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b(.)45 b(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)
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b(211)801 2599 y @beginspecial @setspecial @endspecial
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2943 y @beginspecial @setspecial @endspecial FN(26)33
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3431 y @beginspecial @setspecial @endspecial FN(60)33
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3920 y @beginspecial @setspecial @endspecial(60.3)h(Algebraic)29
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4082 y @beginspecial @setspecial @endspecial(60.4)h(Di\013eren)m(tial)
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47 46 bop 241 299 a @beginspecial @setspecial @endspecial
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FM(3.3.)72 b(BOOLEAN)30 b(EXPRESSIONS)1549 b FQ(55)241
555 y(are)31 b(ob)m(viously)e(in)m(teger)h(expressions.)589
761 y FH(j)44 b(+)f(k)g(-)g(2)g(*)g(j^2)241 967 y FQ(is)25
b(an)i(in)m(teger)g(expression)e(when)h FJ(J)g FQ(and)h
FJ(K)f FQ(ha)m(v)m(e)i(v)-5 b(alues)26 b(that)h(are)g(in)m(tegers,)h
(or)f(if)e(not)241 1067 y(in)m(tegers)30 b(are)h(suc)m(h)f(that)h
(\\the)g(v)-5 b(ariables)29 b(and)h(fractions)g(cancel)h(out",)g(as)g
(in)589 1273 y FH(k)44 b(-)f(7/3)f(-)h(j)g(+)h(2/3)e(+)h(2*j^2.)241
1428 y @beginspecial @setspecial @endspecial 181 x FE(3.3)135
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b(the)g(algebraic)g(mo)s(de)g(of)g(RE-)241 1948 y(DUCE,)c(b)s(o)s
(olean)g(expressions)f(ha)m(v)m(e)i(the)g(syn)m(tactical)g(form:)589
2154 y FH(<expression>)39 b(<relational)g(operator>)h(<expression>)241
2360 y FQ(or)589 2566 y FH(<boolean)h(operator>)f(\(<arguments>\))241
2771 y FQ(or)589 2977 y FH(<boolean)h(expression>)e(<logical)h
(operator>)589 3077 y(<boolean)h(expression>.)241 3296
y FQ(P)m(aren)m(theses)31 b(can)g(also)f(b)s(e)g(used)g(to)h(con)m
(trol)f(the)h(precedence)g(of)f(expressions.)241 3459
y(In)39 b(addition)f(to)j(the)f(logical)f(and)h(relational)f(op)s
(erators)h(de\014ned)e(earlier)h(as)h(in\014x)241 3572
y(op)s(erators,)31 b(the)f(follo)m(wing)f(b)s(o)s(olean)g(op)s(erators)
i(are)g(also)f(de\014ned:)p eop
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56 55 bop 664 299 a @beginspecial @setspecial @endspecial
FQ(56)1625 b FM(CHAPTER)30 b(3.)71 b(EXPRESSIONS)805
622 y FJ(EVENP\(U\))241 b FQ(determines)29 b(if)g(the)i(n)m(um)m(b)s
(er)e FJ(U)h FQ(is)f(ev)m(en)i(or)g(not;)805 848 y FJ(FIXP\(U\))289
b FQ(determines)29 b(if)g(the)i(expression)e FJ(U)h FQ(is)f(in)m(teger)
i(or)f(not;)805 1074 y FJ(FREEOF\(U,V\))97 b FQ(determines)38
b(if)g(the)h(expression)f FJ(U)h FQ(do)s(es)f(not)i(con)m(tain)f(the)
1430 1186 y(k)m(ernel)29 b FJ(V)h FQ(an)m(ywhere)h(in)e(its)h
(structure;)805 1412 y FJ(NUMBERP\(U\))145 b FQ(determines)29
b(if)g FJ(U)h FQ(is)g(a)g(n)m(um)m(b)s(er)f(or)i(not;)805
1638 y FJ(ORDP\(U,V\))193 b FQ(determines)29 b(if)g FJ(U)g
FQ(is)h(ordered)f(ahead)h(of)h FJ(V)e FQ(b)m(y)h(some)h(canon-)1430
1751 y(ical)i(ordering)g(\(based)i(on)f(the)h(expression)e(structure)h
(and)1430 1864 y(an)c(in)m(ternal)f(ordering)g(of)i(iden)m
(ti\014ers\);)805 2090 y FJ(PRIMEP\(U\))193 b FQ(true)30
b(if)f FJ(U)h FQ(is)f(a)i(prime)e(ob)5 b(ject.)664 2279
y FD(Examples:)1013 2485 y FH(j<1)1013 2584 y(x>0)86
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3102 y FQ(Bo)s(olean)d(expressions)f(can)h(only)f(app)s(ear)g(directly)
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FQ(,)g(and)664 3215 y FJ(UNTIL)33 b FQ(statemen)m(ts,)k(as)d(describ)s
(ed)f(in)f(other)j(sections.)52 b(Suc)m(h)33 b(expressions)g(cannot)664
3328 y(b)s(e)28 b(used)f(in)f(place)i(of)g(ordinary)f(algebraic)g
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3491 y(NB:)36 b(F)-8 b(or)35 b(those)g(familiar)d(with)i(sym)m(b)s
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3604 y(op)s(erators)g(is)f(di\013eren)m(t)h(in)f(that)h(mo)s(de.)51
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3717 y(in)m(tegers)e(and)f(reals)f(in)g(sym)m(b)s(olic)g(mo)s(de.)664
3866 y(When)40 b(t)m(w)m(o)i(or)f(more)f(b)s(o)s(olean)g(expressions)f
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3966 y(ev)-5 b(aluated)41 b(one)g(b)m(y)f(one)h(un)m(til)d(a)j
FD(false)48 b FQ(expression)39 b(is)h(found.)69 b(The)40
b(rest)h(are)g(not)664 4065 y(ev)-5 b(aluated.)41 b(Th)m(us)1013
4271 y FH(numberp)g(x)i(and)f(numberp)f(y)i(and)f(x>y)664
4490 y FQ(do)s(es)i(not)g(attempt)h(to)g(mak)m(e)g(the)f
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FQ(are)i(b)s(oth)664 4603 y(v)m(eri\014ed)30 b(to)h(b)s(e)e(n)m(um)m(b)
s(ers.)664 4766 y(Similarly)-8 b(,)31 b(ev)-5 b(aluation)33
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FD(true)37 b FQ(expression)29 b(is)g(found.)p eop
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57 56 bop 241 299 a @beginspecial @setspecial @endspecial
FM(3.4.)72 b(EQUA)-8 b(TIONS)2136 b FQ(57)241 555 y(NB:)42
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(a)g(b)s(o)s(olean)g(expression)241 668 y(is)i(exp)s(ected,)48
b(the)c(algebraic)f(v)-5 b(alue)43 b(0)i(is)e(in)m(terpreted)g(as)h
FD(false)p FQ(,)k(while)42 b(all)g(other)241 781 y(algebraic)c(v)-5
b(alues)38 b(are)h(con)m(v)m(erted)h(to)f FD(true)p FQ(.)65
b(So)38 b(in)g(algebraic)g(mo)s(de)g(a)h(pro)s(cedure)241
894 y(can)31 b(b)s(e)e(written)h(for)g(direct)g(usage)i(in)d(b)s(o)s
(olean)g(expressions,)h(returning)e(sa)m(y)k(1)f(or)f(0)241
1007 y(as)g(its)g(v)-5 b(alue)30 b(as)h(in)589 1238 y
FH(procedure)40 b(polynomialp\(u,x\);)720 1337 y(if)j(den\(u\)=1)d(and)
j(deg\(u,x\)>=1)c(then)j(1)h(else)f(0;)241 1568 y FQ(One)30
b(can)g(then)g(use)g(this)g(in)f(a)i(b)s(o)s(olean)e(construct,)i(suc)m
(h)f(as)589 1774 y FH(if)43 b(polynomialp\(q,z\))37 b(and)43
b(not)f(polynomialp\(q,y\))37 b(then)42 b(...)241 1993
y FQ(In)36 b(addition,)h(an)m(y)g(pro)s(cedure)e(that)j(do)s(es)e(not)h
(ha)m(v)m(e)h(a)f(de\014ned)f(return)f(v)-5 b(alue)36
b(\(for)241 2106 y(example,)f(a)f(blo)s(c)m(k)g(without)f(a)h
FJ(RETURN)e FQ(statemen)m(t)k(in)d(it\))h(has)g(the)g(b)s(o)s(olean)f
(v)-5 b(alue)241 2219 y FD(false)p FQ(.)241 2374 y @beginspecial
@setspecial @endspecial 181 x FE(3.4)135 b(Equations)241
2808 y FQ(Equations)29 b(are)i(a)g(particular)e(t)m(yp)s(e)h(of)h
(expression)e(with)g(the)h(syn)m(tax)589 3039 y FH(<expression>)39
b(=)k(<expression>.)241 3283 y FQ(In)37 b(addition)e(to)k(their)d(role)
i(as)f(b)s(o)s(olean)g(expressions,)h(they)g(can)g(also)f(b)s(e)g(used)
g(as)241 3396 y(argumen)m(ts)27 b(to)h(sev)m(eral)f(op)s(erators)g
(\(e.g.,)j FJ(SOLVE)p FQ(\),)c(and)g(can)i(b)s(e)e(returned)g(as)h(v)-5
b(alues.)241 3558 y(Under)19 b(normal)h(circumstances,)i(the)f(righ)m
(t-hand-side)d(of)j(the)g(equation)f(is)f(ev)-5 b(aluated)241
3671 y(but)33 b(not)h(the)g(left-hand-side.)49 b(This)32
b(also)h(applies)f(to)j(an)m(y)f(substitutions)d(made)j(b)m(y)241
3784 y(the)c FJ(SUB)g FQ(op)s(erator.)41 b(If)30 b(b)s(oth)f(sides)h
(are)g(to)h(b)s(e)f(ev)-5 b(aluated,)31 b(the)f(switc)m(h)g
FJ(EVALLHSEQP)241 3897 y FQ(should)e(b)s(e)i(turned)f(on.)241
4047 y(T)-8 b(o)34 b(facilitate)g(the)f(handling)e(of)j(equations,)h(t)
m(w)m(o)g(selectors,)g FJ(LHS)67 b FQ(and)33 b FJ(RHS)p
FQ(,)g(whic)m(h)241 4146 y(return)23 b(the)i(left-)g(and)f(righ)m
(t-hand)f(sides)h(of)g(a)h(equation)g(resp)s(ectiv)m(ely)-8
b(,)26 b(are)f(pro)m(vided.)241 4246 y(F)-8 b(or)31 b(example,)589
4452 y FH(lhs\(a+b=c\))40 b(->)j(a+b)241 4551 y(and)589
4651 y(rhs\(a+b=c\))d(->)j(c.)241 4795 y @beginspecial
@setspecial @endspecial eop
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58 57 bop 664 299 a @beginspecial @setspecial @endspecial
FQ(58)1625 b FM(CHAPTER)30 b(3.)71 b(EXPRESSIONS)664
555 y FE(3.5)136 b(Prop)t(er)44 b(Statemen)l(ts)j(as)e(Expressions)664
795 y FQ(Sev)m(eral)33 b(kinds)f(of)h(prop)s(er)e(statemen)m(ts)k
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894 y(of)42 b(some)h(kind,)g(whic)m(h)e(can)h(in)f(turn)g(b)s(e)g(used)
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1094 y(the)31 b(v)-5 b(alue)30 b(assigned.)40 b(So)1013
1299 y FH(2)j(*)g(\(x)g(:=)g(a+b\))664 1505 y FQ(is)24
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2030 y FQ(sets)31 b FJ(X)f FQ(to)h FJ(a+b)f FQ(and)f
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59 58 bop 241 299 a @beginspecial @setspecial @endspecial
165 x @beginspecial @setspecial @endspecial 764 x FI(Chapter)64
b(4)241 1693 y FT(Lists)241 2174 y FQ(A)33 b(list)e(is)h(an)g(ob)5
b(ject)34 b(consisting)d(of)i(a)g(sequence)g(of)g(other)g(ob)5
b(jects)33 b(\(including)d(lists)241 2274 y(themselv)m(es\),)i
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b(Examples)30 b(of)241 2373 y(lists)f(are:)589 2579 y
FH({a,b,c})589 2779 y({1,a-b,c=d})589 2978 y({{a},{{b,c},d},e})o(.)241
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4543 y(the)h(ASSIST)f(pac)m(k)-5 b(age.)241 4706 y(T)d(o)40
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b FQ(for)k(example)g(will)d(return)i(the)h FL(n)2986
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5187 y(59)p eop
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60 59 bop 664 299 a @beginspecial @setspecial @endspecial
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61 60 bop 241 299 a @beginspecial @setspecial @endspecial
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145 144 bop 241 299 a @beginspecial @setspecial @endspecial
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146 145 bop 664 299 a @beginspecial @setspecial @endspecial
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147 146 bop 241 299 a @beginspecial @setspecial @endspecial
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4462 y(In)g(order)h(to)h(allo)m(w)f(users)g(relativ)m(ely)f(easy)i
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1110 y(begin)h(scalar)g(seed,deriv,top,fa)o(ct)o(;)895
1209 y(seed:=1/\(y^2)d(-)43 b(2*x*y)f(+1\)^\(1/2\);)895
1309 y(deriv:=df\(seed,)o(y,n)o(\);)895 1409 y(top:=sub\(y=0,de)o(riv)o
(\);)895 1508 y(fact:=for)d(i:=1:n)j(product)e(i;)895
1608 y(return)h(top/fact)677 1708 y(end;)241 1913 y FQ(Pro)s(cedures)32
b(ma)m(y)i(also)f(b)s(e)g(de\014ned)f(recursiv)m(ely)-8
b(.)49 b(In)33 b(other)g(w)m(ords,)h(the)g(pro)s(cedure)241
2013 y(b)s(o)s(dy)27 b(can)i(include)d(references)j(to)g(the)g(pro)s
(cedure)e(name)i(itself,)f(or)g(to)i(other)e(pro)s(ce-)241
2113 y(dures)c(that)i(themselv)m(es)f(reference)h(the)f(giv)m(en)g(pro)
s(cedure.)38 b(As)25 b(an)g(example,)i(w)m(e)e(can)241
2212 y(de\014ne)k(the)i(Legendre)f(p)s(olynomial)e(through)i(its)g
(standard)f(recurrence)h(relation:)589 2418 y FH(procedure)40
b(p\(n,x\);)720 2518 y(if)j(n<0)f(then)g(rederr)f("Invalid)g(argument)f
(to)j(P\(N,X\)")764 2617 y(else)f(if)g(n=0)h(then)f(1)764
2717 y(else)g(if)g(n=1)h(then)f(x)764 2817 y(else)g
(\(\(2*n-1\)*x*p\(n-1)o(,x)o(\)-)o(\(n-)o(1\))o(*p\()o(n-)o(2,)o(x\)\))
o(/n)o(;)241 3036 y FQ(The)31 b(op)s(erator)g FJ(REDERR)f
FQ(in)g(the)i(ab)s(o)m(v)m(e)h(example)e(pro)m(vides)f(for)h(a)h
(simple)e(error)h(exit)241 3149 y(from)42 b(an)g(algebraic)h(pro)s
(cedure)e(\(and)h(also)h(a)g(blo)s(c)m(k\).)77 b(It)43
b(can)g(tak)m(e)h(a)f(string)e(as)241 3262 y(argumen)m(t.)241
3424 y(It)25 b(should)e(b)s(e)h(noted)h(ho)m(w)m(ev)m(er)h(that)f(all)f
(the)h(ab)s(o)m(v)m(e)h(de\014nitions)d(of)i FJ(p\(n,x\))e
FQ(are)i(quite)241 3537 y(ine\016cien)m(t)i(if)h(extensiv)m(e)g(use)g
(is)g(to)h(b)s(e)e(made)i(of)f(suc)m(h)g(p)s(olynomials,)e(since)i(eac)
m(h)h(call)241 3650 y(e\013ectiv)m(ely)40 b(recomputes)f(all)e(lo)m(w)m
(er)j(order)e(p)s(olynomials.)64 b(It)39 b(w)m(ould)e(b)s(e)i(b)s
(etter)g(to)241 3763 y(store)28 b(these)h(expressions)e(in)g(an)h(arra)
m(y)-8 b(,)29 b(and)f(then)g(use)f(sa)m(y)i(the)f(recurrence)g
(relation)241 3876 y(to)h(compute)g(only)f(those)h(p)s(olynomials)d
(that)j(ha)m(v)m(e)h(not)f(already)f(b)s(een)g(deriv)m(ed.)39
b(W)-8 b(e)241 3989 y(lea)m(v)m(e)32 b(it)d(as)i(an)f(exercise)h(for)f
(the)h(reader)f(to)h(write)f(suc)m(h)g(a)g(de\014nition.)241
4126 y @beginspecial @setspecial @endspecial 199 x FE(14.3)135
b(Using)46 b(LET)e(Inside)i(Pro)t(cedures)241 4578 y
FQ(By)32 b(using)e FJ(LET)g FQ(instead)h(of)h(an)f(assignmen)m(t)g(in)f
(the)i(pro)s(cedure)e(b)s(o)s(dy)g(it)h(is)g(p)s(ossible)241
4691 y(to)36 b(b)m(ypass)g(the)g(call-b)m(y-v)-5 b(alue)35
b(protection.)58 b(If)35 b FJ(X)h FQ(is)f(a)h(formal)f(parameter)h(or)g
(lo)s(cal)241 4804 y(v)-5 b(ariable)34 b(of)h(the)h(pro)s(cedure)e
(\(i.e.)55 b(is)34 b(in)g(the)i(heading)e(or)h(in)f(a)i(lo)s(cal)e
(declaration\),)241 4917 y(and)c FJ(LET)f FQ(is)g(used)h(instead)g(of)g
FJ(:=)g FQ(to)h(mak)m(e)g(an)g(assignmen)m(t)f(to)h FJ(X)p
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190 189 bop 664 299 a @beginspecial @setspecial @endspecial
FQ(190)1537 b FM(CHAPTER)30 b(14.)72 b(PR)m(OCEDURES)1013
555 y FH(let)42 b(x)h(=)h(123;)664 799 y FQ(then)39 b(it)g(is)f(the)h
(v)-5 b(ariable)38 b(that)i(is)e(the)h(v)-5 b(alue)39
b(of)g FJ(X)g FQ(that)g(is)g(c)m(hanged.)67 b(This)37
b(e\013ect)664 912 y(also)e(o)s(ccurs)f(with)f(lo)s(cal)h(v)-5
b(ariables)33 b(de\014ned)g(in)g(a)i(blo)s(c)m(k.)53
b(If)34 b(the)g(v)-5 b(alue)34 b(of)h FJ(X)f FQ(is)g(not)664
1025 y(a)e(v)-5 b(ariable,)31 b(but)g(a)h(more)g(general)g(expression,)
f(then)g(it)g(is)g(that)h(expression)f(that)h(is)664
1138 y(used)g(on)g(the)g(left-hand)f(side)g(of)i(the)f
FJ(LET)f FQ(statemen)m(t.)49 b(F)-8 b(or)32 b(example,)h(if)e
FJ(X)h FQ(had)g(the)664 1251 y(v)-5 b(alue)30 b FJ(p*q)p
FQ(,)g(it)g(is)f(as)i(if)e FJ(let)47 b(p*q)g(=)g(123)30
b FQ(had)g(b)s(een)f(executed.)664 1408 y @beginspecial
@setspecial @endspecial 179 x FE(14.4)136 b(LET)44 b(Rules)i(as)f(Pro)t
(cedures)664 1840 y FQ(The)27 b FJ(LET)g FQ(statemen)m(t)j(o\013ers)e
(an)f(alternativ)m(e)h(syn)m(tax)h(and)e(seman)m(tics)h(for)f(pro)s
(cedure)664 1953 y(de\014nition.)664 2102 y(In)j(place)g(of)1013
2308 y FH(procedure)40 b(abc\(x,y,z\);)f(<procedure)g(body>;)664
2514 y FQ(one)31 b(can)g(write)1013 2720 y FH(for)42
b(all)h(x,y,z)e(let)h(abc\(x,y,z\))e(=)j(<procedure)c(body>;)664
2939 y FQ(There)30 b(are)h(sev)m(eral)g(di\013erences)e(to)i(note.)664
3089 y(If)e(the)h(pro)s(cedure)f(b)s(o)s(dy)f(con)m(tains)i(an)f
(assignmen)m(t)h(to)g(one)g(of)g(the)g(formal)e(parame-)664
3188 y(ters,)j(e.g.)1013 3394 y FH(x)43 b(:=)g(123;)664
3613 y FQ(in)f(the)h FJ(PROCEDURE)d FQ(case)k(it)e(is)g(a)h(v)-5
b(ariable)41 b(holding)g(a)i(cop)m(y)h(of)f(the)g(\014rst)f(actual)664
3726 y(argumen)m(t)31 b(that)g(is)e(c)m(hanged.)42 b(The)30
b(actual)g(argumen)m(t)h(is)f(not)g(c)m(hanged.)664 3889
y(In)21 b(the)h FJ(LET)f FQ(case,)k(the)d(actual)g(argumen)m(t)g(is)f
(c)m(hanged.)39 b(Th)m(us,)22 b(if)f FJ(ABC)g FQ(is)g(de\014ned)f
(using)664 4002 y FJ(LET)p FQ(,)33 b(and)g FJ(abc\(u,v,w\))d
FQ(is)j(ev)-5 b(aluated,)34 b(the)g(v)-5 b(alue)33 b(of)h
FJ(U)f FQ(c)m(hanges)h(to)g(123.)51 b(That)34 b(is,)664
4115 y(the)28 b FJ(LET)f FQ(form)g(of)h(de\014nition)e(allo)m(ws)h(the)
h(user)f(to)h(b)m(ypass)f(the)h(protections)g(that)h(are)664
4228 y(enforced)c(b)m(y)h(the)f(call)f(b)m(y)i(v)-5 b(alue)24
b(con)m(v)m(en)m(tions)j(of)e(standard)f FJ(PROCEDURE)f
FQ(de\014nitions.)664 4377 y FD(Example:)54 b FQ(W)-8
b(e)37 b(tak)m(e)h(our)e(earlier)f FJ(FACTORIAL)f FQ(pro)s(cedure)h
(and)h(write)g(it)f(as)i(a)g FJ(LET)664 4477 y FQ(statemen)m(t.)1013
4683 y FH(for)42 b(all)h(n)g(let)f(factorial)e(n)j(=)1536
4782 y(begin)e(scalar)h(m,s;)1536 4882 y(m:=1;)f(s:=n;)p
eop
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191 190 bop 241 299 a @beginspecial @setspecial @endspecial
FM(14.4.)72 b(LET)30 b(R)m(ULES)g(AS)g(PR)m(OCEDURES)1257
b FQ(191)938 555 y FH(l1:)42 b(if)h(s=0)g(then)f(return)f(m;)1112
655 y(m:=m*s;)1112 754 y(s:=s-1;)1112 854 y(go)i(to)g(l1)938
954 y(end;)241 1173 y FQ(The)34 b(reader)h(will)e(notice)i(that)h(w)m
(e)g(in)m(tro)s(duced)d(a)j(new)f(lo)s(cal)f(v)-5 b(ariable,)35
b FJ(S)p FQ(,)g(and)g(set)241 1286 y(it)h(equal)f(to)i
FJ(N)p FQ(.)g(The)e(original)g(form)h(of)g(the)h(pro)s(cedure)e(con)m
(tained)h(the)h(statemen)m(t)241 1399 y FJ(n:=n-1;)p
FQ(.)69 b(If)41 b(the)f(user)g(ask)m(ed)i(for)e(the)h(v)-5
b(alue)40 b(of)h FJ(factorial\(5\))c FQ(then)j FJ(N)h
FQ(w)m(ould)241 1512 y(corresp)s(ond)28 b(to,)k(not)e(just)f(ha)m(v)m
(e)i(the)f(v)-5 b(alue)30 b(of,)g(5,)h(and)e(REDUCE)h(w)m(ould)f(ob)5
b(ject)31 b(to)241 1625 y(trying)e(to)i(execute)h(the)f(statemen)m(t)h
(5)f(:=)f(5)21 b FP(\000)e FQ(1.)241 1774 y(If)30 b FJ(PQR)f
FQ(is)h(a)g(pro)s(cedure)g(with)f(no)h(parameters,)589
1980 y FH(procedure)40 b(pqr;)720 2079 y(<procedure)g(body>;)241
2285 y FQ(it)30 b(can)g(b)s(e)g(written)g(as)g(a)h FJ(LET)e
FQ(statemen)m(t)k(quite)c(simply:)589 2491 y FH(let)43
b(pqr)f(=)h(<procedure)d(body>;)241 2710 y FQ(T)-8 b(o)34
b(call)g FD(pr)-5 b(o)g(c)g(e)g(dur)g(e)44 b FJ(PQR)p
FQ(,)33 b(if)g(de\014ned)g(in)g(the)h(latter)h(form,)f(the)h(empt)m(y)f
(paren)m(theses)241 2823 y(w)m(ould)40 b(not)h(b)s(e)g(used:)61
b(use)41 b FJ(PQR)g FQ(not)g FJ(PQR\(\))f FQ(where)h(a)g(call)g(on)g
(the)g(pro)s(cedure)f(is)241 2936 y(needed.)241 3086
y(The)25 b(t)m(w)m(o)h(notations)g(for)f(a)g(pro)s(cedure)f(with)g(no)h
(argumen)m(ts)h(can)g(b)s(e)e(com)m(bined.)38 b FJ(PQR)241
3185 y FQ(can)30 b(b)s(e)g(de\014ned)f(in)g(the)i(standard)e
FJ(PROCEDURE)f FQ(form.)41 b(Then)29 b(a)i FJ(LET)e FQ(statemen)m(t)589
3391 y FH(let)43 b(pqr)f(=)h(pqr\(\);)241 3610 y FQ(w)m(ould)29
b(allo)m(w)h(a)h(user)e(to)i(use)f FJ(PQR)g FQ(instead)g(of)g
FJ(PQR\(\))f FQ(in)g(calling)g(the)h(pro)s(cedure.)241
3760 y(A)40 b(feature)g(a)m(v)-5 b(ailable)39 b(with)g
FJ(LET)p FQ(-de\014ned)f(pro)s(cedures)h(and)g(not)h(with)f(pro)s
(cedures)241 3859 y(de\014ned)29 b(in)g(the)i(standard)e(w)m(a)m(y)i
(is)f(the)g(p)s(ossibilit)m(y)d(of)k(de\014ning)d(partial)h(functions.)
415 4065 y FH(for)42 b(all)h(x)g(such)f(that)g(numberp)f(x)i(let)f
(uvw\(x\)=<procedur)o(e)c(body>;)241 4285 y FQ(No)m(w)c
FJ(UVW)e FQ(of)i(an)f(in)m(teger)h(w)m(ould)e(b)s(e)g(calculated)i(as)f
(prescrib)s(ed)e(b)m(y)i(the)h(pro)s(cedure)241 4397
y(b)s(o)s(dy)-8 b(,)38 b(while)d FJ(UVW)i FQ(of)g(a)h(general)f
(argumen)m(t,)j(suc)m(h)d(as)g FJ(Z)g FQ(or)g FJ(p+q)g
FQ(\(assuming)f(these)241 4510 y(ev)-5 b(aluate)32 b(to)g(themselv)m
(es\))g(w)m(ould)e(simply)f(sta)m(y)k FJ(uvw\(z\))c FQ(or)j
FJ(uvw\(p+q\))d FQ(as)j(the)f(case)241 4623 y(ma)m(y)g(b)s(e.)241
4778 y @beginspecial @setspecial @endspecial eop
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192 191 bop 664 299 a @beginspecial @setspecial @endspecial
FQ(192)1537 b FM(CHAPTER)30 b(14.)72 b(PR)m(OCEDURES)664
555 y FE(14.5)136 b(REMEMBER)45 b(Statemen)l(t)664 795
y FQ(Setting)30 b(the)h(remem)m(b)s(er)f(option)f(for)i(an)f(algebraic)
g(pro)s(cedure)f(b)m(y)882 1001 y FH(REMEMBER)40 b(\(PROCNAME:procedu)o
(re\))o(;)664 1220 y FQ(sa)m(v)m(es)27 b(all)e(in)m(termediate)g
(results)g(of)h(suc)m(h)f(pro)s(cedure)g(ev)-5 b(aluations,)26
b(including)c(recur-)664 1333 y(siv)m(e)34 b(calls.)50
b(Subsequen)m(t)32 b(calls)h(to)i(the)f(pro)s(cedure)e(can)i(then)g(b)s
(e)f(determined)f(from)664 1446 y(the)k(sa)m(v)m(ed)h(results,)f(and)g
(th)m(us)f(the)h(n)m(um)m(b)s(er)e(of)i(ev)-5 b(aluations)36
b(\(or)g(the)g(complexit)m(y\))664 1558 y(can)e(b)s(e)f(reduced.)50
b(This)32 b(mo)s(de)h(of)h(ev)-5 b(alation)34 b(costs)g(extra)h(memory)
-8 b(,)35 b(of)f(course.)51 b(In)664 1671 y(addition,)29
b(the)i(pro)s(cedure)e(m)m(ust)h(b)s(e)g(free)g(of)h(side{e\013ects.)
664 1834 y(The)i(follo)m(wing)e(examples)i(sho)m(w)g(the)g(e\013ect)i
(of)e(the)g(remem)m(b)s(er)g(statemen)m(t)i(on)e(t)m(w)m(o)664
1947 y(w)m(ell{kno)m(wn)d(examples.)664 2178 y FH(procedure)40
b(H\(n\);)259 b(\045)44 b(Hofstadter's)38 b(function)708
2277 y(if)43 b(numberp)d(n)j(then)708 2377 y(<<)g(cnn)f(:=)h(cnn)f(+1;)
129 b(\045)44 b(counts)d(the)h(calls)708 2477 y(if)h(n)g(<)g(3)g(then)f
(1)h(else)f(H\(n-H\(n-1\)\)+H\(n-)o(H\(n)o(-2)o(\)\)>)o(>;)664
2676 y(remember)e(h;)664 2875 y(>)j(<<)g(cnn)f(:=)h(0;)g(H\(100\);)e
(cnn>>;)664 3074 y(100)664 3274 y(\045)i(H)h(has)e(been)g(called)f(100)
h(times)g(only.)664 3473 y(procedure)e(A\(m,n\);)171
b(\045)44 b(Ackermann)c(function)708 3672 y(if)j(m=0)f(then)g(n+1)g
(else)751 3772 y(if)h(n=0)f(then)g(A\(m-1,1\))f(else)751
3871 y(A\(m-1,A\(m,n-1\)\);)664 4071 y(remember)f(a;)664
4270 y(A\(3,3\);)p eop
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193 192 bop 241 299 a @beginspecial @setspecial @endspecial
165 x @beginspecial @setspecial @endspecial 764 x FI(Chapter)64
b(15)241 1693 y FT(User)76 b(Con)-6 b(tributed)78 b(P)-6
b(ac)g(k)-13 b(ages)241 2187 y FQ(The)30 b(complete)h(REDUCE)f(system)h
(includes)d(a)j(n)m(um)m(b)s(er)e(of)i(pac)m(k)-5 b(ages)32
b(con)m(tributed)241 2300 y(b)m(y)k(users)f(that)h(are)g(pro)m(vided)f
(as)h(a)g(service)g(to)h(the)f(user)f(comm)m(unit)m(y)-8
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b(ages)32 b(should)d(b)s(e)h(directed)f(to)i(their)f(individual)c
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(installation)e(pro)s(cess.)241 2689 y(Ho)m(w)m(ev)m(er,)k(man)m(y)d(m)
m(ust)g(b)s(e)g(sp)s(eci\014cally)e(loaded)i(b)s(efore)g(they)g(can)h
(b)s(e)e(used.)39 b(\(Those)241 2802 y(that)27 b(are)f(loaded)g
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b(Y)-8 b(ou)26 b(should)241 2915 y(also)38 b(consult)f(the)h(user)f
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(necessary)-8 b(.)52 b(If)33 b(it)g(is,)h(the)g(relev)-5
b(an)m(t)34 b(command)f(is)241 3141 y FJ(LOAD)p 439 3141
29 4 v 33 w(PACKAGE)p FQ(,)22 b(whic)m(h)f(tak)m(es)k(a)f(list)e(of)h
(one)g(or)h(more)f(pac)m(k)-5 b(age)25 b(names)e(as)h(argumen)m(t,)241
3253 y(for)30 b(example:)589 3484 y FH(load_package)39
b(algint;)241 3728 y FQ(although)30 b(this)f(syn)m(tax)i(ma)m(y)g(v)-5
b(ary)30 b(from)g(implemen)m(tation)f(to)i(implemen)m(tation.)241
3891 y(Nearly)j(all)e(these)j(pac)m(k)-5 b(ages)36 b(come)f(with)d
(separate)j(do)s(cumen)m(tation)f(and)g(test)h(\014les)241
4004 y(\(except)43 b(those)f(noted)g(here)g(that)h(ha)m(v)m(e)g(no)f
(additional)e(do)s(cumen)m(tation\),)45 b(whic)m(h)241
4117 y(is)33 b(included,)f(along)h(with)g(the)h(source)g(of)g(the)g
(pac)m(k)-5 b(age,)36 b(in)d(the)h(REDUCE)f(system)241
4230 y(distribution.)61 b(These)38 b(items)g(should)e(b)s(e)i(studied)f
(for)h(an)m(y)h(additional)d(details)i(on)241 4343 y(the)30
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(cumen)m(tation)g(for)g(the)h(pac)m(k)-5 b(ages)377 4743
y FP(\017)46 b FQ(ALGINT:)31 b(In)m(tegration)g(of)f(square)g(ro)s(ots)
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4930 y FP(\017)46 b FQ(APPL)-8 b(YSYM:)27 b(In\014nitesimal)d
(symmetries)h(of)i(di\013eren)m(tial)e(equations)i(\(c)m(hap-)1667
5187 y(193)p eop
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194 193 bop 664 299 a @beginspecial @setspecial @endspecial
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b(\(c)m(hapter)g @beginspecial @setspecial @endspecial(22)q(\);)801
930 y FP(\017)45 b FQ(ASSIST:)29 b(Useful)g(utilities)f(for)i(v)-5
b(arious)30 b(applications)e(\(c)m(hapter)k @beginspecial
@setspecial @endspecial(23)q(\);)801 1118 y FP(\017)45
b FQ(A)-10 b(VECTOR:)30 b(A)h(v)m(ector)h(algebra)e(and)g(calculus)f
(pac)m(k)-5 b(age)32 b(\(c)m(hapter)f @beginspecial @setspecial
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b(A)f(pac)m(k)-5 b(age)33 b(for)d(b)s(o)s(olean)f(algebra)i(\(c)m
(hapter)g @beginspecial @setspecial @endspecial(26)q(\);)801
1493 y FP(\017)45 b FQ(CALI:)22 b(A)g(pac)m(k)-5 b(age)24
b(for)d(computational)h(comm)m(utativ)m(e)h(algebra)f(\(c)m(hapter)g
@beginspecial @setspecial @endspecial(27)q(\);)801 1681
y FP(\017)45 b FQ(CAMAL:)31 b(Calculations)e(in)g(celestial)h(mec)m
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801 1869 y FP(\017)45 b FQ(CHANGEVR:)23 b(Change)f(of)f(Indep)s(enden)m
(t)g(V)-8 b(ariable\(s\))21 b(in)g(DEs)h(\(c)m(hapter)g
@beginspecial @setspecial @endspecial(30)q(\);)801 2056
y FP(\017)45 b FQ(COMP)-8 b(A)m(CT:)31 b(P)m(ac)m(k)-5
b(age)33 b(for)d(compacting)h(expressions)e(\(c)m(hapter)j
@beginspecial @setspecial @endspecial(31\);)801 2244
y FP(\017)45 b FQ(CONTFR:)31 b(Appro)m(ximation)f(of)i(a)g(n)m(um)m(b)s
(er)e(b)m(y)h(con)m(tin)m(ued)g(fractions)g(\(c)m(hap-)891
2357 y(ter)g FN(??)q FQ(\);)801 2544 y FP(\017)45 b FQ(CRA)m(CK:)c
(Solving)e(o)m(v)m(erdetermined)h(systems)h(of)g(PDEs)f(or)h(ODEs)f
(\(c)m(hap-)891 2657 y(ter)31 b @beginspecial @setspecial
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3033 y FP(\017)45 b FQ(DEFINT:)31 b(A)g(de\014nite)e(in)m(tegration)h
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@setspecial @endspecial(34)q(\);)801 3220 y FP(\017)45
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b(of)j(irregular)d(and)i(regular)g(singular)e(p)s(oin)m(ts)h(\(c)m
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3521 y FP(\017)45 b FQ(DFP)-8 b(AR)g(T:)32 b(Deriv)-5
b(ativ)m(es)31 b(of)g(generic)f(functions)f(\(c)m(hapter)i
@beginspecial @setspecial @endspecial(36)q(\);)801 3708
y FP(\017)45 b FQ(DUMMY:)27 b(Canonical)c(form)i(of)f(expressions)g
(with)f(dumm)m(y)h(v)-5 b(ariables)23 b(\(c)m(hap-)891
3821 y(ter)31 b @beginspecial @setspecial @endspecial(37)q(\);)801
4009 y FP(\017)45 b FQ(EX)m(CALC:)31 b(A)f(di\013eren)m(tial)f
(geometry)j(pac)m(k)-5 b(age)32 b(\(c)m(hapter)g @beginspecial
@setspecial @endspecial(39)q(\);)801 4197 y FP(\017)45
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(\);)801 4384 y FP(\017)45 b FQ(FIDE:)23 b(Finite)e(di\013erence)h
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(hap-)891 4497 y(ter)31 b @beginspecial @setspecial @endspecial(40)q
(\);)801 4685 y FP(\017)45 b FQ(GENTRAN:)31 b(A)g(co)s(de)f(generation)
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@setspecial @endspecial(42)q(\);)801 4872 y FP(\017)45
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eop
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195 194 bop 241 299 a @beginspecial @setspecial @endspecial
2852 w FQ(195)377 555 y FP(\017)46 b FQ(GR)m(OEBNER:)31
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743 y FP(\017)46 b FQ(IDEALS:)30 b(Arithmetic)g(for)g(p)s(olynomial)d
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(\);)377 930 y FP(\017)46 b FQ(INEQ:)30 b(Supp)s(ort)e(for)j(solving)e
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377 1306 y FP(\017)46 b FQ(LAPLA)m(CE:)30 b(Laplace)h(and)f(in)m(v)m
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@setspecial @endspecial(49\);)377 1493 y FP(\017)46 b
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(real)h(n-dimensional)c(Lie)j(algebras)468 1606 y(\(c)m(hapter)k
@beginspecial @setspecial @endspecial(50)q(\);)377 1794
y FP(\017)46 b FQ(LIMITS:)30 b(A)g(pac)m(k)-5 b(age)32
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2169 y FP(\017)46 b FQ(MODSR:)31 b(Mo)s(dular)d(solv)m(e)j(and)f(ro)s
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377 2357 y FP(\017)46 b FQ(NCPOL)-8 b(Y:)30 b(Non{comm)m(utativ)m(e)j
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2732 y FP(\017)46 b FQ(NUMERIC:)31 b(Solving)d(n)m(umerical)h(problems)
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2920 y FP(\017)46 b FQ(ODESOL)-10 b(VE:)30 b(Ordinary)e(di\013eren)m
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@setspecial @endspecial(61)q(\);)377 3483 y FP(\017)46
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@beginspecial @setspecial @endspecial(62)q(\);)377 3670
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@endspecial(64)q(\);)377 3858 y FP(\017)46 b FQ(REA)m(CTEQN:)32
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m(hap-)468 3971 y(ter)f @beginspecial @setspecial @endspecial(66)q(\);)
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@setspecial @endspecial(68)q(\);)377 4346 y FP(\017)46
b FQ(RESIDUE:)30 b(A)h(residue)e(pac)m(k)-5 b(age)32
b(\(c)m(hapter)f @beginspecial @setspecial @endspecial(69)q(\);)377
4534 y FP(\017)46 b FQ(RLFI:)31 b(REDUCE)f(LaT)-8 b(eX)31
b(form)m(ula)f(in)m(terface)h(\(c)m(hapter)g @beginspecial
@setspecial @endspecial(70)q(\);)377 4721 y FP(\017)46
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377 4909 y FP(\017)46 b FQ(R)m(OOTS:)30 b(A)g(REDUCE)g(ro)s(ot)h
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196 195 bop 664 299 a @beginspecial @setspecial @endspecial
FQ(196)665 b FM(CHAPTER)30 b(15.)72 b(USER)29 b(CONTRIBUTED)h(P)-8
b(A)m(CKA)m(GES)801 555 y FP(\017)45 b FQ(SCOPE:)30 b(REDUCE)g(source)g
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@beginspecial @setspecial @endspecial(73)q(\);)801 743
y FP(\017)45 b FQ(SETS:)30 b(A)g(basic)g(set)h(theory)f(pac)m(k)-5
b(age)33 b(\(c)m(hapter)e @beginspecial @setspecial @endspecial(74)q
(\);)801 930 y FP(\017)45 b FQ(SPDE:)27 b(A)g(pac)m(k)-5
b(age)29 b(for)d(\014nding)e(symmetry)j(groups)f(of)h(PDE's)g(\(c)m
(hapter)g @beginspecial @setspecial @endspecial(76)q(\);)801
1118 y FP(\017)45 b FQ(SPECFN:)30 b(P)m(ac)m(k)-5 b(age)34
b(for)c(sp)s(ecial)f(functions)g(\(c)m(hapter)i @beginspecial
@setspecial @endspecial(77)q(\);)801 1306 y FP(\017)45
b FQ(SPECFN2:)c(P)m(ac)m(k)-5 b(age)33 b(for)d(sp)s(ecial)f(sp)s(ecial)
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@endspecial(78\);)801 1493 y FP(\017)45 b FQ(SUM:)31
b(A)g(pac)m(k)-5 b(age)32 b(for)e(series)g(summation)f(\(c)m(hapter)i
@beginspecial @setspecial @endspecial(79)q(\);)801 1681
y FP(\017)45 b FQ(SYMMETR)-8 b(Y:)31 b(Op)s(erations)e(on)i(symmetric)e
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@endspecial(81)q(\);)801 1869 y FP(\017)45 b FQ(T)-8
b(A)g(YLOR:)31 b(Manipulation)d(of)j(T)-8 b(a)m(ylor)31
b(series)e(\(c)m(hapter)j @beginspecial @setspecial @endspecial(82)q
(\);)801 2056 y FP(\017)45 b FQ(TPS:)30 b(A)h(truncated)f(p)s(o)m(w)m
(er)g(series)g(pac)m(k)-5 b(age)32 b(\(c)m(hapter)g @beginspecial
@setspecial @endspecial(83)q(\);)801 2244 y FP(\017)45
b FQ(TRI:)30 b(T)-8 b(eX)31 b(REDUCE)g(in)m(terface)g(\(c)m(hapter)g
@beginspecial @setspecial @endspecial(84)q(\);)801 2431
y FP(\017)45 b FQ(TRIGSIMP:)28 b(Simpli\014cation)d(and)j
(factorization)i(of)e(trigonometric)h(and)f(h)m(y-)891
2544 y(p)s(erb)s(olic)g(functions)h(\(c)m(hapter)i @beginspecial
@setspecial @endspecial(85)q(\);)801 2732 y FP(\017)45
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(non-ab)s(elian)g(gauge)j(\014eld)891 2845 y(theories)31
b(\(c)m(hapter)g @beginspecial @setspecial @endspecial(87)q(\);)801
3033 y FP(\017)45 b FQ(XIDEAL:)31 b(Gr\177)-45 b(obner)30
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@setspecial @endspecial(88)q(\);)801 3220 y FP(\017)45
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3408 y FP(\017)45 b FQ(ZEILBER)m(G:)36 b(A)g(pac)m(k)-5
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(hap-)891 3521 y(ter)d @beginspecial @setspecial @endspecial(89)q(\);)
801 3708 y FP(\017)45 b FQ(ZTRANS:)30 b FL(Z)7 b FQ(-transform)30
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2300 y(guage)34 b(Lisp)e(kno)m(wn)h(as)g FD(Standar)-5
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245 244 bop 241 299 a @beginspecial @setspecial @endspecial
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247 246 bop 241 299 a @beginspecial @setspecial @endspecial
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1684 y(an)38 b(indeterminate)e(of)i(a)h(p)s(olynomial.)60
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1797 y(prop)s(ert)m(y)29 b(to)j(b)s(e)d(a)i FD(c)-5 b(omp)g(osite)33
b FQ(ob)5 b(ject.)241 1952 y FN(De\014nition)p FQ(:)p
241 1965 479 4 v 241 2098 a(A)30 b(bag)h(is)e(an)i(ob)5
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2329 a(1.)46 b(It)c(is)f(a)i FJ(KERNEL)d FQ(comp)s(osed)i(of)g(an)g
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2442 y(con)m(ten)m(t)32 b(\(miscellaneous)d(ob)5 b(jects\).)241
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y @beginspecial @setspecial @endspecial 352 2925 a(3.)46
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3038 y(it)30 b FJ(NONCOM)f FQ(or)h FJ(SYMMETRIC)e FQ(etc.)k
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3928 y(a)38 b(bag.)65 b FN(When)43 b(and)h(only)g(when)38
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4028 y(\014ned)25 b(function)h(do)s(es)g FJ(PUTBAG)f
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3237 y(thanks)f(to)g FJ(KERNLIST)e FQ(whic)m(h)g(transforms)h(a)h(bag)g
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4475 y(\014rst)e(one,)i(if)e(their)g(argumen)m(t)h(is)f(a)h(list)e(of)i
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y(for)k(the)f(second)h(one.)p eop
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249 248 bop 241 299 a @beginspecial @setspecial @endspecial
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2256 y(sage)32 b(is)d(issued.)241 2408 y @beginspecial
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2719 2842 29 4 v 33 w(TO)p 2848 2842 V 34 w(IDS)g FQ(han-)468
2955 y(dle)d(iden)m(ti\014ers.)38 b FJ(MKIDNEW)29 b FQ(is)g(a)i(v)-5
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250 249 bop 664 299 a @beginspecial @setspecial @endspecial
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FL(p)e FQ(at)h(a)468 655 y(time.)68 b(The)38 b(\014rst)h(argumen)m(t)h
(is)e(a)i(list)e(\(or)i(a)g(bag\))g(and)f(the)g(second)h(is)e(the)468
754 y(in)m(teger)31 b FL(p)p FQ(.)817 959 y FH(COMBINATIONS\({1,)o(2,)o
(3})o(,2\))37 b(==>)42 b({{2,3},{1,3},{1,2)o(}})468 1177
y FJ(REMSYM)22 b FQ(is)h(a)i(command)e(that)i(erases)f(the)h(REDUCE)e
(commands)h FJ(symmetric)468 1289 y FQ(or)30 b FJ(antisymmetric)p
FQ(.)468 1425 y FJ(SYMMETRIZE)21 b FQ(is)h(a)i(p)s(o)m(w)m(erful)e
(function)g(whic)m(h)h(generate)i(a)f(symmetric)e(expres-)468
1525 y(sion.)38 b(It)24 b(has)g(3)h(argumen)m(ts.)39
b(The)24 b(\014rst)g(is)f(a)i(list)e(\(or)h(a)h(list)e(of)i(lists\))e
(con)m(taining)468 1625 y(the)i(expressions)e(whic)m(h)h(will)e(app)s
(ear)i(as)h(v)-5 b(ariables)23 b(for)i(a)g(k)m(ernel.)38
b(The)24 b(second)468 1724 y(argumen)m(t)33 b(is)f(the)g(k)m
(ernel-name)h(and)f(the)h(third)e(is)g(a)i(p)s(erm)m(utation)f
(function)468 1824 y(whic)m(h)24 b(either)h(exist)g(in)f(the)i
(algebraic)f(or)g(in)f(the)i(sym)m(b)s(olic)e(mo)s(de.)38
b(This)24 b(func-)468 1923 y(tion)30 b(ma)m(y)h(ha)m(v)m(e)g(b)s(een)f
(constructed)g(b)m(y)h(the)f(user.)40 b(Within)29 b(this)g(pac)m(k)-5
b(age)32 b(the)468 2023 y(t)m(w)m(o)g(functions)d FJ(PERMUTATIONS)e
FQ(and)i FJ(CYCLICPERMLIST)e FQ(ma)m(y)k(b)s(e)f(used.)817
2227 y FH(ll:={a,b,c}$)817 2327 y(SYMMETRIZE\(ll,op)o(,c)o(yc)o(lic)o
(pe)o(rml)o(is)o(t\))o(;)38 b(==>)1165 2427 y(OP\(A,B,C\))i(+)j
(OP\(B,C,A\))d(+)j(OP\(C,A,B\))817 2526 y(SYMMETRIZE\(list)37
b(ll,op,cyclicperm)o(lis)o(t\))o(;)h(==>)1165 2626 y(OP\({A,B,C}\))h(+)
44 b(OP\({B,C,A}\))39 b(+)k(OP\({C,A,B}\))468 2830 y
FQ(Notice)31 b(that)f(taking)g(for)g(the)g(\014rst)f(argumen)m(t)h(a)g
(list)f(of)h(lists)e(giv)m(es)i(rise)f(to)i(an)468 2930
y(expression)36 b(where)g(eac)m(h)i(k)m(ernel)f(has)g(a)g
FD(list)i(as)g(ar)-5 b(gument)p FQ(.)62 b(Another)37
b(p)s(ecu-)468 3030 y(liarit)m(y)c(of)h(this)g(function)f(is)g(that,)j
(unless)d(a)i(pattern)f(matc)m(hing)h(is)e(made)i(on)468
3129 y(the)c(op)s(erator)f FJ(OP)p FQ(,)g(it)g(needs)g(to)h(b)s(e)f
(reev)-5 b(aluated.)41 b(Here)31 b(is)e(an)i(illustration:)817
3334 y FH(op\(a,b,c\):=a*b*c)o($)817 3433 y(SYMMETRIZE\(ll,op)o(,c)o
(yc)o(lic)o(pe)o(rml)o(is)o(t\))o(;)38 b(==>)1209 3533
y(OP\(A,B,C\))i(+)j(OP\(B,C,A\))d(+)j(OP\(C,A,B\))817
3633 y(for)f(all)g(x)i(let)e(op\(x,a,b\)=sin\(x*)o(a*)o(b\);)817
3732 y(SYMMETRIZE\(ll,op)o(,c)o(yc)o(lic)o(pe)o(rml)o(is)o(t\))o(;)c
(==>)1253 3832 y(OP\(B,C,A\))h(+)44 b(SIN\(A*B*C\))39
b(+)k(OP\(A,B,C\))468 4050 y FQ(The)d(functions)f FJ(SORTNUMLIST)f
FQ(and)i FJ(SORTLIST)f FQ(are)i(functions)e(whic)m(h)g(sort)468
4162 y(lists.)g(They)30 b(use)g FD(bubblesort)h FQ(and)f
FD(quicksort)g FQ(algorithms.)468 4312 y FJ(SORTNUMLIST)35
b FQ(tak)m(es)k(as)f(argumen)m(t)g(a)g(list)e(of)i(n)m(um)m(b)s(ers.)61
b(It)37 b(sorts)h(it)f(in)f(in-)468 4424 y(creasing)30
b(order.)468 4560 y FJ(SORTLIST)36 b FQ(is)h(a)i(generalisation)e(of)h
(the)h(ab)s(o)m(v)m(e)g(function.)63 b(It)38 b(sorts)g(the)h(list)468
4660 y(according)d(to)i(an)m(y)e(w)m(ell)g(de\014ned)f(ordering.)58
b(Its)36 b(\014rst)g(argumen)m(t)h(is)e(the)i(list)468
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(function.)83 b(The)44 b(con)m(ten)m(t)j(of)468 4859
y(the)33 b(list)e(is)h(not)h(necessary)g(n)m(um)m(b)s(ers)e(but)h(m)m
(ust)g(b)s(e)g(suc)m(h)h(that)g(the)g(ordering)468 4959
y(function)c(has)h(a)h(meaning.)p eop
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252 251 bop 664 299 a @beginspecial @setspecial @endspecial
FQ(252)497 b FM(CHAPTER)29 b(23.)72 b(ASSIST:)29 b(V)-10
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b(SORTNUMLIST)39 b(l;)261 b(==>)42 b({0,1,3,4})1240 655
y(ll:={1,a,tt,z}$)c(SORTLIST\(ll,ord)o(p\))o(;)g(==>)k({a,z,tt,1})891
880 y FQ(Note:)e(using)23 b(these)i(functions)e(for)h(k)m(ernels)g(or)h
(bags)f(ma)m(y)h(b)s(e)f(dangerous)h(since)891 993 y(they)33
b(are)f(destructiv)m(e.)47 b(If)31 b(it)h(is)f(needed,)i(it)f(is)f
(recommended)h(\014rst)f(to)i(apply)891 1106 y FJ(KERNLIST)c
FQ(on)h(them.)891 1243 y(The)39 b(function)g FJ(EXTREMUM)e
FQ(is)h(a)i(generalisation)f(of)g(the)h(functions)e FJ(MIN)h
FQ(and)891 1342 y FJ(MAX)d FQ(to)h(include)d(general)i(orderings.)57
b(It)36 b(is)g(a)g(2)h(argumen)m(ts)f(function.)57 b(The)891
1442 y(\014rst)32 b(is)g(the)h(list)f(and)g(the)h(second)f(is)g(the)h
(ordering)f(function.)46 b(With)32 b(the)h(list)891 1542
y FJ(ll)d FQ(de\014ned)f(in)g(the)i(last)f(example,)g(one)h(gets)1240
1753 y FH(EXTREMUM\(ll,ordp\))o(;)37 b(==>)43 b(1)745
1965 y FQ(iii.)g(There)30 b(are)h(four)f(functions)f(to)i(iden)m(tify)e
(dep)s(endencies.)39 b FJ(FUNCVAR)29 b FQ(tak)m(es)j(an)m(y)891
2065 y(expression)38 b(as)g(argumen)m(t)h(and)f(returns)f(the)i(set)f
(of)h(v)-5 b(ariables)37 b(on)h(whic)m(h)f(it)891 2164
y(dep)s(ends.)i(Constan)m(ts)31 b(are)g(eliminated.)1240
2376 y FH(FUNCVAR\(e+pi+sin\()o(lo)o(g\()o(y\)\))o(;)37
b(==>)43 b({y})891 2588 y FJ(DEPATOM)31 b FQ(has)i(an)g
FN(atom)e FQ(as)i(argumen)m(t.)49 b(It)33 b(returns)e(its)h(argumen)m
(t)i(if)d(it)i(is)f(a)891 2687 y(n)m(um)m(b)s(er)c(or)g(if)f(no)i(dep)s
(endency)e(has)h(previously)e(b)s(een)h(declared.)40
b(Otherwise,)891 2787 y(it)45 b(returns)f(the)h(list)f(of)h(v)-5
b(ariables)44 b(on)h(whic)m(h)f(in)g(dep)s(ends)f(as)j(declared)e(in)
891 2886 y(v)-5 b(arious)30 b FJ(DEPEND)e FQ(declarations.)1240
3098 y FH(DEPEND)41 b(a,x,y;)1240 3198 y(DEPATOM)g(a;)304
b(==>)42 b({x,y})891 3409 y FQ(The)36 b(functions)f FJ(EXPLICIT)f
FQ(and)i FJ(IMPLICIT)e FQ(mak)m(e)j(explicit)d(or)j(implicit)c(the)891
3509 y(dep)s(endencies.)1240 3721 y FH(depend)41 b(a,x;)h(depend)f
(x,y,z;)1240 3820 y(EXPLICIT)f(a;)261 b(==>)42 b(a\(x\(y,z\)\))1240
3920 y(IMPLICIT)e(ws;)217 b(==>)42 b(a)891 4145 y FQ(These)34
b(are)f(useful)f(when)g(one)i(do)s(es)f(not)h(kno)m(w)f(the)h(names)f
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(of)h(the)f(dep)s(endencies.)891 4395 y FJ(KORDERLIST)g
FQ(is)i(a)h(zero)g(argumen)m(t)g(function)f(whic)m(h)f(displa)m(y)g
(the)i(actual)g(or-)891 4495 y(dering.)1240 4706 y FH(KORDER)41
b(x,y,z;)1240 4806 y(KORDERLIST;)257 b(==>)42 b(\(x,y,z\))p
eop
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253 252 bop 241 299 a @beginspecial @setspecial @endspecial
FM(23.6.)72 b(PR)m(OPER)-8 b(TIES)30 b(AND)h(FLA)m(GS)1434
b FQ(253)324 555 y(iv.)45 b(A)32 b(function)f FJ(SIMPLIFY)f
FQ(whic)m(h)h(tak)m(es)i(an)f(arbitrary)f(expression)g(is)g(a)m(v)-5
b(ailable)468 655 y(whic)m(h)39 b FD(for)-5 b(c)g(es)41
b FQ(do)m(wn-to-the-b)s(ottom)h(simpli\014cation)36 b(of)k(an)g
(expression.)68 b(It)468 754 y(is)31 b(useful)f(with)h
FJ(SYMMETRIZE)p FQ(.)e(It)k(has)e(also)h(pro)m(v)m(ed)h(useful)d(to)j
(simplify)28 b(some)468 854 y(output)i(expressions)f(of)i(the)f(pac)m
(k)-5 b(age)32 b(EX)m(CALC)f(\(c)m(hapter)g @beginspecial
@setspecial @endspecial(39)q(\).)817 1058 y FH(l:=op\(x,y,z\)$)817
1158 y(op\(x,y,z\):=x*y*z)o($)817 1258 y(SYMMETRIZE\(l,op,)o(cy)o(cl)o
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(z,x)o(\)+)o(op\()o(z,)o(x,)o(y\))817 1457 y(SIMPLIFY)j(ws;)260
b(==>)43 b(op\(y,z,x\)+op\(z,)o(x,y)o(\)+)o(x*y)o(*z)349
1675 y FQ(v.)j(Filtering)29 b(functions)g(for)h(lists.)468
1824 y FJ(CHECKPROLIST)d FQ(is)i(a)h(b)s(o)s(olean)f(function)g(whic)m
(h)f(c)m(hec)m(ks)k(if)d(the)h(elemen)m(ts)g(of)g(a)468
1937 y(list)19 b(ha)m(v)m(e)j(a)f(de\014nite)e(prop)s(ert)m(y)-8
b(.)38 b(Its)20 b(\014rst)g(argumen)m(t)h(is)e(the)i(list,)h(and)d(its)
h(second)468 2050 y(argumen)m(t)43 b(is)f(a)h(b)s(o)s(olean)f(function)
f(\()p FJ(FIXP)47 b(NUMBERP)f FL(:)15 b(:)g(:)q FQ(\))43
b(or)g(an)g(ordering)468 2162 y(function)29 b(\(as)i
FJ(ORDP)p FQ(\).)468 2298 y FJ(EXTRACTLIST)25 b FQ(extracts)k(from)f
(the)g(list)e(giv)m(en)i(as)g(its)g(\014rst)f(argumen)m(t)h(the)g(ele-)
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(function)f(giv)m(en)h(as)h(its)e(second)i(argumen)m(t.)817
2602 y FH(l:={1,a,b,"st"\)$)817 2702 y(EXTRACTLIST\(l,fi)o(xp)o(\);)168
b(==>)42 b({1})817 2802 y(EXTRACTLIST\(l,st)o(ri)o(ng)o(p\);)37
b(==>)42 b({st})241 2956 y @beginspecial @setspecial
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3389 y FQ(It)38 b(ma)m(y)g(b)s(e)g(useful)e(to)i(pro)m(vide)f
(analogous)i(functions)d(in)h(algebraic)g(mo)s(de)h(to)g(the)241
3502 y(prop)s(erties)j(and)h(\015ags)h(of)g(LISP)-8 b(.)42
b(Just)g(using)f(the)i(sym)m(b)s(olic)e(mo)s(de)i(functions)e(to)241
3615 y(alter)26 b(prop)s(ert)m(y)h(lists)e(of)i(ob)5
b(jects)27 b(ma)m(y)g(easily)f(destro)m(y)i(the)f(in)m(tegrit)m(y)f(of)
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(describ)s(ed)d FN(do)47 b(ignore)41 b FQ(the)g(prop)s(ert)m(y)f(list)f
(and)241 3841 y(\015ags)44 b(already)f(de\014ned)f(b)m(y)i(the)g
(system)g(itself.)79 b(They)43 b(generate)i(and)e(trac)m(k)i(the)241
3954 y FD(additional)38 b(pr)-5 b(op)g(erties)39 b(and)d(\015ags)f
FQ(that)f(the)g(user)g(issues)e(using)h(them.)51 b(They)33
b(o\013er)241 4067 y(the)d(p)s(ossibilit)m(y)d(of)k(w)m(orking)e(on)i
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4298 y FN(i.)46 b(Flags)g FQ(T)-8 b(o)33 b(a)g(giv)m(en)f(iden)m
(ti\014er,)g(one)h(ma)m(y)g(asso)s(ciates)g(another)g(one)g(link)m(ed)e
(to)i(it)468 4411 y(\\in)27 b(the)h(bac)m(kground".)40
b(The)27 b(three)h(functions)e FJ(PUTFLAG)p FQ(,)g FJ(DISPLAYFLAG)e
FQ(and)468 4524 y FJ(CLEARFLAG)k FQ(handle)h(them.)468
4660 y FJ(PUTFLAG)i FQ(has)i(3)g(argumen)m(ts.)48 b(The)33
b(\014rst)f(is)g(the)h(iden)m(ti\014er)e(or)i(a)g(list)f(of)h(iden-)468
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(\015ag,)j(the)e(third)d(is)i(T)g(\(true\))h(or)f(0)468
4859 y(\(zero\).)42 b(When)29 b(the)g(third)e(argumen)m(t)i(is)f(T,)h
(it)f(creates)j(the)e(\015ag,)h(when)e(it)g(is)g(0)468
4959 y(it)i(destro)m(ys)h(it.)p eop
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254 253 bop 664 299 a @beginspecial @setspecial @endspecial
FQ(254)497 b FM(CHAPTER)29 b(23.)72 b(ASSIST:)29 b(V)-10
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y(PUTFLAG\(z2,flag1_)o(na)o(me)o(,0\))o(;)255 b(==>)891
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1277 y(DISPLAYFLAG)c(z2;)173 b(==>)43 b({})891 1502 y
FJ(CLEARFLAG)26 b FQ(is)h(a)h(command)g(whic)m(h)f(clears)h
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1615 y(ti\014ers)i FL(id)1223 1629 y FO(1)1263 1615 y
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4810 y(functions.)i(They)30 b(are:)p eop
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255 254 bop 241 299 a @beginspecial @setspecial @endspecial
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FJ(ALATOMP)27 b FQ(has)j(the)f(v)-5 b(alue)29 b(T)g(i\013)g(x)g(is)f
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f(the)i(expression)e(x)h(dep)s(ends)f(on)h(v)g(at)h FN(an)m(y)k(lev)m
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1816 y(functions)j(to)i(ease)g(the)g(v)m(eri\014cation)f(of)h(their)e
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2236 y(ii.)44 b(The)28 b(next)g(functions)f(allo)m(w)h(one)h(to)g
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(t)468 2336 y(of)i(REDUCE)f(whic)m(h)f(is)g(created)i(b)m(y)g(the)f
(user)g(while)e(w)m(orking)i(in)m(teractiv)m(ely)-8 b(.)468
2436 y(Tw)m(o)31 b(functions)e(are)h(pro)m(vided:)468
2535 y FJ(SHOW)j FQ(allo)m(ws)g(to)h(get)h(the)f(v)-5
b(arious)32 b(iden)m(ti\014ers)g(already)h(assigned)g(and)g(to)i(see)
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(clears)468 2735 y(them)34 b(all.)49 b(It)34 b(is)e(to)j(b)s(e)d
(stressed)i(that)g(iden)m(ti\014ers)e(assigned)h(from)g(the)g(input)468
2834 y(of)c(\014les)f(are)i FN(ignored)p FQ(.)40 b(Both)30
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2934 y(options)h(for)g(this)f(argumen)m(t:)773 3111 y
FH(SHOW)42 b(\(SUPPRESS\))e(all)773 3210 y(SHOW)i(\(SUPPRESS\))e
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y(SHOW)i(\(SUPPRESS\))e(saveids)171 b(\(for)42 b(saved)f(expressions\))
773 3509 y(SHOW)h(\(SUPPRESS\))e(matrices)773 3609 y(SHOW)i
(\(SUPPRESS\))e(arrays)773 3708 y(SHOW)i(\(SUPPRESS\))e(vectors)1471
3808 y(\(contains)f(vector,)i(index)h(and)g(tvector\))773
3908 y(SHOW)g(\(SUPPRESS\))e(forms)468 4084 y FQ(The)28
b(option)g FJ(all)f FQ(is)h(the)g(most)h(con)m(v)m(enien)m(t)g(for)f
FJ(SHOW)g FQ(but)f(it)h(ma)m(y)h(tak)m(es)h(time)468
4184 y(to)j(get)f(the)g(answ)m(er)g(after)g(one)g(has)g(w)m(ork)m(ed)g
(sev)m(eral)g(hours.)44 b(When)32 b(en)m(tering)468 4284
y(REDUCE)e(the)h(option)f FJ(all)f FQ(for)h FJ(SHOW)g
FQ(giv)m(es:)817 4461 y FH(SHOW)42 b(all;)390 b(==>)43
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4660 y(lists)f(are:)h(NIL)1776 4759 y(matrices)e(are:)i(NIL)1776
4859 y(vectors)e(are:)i(NIL)1776 4959 y(forms)f(are:)h(NIL)p
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256 255 bop 664 299 a @beginspecial @setspecial @endspecial
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b(arious)26 b(options.)39 b(Starting)26 b(from)891 655
y(a)31 b(fresh)f(en)m(vironmen)m(t)1240 864 y FH(a:=b:=1$)1240
964 y(SHOW)42 b(scalars;)215 b(==>)86 b(scalars)40 b(are:)i(\(A)h(B\))
1240 1063 y(SUPPRESS)d(scalars;)h(==>)h(t)1240 1163 y(SHOW)g(scalars;)
215 b(==>)86 b(scalars)40 b(are:)i(NIL)745 1385 y FQ(iii.)h(The)e
FJ(CLEAR)e FQ(function)g(of)i(the)f(system)h(do)s(es)f(not)h(do)g(a)g
(complete)g(cleaning)891 1498 y(of)31 b FJ(OPERATORS)d
FQ(and)i FJ(FUNCTIONS)p FQ(.)f(The)h(follo)m(wing)f(t)m(w)m(o)j
(functions)d(do)i(a)g(more)891 1611 y(complete)f(cleaning)f(and,)g
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FD(user)891 1724 y FQ(\015ag)d(and)f(prop)s(erties)e(that)j(the)f
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891 1837 y(in)m(tro)s(duced.)891 1973 y(Their)40 b(names)h(are)g
FJ(CLEAROP)e FQ(and)i FJ(CLEARFUNCTIONS)p FQ(.)c FJ(CLEAROP)i
FQ(tak)m(es)k(one)891 2073 y(op)s(erator)27 b(as)f(its)f(argumen)m(t.)
40 b FJ(CLEARFUNCTIONS)22 b FQ(is)j(a)i(nary)e(command.)39
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664 3531 y(and)30 b(sev)m(eral)h(new)f(facilities)e(to)j(manipulate)e
(p)s(olynomials.)795 3753 y(i.)45 b(Tw)m(o)d(functions)d
FJ(ALG)p 1659 3753 29 4 v 34 w(TO)p 1789 3753 V 34 w(SYMB)g
FQ(and)i FJ(SYMB)p 2434 3753 V 33 w(TO)p 2563 3753 V
34 w(ALG)f FQ(allo)m(w)h(the)g(c)m(hanging)g(of)891 3853
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(and)g(vice-v)m(ersa.)70 b(This)37 b(is)i(made)h(in)e(suc)m(h)i(a)g(w)m
(a)m(y)g(that)891 4052 y(the)h(sym)m(b)s(ol)d FJ(list)h
FQ(whic)m(h)g(app)s(ears)g(in)g(the)h(algebraic)g(mo)s(de)f(disapp)s
(ear)f(in)891 4152 y(the)44 b(sym)m(b)s(olic)e(form)h(\(there)h(it)f(b)
s(ecomes)h(a)g(paren)m(thesis)e(\\\(\)")j(\))f(and)f(it)g(is)891
4251 y(rein)m(tro)s(duced)30 b(in)h(the)g(translation)g(from)g(a)h(sym)
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m(w)h(the)f(w)m(ell-kno)m(wn)891 4451 y(lisp)21 b(function)g
FJ(FLATTENS)g FQ(can)i(b)s(e)f(trivially)e(transp)s(ortd)h(in)m(to)i
(algebraic)f(mo)s(de:)1109 4660 y FH(algebraic)40 b(procedure)g(ecrase)
h(x;)1109 4759 y(lisp)h(symb_to_alg)d(flattens1)h(alg_to_symb)f
(algebraic)h(x;)1153 4959 y(symbolic)g(procedure)g(flattens1)g(x;)p
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257 256 bop 241 299 a @beginspecial @setspecial @endspecial
FM(23.8.)72 b(HANDLING)32 b(OF)e(POL)-8 b(YNOMIALS)1220
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754 y(if)f(atom)g(x)i(then)e(list)f(x)j(else)817 854
y(if)e(cdr)h(x)g(then)991 954 y(append\(flattens1)37
b(car)42 b(x,)h(flattens1)d(cdr)i(x\))904 1053 y(else)g(flattens1)e
(car)i(x;)468 1265 y FQ(giv)m(es,)31 b(for)f(instance,)817
1477 y FH(ll:={a,{b,{c},d,)o(e})o(,{)o({{z)o(}})o(}}$)817
1576 y(ECRASE)41 b(ll;)h(==>)h({A,)f(B,)h(C,)f(D,)h(E,)g(Z})347
1788 y FQ(ii.)h FJ(LEADTERM)37 b FQ(and)h FJ(REDEXPR)f
FQ(are)i(the)h(algebraic)e(equiv)-5 b(alen)m(t)39 b(of)g(the)g(sym)m(b)
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FQ(.)f(They)h(giv)m(e)g(the)h FD(le)-5 b(ading)40 b(term)d
FQ(and)g(the)g FD(r)-5 b(e)g(ductum)468 1987 y FQ(of)29
b(a)h(p)s(olynomial.)37 b(They)29 b(also)g(w)m(ork)g(for)g(rational)f
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(v)-5 b(ariable.)468 2187 y(They)30 b(w)m(ork)g(according)h(to)g(the)f
(curren)m(t)h(ordering)e(of)h(the)h(system:)817 2398
y FH(pol:=x+y+z$)817 2498 y(LEADTERM)40 b(pol;)i(==>)g(x)817
2598 y(korder)f(y,x,z;)817 2697 y(LEADTERM)f(pol;)i(==>)g(y)817
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b(p)s(olynomials)e(is)i(recur-)468 3135 y(siv)m(e.)81
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3473 y(Ho)m(w)m(ev)m(er,)35 b(v)m(ery)e(often)g(one)g(needs)f(to)i
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3699 y(is)i(pro)m(vided)f(b)m(y)i(the)g(pac)m(k)-5 b(age)42
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3925 y(can)37 b(b)s(e)e(a)i(problem.)57 b(So,)38 b(a)f(new)f(switc)m(h)
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4038 y FQ(p)s(olynomials.)38 b(It)29 b(is)g(called)g
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4677 y FJ(SPLITTERMS)h FQ(is)i(analoguous)h(to)h FJ(MONOM)d
FQ(except)j(that)g(it)f(giv)m(es)g(a)g(list)f(of)h(t)m(w)m(o)468
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258 257 bop 664 299 a @beginspecial @setspecial @endspecial
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y(4)1056 4307 y(TRIGEXPAND)c(ws;)i(==>)1362 4407 y(3)784
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261 260 bop 241 299 a @beginspecial @setspecial @endspecial
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262 261 bop 664 299 a @beginspecial @setspecial @endspecial
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2449 y(as)i(a)g(bag.)745 2635 y(iii.)43 b(F)-8 b(unctions)34
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263 262 bop 241 299 a @beginspecial @setspecial @endspecial
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326 325 bop 664 299 a @beginspecial @setspecial @endspecial
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eop
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eop
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eop
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335 334 bop 241 299 a @beginspecial @setspecial @endspecial
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eop
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338 337 bop 664 299 a @beginspecial @setspecial @endspecial
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339 338 bop 241 299 a @beginspecial @setspecial @endspecial
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340 339 bop 664 299 a @beginspecial @setspecial @endspecial
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eop
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389 388 bop 241 299 a @beginspecial @setspecial @endspecial
165 x @beginspecial @setspecial @endspecial 764 x FI(Chapter)64
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390 389 bop 664 299 a @beginspecial @setspecial @endspecial
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3854 y FH(INVTORDER)i(REVGRADLEX,)f({x,y,z};)664 4054
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4153 y(2*x)f(+)h(y**2*z)e(+)j(1/2,)1231 4253 y(x**2*z)d(-)i(1/2*x)f(-)h
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y(g)43 b(:=)g({8*x*y*z)84 b(-)43 b(2*x*y*z)84 b(+)44
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b(-)43 b(96*x)f(+)h(20*z)f(-)h(9,)p eop
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391 390 bop 241 299 a @beginspecial @setspecial @endspecial
FM(48.1.)72 b(THE)30 b(BASIC)g(OPERA)-8 b(TORS)1480 b
FQ(391)633 555 y FH(3)502 655 y(2*y)43 b(*z)f(+)i(4*x*y)d(+)i(y,)720
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4280 y(7)261 b(6)174 b(5)304 b(4)h(3)348 b(2)502 4379
y(16*z)86 b(-)43 b(8*z)86 b(+)43 b(z)87 b(+)43 b(52*z)86
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4578 y(-)f(60})p eop
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392 391 bop 664 299 a @beginspecial @setspecial @endspecial
FQ(392)792 b FM(CHAPTER)30 b(48.)72 b(INVBASE:)30 b(INV)m(OLUTIVE)h
(BASES)p eop
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393 392 bop 241 299 a @beginspecial @setspecial @endspecial
165 x @beginspecial @setspecial @endspecial 764 x FI(Chapter)64
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y FQ(393)p eop
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394 393 bop 664 299 a @beginspecial @setspecial @endspecial
FQ(394)322 b FM(CHAPTER)30 b(49.)72 b(LAPLA)m(CE:)30
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b(-)1013 1153 y(for)42 b(i:=n-1)f(step)h(-1)h(until)f(0)h(sum)1100
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y(17)664 2938 y(----------)751 3038 y(2)708 3137 y(p)87
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3934 y(4)664 4034 y(-----------------)o(--)o(--)o(-)751
4133 y(k*p)708 4233 y(e)130 b(*sqrt\()41 b(-)i(a)h(+)f(p\))664
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b(t\);)882 4632 y(a*t)173 b(b*t)708 4731 y(c*\(e)f(-)44
b(e)130 b(\))664 4831 y(-----------------)926 4930 y(a)43
b(-)g(b)p eop
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395 394 bop 241 299 a @beginspecial @setspecial @endspecial
2852 w FQ(395)241 655 y FH(invlap\(p**\(-7/3\))o(,)37
b(p,)43 b(t\);)415 854 y(1/3)372 954 y(t)130 b(*t)241
1053 y(------------)589 1153 y(7)284 1253 y(gamma\(---\))589
1352 y(3)p eop
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396 395 bop 664 299 a @beginspecial @setspecial @endspecial
FQ(396)322 b FM(CHAPTER)30 b(49.)72 b(LAPLA)m(CE:)30
b(LAPLA)m(CE)h(TRANSF)m(ORMS)f(ETC.)p eop
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397 396 bop 241 299 a @beginspecial @setspecial @endspecial
165 x @beginspecial @setspecial @endspecial 764 x FI(Chapter)64
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407 406 bop 241 299 a @beginspecial @setspecial @endspecial
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408 407 bop 664 299 a @beginspecial @setspecial @endspecial
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3366 y(@)2746 3141 y FQ(0)e(0)h(0)f FP(\000)p FQ(11)2746
3254 y(1)g(0)h(0)142 b(0)2746 3367 y(0)83 b(1)h(0)142
b(9)2746 3480 y(0)83 b(0)h(1)f FP(\000)p FQ(17)3335 3067
y FB(1)3335 3213 y(C)3335 3263 y(C)3335 3313 y(C)3335
3366 y(A)664 3716 y FQ(The)37 b(p)s(olynomial)e(asso)s(ciated)j(with)f
(a)h(companion)f(matrix)g(can)h(b)s(e)f(reco)m(v)m(ered)i(b)m(y)664
3829 y(calling)29 b FJ(FIND)p 1150 3829 29 4 v 33 w(COMPANION)p
FQ(.)664 3992 y FJ(HESSIAN)p FQ(\(expr,)23 b(v)-5 b(ar)p
1387 3992 28 4 v 33 w(list\))22 b(calculates)h(the)g(Hessian)g(matrix)f
(of)h(the)h(expressions)d(with)664 4105 y(resp)s(ect)27
b(to)h(the)f(v)-5 b(ariables)25 b(in)h(the)h(list,)g(or)g(the)g(single)
e(v)-5 b(ariable.)39 b(That)26 b(is)g(the)i(matrix)664
4217 y(with)33 b(the)h(\(i,)15 b(j\))34 b(elemen)m(t)h(the)f
FL(j)1775 4185 y FF(th)1880 4217 y FQ(deriv)-5 b(ativ)m(e)34
b(of)g(the)h(expressions)d(with)h(resp)s(ect)h(to)664
4330 y(the)d FL(i)852 4297 y FF(th)953 4330 y FQ(v)-5
b(ariable.)796 4718 y FJ(hessian)n FQ(\()p FL(x)21 b
FP(\003)f FL(y)j FP(\003)e FL(z)j FQ(+)c FL(x)1646 4685
y FO(2)1686 4718 y FL(;)15 b FP(f)p FL(w)r(;)g(x;)g(y)s(;)g(z)t
FP(g)p FQ(\))86 b(=)2424 4475 y FB(0)2424 4621 y(B)2424
4671 y(B)2424 4721 y(B)2424 4774 y(@)2538 4549 y FQ(0)f(0)j(0)i(0)2538
4662 y(0)85 b(2)i FL(z)92 b(y)2538 4775 y FQ(0)84 b FL(z)92
b FQ(0)86 b FL(x)2538 4888 y FQ(0)e FL(y)h(x)i FQ(0)3026
4475 y FB(1)3026 4621 y(C)3026 4671 y(C)3026 4721 y(C)3026
4774 y(A)p eop
%%Page: 409 409
409 408 bop 241 299 a @beginspecial @setspecial @endspecial
FM(52.4.)72 b(CONSTR)m(UCTORS)1820 b FQ(409)241 555 y(Hilb)s(ert's)21
b(matrix,)k(that)f(is)f(where)g(the)h(\(i,)15 b(j\))23
b(elemen)m(t)h(is)f(1)p FL(=)p FQ(\()p FL(i)7 b FQ(+)g
FL(j)12 b FP(\000)7 b FL(x)p FQ(\))24 b(is)e(constructed)241
668 y(b)m(y)30 b FJ(HILBERT)p FQ(\(n,x\).)241 831 y(The)23
b(Jacobian)g(of)h(an)g(expression)e(list)g(with)h(resp)s(ect)h(to)g(a)g
(v)-5 b(ariable)23 b(list)f(is)h(calculated)241 944 y(b)m(y)38
b FJ(JACOBIAN)p FQ(\(expr)p 974 944 28 4 v 31 w(list,v)-5
b(ariable)p 1465 944 V 30 w(list\).)66 b(This)37 b(is)g(a)j(matrix)e
(whose)g(\(i,)15 b(j\))39 b(en)m(try)g(is)241 1057 y(df\(expr)p
535 1057 V 32 w(list\(i\),v)-5 b(ariable)p 1123 1057
V 30 w(list\(j\)\).)241 1219 y(The)24 b(square)g(Jordan)f(blo)s(c)m(k)h
(matrix)g(of)h(dimension)c FL(n)j FQ(is)g(calculated)g(b)m(y)g(the)h
(function)241 1332 y FJ(JORDAN)p 535 1332 29 4 v 32 w(BLOCK)p
FQ(\(exp,n\).)46 b(The)31 b(en)m(tries)h(of)h(the)f(Jordan)p
2182 1332 28 4 v 32 w(blo)s(c)m(k)g(matrix)f(are)i FP(J)16
b FQ(\(i,i\))32 b(=)241 1445 y(expr)e(for)g(i=1)f(.)16
b(.)f(.)h(n,)30 b FP(J)16 b FQ(\(i,i+1\))30 b(=)g(1)h(for)f(i=1)g(.)15
b(.)g(.)h(n-1,)31 b(and)e(all)h(other)g(en)m(tries)h(are)f(0.)373
1912 y FJ(jordan)p 666 1912 V 31 w(block)p FQ(\()p FJ(x)p
FL(;)15 b FJ(5)p FQ(\))82 b(=)1374 1619 y FB(0)1374 1765
y(B)1374 1815 y(B)1374 1865 y(B)1374 1915 y(B)1374 1964
y(B)1374 2018 y(@)1488 1686 y FL(x)k FQ(1)k(0)g(0)g(0)1491
1799 y(0)d FL(x)f FQ(1)k(0)g(0)1491 1912 y(0)g(0)d FL(x)f
FQ(1)k(0)1491 2025 y(0)g(0)g(0)d FL(x)f FQ(1)1491 2138
y(0)k(0)g(0)g(0)d FL(x)2121 1619 y FB(1)2121 1765 y(C)2121
1815 y(C)2121 1865 y(C)2121 1915 y(C)2121 1964 y(C)2121
2018 y(A)241 2380 y FJ(MAKE)p 439 2380 29 4 v 33 w(IDENTITY)p
FQ(\(n\))28 b(generates)k(the)f FL(n)19 b FP(\002)h FL(n)30
b FQ(iden)m(tit)m(y)g(matrix.)241 2542 y FJ(RANDOM)p
535 2542 V 32 w(MATRIX)p FQ(\(r,c,limit\))39 b(generates)k(and)d
FL(r)30 b FP(\002)d FL(c)41 b FQ(matrix)g(with)f(random)g(v)-5
b(alues)241 2655 y(limited)25 b(b)m(y)i FJ(limit)p FQ(.)38
b(The)27 b(t)m(yp)s(e)g(of)h(en)m(tries)f(is)f(con)m(trolled)h(b)m(y)g
(a)h(n)m(um)m(b)s(er)e(of)i(switc)m(hes.)241 2918 y FJ(IMAGINARY)43
b FQ(If)20 b(on)g(then)h(matrix)e(en)m(tries)i(are)g
FL(x)q FQ(+)q FL(i)q FP(\003)q FL(y)h FQ(where)e FP(\000)p
FL(l)r(imit)25 b(<)g(x;)15 b(y)28 b(<)d(l)r(imit)p FQ(.)241
3105 y FJ(NOT)p 391 3105 V 33 w(NEGATIVE)44 b FQ(If)27
b(on)g(then)h(0)e FL(<)f(entr)s(y)i(<)e(l)r(imit)p FQ(.)40
b(In)27 b(the)h(imaginary)e(case)j(w)m(e)f(ha)m(v)m(e)468
3218 y(0)e FL(<)f(x;)15 b(y)28 b(<)d(l)r(imit)p FQ(.)241
3406 y FJ(ONLY)p 439 3406 V 33 w(INTEGER)44 b FQ(If)31
b(on)h(then)g(eac)m(h)h(en)m(try)f(is)f(an)h(in)m(teger.)46
b(In)31 b(the)h(imaginary)f(case)i FL(x)468 3519 y FQ(and)d
FL(y)j FQ(are)e(in)m(tegers.)41 b(If)30 b(o\013)g(the)h(v)-5
b(alues)30 b(are)g(rounded.)241 3706 y FJ(SYMMETRIC)43
b FQ(If)30 b(on)g(then)g(the)h(matrix)e(is)h(symmetric.)241
3894 y FJ(UPPER)p 487 3894 V 33 w(MATRIX)44 b FQ(If)29
b(on)i(then)f(the)g(matrix)g(is)g(upp)s(er)e(triangular.)241
4082 y FJ(LOWER)p 487 4082 V 33 w(MATRIX)44 b FQ(If)29
b(on)i(then)f(the)g(matrix)g(is)g(lo)m(w)m(er)g(triangular.)373
4436 y FJ(random)p 666 4436 28 4 v 31 w(matrix)n FQ(\(3)p
FL(;)15 b FQ(3)p FL(;)g FQ(10\))86 b(=)1548 4242 y FB(0)1548
4388 y(B)1548 4441 y(@)1662 4323 y FP(\000)p FQ(4)p FL(:)p
FQ(729721)99 b(6)p FL(:)p FQ(987047)134 b(7)p FL(:)p
FQ(521383)1662 4436 y FP(\000)p FQ(5)p FL(:)p FQ(224177)99
b(5)p FL(:)p FQ(797709)g FP(\000)p FQ(4)p FL(:)p FQ(321952)1662
4549 y FP(\000)p FQ(9)p FL(:)p FQ(418455)86 b FP(\000)p
FQ(9)p FL(:)p FQ(94318)g FP(\000)p FQ(0)p FL(:)p FQ(730980)3067
4242 y FB(1)3067 4388 y(C)3067 4441 y(A)370 4902 y FJ(on)47
b(only)p 711 4902 29 4 v 34 w(integer,)e(not)p 1318 4902
V 34 w(negative,)g(upper)p 2069 4902 V 33 w(matrix,)h(imaginary;)p
eop
%%Page: 410 410
410 409 bop 664 299 a @beginspecial @setspecial @endspecial
FQ(410)440 b FM(CHAPTER)30 b(52.)72 b(LINALG:)31 b(LINEAR)f(ALGEBRA)h
(P)-8 b(A)m(CKA)m(GE)706 812 y FJ(random)p 999 812 28
4 v 31 w(matrix)n FQ(\(4)p FL(;)15 b FQ(4)p FL(;)g FQ(10\))86
b(=)1881 568 y FB(0)1881 715 y(B)1881 764 y(B)1881 814
y(B)1881 867 y(@)1995 643 y FQ(2)21 b FP(\003)g FL(i)f
FQ(+)g(5)84 b(3)20 b FP(\003)h FL(i)f FQ(+)g(7)84 b(7)20
b FP(\003)h FL(i)g FQ(+)f(3)220 b(6)2132 755 y(0)h(2)20
b FP(\003)h FL(i)f FQ(+)g(5)84 b(5)20 b FP(\003)h FL(i)g
FQ(+)f(1)83 b(2)21 b FP(\003)f FL(i)h FQ(+)f(1)2132 868
y(0)357 b(0)h(8)364 b FL(i)2132 981 y FQ(0)357 b(0)h(0)220
b(5)21 b FP(\003)f FL(i)h FQ(+)f(9)3563 568 y FB(1)3563
715 y(C)3563 764 y(C)3563 814 y(C)3563 867 y(A)664 1193
y FJ(TOEPLITZ)33 b FQ(creates)j(the)g(T)-8 b(o)s(eplitz)34
b(matrix)g(from)h(the)g(giv)m(en)g(expression)e(list.)54
b(This)664 1306 y(is)31 b(a)i(square)f(symmetric)f(matrix)g(in)g(whic)m
(h)g(the)h(\014rst)f(expression)g(is)g(placed)h(on)g(the)664
1419 y(diagonal)k(and)g(the)h FL(i)1411 1386 y FF(th)1519
1419 y FQ(expression)e(is)h(placed)g(on)h(the)g(\()p
FL(i)25 b FP(\000)f FQ(1\))2912 1386 y FF(th)3020 1419
y FQ(sub-)36 b(and)g(sup)s(er-)664 1532 y(diagonals.)k(It)31
b(has)f(dimension)d(equal)j(to)h(the)g(n)m(um)m(b)s(er)e(of)i
(expressions.)706 1937 y FJ(toeplitz)n FQ(\()p FP(f)p
FL(w)r(;)15 b(x;)g(y)s(;)g(z)t FP(g)p FQ(\))86 b(=)1821
1694 y FB(0)1821 1840 y(B)1821 1890 y(B)1821 1939 y(B)1821
1993 y(@)1935 1768 y FL(w)93 b(x)101 b(y)106 b(z)1943
1881 y(x)90 b(w)k(x)100 b(y)1945 1994 y(y)j(x)91 b(w)i(x)1945
2106 y(z)108 b(y)c(x)90 b(w)2496 1694 y FB(1)2496 1840
y(C)2496 1890 y(C)2496 1939 y(C)2496 1993 y(A)664 2343
y FJ(VANDERMONDE)26 b FQ(creates)31 b(the)e(V)-8 b(andermonde)28
b(matrix)h(from)f(the)i(expression)d(list;)i(the)664
2456 y(square)h(matrix)g(in)f(whic)m(h)g(the)i(\(i,)15
b(j\))30 b(en)m(try)h(is)e(expr)p 2472 2456 V 32 w(list\(i\))2747
2423 y FO(\()p FF(j)t Fu(\000)p FO(1\))2929 2456 y FQ(.)796
2815 y FJ(vandermonde)m FQ(\()p FP(f)p FL(x;)15 b FQ(2)22
b FP(\003)e FL(y)s(;)15 b FQ(3)21 b FP(\003)g FL(z)t
FP(g)p FQ(\))84 b(=)2209 2621 y FB(0)2209 2768 y(B)2209
2821 y(@)2323 2702 y FQ(1)147 b FL(x)210 b(x)2829 2669
y FO(2)2323 2815 y FQ(1)83 b(2)21 b FP(\003)g FL(y)86
b FQ(4)20 b FP(\003)h FL(y)2893 2782 y FO(2)2323 2928
y FQ(1)84 b(3)21 b FP(\003)g FL(z)88 b FQ(9)21 b FP(\003)g
FL(z)2892 2895 y FO(2)2974 2621 y FB(1)2974 2768 y(C)2974
2821 y(A)664 3174 y FQ(The)h(direct)f(pro)s(duct)g(\(or)h(tensor)g(pro)
s(duct\))f(is)g(created)i(b)m(y)f(the)g FJ(KRONECKER)p
3293 3174 29 4 v 32 w(PRODUCT)664 3287 y FQ(function.)664
3518 y FH(a1)43 b(:=)g(mat\(\(1,2\),\(3,4\))o(,\(5)o(,6)o(\)\)$)664
3618 y(a2)g(:=)g(mat\(\(1,1,1\),\(2,)o(z,2)o(\),)o(\(3,)o(3,)o(3\)\))o
($)664 3717 y(kronecker_product)o(\(a)o(1,)o(a2\))o(;)796
3889 y FB(0)796 4035 y(B)796 4085 y(B)796 4134 y(B)796
4184 y(B)796 4234 y(B)796 4284 y(B)796 4334 y(B)796 4383
y(B)796 4433 y(B)796 4483 y(B)796 4533 y(B)796 4583 y(B)796
4632 y(B)796 4682 y(B)796 4735 y(@)933 3954 y FQ(1)172
b(1)g(1)129 b(2)173 b(2)f(2)933 4067 y(2)g FL(z)j FQ(2)129
b(4)107 b(2)20 b FP(\003)h FL(z)110 b FQ(4)933 4180 y(3)172
b(3)g(3)129 b(6)173 b(6)f(6)933 4293 y(3)g(3)g(3)129
b(4)173 b(4)f(4)933 4406 y(6)106 b(3)21 b FP(\003)f FL(z)110
b FQ(6)129 b(8)107 b(4)20 b FP(\003)h FL(z)110 b FQ(8)933
4519 y(9)172 b(9)g(9)107 b(12)127 b(12)g(12)933 4632
y(5)172 b(5)g(5)129 b(6)173 b(6)f(6)910 4745 y(10)84
b(5)21 b FP(\003)f FL(z)88 b FQ(10)c(12)g(6)20 b FP(\003)h
FL(z)87 b FQ(12)910 4858 y(15)127 b(15)h(15)84 b(18)127
b(18)g(18)2086 3889 y FB(1)2086 4035 y(C)2086 4085 y(C)2086
4134 y(C)2086 4184 y(C)2086 4234 y(C)2086 4284 y(C)2086
4334 y(C)2086 4383 y(C)2086 4433 y(C)2086 4483 y(C)2086
4533 y(C)2086 4583 y(C)2086 4632 y(C)2086 4682 y(C)2086
4735 y(A)p eop
%%Page: 411 411
411 410 bop 241 299 a @beginspecial @setspecial @endspecial
FM(52.5.)72 b(HIGHER)31 b(ALGORITHMS)1560 b FQ(411)241
464 y @beginspecial @setspecial @endspecial 91 x FE(52.5)135
b(Higher)46 b(Algorithms)241 808 y FQ(The)23 b(Cholesky)g(decomp)s
(osition)g(of)h(a)g(matrix)g(can)g(b)s(e)f(calculated)h(with)f(the)h
(function)241 921 y FJ(CHOLESKY)p FQ(.)d(It)i(returns)f
FP(fL)p FL(;)15 b FP(U)10 b(g)24 b FQ(where)e FP(L)h
FQ(is)g(a)g(lo)m(w)m(er)h(matrix,)g FP(U)32 b FQ(is)22
b(an)i(upp)s(er)d(matrix,)241 1034 y(and)30 b FP(A)24
b FQ(=)h FP(LU)9 b FQ(,)31 b(and)e FP(U)34 b FQ(=)25
b FP(L)1222 1001 y FF(T)1277 1034 y FQ(.)241 1196 y(Gram{Sc)m(hmidt)36
b(orthonormalisation)f(can)j(b)s(e)e(calculated)h(b)m(y)g
FJ(GRAM)p 2738 1196 29 4 v 33 w(SCHMIDT)p FQ(.)e(It)241
1309 y(accepts)30 b(a)f(list)f(of)h(linearly)e(indep)s(enden)m(t)g(v)m
(ectors,)k(written)d(as)h(lists,)f(and)g(returns)g(a)241
1422 y(list)h(of)h(orthogonal)h(normalised)d(v)m(ectors.)241
1653 y FH(gram_schmidt\({{1)o(,0)o(,0)o(},{)o(1,)o(1,0)o(},)o({1,)o(1,)
o(1})o(}\);)241 1852 y({{1,0,0},{0,1,0})o(,{)o(0,)o(0,1)o(}})241
2052 y(gram_schmidt\({{1)o(,2)o(},)o({3,)o(4})o(}\);)502
2251 y(1)392 b(2)348 b(2*sqrt\(5\))171 b(-)43 b(sqrt\(5\))241
2350 y({{---------,----)o(--)o(--)o(-},)o({-)o(---)o(--)o(---)o(--)o
(,-)o(---)o(--)o(---)o(--)o(-})o(})372 2450 y(sqrt\(5\))127
b(sqrt\(5\))390 b(5)479 b(5)241 2694 y FQ(The)26 b(LU)g(decomp)s
(osition)f(of)h(a)h(real)f(or)g(imaginary)f(matrix)h(with)f(n)m(umeric)
g(en)m(tries)h(is)241 2807 y(p)s(erformed)31 b(b)m(y)h
FJ(LU)p 908 2807 V 34 w(DECOM\()p FP(A)p FJ(\))p FQ(.)45
b(It)33 b(returns)e FP(fL)p FL(;)15 b FP(U)10 b(g)33
b FQ(where)f FP(L)g FQ(is)f(a)i(lo)m(w)m(er)g(diagonal)241
2920 y(matrix,)d FP(U)39 b FQ(an)30 b(upp)s(er)f(diagonal)g(matrix)h
(and)g FP(A)25 b FQ(=)f FP(LU)9 b FQ(.)241 3083 y(Note:)56
b(the)37 b(algorithm)g(used)f(can)i(sw)m(ap)f(the)h(ro)m(ws)f(of)g
FP(A)g FQ(during)e(the)j(calculation.)241 3196 y(This)33
b(means)j(that)g FP(LU)44 b FQ(do)s(es)35 b(not)h(equal)f
FP(A)g FQ(but)g(a)h(ro)m(w)g(equiv)-5 b(alen)m(t)35 b(of)g(it.)56
b(Due)36 b(to)241 3309 y(this,)41 b FJ(lu)p 557 3309
V 34 w(decom)e FQ(returns)g FP(fL)p FL(;)15 b FP(U)9
b FQ(,v)m(ec)p FP(g)p FQ(.)72 b(The)40 b(call)f FJ(CONVERT\()p
FP(A)p FJ(,vec\))d FQ(will)i(return)241 3421 y(the)30
b(matrix)g(that)h(has)f(b)s(een)g(decomp)s(osed,)g FD(i.e.)72
b FP(LU)34 b FQ(=)c FJ(convert\()p FP(A)p FJ(,vec\))p
FQ(.)376 3776 y FP(K)d FQ(=)568 3582 y FB(0)568 3728
y(B)568 3781 y(@)717 3663 y FQ(1)119 b(3)84 b(5)682 3776
y FP(\000)p FQ(4)f(3)h(7)717 3888 y(8)119 b(6)84 b(4)1097
3582 y FB(1)1097 3728 y(C)1097 3781 y(A)282 4272 y FJ(lu)p
384 4272 V 34 w(decom)p FQ(\()p FP(K)q FQ(\))f(=)1029
4075 y FB(8)1029 4150 y(>)1029 4175 y(<)1029 4324 y(>)1029
4349 y(:)1103 4078 y(0)1103 4225 y(B)1103 4278 y(@)1252
4159 y FQ(8)177 b(0)245 b(0)1217 4272 y FP(\000)p FQ(4)141
b(6)245 b(0)1252 4385 y(1)119 b(2)p FL(:)p FQ(25)85 b(1)p
FL(:)p FQ(1251)1955 4078 y FB(1)1955 4225 y(C)1955 4278
y(A)2042 4272 y FL(;)2082 4078 y FB(0)2083 4225 y(B)2083
4278 y(@)2197 4159 y FQ(1)e(0)p FL(:)p FQ(75)i(0)p FL(:)p
FQ(5)2197 4272 y(0)141 b(1)h(1)p FL(:)p FQ(5)2197 4385
y(0)f(0)177 b(1)2728 4078 y FB(1)2728 4225 y(C)2728 4278
y(A)2816 4272 y FL(;)15 b FQ([)25 b(3)h(2)g(3)g(])3144
4075 y FB(9)3144 4150 y(>)3144 4175 y(=)3144 4324 y(>)3144
4349 y(;)241 4626 y FJ(PSEUDO)p 535 4626 V 32 w(INVERSE)p
FQ(,)35 b(also)h(kno)m(wn)f(as)i(the)f(Mo)s(ore{P)m(enrose)i(in)m(v)m
(erse,)f(computes)f(the)241 4739 y(pseudo)43 b(in)m(v)m(erse)i(of)f
FP(A)p FQ(.)83 b(Giv)m(en)45 b(the)f(singular)f(v)-5
b(alue)44 b(decomp)s(osition)f(of)h FP(A)p FQ(,)k FD(i.e.)241
4852 y FP(A)25 b FQ(=)g FP(U)516 4788 y FB(P)618 4852
y FP(V)681 4819 y FF(T)737 4852 y FQ(,)30 b(then)g(the)h(pseudo)e(in)m
(v)m(erse)i FP(A)1834 4819 y Fu(\000)p FO(1)1958 4852
y FQ(is)e(de\014ned)g(b)m(y)i FP(A)2562 4819 y Fu(\000)p
FO(1)2681 4852 y FQ(=)25 b FP(V)2840 4819 y FF(T)2910
4788 y FB(P)2998 4814 y Fu(\000)p FO(1)3107 4852 y FP(U)9
b FQ(.)p eop
%%Page: 412 412
412 411 bop 664 299 a @beginspecial @setspecial @endspecial
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b(The)28 b(m)m(ultiplication)p eop
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413 412 bop 241 299 a @beginspecial @setspecial @endspecial
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1311 3210 V 35 w(ro)m(ws)151 b(ro)m(ws)p 1857 3210 V
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414 413 bop 664 299 a @beginspecial @setspecial @endspecial
FQ(414)440 b FM(CHAPTER)30 b(52.)72 b(LINALG:)31 b(LINEAR)f(ALGEBRA)h
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415 414 bop 241 299 a @beginspecial @setspecial @endspecial
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416 415 bop 664 299 a @beginspecial @setspecial @endspecial
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417 416 bop 241 299 a @beginspecial @setspecial @endspecial
2852 w FQ(417)502 555 y FH(<mathml>)633 655 y(<apply><plus/>)764
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418 417 bop 664 299 a @beginspecial @setspecial @endspecial
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eop
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419 418 bop 241 299 a @beginspecial @setspecial @endspecial
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4 v 2086 1187 a(y)1338 1255 y Fu(\000)p FF(x)1433 1232
y Fy(2)1467 1255 y Fu(\000)p FF(x)p FO(+)p FF(y)1654
1232 y Fy(2)1688 1255 y FO(+)p FF(y)p 1338 1275 V 1541
1327 a(y)1884 1255 y Fu(\000)p FF(x)1979 1232 y Fy(2)2013
1255 y FO(+)p FF(x)p FO(+)p FF(y)2200 1232 y Fy(2)2234
1255 y Fu(\000)p FF(y)p 1884 1275 V 2086 1327 a(y)2378
1054 y FB(1)2378 1203 y(A)241 1567 y FJ(frobenius)p FQ(\()p
FP(A)p FQ(\))j(=)374 1795 y FB(8)374 1870 y(<)374 2020
y(:)447 1799 y(0)447 1948 y(@)561 1902 y FQ(0)700 1858
y FF(x)p Fu(\003)p FO(\()p FF(x)842 1835 y Fy(2)877 1858
y Fu(\000)p FF(x)p Fu(\000)p FF(y)1064 1835 y Fy(2)1098
1858 y FO(+)p FF(y)r FO(\))p 700 1881 518 4 v 940 1934
a FF(y)561 2043 y FQ(1)713 2002 y Fu(\000)p FO(2)p Fu(\003)p
FF(x)878 1979 y Fy(2)913 2002 y FO(+)p FF(x)p FO(+2)p
Fu(\003)p FF(y)1170 1979 y Fy(2)p 713 2022 492 4 v 940
2074 a FF(y)1269 1799 y FB(1)1269 1948 y(A)1357 1968
y FL(;)1397 1799 y FB(0)1397 1948 y(@)1511 1901 y FQ(1)1697
1860 y Fu(\000)p FF(x)1792 1837 y Fy(2)1826 1860 y FO(+)p
FF(y)1918 1837 y Fy(2)1953 1860 y FO(+)p FF(y)p 1697
1880 349 4 v 1853 1932 a(y)1511 2041 y FQ(0)1650 2000
y Fu(\000)p FF(x)1745 1977 y Fy(2)1779 2000 y Fu(\000)p
FF(x)p FO(+)p FF(y)1966 1977 y Fy(2)2000 2000 y FO(+)p
FF(y)p 1650 2020 443 4 v 1853 2072 a(y)2144 1799 y FB(1)2144
1948 y(A)2232 1968 y FL(;)2272 1824 y FB( )2380 1906
y FQ(1)2538 1866 y Fu(\000)p FF(x)2633 1842 y Fy(2)2667
1866 y FO(+)p FF(y)2759 1842 y Fy(2)2794 1866 y FO(+)p
FF(y)p 2518 1885 388 4 v 2518 1940 a(x)2558 1921 y Fy(2)2592
1940 y FO(+)p FF(x)p Fu(\000)p FF(y)2779 1921 y Fy(2)2814
1940 y Fu(\000)p FF(y)2380 2033 y FQ(0)2666 1993 y Fu(\000)p
FF(y)p 2518 2012 V 2518 2067 a(x)2558 2048 y Fy(2)2592
2067 y FO(+)p FF(x)p Fu(\000)p FF(y)2779 2048 y Fy(2)2814
2067 y Fu(\000)p FF(y)2957 1824 y FB(!)3023 1795 y(9)3023
1870 y(=)3023 2020 y(;)241 2231 y @beginspecial @setspecial
@endspecial 141 x FE(57.4)135 b(Ratjordan)241 2625 y
FJ(Ratjordan)p FQ(\()p FP(A)p FQ(\))30 b(computes)k(the)f(rational)f
(Jordan)g(normal)g(form)g FP(R)h FQ(of)g(the)g(matrix)241
2738 y FP(A)p FQ(.)241 2901 y(It)d(returns)f FP(fR)p
FL(;)15 b FP(P)7 b FL(;)15 b FP(P)995 2868 y Fu(\000)p
FO(1)1092 2901 y FP(g)31 b FQ(where)f FP(R)p FL(;)15
b FP(P)7 b FQ(,)32 b(and)e FP(P)1922 2868 y Fu(\000)p
FO(1)2047 2901 y FQ(are)h(suc)m(h)f(that)h FP(P)7 b(RP)2819
2865 y Fu(\000)p FO(1)2939 2901 y FQ(=)25 b FP(A)p FQ(.)241
3064 y FP(A)30 b FQ(is)f(a)i(square)f(matrix.)241 3226
y FJ(load)p 439 3226 29 4 v 33 w(package)46 b(normform;)1338
3543 y FP(A)25 b FQ(=)1532 3399 y FB( )1639 3487 y FL(x)c
FQ(+)e FL(y)109 b FQ(5)1721 3599 y FL(y)167 b(x)1985
3566 y FO(2)2066 3399 y FB(!)241 3863 y FJ(ratjordan)p
FQ(\()p FP(A)p FQ(\))28 b(=)468 4101 y FB(\( )642 4188
y FQ(0)83 b FP(\000)p FL(x)893 4155 y FO(3)953 4188 y
FP(\000)20 b FL(x)1096 4155 y FO(2)1155 4188 y FP(\003)h
FL(y)i FQ(+)d(5)g FP(\003)h FL(y)642 4301 y FQ(1)271
b FL(x)1010 4268 y FO(2)1070 4301 y FQ(+)19 b FL(x)i
FQ(+)f FL(y)1600 4101 y FB(!)1681 4245 y FL(;)1721 4101
y FB( )1829 4188 y FQ(1)83 b FL(x)21 b FQ(+)f FL(y)1829
4301 y FQ(0)165 b FL(y)2210 4101 y FB(!)2291 4245 y FL(;)2331
4101 y FB( )2438 4185 y FQ(1)2577 4141 y Fu(\000)p FO(\()p
FF(x)p FO(+)p FF(y)r FO(\))p 2577 4164 242 4 v 2679 4217
a FF(y)2438 4309 y FQ(0)2740 4273 y FO(1)p 2739 4288
38 4 v 2739 4340 a FF(y)2870 4101 y FB(!\))241 4490 y
@beginspecial @setspecial @endspecial 141 x FE(57.5)135
b(Jordansym)l(b)t(olic)241 4884 y FJ(Jordansymbolic)p
FQ(\()p FP(A)p FQ(\))56 b(computes)30 b(the)g(Jordan)f(normal)g(form)h
FP(J)16 b FQ(of)30 b(the)g(matrix)g FP(A)p FQ(.)p eop
%%Page: 434 434
434 433 bop 664 299 a @beginspecial @setspecial @endspecial
FQ(434)375 b FM(CHAPTER)30 b(57.)72 b(NORMF)m(ORM:)31
b(MA)-8 b(TRIX)31 b(NORMAL)g(F)m(ORMS)664 555 y FQ(It)c(returns)e
FP(fJ)17 b FL(;)e FP(L)p FL(;)g FP(P)7 b FL(;)15 b FP(P)1516
522 y Fu(\000)p FO(1)1613 555 y FP(g)p FQ(,)28 b(where)e
FP(J)17 b FL(;)e FP(P)7 b FQ(,)28 b(and)e FP(P)2455 522
y Fu(\000)p FO(1)2577 555 y FQ(are)h(suc)m(h)f(that)i
FP(P)7 b(J)17 b(P)3340 519 y Fu(\000)p FO(1)3459 555
y FQ(=)25 b FP(A)p FQ(.)664 668 y FP(L)k FQ(=)f FP(f)h
FD(l)5 b(l)p FQ(,)29 b FL(\030)k FP(g)p FQ(,)c(where)g
FL(\030)j FQ(is)c(a)h(name)g(and)f FD(l)5 b(l)29 b FQ(is)f(a)h(list)e
(of)i(irreducible)c(factors)30 b(of)f FD(p)6 b FQ(\()p
FL(\030)t FQ(\).)664 831 y FP(A)30 b FQ(is)f(a)i(square)f(matrix.)664
994 y FJ(load)p 862 994 29 4 v 33 w(package)46 b(normform;)1845
1388 y FP(A)25 b FQ(=)2039 1244 y FB( )2167 1331 y FQ(1)105
b FL(y)2146 1444 y(y)2194 1411 y FO(2)2318 1444 y FQ(3)2406
1244 y FB(!)664 1692 y FJ(jordansymbolic)p FQ(\()p FP(A)p
FQ(\))27 b(=)1039 1946 y @beginspecial @setspecial @endspecial
1205 1802 a FB(\( )1380 1890 y FL(\030)1420 1904 y FO(11)1612
1890 y FQ(0)1414 2003 y(0)118 b FL(\030)1617 2017 y FO(12)1733
1802 y FB(!)1814 1946 y FL(;)1854 1852 y FB(n)q(n)1965
1946 y FP(\000)p FL(y)2084 1909 y FO(3)2143 1946 y FQ(+)20
b FL(\030)2278 1909 y FO(2)2338 1946 y FP(\000)g FQ(4)g
FP(\003)h FL(\030)j FQ(+)c(3)2760 1852 y FB(o)2831 1946
y FL(;)15 b(\030)2915 1852 y FB(o)2986 1946 y FL(;)1275
2109 y FB( )1383 2197 y FL(\030)1423 2211 y FO(11)1517
2197 y FP(\000)20 b FQ(3)84 b FL(\030)1777 2211 y FO(12)1871
2197 y FP(\000)20 b FQ(3)1475 2310 y FL(y)1523 2277 y
FO(2)1829 2310 y FL(y)1877 2277 y FO(2)2049 2109 y FB(!)2130
2253 y FL(;)2170 2085 y FB(0)2171 2234 y(@)2345 2140
y FF(\030)2376 2149 y Fy(11)2441 2140 y Fu(\000)p FO(2)p
2295 2160 288 4 v 2295 2214 a(2)p Fu(\003)p FO(\()p FF(y)2429
2195 y Fy(3)2465 2214 y Fu(\000)p FO(1\))2726 2140 y
FF(\030)2757 2149 y Fy(11)2822 2140 y FO(+)p FF(y)2914
2117 y Fy(3)2949 2140 y Fu(\000)p FO(1)p 2685 2160 395
4 v 2685 2214 a(2)p Fu(\003)p FF(y)2792 2195 y Fy(2)2828
2214 y Fu(\003)p FO(\()p FF(y)2927 2195 y Fy(3)2962 2214
y FO(+1\))2345 2286 y FF(\030)2376 2295 y Fy(12)2441
2286 y Fu(\000)p FO(2)p 2295 2306 288 4 v 2295 2360 a(2)p
Fu(\003)p FO(\()p FF(y)2429 2341 y Fy(3)2465 2360 y Fu(\000)p
FO(1\))2726 2286 y FF(\030)2757 2295 y Fy(12)2822 2286
y FO(+)p FF(y)2914 2263 y Fy(3)2949 2286 y Fu(\000)p
FO(1)p 2685 2306 395 4 v 2685 2360 a(2)p Fu(\003)p FF(y)2792
2341 y Fy(2)2828 2360 y Fu(\003)p FO(\()p FF(y)2927 2341
y Fy(3)2962 2360 y FO(+1\))3131 2085 y FB(1)3131 2234
y(A)3204 2081 y(9)3204 2156 y(=)3204 2305 y(;)664 2787
y FJ(solve)p FQ(\()p FP(\000)p FJ(y)1058 2754 y Fm(3)1116
2787 y FQ(+)g FJ(xi)1303 2754 y Fm(2)1362 2787 y FP(\000)g
FJ(4)g FP(\003)h FJ(xi)e FQ(+)h FJ(3)p FL(;)15 b FJ(xi)p
FQ(\))p FJ(;)1401 3167 y FP(f)p FL(\030)30 b FQ(=)1612
3091 y FB(p)p 1695 3091 244 4 v 76 x FL(y)1743 3141 y
FO(3)1803 3167 y FQ(+)19 b(1)i(+)f(2)p FL(;)31 b(\030)e
FQ(=)c FP(\000)2387 3091 y FB(p)p 2470 3091 V 76 x FL(y)2518
3141 y FO(3)2577 3167 y FQ(+)20 b(1)h(+)f(2)p FP(g)664
3468 y(J)42 b FQ(=)25 b FJ(sub)o FQ(\()p FP(f)p FJ(xi)p
FQ(\()p FJ(1)p FL(;)15 b FJ(1)p FQ(\))26 b(=)f FJ(sqrt)p
FQ(\()p FJ(y)1786 3435 y Fm(3)1845 3468 y FQ(+)20 b FJ(1)p
FQ(\))g(+)g FJ(2)p FL(;)30 b FJ(xi)p FQ(\()p FJ(1)p FL(;)15
b FJ(2)p FQ(\))25 b(=)g FP(\000)p FJ(sqrt)p FQ(\()p FJ(y)3002
3435 y Fm(3)3061 3468 y FQ(+)19 b FJ(1)p FQ(\))i(+)f
FJ(2)p FP(g)p FL(;)868 3581 y FJ(first)47 b(jordansymbolic)d(\()p
FP(A)p FJ(\)\);)1391 4003 y FP(J)e FQ(=)1591 3859 y FB( )1698
3870 y(p)p 1781 3870 V 76 x FL(y)1829 3920 y FO(3)1889
3946 y FQ(+)19 b(1)i(+)f(2)338 b(0)1917 4063 y(0)303
b FP(\000)2336 3987 y FB(p)p 2418 3987 V 2418 4063 a
FL(y)2466 4037 y FO(3)2526 4063 y FQ(+)20 b(1)g(+)g(2)2860
3859 y FB(!)664 4239 y @beginspecial @setspecial @endspecial
141 x FE(57.6)136 b(Jordan)664 4633 y FJ(Jordan)p FQ(\()p
FP(A)p FQ(\))29 b(computes)i(the)f(Jordan)g(normal)f(form)h
FP(J)47 b FQ(of)30 b(the)h(matrix)f FP(A)p FQ(.)664 4796
y(It)h(returns)e FP(fJ)17 b FL(;)e FP(P)7 b FL(;)15 b
FP(P)1421 4763 y Fu(\000)p FO(1)1517 4796 y FP(g)p FQ(,)31
b(where)f FP(J)17 b FL(;)e FP(P)7 b FQ(,)31 b(and)f FP(P)2373
4763 y Fu(\000)p FO(1)2498 4796 y FQ(are)h(suc)m(h)f(that)h
FP(P)7 b(J)17 b(P)3272 4760 y Fu(\000)p FO(1)3391 4796
y FQ(=)25 b FP(A)p FQ(.)664 4959 y FP(A)30 b FQ(is)f(a)i(square)f
(matrix.)p eop
%%Page: 435 435
435 434 bop 241 299 a @beginspecial @setspecial @endspecial
FM(57.6.)72 b(JORD)m(AN)2208 b FQ(435)241 555 y FJ(load)p
439 555 29 4 v 33 w(package)46 b(normform;)1006 1086
y FP(A)25 b FQ(=)1200 743 y FB(0)1200 889 y(B)1200 939
y(B)1200 989 y(B)1200 1039 y(B)1200 1088 y(B)1200 1138
y(B)1200 1188 y(B)1200 1241 y(@)1337 804 y FP(\000)p
FQ(9)106 b FP(\000)p FQ(21)83 b FP(\000)p FQ(15)h(4)f(2)h(0)1314
917 y FP(\000)p FQ(10)119 b(21)g FP(\000)p FQ(14)84 b(4)f(2)h(0)1337
1030 y FP(\000)p FQ(8)141 b(16)119 b FP(\000)p FQ(11)84
b(4)f(2)h(0)1337 1143 y FP(\000)p FQ(6)141 b(12)h FP(\000)p
FQ(9)106 b(3)83 b(3)h(0)1337 1256 y FP(\000)p FQ(4)164
b(8)g FP(\000)p FQ(6)106 b(0)83 b(5)h(0)1337 1368 y FP(\000)p
FQ(2)164 b(4)g FP(\000)p FQ(3)106 b(0)83 b(1)h(3)2392
743 y FB(1)2392 889 y(C)2392 939 y(C)2392 989 y(C)2392
1039 y(C)2392 1088 y(C)2392 1138 y(C)2392 1188 y(C)2392
1241 y(A)241 1610 y FP(J)64 b FJ(=)47 b(first)g(jordan)p
FQ(\()p FP(A)p FQ(\))p FJ(;)999 2225 y FP(J)42 b FQ(=)1199
1882 y FB(0)1199 2028 y(B)1199 2078 y(B)1199 2127 y(B)1199
2177 y(B)1199 2227 y(B)1199 2277 y(B)1199 2327 y(B)1199
2380 y(@)1313 1943 y FQ(3)84 b(0)f(0)h(0)154 b(0)262
b(0)1313 2055 y(0)84 b(3)f(0)h(0)154 b(0)262 b(0)1313
2168 y(0)84 b(0)f(1)h(1)154 b(0)262 b(0)1313 2281 y(0)84
b(0)f(0)h(1)154 b(0)262 b(0)1313 2394 y(0)84 b(0)f(0)h(0)f
FL(i)21 b FQ(+)f(2)190 b(0)1313 2507 y(0)84 b(0)f(0)h(0)154
b(0)h FP(\000)p FL(i)20 b FQ(+)g(2)2398 1882 y FB(1)2398
2028 y(C)2398 2078 y(C)2398 2127 y(C)2398 2177 y(C)2398
2227 y(C)2398 2277 y(C)2398 2327 y(C)2398 2380 y(A)p
eop
%%Page: 436 436
436 435 bop 664 299 a @beginspecial @setspecial @endspecial
FQ(436)375 b FM(CHAPTER)30 b(57.)72 b(NORMF)m(ORM:)31
b(MA)-8 b(TRIX)31 b(NORMAL)g(F)m(ORMS)p eop
%%Page: 437 437
437 436 bop 241 299 a @beginspecial @setspecial @endspecial
165 x @beginspecial @setspecial @endspecial 764 x FI(Chapter)64
b(58)241 1693 y FT(NUMERIC:)76 b(Solving)241 1942 y(n)-6
b(umerical)76 b(problems)1470 2424 y Fx(Herb)r(ert)26
b(Melenk)826 2515 y(Konrad{Zuse{Zen)n(trum)f(f)r(\177)-41
b(ur)26 b(Informationstec)n(hnik)f(Berlin)1521 2607 y(T)-6
b(akustra)l(\177)-34 b(se)27 b(7)1150 2698 y(D{14195)g(Berlin{Dahlem,)g
(German)n(y)1352 2819 y(e{mail:)35 b(melenk@zib.de)241
3063 y FQ(The)g Fk(NUMERIC)h FQ(pac)m(k)-5 b(age)38 b(implemen)m(ts)c
(some)j(n)m(umerical)d(\(appro)m(ximativ)m(e\))j(algo-)241
3176 y(rithms)43 b(for)h(REDUCE)60 b(based)44 b(on)g(the)h(REDUCE)g
(rounded)e(mo)s(de)h(arithmetic.)241 3289 y(These)f(algorithms)g(are)i
(implemen)m(ted)d(for)i(standard)f(cases.)82 b(They)43
b(should)f(not)241 3402 y(b)s(e)h(called)f(for)i(ill-conditioned)c
(problems;)49 b(please)43 b(use)g(standard)g(mathematical)241
3515 y(libraries)27 b(for)j(these.)241 3652 y @beginspecial
@setspecial @endspecial 199 x FE(58.1)135 b(Syn)l(tax)241
3964 y @beginspecial @setspecial @endspecial 143 x FR(58.1.1)112
b(In)m(terv)-6 b(als,)37 b(Starting)f(P)m(oin)m(ts)241
4329 y FQ(In)m(terv)-5 b(als)25 b(are)i(generally)e(co)s(ded)g(as)i(lo)
m(w)m(er)f(b)s(ound)e(and)h(upp)s(er)f(b)s(ound)g(connected)j(b)m(y)241
4442 y(the)j(op)s(erator)h FJ(`..')p FQ(,)e(usually)g(asso)s(ciated)h
(to)i(a)e(v)-5 b(ariable)29 b(in)g(an)i(equation.)459
4672 y FH(x=)42 b(\(2.5)g(..)h(3.5\))241 4916 y FQ(means)35
b(that)h(the)g(v)-5 b(ariable)34 b(x)i(is)f(tak)m(en)h(in)e(the)i
(range)g(from)f(2.5)i(up)d(to)j(3.5.)57 b(Note,)1667
5187 y(437)p eop
%%Page: 438 438
438 437 bop 664 299 a @beginspecial @setspecial @endspecial
FQ(438)121 b FM(CHAPTER)30 b(58.)72 b(NUMERIC:)30 b(SOL)-10
b(VING)30 b(NUMERICAL)g(PR)m(OBLEMS)664 555 y FQ(that)24
b(the)g(b)s(ounds)d(can)j(b)s(e)f(algebraic)g(expressions,)h(whic)m(h,)
f(ho)m(w)m(ev)m(er,)k(m)m(ust)c(ev)-5 b(aluate)664 668
y(to)32 b(n)m(umeric)e(results.)43 b(In)30 b(cases)i(where)f(an)g(in)m
(terv)-5 b(al)31 b(is)f(returned)g(as)i(the)f(result,)g(the)664
781 y(lo)m(w)m(er)h(and)e(upp)s(er)f(b)s(ounds)g(can)i(b)s(e)g
(extracted)h(b)m(y)f(the)h FJ(PART)e FQ(op)s(erator)h(as)g(the)h
(\014rst)664 894 y(and)j(second)h(part)g(resp)s(ectiv)m(ely)-8
b(.)57 b(A)36 b(starting)g(p)s(oin)m(t)e(is)h(sp)s(eci\014ed)g(b)m(y)g
(an)h(equation)664 1007 y(with)29 b(a)i(n)m(umeric)e(righ)m(thand)g
(side,)882 1235 y FH(x=3.0)664 1476 y FQ(If)i(for)h(m)m(ultiv)-5
b(ariate)30 b(applications)g(sev)m(eral)i(co)s(ordinates)g(m)m(ust)f(b)
s(e)g(sp)s(eci\014ed)f(b)m(y)i(in-)664 1589 y(terv)-5
b(als)39 b(or)g(as)g(a)g(starting)g(p)s(oin)m(t,)h(these)f(sp)s
(eci\014cations)f(can)h(b)s(e)f(collected)h(in)f(one)664
1701 y(parameter)27 b(\(whic)m(h)e(is)f(then)i(a)g(list\))f(or)h(they)g
(can)g(b)s(e)g(giv)m(en)g(as)g(separate)h(parameters)664
1814 y(alternativ)m(ely)-8 b(.)62 b(The)37 b(list)f(form)h(is)f(more)i
(appropriate)e(when)g(the)i(parameters)g(are)664 1927
y(built)26 b(from)i(other)g(REDUCE)g(calculations)f(in)g(an)g
(automatic)i(st)m(yle,)g(while)d(the)j(\015at)664 2040
y(form)h(is)f(more)i(con)m(v)m(enien)m(t)h(for)e(direct)f(in)m
(teractiv)m(e)j(input.)664 2182 y @beginspecial @setspecial
@endspecial 149 x FR(58.1.2)113 b(Accuracy)37 b(Con)m(trol)664
2552 y FQ(The)i(k)m(eyw)m(ord)i(parameters)f FL(accur)s(acy)k
FQ(=)c FL(a)g FQ(and)f FL(iter)s(ations)i FQ(=)f FL(i)p
FQ(,)j(where)c FL(a)h FQ(and)664 2665 y FL(i)h FQ(m)m(ust)g(b)s(e)f(p)s
(ositiv)m(e)f(in)m(teger)i(n)m(um)m(b)s(ers,)h(con)m(trol)g(the)e
(iterativ)m(e)i(algorithms:)60 b(the)664 2778 y(iteration)25
b(is)e(con)m(tin)m(ued)i(un)m(til)e(the)i(lo)s(cal)f(error)g(is)g(b)s
(elo)m(w)g(10)2736 2745 y Fu(\000)p FF(a)2834 2778 y
FQ(;)i(if)e(that)i(is)d(imp)s(ossible)664 2891 y(within)g
FL(i)i FQ(steps,)h(the)f(iteration)g(is)f(terminated)h(with)e(an)i
(error)g(message.)40 b(The)25 b(v)-5 b(alues)664 3004
y(reac)m(hed)31 b(so)g(far)f(are)h(then)f(returned)f(as)i(the)f
(result.)664 3138 y @beginspecial @setspecial @endspecial
199 x FE(58.2)136 b(Minima)664 3590 y FQ(The)26 b(function)g(to)h(b)s
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3929 y(general)c(\014nd)d(only)i(lo)s(cal)g(minima.)664
4091 y(Syn)m(tax:)664 4335 y FN(NUM)p 931 4335 32 4 v
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439 438 bop 241 299 a @beginspecial @setspecial @endspecial
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440 439 bop 664 299 a @beginspecial @setspecial @endspecial
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3438 y(jacobian;)839 3637 y([COS\(X\))84 b(SIN\(Y\)])839
3737 y([)609 b(])839 3836 y([)86 b(1)305 b(1)130 b(])664
3980 y @beginspecial @setspecial @endspecial 192 x FE(58.4)136
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441 440 bop 241 299 a @beginspecial @setspecial @endspecial
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2701 y(tion)h(of)g(a)h(ordinary)e(di\013eren)m(tial)f(equation)j(real)f
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442 441 bop 664 299 a @beginspecial @setspecial @endspecial
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443 442 bop 241 299 a @beginspecial @setspecial @endspecial
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446 445 bop 664 299 a @beginspecial @setspecial @endspecial
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h(co)s(e\016cien)m(ts)g(in)e(the)i(range)f([)p FP(\000)p
FL(n;)15 b(n)p FQ(].)p eop
%%Page: 484 484
484 483 bop 664 299 a @beginspecial @setspecial @endspecial
FQ(484)463 b FM(CHAPTER)29 b(64.)72 b(RANDPOL)-8 b(Y:)31
b(RANDOM)g(POL)-8 b(YNOMIALS)664 555 y FQ(F)g(urther)34
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b(2*x)g(*y)f(-)i(44*x)85 b(+)43 b(83*x*y)85 b(+)43 b(85*x*y)85
b(+)43 b(55*x*y)1667 2639 y(5)304 b(4)261 b(3)305 b(2)708
2738 y(-)43 b(27*x*y)e(+)i(33*x)f(-)h(98*y)86 b(+)43
b(51*y)86 b(-)43 b(2*y)86 b(+)43 b(70*y)85 b(-)43 b(60*y)f(-)i(10)p
eop
%%Page: 485 485
485 484 bop 241 299 a @beginspecial @setspecial @endspecial
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(76*sin\(x\)*x)c(+)k(96*sin\(x\)\))p eop
%%Page: 486 486
486 485 bop 664 299 a @beginspecial @setspecial @endspecial
FQ(486)463 b FM(CHAPTER)29 b(64.)72 b(RANDPOL)-8 b(Y:)31
b(RANDOM)g(POL)-8 b(YNOMIALS)p eop
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487 486 bop 241 299 a @beginspecial @setspecial @endspecial
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488 487 bop 664 299 a @beginspecial @setspecial @endspecial
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489 488 bop 241 299 a @beginspecial @setspecial @endspecial
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eop
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490 489 bop 664 299 a @beginspecial @setspecial @endspecial
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491 490 bop 241 299 a @beginspecial @setspecial @endspecial
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y FJ(EQUAL)98 b(NEQ)h(DIV)g(SDIV)f(ASSOC)h(NASSOC)664
4611 y @beginspecial @setspecial @endspecial eop
%%Page: 499 499
499 498 bop 241 299 a @beginspecial @setspecial @endspecial
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eop
%%Page: 500 500
500 499 bop 664 299 a @beginspecial @setspecial @endspecial
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%%Page: 501 501
501 500 bop 241 299 a @beginspecial @setspecial @endspecial
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502 501 bop 664 299 a @beginspecial @setspecial @endspecial
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y(2*a)664 2903 y @beginspecial @setspecial @endspecial
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3629 y(a)m(v)-5 b(ailable:)40 b FJ(RLGQEA)p FQ(.)664
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4735 y @beginspecial @setspecial @endspecial eop
%%Page: 503 503
503 502 bop 241 299 a @beginspecial @setspecial @endspecial
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%%Page: 504 504
504 503 bop 664 299 a @beginspecial @setspecial @endspecial
FQ(504)1018 b FM(CHAPTER)30 b(67.)72 b(REDLOG:)30 b(LOGIC)g(SYSTEM)p
eop
%%Page: 505 505
505 504 bop 241 299 a @beginspecial @setspecial @endspecial
165 x @beginspecial @setspecial @endspecial 764 x FI(Chapter)64
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5187 y(505)p eop
%%Page: 506 506
506 505 bop 664 299 a @beginspecial @setspecial @endspecial
FQ(506)24 b FM(CHAPTER)30 b(68.)72 b(RESET:)29 b(RESET)g(REDUCE)i(TO)e
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%%Page: 507 507
507 506 bop 241 299 a @beginspecial @setspecial @endspecial
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5187 y(507)p eop
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508 507 bop 664 299 a @beginspecial @setspecial @endspecial
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511 510 bop 241 299 a @beginspecial @setspecial @endspecial
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b(It)891 4504 y(will)31 b(\014nd)g(all)h(ro)s(ots,)i(real)f(and)f
(complex,)i(of)f(the)g(p)s(olynomial)e(p)h(to)i(an)f(accu-)891
4617 y(racy)40 b(that)g(is)e(su\016cien)m(t)g(to)i(separate)g(them)f
(and)g(whic)m(h)f(is)g(a)h(minim)m(um)e(of)891 4730 y(6)i(decimal)e
(places.)63 b(The)38 b(v)-5 b(alue)37 b(returned)g(b)m(y)h(R)m(OOTS)f
(is)g(a)h(list)f(of)h(equat-)891 4843 y(ions)i(for)h(all)e(ro)s(ots.)72
b(In)40 b(addition,)i(R)m(OOTS)d(stores)j(separate)f(lists)e(of)i(real)
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515 514 bop 241 299 a @beginspecial @setspecial @endspecial
FM(71.1.)72 b(TOP)30 b(LEVEL)g(FUNCTIONS)1480 b FQ(515)468
555 y(ro)s(ots)43 b(and)e(complex)h(ro)s(ots)h(in)e(the)h(global)g(v)-5
b(ariables)41 b(R)m(OOTSREAL)g(and)468 668 y(R)m(OOTSCOMPLEX.)468
812 y(The)23 b(output)g(of)h(R)m(OOTS)e(is)h(normally)f(sorted)h(in)m
(to)h(a)g(standard)e(order:)37 b(a)24 b(ro)s(ot)468 925
y(with)i(smaller)f(real)i(part)f(precedes)h(a)h(ro)s(ot)f(with)e
(larger)i(real)g(part;)h(ro)s(ots)f(with)468 1038 y(iden)m(tical)33
b(real)g(parts)h(are)g(sorted)g(so)g(that)h(larger)e(imaginary)g(part)g
(precedes)468 1151 y(smaller)c(imaginary)g(part.)468
1295 y(Ho)m(w)m(ev)m(er,)j(when)e(a)g(p)s(olynomial)e(has)h(b)s(een)h
(factored)h(algebraically)d(then)i(the)468 1408 y(ro)s(ot)h(sorting)g
(is)f(applied)f(to)i(eac)m(h)h(factor)g(separately)-8
b(.)44 b(This)29 b(mak)m(es)j(the)f(\014nal)468 1521
y(resulting)e(order)g(less)h(ob)m(vious.)241 1697 y FN(R)m(OOTS)p
611 1697 32 4 v 37 w(A)-9 b(T)p 791 1697 V 37 w(PREC)35
b(p;)46 b FQ(Same)30 b(as)g(R)m(OOTS)f(except)i(that)g(ro)s(ots)f(v)-5
b(alues)30 b(are)g(re-)468 1810 y(turned)38 b(to)h(a)g(minim)m(um)d(of)
j(the)g(n)m(um)m(b)s(er)f(of)h(decimal)f(places)g(equal)h(to)g(the)468
1923 y(curren)m(t)30 b(system)h(precision.)241 2098 y
FN(R)m(OOT)p 553 2098 V 37 w(V)-12 b(AL)35 b(p;)45 b
FQ(Same)e(as)f(R)m(OOTS)p 1666 2098 28 4 v 32 w(A)-8
b(T)p 1824 2098 V 33 w(PREC,)42 b(except)h(that)g(instead)f(of)g(re-)
468 2211 y(turning)e(a)j(list)e(of)h(equations)g(for)g(the)h(ro)s(ots,)
j(a)c(list)f(of)i(the)f(ro)s(ot)h(v)-5 b(alue)41 b(is)468
2324 y(returned.)f(This)28 b(is)i(the)g(function)f(that)i(SOL)-10
b(VE)29 b(calls.)241 2500 y FN(NEARESTR)m(OOT\(p,s\);)44
b FQ(This)34 b(top)j(lev)m(el)g(function)e(\014nds)g(the)i(ro)s(ot)f
(to)i(whic)m(h)468 2613 y(the)31 b(metho)s(d)f(con)m(v)m(erges)i(giv)m
(en)f(the)f(initial)e(starting)i(origin)f(s,)i(whic)m(h)e(can)i(b)s(e)
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(in)e(the)h(vicinit)m(y)f(of)h(s)g(and)g(s)g(is)f(not)468
2839 y(signi\014can)m(tly)26 b(closer)i(to)h(one)f(ro)s(ot)g(than)g(it)
f(is)g(to)h(all)f(others,)i(the)f(con)m(v)m(ergence)468
2952 y(could)f(arriv)m(e)h(at)h(a)f(ro)s(ot)g(that)h(is)e(not)h(truly)f
(the)h(nearest)g(ro)s(ot.)41 b(This)26 b(function)468
3064 y(should)36 b(therefore)i(b)s(e)f(used)g(only)g(when)g(the)h(user)
f(is)f(certain)i(that)g(there)g(is)468 3177 y(only)30
b(one)g(ro)s(ot)h(in)e(the)i(immediate)e(vicinit)m(y)g(of)h(the)h
(starting)f(p)s(oin)m(t)f(s.)241 3353 y FN(FIRSTR)m(OOT)34
b(p;)45 b FQ(R)m(OOTS)29 b(is)h(called,)g(but)f(only)h(a)h(single)e(ro)
s(ot)h(is)g(computed.)241 3492 y @beginspecial @setspecial
@endspecial 149 x FR(71.1.3)112 b(Other)38 b(top)f(lev)m(el)f
(functions)241 3862 y FN(GETR)m(OOT\(n,rr\);)44 b FQ(If)38
b(rr)f(has)i(the)f(form)h(of)f(the)h(output)f(of)h(R)m(OOTS,)e(REAL-)
468 3975 y(R)m(OOTS,)21 b(or)i(NEARESTR)m(OOTS;)d(GETR)m(OOT)i(returns)
f(the)h(rational,)i(real,)468 4088 y(or)i(complex)g(v)-5
b(alue)26 b(of)g(the)g(ro)s(ot)h(equation.)39 b(An)26
b(error)g(o)s(ccurs)f(if)h FL(n)e(<)h FQ(1)i(or)f FL(n)f(>)468
4201 y FQ(the)31 b(n)m(um)m(b)s(er)e(of)h(ro)s(ots)h(in)e(rr.)241
4376 y FN(MKPOL)-9 b(Y)35 b(rr;)46 b FQ(This)j(function)h(can)h(b)s(e)f
(used)h(to)g(reconstruct)h(a)f(p)s(olynomial)468 4489
y(whose)33 b(ro)s(ot)g(equation)g(list)f(is)g(rr)g(and)h(whose)g
(denominator)f(is)g(1.)49 b(Th)m(us)32 b(one)468 4602
y(can)23 b(v)m(erify)e(that)i(if)e FL(r)s(r)27 b FQ(:=)f
FL(R)q(O)s(O)s(T)13 b(S)26 b(p)p FQ(,)e(and)d FL(r)s(r)s
FQ(1)k(:=)g FL(R)q(O)s(O)s(T)13 b(S)27 b(M)10 b(K)d(P)13
b(O)s(LY)41 b(r)s(r)s FQ(,)468 4715 y(then)31 b FL(r)s(r)s
FQ(1)c(=)f FL(r)s(r)s FQ(.)43 b(\(This)30 b(will)f(b)s(e)i(true)g(if)f
FJ(MULTIROOT)f FQ(and)i FJ(RATROOT)f FQ(are)h(ON,)468
4828 y(and)i FJ(ROUNDED)g FQ(is)g(o\013.\))52 b(Ho)m(w)m(ev)m(er,)37
b FL(M)10 b(K)d(P)13 b(O)s(LY)54 b(r)s(r)25 b FP(\000)d
FL(N)10 b(U)g(M)44 b(p)31 b FQ(=)g(0)k(will)c(b)s(e)468
4941 y(true)f(if)g(and)f(only)h(if)f(all)g(ro)s(ots)i(of)f(p)g(ha)m(v)m
(e)i(b)s(een)e(computed)g(exactly)-8 b(.)p eop
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516 515 bop 664 299 a @beginspecial @setspecial @endspecial
FQ(516)89 b FM(CHAPTER)29 b(71.)72 b(R)m(OOTS:)30 b(A)g(REDUCE)h(R)m
(OOT)e(FINDING)j(P)-8 b(A)m(CKA)m(GE)664 464 y @beginspecial
@setspecial @endspecial 91 x FE(71.2)136 b(Switc)l(hes)45
b(Used)h(in)f(Input)664 808 y FQ(The)g(input)e(of)j(p)s(olynomials)c
(in)j(algebraic)g(mo)s(de)g(is)f(sensitiv)m(e)h(to)h(the)f(switc)m(hes)
664 921 y FJ(COMPLEX)p FQ(,)e FJ(ROUNDED)p FQ(,)g(and)i
FJ(ADJPREC)p FQ(.)e(The)h(correct)i(c)m(hoice)g(of)f(input)e(metho)s(d)
h(is)664 1034 y(imp)s(ortan)m(t)e(since)h(incorrect)g(c)m(hoices)g
(will)e(result)h(in)f(undesirable)g(truncation)h(or)664
1147 y(rounding)28 b(of)j(the)f(input)f(co)s(e\016cien)m(ts.)664
1309 y(T)-8 b(runcation)27 b(or)g(rounding)e(ma)m(y)j(o)s(ccur)f(if)g
FJ(ROUNDED)e FQ(is)i(on)g(and)g(one)g(of)h(the)f(follo)m(wing)664
1422 y(is)j(true:)664 1523 y @beginspecial @setspecial
@endspecial 775 1672 a(1.)46 b(a)31 b(co)s(e\016cien)m(t)g(is)f(en)m
(tered)h(in)e(\015oating)h(p)s(oin)m(t)g(form)f(or)i(rational)e(form.)
664 1724 y @beginspecial @setspecial @endspecial 775
1855 a(2.)46 b FJ(COMPLEX)29 b FQ(is)g(on)i(and)e(a)i(co)s(e\016cien)m
(t)g(is)f(imaginary)f(or)h(complex.)664 2104 y(Therefore,)h(to)g(a)m(v)
m(oid)g(undesirable)c(truncation)j(or)g(rounding,)f(then:)664
2223 y @beginspecial @setspecial @endspecial 775 2353
a(1.)46 b FJ(ROUNDED)25 b FQ(should)g(b)s(e)i(o\013)g(and)f(input)f
(should)g(b)s(e)h(in)g(in)m(teger)h(or)g(rational)f(form;)891
2466 y(or)664 2501 y @beginspecial @setspecial @endspecial
775 2649 a(2.)46 b FJ(ROUNDED)25 b FQ(can)h(b)s(e)g(on)g(if)f(it)h(is)f
(acceptable)i(to)g(truncate)g(or)f(round)f(input)f(to)j(the)891
2762 y(curren)m(t)34 b(v)-5 b(alue)33 b(of)g(system)h(precision;)f(or)h
(b)s(oth)f FJ(ROUNDED)e FQ(and)i FJ(ADJPREC)f FQ(can)891
2875 y(b)s(e)24 b(on,)h(in)e(whic)m(h)f(case)j(system)f(precision)f
(will)e(b)s(e)i(adjusted)g(to)i(accommo)s(date)891 2988
y(the)31 b(largest)g(co)s(e\016cien)m(t)g(whic)m(h)e(is)g(input;)g(or)
664 3041 y @beginspecial @setspecial @endspecial 775
3171 a(3.)46 b(if)21 b(the)h(input)e(con)m(tains)i(complex)f(co)s
(e\016cien)m(ts)h(with)f(v)m(ery)h(di\013eren)m(t)f(magnitude)891
3284 y(for)45 b(the)f(real)g(and)g(imaginary)f(parts,)48
b(then)c(all)g(three)g(switc)m(hes)h FJ(ROUNDED)p FQ(,)891
3397 y FJ(ADJPREC)29 b FQ(and)h FJ(COMPLEX)e FQ(m)m(ust)i(b)s(e)g(on.)
664 3646 y FN(in)m(teger)35 b(and)g(complex)g(mo)s(des)45
b FQ(\(o\013)39 b FJ(ROUNDED)p FQ(\))e(an)m(y)h(real)g(p)s(olynomial)e
(can)j(b)s(e)891 3759 y(input)c(using)g(in)m(teger)h(co)s(e\016cien)m
(ts)h(of)g(an)m(y)f(size;)k(in)m(teger)c(or)h(rational)e(co)s(e\016-)
891 3872 y(cien)m(ts)c(can)g(b)s(e)f(used)g(to)h(input)e(an)m(y)i(real)
f(or)h(complex)f(p)s(olynomial,)e(indep)s(en-)891 3985
y(den)m(t)e(of)g(the)g(setting)g(of)g(the)g(switc)m(h)f
FJ(COMPLEX)p FQ(.)f(These)i(are)g(the)g(most)g(v)m(ersatile)891
4098 y(input)34 b(mo)s(des,)i(since)e(an)m(y)h(real)g(or)g(complex)g(p)
s(olynomial)d(can)k(b)s(e)e(input)f(ex-)891 4211 y(actly)-8
b(.)664 4394 y FN(mo)s(des)35 b(rounded)g(and)g(complex-rounded)46
b FQ(\(on)36 b FJ(ROUNDED)p FQ(\))e(p)s(olynomials)g(can)891
4507 y(b)s(e)41 b(input)e(using)g(in)m(teger)j(co)s(e\016cien)m(ts)f
(of)g(an)m(y)h(size.)72 b(Floating)41 b(p)s(oin)m(t)f(co)s(ef-)891
4620 y(\014cien)m(ts)f(will)e(b)s(e)i(truncated)g(or)g(rounded,)i(to)f
(a)f(size)h(dep)s(enden)m(t)e(up)s(on)g(the)891 4733
y(system.)54 b(If)34 b(complex)g(is)g(on,)h(real)g(co)s(e\016cien)m(ts)
g(can)g(b)s(e)f(input)e(to)k(an)m(y)e(preci-)891 4846
y(sion)27 b(using)g(in)m(teger)h(form,)g(but)f(co)s(e\016cien)m(ts)i
(of)f(imaginary)f(parts)g(of)h(complex)891 4959 y(co)s(e\016cien)m(ts)k
(will)27 b(b)s(e)j(rounded)f(or)h(truncated.)p eop
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517 516 bop 241 299 a @beginspecial @setspecial @endspecial
FM(71.3.)72 b(R)m(OOT)30 b(P)-8 b(A)m(CKA)m(GE)32 b(SWITCHES)1317
b FQ(517)241 464 y @beginspecial @setspecial @endspecial
91 x FE(71.3)135 b(Ro)t(ot)46 b(P)l(ac)l(k)-7 b(age)46
b(Switc)l(hes)241 808 y FN(RA)-9 b(TR)m(OOT)45 b FQ(\(Default)29
b(OFF\))g(If)f FJ(RATROOT)f FQ(is)g(on)i(all)e(ro)s(ot)i(equations)f
(are)h(output)468 921 y(in)i(rational)g(form.)46 b(Assuming)30
b(that)j(the)g(mo)s(de)e(is)h FJ(COMPLEX)e FQ(\()p FD(i.e.)79
b FJ(ROUNDED)468 1034 y FQ(is)33 b(o\013,\))j(the)d(ro)s(ot)i
(equations)e(are)h(guaran)m(teed)h(to)g(b)s(e)e(able)g(to)i(b)s(e)e
(input)f(in)m(to)468 1147 y(REDUCE)38 b(without)e(truncation)h(or)h
(rounding)d(errors.)63 b(\(Cf.)f(the)38 b(function)468
1260 y(MKPOL)-8 b(Y)30 b(describ)s(ed)f(ab)s(o)m(v)m(e.\))241
1447 y FN(MUL)-9 b(TIR)m(OOT)45 b FQ(\(Default)26 b(ON\))g(Whenev)m(er)
h(the)f(p)s(olynomial)d(has)j(complex)g(co)s(ef-)468
1560 y(\014cien)m(ts)31 b(or)g(has)g(real)f(co)s(e\016cien)m(ts)i(and)e
(has)h(m)m(ultiple)e(ro)s(ots,)j(as)62 b(determined)468
1673 y(b)m(y)34 b(the)g(Sturm)e(function,)i(the)g(function)e
FJ(SQFRF)g FQ(is)h(called)g(automatically)h(to)468 1786
y(factor)29 b(the)f(p)s(olynomial)e(in)m(to)i(square-free)g(factors.)41
b(If)27 b FJ(MULTIROOT)f FQ(is)h(on,)h(the)468 1899 y(m)m(ultiplicit)m
(y)f(of)j(the)h(ro)s(ots)f(will)d(b)s(e)j(indicated)e(in)h(the)i
(output)e(of)i(R)m(OOTS)d(or)468 2012 y(REALR)m(OOTS)c(b)m(y)h(prin)m
(ting)e(the)i(ro)s(ot)h(output)f(rep)s(eatedly)-8 b(,)26
b(according)f(to)h(its)468 2125 y(m)m(ultiplicit)m(y)-8
b(.)52 b(If)34 b FJ(MULTIROOT)e FQ(is)i(o\013,)j(eac)m(h)f(ro)s(ot)f
(will)d(b)s(e)j(prin)m(ted)e(once,)k(and)468 2238 y(all)32
b(ro)s(ots)h(should)d(b)s(e)i(normally)f(b)s(e)h(distinct.)47
b(\(Tw)m(o)33 b(iden)m(tical)f(ro)s(ots)g(should)468
2350 y(not)c(app)s(ear.)39 b(If)27 b(the)g(initial)e(precision)h(of)h
(the)h(computation)f(or)h(the)f(accuracy)468 2463 y(of)g(the)f(output)h
(w)m(as)g(insu\016cien)m(t)d(to)k(separate)f(t)m(w)m(o)h
(closely-spaced)f(ro)s(ots,)g(the)468 2576 y(program)35
b(attempts)i(to)f(increase)f(accuracy)i(and/or)e(precision)f(if)g(it)h
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(the)d(initial)c(accuracy)k(sp)s(eci\014ed)e(w)m(as)i(to)s(o)f(lo)m(w,)
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165 x @beginspecial @setspecial @endspecial 764 x FI(Chapter)64
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b(teger)77 b(p)6 b(olynomial)241 2191 y(solv)-6 b(ers)1443
2664 y Fx(F)g(rancis)26 b(J.)g(W)-6 b(righ)n(t)580 2755
y(Sc)n(ho)r(ol)27 b(of)f(Mathematical)h(Sciences,)f(Queen)f(Mary)h(and)
f(W)-6 b(est\014eld)26 b(College)1380 2847 y(Univ)n(ersit)n(y)f(of)h
(London)1479 2938 y(Mile)h(End)e(Road)1306 3029 y(London)g(E1)h(4NS,)g
(England)1183 3151 y(e{mail:)35 b(F.J.W)-6 b(righ)n(t@QMW.ac.uk)241
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3504 y(metho)s(ds)39 b(can)i(b)s(e)f(calculated.)70 b(The)40
b(op)s(erator)h FJ(r_solve)d FQ(computes)j(all)e(rational)241
3617 y(zeros)31 b(and)f(the)g(op)s(erator)h FJ(i_solve)59
b FQ(computes)30 b(only)g(in)m(teger)h(zeros)g(in)e(a)i(w)m(a)m(y)g
(that)241 3730 y(is)e(sligh)m(tly)g(more)h(e\016cien)m(t)h(than)f
(extracting)h(them)g(from)f(the)g(rational)g(zeros.)241
3893 y(The)f(\014rst)g(argumen)m(t)i(is)e(either)g(a)h(univ)-5
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4006 y(with)h(in)m(teger,)i(rational)f(or)g(rounded)f(co)s(e\016cien)m
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4119 y(allo)m(w)m(ed.)68 b(The)39 b(argumen)m(t)h(is)f(simpli\014ed)d
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4231 y(and)30 b(the)g(denominator)g(is)f(silen)m(tly)g(ignored.)241
4394 y(Subsequen)m(t)43 b(argumen)m(ts)i(are)g(optional.)83
b(If)44 b(the)h(p)s(olynomial)d(v)-5 b(ariable)43 b(is)h(to)h(b)s(e)241
4507 y(sp)s(eci\014ed)36 b(then)h(it)g(m)m(ust)g(b)s(e)g(the)h(\014rst)
f(optional)f(argumen)m(t.)63 b(Ho)m(w)m(ev)m(er,)41 b(since)c(the)241
4620 y(v)-5 b(ariable)33 b(in)g(a)i(non-constan)m(t)g(univ)-5
b(ariate)33 b(p)s(olynomial)f(can)j(b)s(e)f(deduced)f(from)h(the)241
4733 y(p)s(olynomial)19 b(it)i(is)g(unnecessary)g(to)i(sp)s(ecify)d(it)
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2044 580 V 727 w(Op)s(eration)p 3381 580 V 935 583 2449
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3389 1762 V 927 1766 2464 4 v 925 1879 4 113 v 1020 1845
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2592 y(deq)k(1:=u\(1,1\)+u\(1,2)o(,2)o(\);)664 2791 y(deq\(1\))e(:=)i
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(GL\(6\):=2*df\(xi\(2\))o(,x)o(\(2)o(\)\))37 b(-)43 b
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537 536 bop 241 299 a @beginspecial @setspecial @endspecial
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538 537 bop 664 299 a @beginspecial @setspecial @endspecial
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539 538 bop 241 299 a @beginspecial @setspecial @endspecial
165 x @beginspecial @setspecial @endspecial 764 x FI(Chapter)64
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540 539 bop 664 299 a @beginspecial @setspecial @endspecial
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3182 y FP(\017)45 b FQ(Asso)s(ciated)31 b(Legendre)f(F)-8
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3745 y FP(\017)45 b FQ(Gegen)m(bauer)32 b(P)m(olynomials;)801
3933 y FP(\017)45 b FQ(Lam)m(b)s(ert's)31 b FL(!)i FQ(function;)801
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(ell-kno)m(wn)e(constan)m(ts.)p eop
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541 540 bop 241 299 a @beginspecial @setspecial @endspecial
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3361 V 32 w(Ratio)31 b(:)1109 3326 y FO(1+)1199 3270
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eop
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542 541 bop 664 299 a @beginspecial @setspecial @endspecial
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V 1125 3421 2068 4 v eop
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543 542 bop 241 299 a @beginspecial @setspecial @endspecial
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%%Page: 544 544
544 543 bop 664 299 a @beginspecial @setspecial @endspecial
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545 544 bop 241 299 a @beginspecial @setspecial @endspecial
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%%Page: 546 546
546 545 bop 664 299 a @beginspecial @setspecial @endspecial
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%%Page: 547 547
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%%Page: 548 548
548 547 bop 664 299 a @beginspecial @setspecial @endspecial
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%%Page: 549 549
549 548 bop 241 299 a @beginspecial @setspecial @endspecial
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%%Page: 550 550
550 549 bop 664 299 a @beginspecial @setspecial @endspecial
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eop
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551 550 bop 241 299 a @beginspecial @setspecial @endspecial
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3801 y(the)e(same)h(v)-5 b(alue)30 b(and)g(t)m(yp)s(e.)241
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b(eval,)33 b(spr)-5 b(e)g(ad)391 4321 y FQ(Returns)42
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624 623 bop 664 299 a @beginspecial @setspecial @endspecial
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b(eval,)33 b(spr)-5 b(e)g(ad)814 736 y FQ(Returns)30
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b(e)g(ad)814 1261 y FQ(Returns)30 b(T)g(if)f(U)h(is)g(a)h(\015oating)f
(p)s(oin)m(t)f(n)m(um)m(b)s(er.)664 1668 y FJ(IDP)p FQ(\()p
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b(eval,)33 b(spr)-5 b(e)g(ad)814 2283 y FQ(Returns)28
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2396 y(is)i(a)g(p)s(ositiv)m(e)g(n)m(um)m(b)s(er,)f(NIL)h(is)g
(returned.)814 2590 y FJ(EXPR)47 b(PROCEDURE)e(MINUSP\(U\);)957
2703 y(IF)j(NUMBERP)d(U)j(THEN)e(LESSP\(U,)g(0\))h(ELSE)g(NIL;)664
3126 y(NULL)p FQ(\()p FN(U)p FQ(:)p FD(any)p FQ(\):)p
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3239 y FQ(Returns)30 b(T)g(if)f(U)h(is)g(NIL.)814 3433
y FJ(EXPR)47 b(PROCEDURE)e(NULL\(U\);)957 3546 y(U)j(EQ)f(NIL;)664
3969 y(NUMBERP)p FQ(\()p FN(U)p FQ(:)p FD(any)p FQ(\):)p
FD(b)-5 b(o)g(ole)g(an)1570 b(eval,)33 b(spr)-5 b(e)g(ad)814
4082 y FQ(Returns)30 b(T)g(if)f(U)h(is)g(a)h(n)m(um)m(b)s(er)e(\(in)m
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625 624 bop 241 299 a @beginspecial @setspecial @endspecial
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1252 1080 4 v 495 1305 a Fa(a)529 1337 y @beginspecial
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534 3920 y(OR\(EQN\(U,)f(0\),)i(EQN\(U,)f(0.0\)\);)p
391 4015 V 495 4069 a Fa(a)529 4101 y @beginspecial @setspecial
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eop
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626 625 bop 664 299 a @beginspecial @setspecial @endspecial
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b(CAAAR)f(CAAR)1314 2251 y(CAAADR)g(CAADR)f(CADR)1314
2364 y(CAAD)m(AR)k(CAD)m(AR)f(CD)m(AR)1314 2477 y(CAADDR)d(CADDR)f
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y(CAD)m(ADR)f(CD)m(ADR)1314 2816 y(CADD)m(AR)g(CDD)m(AR)1314
2929 y(CADDDR)c(CDDDR)1314 3041 y(CD)m(AAAR)1314 3154
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3493 y(CDD)m(AAR)1314 3606 y(CDD)m(ADR)1314 3719 y(CDDD)m(AR)1314
3832 y(CDDDDR)664 4142 y FJ(CONS)p FQ(\()p FN(U)p FQ(:)p
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b(d-p)g(air)1273 b(eval,)33 b(spr)-5 b(e)g(ad)814 4255
y FQ(Returns)29 b(a)h(dotted-pair)g(whic)m(h)e(is)h(not)h(EQ)f(to)i(an)
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627 626 bop 241 299 a @beginspecial @setspecial @endspecial
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(implies.)p @beginspecial @setspecial @endspecial -33
x Fb(a)391 1043 y FJ(FEXPR)46 b(PROCEDURE)f(LIST\(U\);)534
1156 y(EVLIS)h(U;)p 391 1252 1080 4 v 495 1305 a Fa(a)529
1337 y @beginspecial @setspecial @endspecial Fx(The)26
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2991 y @beginspecial @setspecial @endspecial 166 x FR(91.3.3)112
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3718 y(created)31 b(b)m(y)f(READ)h(whic)m(h)e(ha)m(v)m(e)j(the)e(same)h
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3830 y(the)g(same)h(ob)5 b(ject)31 b(\(see)h(the)e(EQ)g(function)f(in)g
(\\Elemen)m(tary)i(Predicates",)241 3943 y(section)f
@beginspecial @setspecial @endspecial(91.3.1)j(on)d(page)h
@beginspecial @setspecial @endspecial(622)r(\).)p eop
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628 627 bop 664 299 a @beginspecial @setspecial @endspecial
FQ(628)787 b FM(CHAPTER)30 b(91.)72 b(THE)30 b(ST)-8
b(AND)m(ARD)31 b(LISP)f(REPOR)-8 b(T)664 623 y FJ(COMPRESS)p
FQ(\()p FN(U)p FQ(:)p FD(id-list)p FQ(\):)p FP(f)p FD(atom)p
FQ(-)p FD(ve)j(ctor)p FP(g)1168 b FD(eval,)33 b(spr)-5
b(e)g(ad)814 736 y FQ(U)32 b(is)f(a)h(list)f(of)h(single)f(c)m
(haracter)i(iden)m(ti\014ers)d(whic)m(h)h(is)g(built)e(in)m(to)j(a)h
(Stand-)814 849 y(ard)45 b(LISP)g(en)m(tit)m(y)h(and)f(returned.)85
b(Recognized)46 b(are)g(n)m(um)m(b)s(ers,)i(strings,)814
962 y(and)43 b(iden)m(ti\014ers)e(with)g(the)j(escap)s(e)f(c)m
(haracter)i(pre\014xing)c(sp)s(ecial)h(c)m(harac-)814
1075 y(ters.)47 b(The)32 b(formats)h(of)f(these)h(items)f(app)s(ear)g
(in)f(\\Primitiv)m(e)g(Data)j(T)m(yp)s(es")814 1188 y(section)h
@beginspecial @setspecial @endspecial(91.2.1)h(on)e(page)h
@beginspecial @setspecial @endspecial(615)r(.)52 b(Iden)m(ti\014ers)33
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(but)g(this)f(is)h(an)g(unde\014ned)814 1414 y(use.)39
b(If)25 b(an)h(en)m(tit)m(y)g(cannot)g(b)s(e)f(parsed)g(out)h(of)g(U)g
(or)f(c)m(haracters)i(are)f(left)g(o)m(v)m(er)814 1527
y(after)31 b(parsing)e(an)h(error)g(o)s(ccurs:)814 1700
y FJ(*****)47 b(Poorly)f(formed)g(atom)g(in)i(COMPRESS)664
2262 y(EXPLODE)p FQ(\()p FN(U)p FQ(:)p FP(f)p FD(atom)p
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FD(id-list)1126 b(eval,)33 b(spr)-5 b(e)g(ad)814 2375
y FQ(Returned)20 b(is)g(a)h(list)e(of)i(in)m(terned)f(c)m(haracters)i
(represen)m(ting)e(the)h(c)m(haracters)h(to)814 2488
y(prin)m(t)k(of)h(the)g(v)-5 b(alue)27 b(of)g(U.)h(The)e(primitiv)m(e)f
(data)j(t)m(yp)s(es)f(ha)m(v)m(e)h(these)g(formats:)814
2700 y FN(in)m(teger)46 b FQ(Leading)24 b(zero)s(es)i(are)f(suppressed)
e(and)h(a)i(min)m(us)d(sign)h(pre\014xes)g(the)1041 2813
y(digits)29 b(if)h(the)g(in)m(teger)h(is)f(negativ)m(e.)814
3001 y FN(\015oating)46 b FQ(The)34 b(v)-5 b(alue)34
b(app)s(ears)g(in)f(the)i(format)f([-]0.nn...nnE[-]mm)h(if)f(the)1041
3114 y(magnitude)40 b(of)h(the)g(n)m(um)m(b)s(er)f(is)g(to)s(o)h(large)
g(or)g(small)e(to)i(displa)m(y)e(in)1041 3226 y([-]nnnn.nnnn)24
b(format.)39 b(The)26 b(crosso)m(v)m(er)i(p)s(oin)m(t)d(is)h
(determined)f(b)m(y)h(the)1041 3339 y(implemen)m(tation.)814
3527 y FN(id)46 b FQ(The)36 b(c)m(haracters)i(of)e(the)h(prin)m(t)e
(name)h(of)h(the)f(iden)m(ti\014er)f(are)i(pro)s(duced)1041
3640 y(with)30 b(sp)s(ecial)e(c)m(haracters)k(pre\014xed)e(with)f(the)h
(escap)s(e)h(c)m(haracter.)814 3827 y FN(string)46 b
FQ(The)21 b(c)m(haracters)j(of)e(the)g(string)f(are)i(pro)s(duced)d
(surrounded)g(b)m(y)h(dou-)1041 3940 y(ble)30 b(quotes)h(".)16
b(.)f(.)g(".)814 4128 y FN(function-p)s(oin)m(ter)46
b FQ(The)30 b(v)-5 b(alue)29 b(of)i(the)f(function-p)s(oin)m(ter)e(is)h
(created)i(as)g(a)1041 4241 y(list)h(of)h(c)m(haracters)h(conforming)e
(to)i(the)f(con)m(v)m(en)m(tions)h(of)f(the)g(system)1041
4354 y(site.)814 4566 y(The)43 b(t)m(yp)s(e)h(mismatc)m(h)f(error)h(o)s
(ccurs)f(if)g(U)g(is)g(not)h(a)g(n)m(um)m(b)s(er,)i(iden)m(ti\014er,)
814 4679 y(string,)30 b(or)g(function-p)s(oin)m(ter.)p
eop
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629 628 bop 241 299 a @beginspecial @setspecial @endspecial
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(EQ)g(to)h(an)m(ything)f(else.)241 1256 y FJ(INTERN)p
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FD(id)1547 b(eval,)33 b(spr)-5 b(e)g(ad)391 1369 y FQ(INTERN)29
b(searc)m(hes)i(the)e(OBLIST)g(for)g(an)h(iden)m(ti\014er)e(with)g(the)
i(same)g(prin)m(t)391 1482 y(name)44 b(as)g(U)f(and)h(returns)e(the)i
(iden)m(ti\014er)e(on)h(the)h(OBLIST)f(if)g(a)h(matc)m(h)391
1595 y(is)35 b(found.)59 b(An)m(y)37 b(prop)s(erties)e(and)h(global)g
(v)-5 b(alues)36 b(asso)s(ciated)h(with)e(U)i(ma)m(y)391
1708 y(b)s(e)g(lost.)64 b(If)37 b(U)i(do)s(es)e(not)i(matc)m(h)f(an)m
(y)h(en)m(try)-8 b(,)41 b(a)d(new)g(one)g(is)f(created)i(and)391
1821 y(returned.)61 b(If)37 b(U)h(has)f(more)h(than)f(the)h(maxim)m(um)
e(n)m(um)m(b)s(er)h(of)g(c)m(haracters)391 1934 y(p)s(ermitted)g(b)m(y)
h(the)h(implemen)m(tation)e(\(the)i(minim)m(um)d(n)m(um)m(b)s(er)h(is)g
(24\))j(an)391 2046 y(error)30 b(o)s(ccurs:)391 2219
y FJ(*****)46 b(Too)h(many)g(characters)e(to)i(INTERN)241
2781 y(REMOB)p FQ(\()p FN(U)p FQ(:)p FD(id)p FQ(\):)p
FD(id)1939 b(eval,)33 b(spr)-5 b(e)g(ad)391 2894 y FQ(If)28
b(U)i(is)e(presen)m(t)h(on)g(the)g(OBLIST)f(it)g(is)g(remo)m(v)m(ed.)42
b(This)27 b(do)s(es)i(not)g(a\013ect)i(U)391 3007 y(ha)m(ving)f(prop)s
(erties,)f(\015ags,)i(functions)d(and)i(the)h(lik)m(e.)40
b(U)30 b(is)g(returned.)241 3160 y @beginspecial @setspecial
@endspecial 167 x FR(91.3.4)112 b(Prop)s(ert)m(y)37 b(List)g(F)-9
b(unctions)241 3548 y FQ(With)30 b(eac)m(h)h(id)e(in)g(the)i(system)f
(is)g(a)h(\\prop)s(ert)m(y)f(list",)f(a)i(set)g(of)g(en)m(tities)f
(whic)m(h)f(are)241 3661 y(asso)s(ciated)i(with)e(the)h(id)f(for)h
(fast)h(access.)42 b(These)30 b(en)m(tities)h(are)f(called)g
(\\\015ags")h(if)241 3774 y(their)e(use)h(giv)m(es)h(the)g(id)e(a)h
(single)f(v)-5 b(alued)30 b(prop)s(ert)m(y)-8 b(,)30
b(and)g(\\prop)s(erties")g(if)f(the)i(id)e(is)241 3887
y(to)i(ha)m(v)m(e)g(a)g(m)m(ultiv)-5 b(alued)28 b(attribute:)41
b(an)30 b(indicator)f(with)g(a)i(prop)s(ert)m(y)-8 b(.)241
4049 y(Flags)29 b(and)g(indicators)f(ma)m(y)i(clash,)g(consequen)m(tly)
f(care)h(should)e(b)s(e)g(tak)m(en)j(to)f(a)m(v)m(oid)241
4162 y(this)f(o)s(ccurrence.)41 b(Flagging)30 b(X)h(with)e(an)h(id)f
(whic)m(h)g(already)h(is)g(an)g(indicator)f(for)h(X)241
4275 y(ma)m(y)h(result)e(in)g(that)i(indicator)e(and)h(asso)s(ciated)h
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4388 y(adding)29 b(an)h(indicator)f(whic)m(h)g(is)h(the)g(same)h(id)e
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4501 y(b)s(eing)e(destro)m(y)m(ed.)p eop
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630 629 bop 664 299 a @beginspecial @setspecial @endspecial
FQ(630)787 b FM(CHAPTER)30 b(91.)72 b(THE)30 b(ST)-8
b(AND)m(ARD)31 b(LISP)f(REPOR)-8 b(T)664 623 y FJ(FLAG)p
FQ(\()p FN(U)p FQ(:)p FD(id-list)p FQ(,)31 b FN(V)p FQ(:)p
FD(id)p FQ(\):)p FD(NIL)1517 b(eval,)33 b(spr)-5 b(e)g(ad)814
736 y FQ(U)38 b(is)f(a)h(list)f(of)g(ids)g(whic)m(h)f(are)j(\015agged)f
(with)e(V.)j(The)e(e\013ect)i(of)f(FLA)m(G)h(is)814 849
y(that)i(FLA)m(GP)g(will)d(ha)m(v)m(e)j(the)g(v)-5 b(alue)39
b(T)h(for)g(those)h(ids)e(of)h(U)h(whic)m(h)e(w)m(ere)814
962 y(\015agged.)i(Both)31 b(V)f(and)f(all)g(the)h(elemen)m(ts)h(of)f
(U)g(m)m(ust)g(b)s(e)f(iden)m(ti\014ers)f(or)i(the)814
1075 y(t)m(yp)s(e)h(mismatc)m(h)f(error)g(o)s(ccurs.)664
1482 y FJ(FLAGP)p FQ(\()p FN(U)p FQ(:)p FD(any)p FQ(,)h
FN(V)p FQ(:)p FD(any)p FQ(\):)p FD(b)-5 b(o)g(ole)g(an)1365
b(eval,)33 b(spr)-5 b(e)g(ad)814 1595 y FQ(Returns)23
b(T)h(if)f(U)h(has)g(b)s(een)g(previously)e(\015agged)j(with)d(V,)j
(else)f(NIL.)g(Returns)814 1708 y(NIL)30 b(if)g(either)f(U)i(or)f(V)h
(is)e(not)i(an)f(id.)664 2097 y FJ(GET)p FQ(\()p FN(U)p
FQ(:)p FD(any)p FQ(,)i FN(IND)p FQ(:)p FD(any)p FQ(\):)p
FD(any)1477 b(eval,)33 b(spr)-5 b(e)g(ad)814 2210 y FQ(Returns)32
b(the)g(prop)s(ert)m(y)g(asso)s(ciated)h(with)e(indicator)g(IND)h(from)
g(the)h(prop-)814 2323 y(ert)m(y)40 b(list)e(of)h(U.)h(If)e(U)i(do)s
(es)e(not)i(ha)m(v)m(e)g(indicator)e(IND,)i(NIL)f(is)f(returned.)814
2436 y(GET)30 b(cannot)h(b)s(e)f(used)g(to)h(access)g(functions)e
(\(use)i(GETD)f(instead\).)664 2848 y FJ(PUT)p FQ(\()p
FN(U)p FQ(:)p FD(id)p FQ(,)h FN(IND)p FQ(:)p FD(id)p
FQ(,)g FN(PR)m(OP)p FQ(:)p FD(any)p FQ(\):)p FD(any)1094
b(eval,)33 b(spr)-5 b(e)g(ad)814 2961 y FQ(The)21 b(indicator)g(IND)h
(with)f(the)g(prop)s(ert)m(y)h(PR)m(OP)f(is)g(placed)g(on)h(the)g(prop)
s(ert)m(y)814 3073 y(list)33 b(of)h(the)g(id)f(U.)i(If)e(the)i(action)f
(of)g(PUT)g(o)s(ccurs,)h(the)f(v)-5 b(alue)34 b(of)g(PR)m(OP)g(is)814
3186 y(returned.)k(If)26 b(either)f(of)h(U)g(and)g(IND)g(are)h(not)f
(ids)e(the)j(t)m(yp)s(e)f(mismatc)m(h)f(error)814 3299
y(will)32 b(o)s(ccur)i(and)g(no)h(prop)s(ert)m(y)f(will)e(b)s(e)i
(placed.)52 b(PUT)35 b(cannot)g(b)s(e)f(used)f(to)814
3412 y(de\014ne)d(functions)f(\(use)h(PUTD)h(instead\).)664
3824 y FJ(REMFLAG)p FQ(\()p FN(U)p FQ(:)p FD(any-list)p
FQ(,)g FN(V)p FQ(:)p FD(id)p FQ(\):)p FD(NIL)1306 b(eval,)33
b(spr)-5 b(e)g(ad)814 3937 y FQ(Remo)m(v)m(es)42 b(the)e(\015ag)g(V)g
(from)f(the)h(prop)s(ert)m(y)f(list)g(of)h(eac)m(h)h(mem)m(b)s(er)e(of)
h(the)814 4050 y(list)e(U.)i(Both)g(V)f(and)g(all)f(the)h(elemen)m(ts)h
(of)f(U)h(m)m(ust)f(b)s(e)f(ids)g(or)h(the)h(t)m(yp)s(e)814
4163 y(mismatc)m(h)30 b(error)g(will)e(o)s(ccur.)664
4552 y FJ(REMPROP)p FQ(\()p FN(U)p FQ(:)p FD(any)p FQ(,)j
FN(IND)p FQ(:)p FD(any)p FQ(\):)p FD(any)1286 b(eval,)33
b(spr)-5 b(e)g(ad)814 4665 y FQ(Remo)m(v)m(es)24 b(the)e(prop)s(ert)m
(y)g(with)f(indicator)g(IND)h(from)g(the)g(prop)s(ert)m(y)g(list)e(of)j
(U.)814 4778 y(Returns)j(the)i(remo)m(v)m(ed)g(prop)s(ert)m(y)e(or)h
(NIL)g(if)f(there)i(w)m(as)f(no)g(suc)m(h)g(indicator.)664
4931 y @beginspecial @setspecial @endspecial eop
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631 630 bop 241 299 a @beginspecial @setspecial @endspecial
FM(91.3.)72 b(FUNCTIONS)2045 b FQ(631)241 555 y FR(91.3.5)112
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b(unctions)30 b(in)f(Standard)g(LISP)g(are)i(global)f(en)m(tities.)40
b(T)-8 b(o)31 b(a)m(v)m(oid)g(function-v)-5 b(ariable)241
890 y(naming)29 b(clashes)h(no)g(v)-5 b(ariable)29 b(ma)m(y)i(ha)m(v)m
(e)h(the)f(same)f(name)h(as)f(a)h(function.)241 1270
y FJ(DE)p FQ(\()p FN(FNAME)p FQ(:)p FD(id)p FQ(,)f FN(P)-9
b(ARAMS)p FQ(:)p FD(id-list)p FQ(,)33 b FN(FN)p FQ(:)p
FD(any)p FQ(\):)p FD(id)446 b(no)-5 b(eval,)34 b(nospr)-5
b(e)g(ad)391 1383 y FQ(The)31 b(function)f(FN)i(with)f(the)g(formal)g
(parameter)h(list)f(P)-8 b(ARAMS)32 b(is)e(added)391
1496 y(to)36 b(the)f(set)h(of)g(de\014ned)e(functions)g(with)g(the)h
(name)h(FNAME.)g(An)m(y)g(previ-)391 1609 y(ous)h(de\014nitions)f(of)i
(the)g(function)e(are)i(lost.)63 b(The)37 b(function)g(created)i(is)e
(of)391 1722 y(t)m(yp)s(e)c(EXPR.)h(If)f(the)g(!*COMP)h(v)-5
b(ariable)32 b(is)h(non-NIL,)g(the)h(EXPR)f(is)f(\014rst)391
1835 y(compiled.)39 b(The)30 b(name)g(of)h(the)f(de\014ned)f(function)h
(is)f(returned.)391 2029 y FJ(FEXPR)46 b(PROCEDURE)f(DE\(U\);)534
2142 y(PUTD\(CAR)g(U,)j('EXPR,)e(LIST\('LAMBDA,)e(CADR)j(U,)g(CADDR)f
(U\)\);)241 2565 y(DF)p FQ(\()p FN(FNAME)p FQ(:)p FD(id)p
FQ(,)30 b FN(P)-9 b(ARAM)p FQ(:)p FD(id-list)p FQ(,)33
b FN(FN)p FQ(:)p FD(any)p FQ(\):)p FD(id)504 b(no)-5
b(eval,)34 b(nospr)-5 b(e)g(ad)391 2678 y FQ(The)26 b(function)g(FN)h
(with)f(formal)g(parameter)h(P)-8 b(ARAM)28 b(is)e(added)g(to)i(the)f
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(FNAME.)h(An)m(y)f(previous)e(de\014nitions)391 2904
y(of)30 b(the)h(function)e(are)h(lost.)41 b(The)30 b(function)f
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3017 y(the)33 b(!*COMP)g(v)-5 b(ariable)31 b(is)h(T)g(the)h(FEXPR)g(is)
e(\014rst)h(compiled.)46 b(The)33 b(name)391 3130 y(of)d(the)h
(de\014ned)e(function)g(is)g(returned.)391 3324 y FJ(FEXPR)46
b(PROCEDURE)f(DF\(U\);)534 3437 y(PUTD\(CAR)g(U,)j('FEXPR,)d
(LIST\('LAMBDA,)g(CADR)h(U,)h(CADDR)g(U\)\);)241 3973
y(DM)p FQ(\()p FN(MNAME)p FQ(:)p FD(id)p FQ(,)31 b FN(P)-9
b(ARAM)p FQ(:)p FD(id-list)p FQ(,)32 b FN(FN)p FQ(:)p
FD(any)p FQ(\):)p FD(id)471 b(no)-5 b(eval,)34 b(nospr)-5
b(e)g(ad)391 4086 y FQ(The)32 b(macro)i(FN)g(with)e(the)h(formal)f
(parameter)i(P)-8 b(ARAM)34 b(is)e(added)h(to)h(the)391
4199 y(set)e(of)h(de\014ned)e(functions)f(with)h(the)i(name)f(MNAME.)h
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(are)i(o)m(v)m(erwritten.)57 b(The)36 b(function)e(created)j(is)e(of)
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(macro)g(is)e(returned.)391 4619 y FJ(FEXPR)46 b(PROCEDURE)f(DM\(U\);)
534 4732 y(PUTD\(CAR)g(U,)j('MACRO,)d(LIST\('LAMBDA,)g(CADR)h(U,)h
(CADDR)g(U\)\);)p eop
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632 631 bop 664 299 a @beginspecial @setspecial @endspecial
FQ(632)787 b FM(CHAPTER)30 b(91.)72 b(THE)30 b(ST)-8
b(AND)m(ARD)31 b(LISP)f(REPOR)-8 b(T)664 623 y FJ(GETD)p
FQ(\()p FN(FNAME)p FQ(:)p FD(any)p FQ(\):)p FP(f)p FQ(NIL,)31
b FD(dotte)-5 b(d-p)g(air)p FP(g)955 b FD(eval,)33 b(spr)-5
b(e)g(ad)814 736 y FQ(If)27 b(FNAME)i(is)e(not)h(the)f(name)h(of)g(a)g
(de\014ned)f(function,)g(NIL)g(is)g(returned.)39 b(If)814
849 y(FNAME)31 b(is)f(a)h(de\014ned)e(function)g(then)h(the)g
(dotted-pair)814 1052 y(\()p FN(TYPE)p FQ(:)p FD(ftyp)-5
b(e)32 b FQ(.)41 b FN(DEF)p FQ(:)p FP(f)p FD(function-p)-5
b(ointer,)34 b(lamb)-5 b(da)p FP(g)p FQ(\))814 1255 y(is)30
b(returned.)664 1644 y FJ(PUTD)p FQ(\()p FN(FNAME)p FQ(:)p
FD(id)p FQ(,)g FN(TYPE)p FQ(:)p FD(ftyp)-5 b(e)p FQ(,)32
b FN(BOD)m(Y)p FQ(:)p FD(function)p FQ(\):)p FD(id)400
b(eval,)33 b(spr)-5 b(e)g(ad)814 1757 y FQ(Creates)27
b(a)g(function)e(with)g(name)h(FNAME)h(and)f(de\014nition)e(BOD)m(Y)j
(of)g(t)m(yp)s(e)814 1870 y(TYPE.)40 b(If)g(PUTD)h(succeeds)f(the)h
(name)f(of)h(the)f(de\014ned)f(function)g(is)h(re-)814
1983 y(turned.)73 b(The)41 b(e\013ect)i(of)f(PUTD)g(is)e(that)i(GETD)g
(will)d(return)h(a)i(dotted-)814 2096 y(pair)25 b(with)g(the)h
(functions)f(t)m(yp)s(e)h(and)g(de\014nition.)37 b(Lik)m(ewise)25
b(the)h(GLOBALP)814 2209 y(predicate)k(will)58 b(return)30
b(T)g(when)f(queried)g(with)g(the)i(function)e(name.)814
2322 y(If)f(the)h(function)f(FNAME)h(has)g(already)f(b)s(een)g
(declared)g(as)h(a)g(GLOBAL)g(or)814 2435 y(FLUID)i(v)-5
b(ariable)29 b(the)i(error:)814 2608 y FJ(*****)47 b(FNAME)f(is)h(a)h
(non-local)d(variable)814 2893 y FQ(o)s(ccurs)d(and)f(the)h(function)e
(will)f(not)j(b)s(e)f(de\014ned.)74 b(If)41 b(function)f(FNAME)814
3006 y(already)30 b(exists)g(a)h(w)m(arning)e(message)j(will)27
b(app)s(ear:)814 3179 y FJ(***)47 b(FNAME)f(redefined)814
3465 y FQ(The)31 b(function)g(de\014ned)f(b)m(y)i(PUTD)f(will)e(b)s(e)i
(compiled)g(b)s(efore)g(de\014nition)e(if)814 3578 y(the)i(!*COMP)f
(global)g(v)-5 b(ariable)29 b(is)h(non-NIL.)664 3985
y FJ(REMD)p FQ(\()p FN(FNAME)p FQ(:)p FD(id)p FQ(\):)p
FP(f)p FQ(NIL,)h FD(dotte)-5 b(d-p)g(air)p FP(g)1022
b FD(eval,)33 b(spr)-5 b(e)g(ad)814 4098 y FQ(Remo)m(v)m(es)34
b(the)e(function)f(named)g(FNAME)i(from)e(the)h(set)h(of)f(de\014ned)f
(func-)814 4211 y(tions.)73 b(Returns)41 b(the)g(\(ft)m(yp)s(e)h(.)74
b(function\))40 b(dotted-pair)h(or)h(NIL)f(as)g(do)s(es)814
4323 y(GETD.)i(The)e(global/function)f(attribute)i(of)g(FNAME)h(is)e
(remo)m(v)m(ed)i(and)814 4436 y(the)31 b(name)f(ma)m(y)h(b)s(e)f(used)f
(subsequen)m(tly)g(as)i(a)g(v)-5 b(ariable.)664 4590
y @beginspecial @setspecial @endspecial eop
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633 632 bop 241 299 a @beginspecial @setspecial @endspecial
FM(91.3.)72 b(FUNCTIONS)2045 b FQ(633)241 555 y FR(91.3.6)112
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890 y(b)s(ound)d(to)j(the)g(v)-5 b(ariable.)39 b(The)30
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(er)g(whic)m(h)f(the)241 1002 y(v)-5 b(ariable)29 b(has)h(a)h
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g(binding)d(mec)m(hanisms)241 1115 y(in)i(Standard)g(LISP)-8
b(.)241 1378 y FN(Lo)s(cal)35 b(Binding)46 b FQ(This)29
b(t)m(yp)s(e)i(of)f(binding)d(o)s(ccurs)j(only)g(in)f(compiled)g
(functions.)468 1491 y(Lo)s(cal)h(v)-5 b(ariables)29
b(o)s(ccur)h(as)h(formal)f(parameters)g(in)f(lam)m(b)s(da)h
(expressions)468 1604 y(and)g(as)g(PR)m(OG)h(form)f(v)-5
b(ariables.)39 b(The)30 b(binding)d(o)s(ccurs)k(when)e(a)i(lam)m(b)s
(da)468 1716 y(expression)c(is)h(ev)-5 b(aluated)29 b(or)g(when)e(a)i
(PR)m(OG)g(form)f(is)g(executed.)41 b(The)28 b(scop)s(e)468
1829 y(of)j(a)f(lo)s(cal)g(v)-5 b(ariable)29 b(is)h(the)g(b)s(o)s(dy)f
(of)h(the)h(function)e(in)g(whic)m(h)g(it)h(is)g(de\014ned.)241
2017 y FN(Global)35 b(Binding)46 b FQ(Only)29 b(one)i(binding)c(of)k(a)
f(global)g(v)-5 b(ariable)29 b(exists)h(at)h(an)m(y)g(time)468
2130 y(allo)m(wing)e(direct)h(access)i(to)f(the)f(v)-5
b(alue)30 b(b)s(ound)e(to)k(the)e(v)-5 b(ariable.)40
b(The)30 b(scop)s(e)468 2243 y(of)h(a)f(global)g(v)-5
b(ariable)29 b(is)h(univ)m(ersal.)39 b(V)-8 b(ariables)29
b(declared)h(GLOBAL)h(ma)m(y)468 2356 y(not)g(app)s(ear)e(as)i
(parameters)g(in)e(lam)m(b)s(da)g(expressions)g(or)h(as)h(PR)m(OG)g
(form)468 2469 y(v)-5 b(ariables.)39 b(A)31 b(v)-5 b(ariable)29
b(m)m(ust)h(b)s(e)g(declared)g(GLOBAL)g(prior)f(to)i(its)f(use)g(as)h
(a)468 2582 y(global)f(v)-5 b(ariable)29 b(since)h(the)g(default)g(t)m
(yp)s(e)g(for)g(undeclared)f(v)-5 b(ariables)29 b(is)468
2694 y(FLUID.)241 2882 y FN(Fluid)35 b(Binding)46 b FQ(Fluid)28
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3108 y(all)f(formal)h(parameters)h(and)e(PR)m(OG)i(form)f(v)-5
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3447 y(suc)m(h)h(a)h(w)m(a)m(y)g(that)g(the)g(previous)e(binding)e(ma)m
(y)k(b)s(e)f(restored.)40 b(All)29 b(references)468 3560
y(to)i(\015uid)d(v)-5 b(ariables)29 b(are)i(to)g(the)g(curren)m(tly)e
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4379 y(ready)28 b(declared)h(FLUID)g(are)g(ignored.)40
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634 633 bop 664 299 a @beginspecial @setspecial @endspecial
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1464 y(b)s(een)f(declared)f(previously)f(it)i(is)f(initialized)e(to)k
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b(t)m(yp)s(e)h(from)h(FLUID)814 1690 y(to)31 b(GLOBAL)g(is)e(not)i(p)s
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2425 y(GLOBALP)p FQ(\()p FN(U)p FQ(:)p FD(any)p FQ(\):)p
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3058 y FJ(SET)p FQ(\()p FN(EXP)p FQ(:)p FD(id)p FQ(,)h
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b(eval,)33 b(spr)-5 b(e)g(ad)814 3171 y FQ(EXP)40 b(m)m(ust)f(b)s(e)g
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814 3397 y(V)-10 b(ALUE.)34 b(If)g(the)g(iden)m(ti\014er)e(is)h(not)h
(a)h(lo)s(cal)e(v)-5 b(ariable)33 b(or)h(has)g(not)g(b)s(een)f(de-)814
3509 y(clared)26 b(GLOBAL)h(it)f(is)g(automatically)g(declared)g(FLUID)
h(with)e(the)i(result-)814 3622 y(ing)j(w)m(arning)f(message:)814
3795 y FJ(***)47 b(EXP)g(declared)f(FLUID)814 4081 y
FQ(EXP)30 b(m)m(ust)h(not)f(ev)-5 b(aluate)31 b(to)g(T)f(or)h(NIL)f(or)
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635 634 bop 241 299 a @beginspecial @setspecial @endspecial
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2949 y(This)k(a\013ects)j(only)e(compiled)f(functions)g(as)i(free)g(v)
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@setspecial @endspecial(10)q(].)241 3220 y @beginspecial
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636 635 bop 664 299 a @beginspecial @setspecial @endspecial
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1137 y @beginspecial @setspecial @endspecial 925 1288
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1400 y(p)s(ears)f(at)h(the)g(top)f(lev)m(el)g(of)h(the)g(same)f(PR)m
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925 1588 a(2.)46 b(As)33 b(the)g(consequen)m(t)g(of)g(a)g(COND)f(item)h
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(of)g(a)h(PR)m(OG.)814 1756 y @beginspecial @setspecial
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2002 y(sequen)m(t)g(of)g(a)g(COND)f(item)g(to)h(an)m(y)g(lev)m(el.)814
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1041 2415 y(of)g(a)g(COND)f(to)h(an)m(y)g(lev)m(el)f(sub)5
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2470 y @beginspecial @setspecial @endspecial 925 2603
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3726 y(another)31 b(error)f(is)f(detected:)814 3898 y
FJ(*****)47 b(Illegal)e(use)i(of)g(GO)h(to)f(LABEL)p
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637 636 bop 241 299 a @beginspecial @setspecial @endspecial
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1108 y FQ(NUMBER)42 b(and)f(MESSA)m(GE)h(are)g(passed)f(bac)m(k)h(to)g
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b(EMSG!*)j(and)e(the)h(error)f(n)m(um)m(b)s(er)814 1446
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(ORSET.)i(FLUID)i(v)-5 b(ariables)814 1559 y(and)30 b(lo)s(cal)g
(bindings)e(are)j(un)m(b)s(ound)d(to)k(return)d(to)j(the)f(en)m
(vironmen)m(t)f(of)h(the)814 1672 y(ERR)m(ORSET.)f(Global)f(v)-5
b(ariables)29 b(are)i(not)g(a\013ected)g(b)m(y)g(the)f(pro)s(cess.)664
2079 y FJ(ERRORSET)p FQ(\()p FN(U)p FQ(:)p FD(any)p FQ(,)g
FN(MSGP)p FQ(:)p FD(b)-5 b(o)g(ole)g(an)p FQ(,)35 b FN(TR)p
FQ(:)p FD(b)-5 b(o)g(ole)g(an)p FQ(\):)p FD(any)474 b(eval,)33
b(spr)-5 b(e)g(ad)814 2192 y FQ(If)27 b(an)g(error)g(o)s(ccurs)g
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b(alue)27 b(of)g(NUMBER)814 2305 y(from)38 b(the)g(ERR)m(OR)g(call)g
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2418 y(addition,)28 b(if)g(the)h(v)-5 b(alue)29 b(of)g(MSGP)g(is)f
(non-NIL,)h(the)g(MESSA)m(GE)g(from)g(the)814 2531 y(ERR)m(OR)g(call)f
(is)f(displa)m(y)m(ed)h(up)s(on)f(b)s(oth)h(the)h(standard)f(output)g
(device)h(and)814 2644 y(the)k(curren)m(tly)e(selected)i(output)f
(device)g(unless)f(the)h(standard)g(output)g(de-)814
2757 y(vice)25 b(is)f(not)h(op)s(en.)38 b(The)24 b(message)i(app)s
(ears)e(pre\014xed)g(with)f(5)i(asterisks.)39 b(The)814
2870 y(MESSA)m(GE)23 b(list)f(is)g(displa)m(y)m(ed)g(without)h(top)g
(lev)m(el)g(paren)m(theses.)38 b(The)23 b(MES-)814 2982
y(SA)m(GE)32 b(from)f(the)g(ERR)m(OR)g(call)g(will)e(b)s(e)h(a)m(v)-5
b(ailable)31 b(in)f(the)i(global)e(v)-5 b(ariable)814
3095 y(EMSG!*.)40 b(The)25 b(exact)i(format)e(of)h(error)f(messages)h
(generated)g(b)m(y)f(Standard)814 3208 y(LISP)30 b(functions)f(describ)
s(ed)g(in)g(this)h(do)s(cumen)m(t)g(are)h(not)g(\014xed)f(and)g(should)
814 3321 y(not)44 b(b)s(e)e(relied)g(up)s(on)g(to)i(b)s(e)e(in)g(an)m
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3414 y(GREATERP)p FQ(\()p FN(U)p FQ(:)p FD(numb)-5 b(er)p
FQ(,)30 b FN(V)p FQ(:)p FD(numb)-5 b(er)p FQ(\):)p FD(b)g(o)g(ole)g(an)
921 b(eval,)33 b(spr)-5 b(e)g(ad)391 3527 y FQ(Returns)29
b(T)h(if)g(U)g(is)f(strictly)h(greater)h(than)f(V,)h(otherwise)f
(returns)f(NIL.)241 3934 y FJ(LESSP)p FQ(\()p FN(U)p
FQ(:)p FD(numb)-5 b(er)p FQ(,)31 b FN(V)p FQ(:)p FD(numb)-5
b(er)p FQ(\):)p FD(b)g(o)g(ole)g(an)1064 b(eval,)33 b(spr)-5
b(e)g(ad)391 4047 y FQ(Returns)29 b(T)h(if)g(U)g(is)f(strictly)h(less)f
(than)i(V,)f(otherwise)g(returns)f(NIL.)p eop
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644 643 bop 664 299 a @beginspecial @setspecial @endspecial
FQ(644)787 b FM(CHAPTER)30 b(91.)72 b(THE)30 b(ST)-8
b(AND)m(ARD)31 b(LISP)f(REPOR)-8 b(T)664 623 y FJ(MAX)p
FQ(\([)p FN(U)p FQ(:)p FD(numb)j(er)p FQ(]\):)p FD(numb)g(er)941
b(no)-5 b(eval,)33 b(nospr)-5 b(e)g(ad,)36 b(or)d(macr)-5
b(o)814 736 y FQ(Returns)29 b(the)h(largest)g(of)h(the)f(v)-5
b(alues)29 b(in)f(U.)j(If)e(t)m(w)m(o)i(or)f(more)g(v)-5
b(alues)30 b(are)g(the)814 849 y(same)h(the)g(\014rst)e(is)h(returned.)
814 1043 y FJ(MACRO)47 b(PROCEDURE)e(MAX\(U\);)957 1156
y(EXPAND\(CDR)g(U,)j('MAX2\);)664 1579 y(MAX2)p FQ(\()p
FN(U)p FQ(:)p FD(numb)-5 b(er)p FQ(,)31 b FN(V)p FQ(:)p
FD(numb)-5 b(er)p FQ(\):)p FD(numb)g(er)1103 b(eval,)33
b(spr)-5 b(e)g(ad)814 1692 y FQ(Returns)32 b(the)h(larger)g(of)g(U)g
(and)g(V.)g(If)g(U)g(and)f(V)h(are)h(the)f(same)g(v)-5
b(alue)33 b(U)g(is)814 1805 y(returned)c(\(U)i(and)f(V)g(migh)m(t)h(b)s
(e)e(of)i(di\013eren)m(t)f(t)m(yp)s(es\).)814 2000 y
FJ(EXPR)47 b(PROCEDURE)e(MAX2\(U,)h(V\);)957 2112 y(IF)i(LESSP\(U,)d
(V\))i(THEN)g(V)g(ELSE)g(U;)664 2536 y(MIN)p FQ(\([)p
FN(U)p FQ(:)p FD(numb)-5 b(er)p FQ(]\):)p FD(numb)g(er)941
b(no)-5 b(eval,)33 b(nospr)-5 b(e)g(ad,)36 b(or)d(macr)-5
b(o)814 2648 y FQ(Returns)25 b(the)h(smallest)f(of)h(the)h(v)-5
b(alues)25 b(in)f(U.)j(If)e(t)m(w)m(o)i(or)f(more)g(v)-5
b(alues)26 b(are)g(the)814 2761 y(same)31 b(the)g(\014rst)e(of)i(these)
g(is)e(returned.)814 2956 y FJ(MACRO)47 b(PROCEDURE)e(MIN\(U\);)957
3069 y(EXPAND\(CDR)g(U,)j('MIN2\);)664 3492 y(MIN2)p
FQ(\()p FN(U)p FQ(:)p FD(numb)-5 b(er)p FQ(,)31 b FN(V)p
FQ(:)p FD(numb)-5 b(er)p FQ(\):)p FD(numb)g(er)1103 b(eval,)33
b(spr)-5 b(e)g(ad)814 3605 y FQ(Returns)25 b(the)h(smaller)f(of)h(its)f
(argumen)m(ts.)40 b(If)25 b(U)h(and)g(V)g(are)g(the)g(same)g(v)-5
b(alue,)814 3717 y(U)31 b(is)e(returned)g(\(U)i(and)f(V)g(migh)m(t)g(b)
s(e)g(of)h(di\013eren)m(t)f(t)m(yp)s(es\).)814 3912 y
FJ(EXPR)47 b(PROCEDURE)e(MIN2\(U,)h(V\);)957 4025 y(IF)i(GREATERP\(U,)c
(V\))j(THEN)g(V)h(ELSE)e(U;)664 4448 y(MINUS)p FQ(\()p
FN(U)p FQ(:)p FD(numb)-5 b(er)p FQ(\):)p FD(numb)g(er)1506
b(eval,)33 b(spr)-5 b(e)g(ad)814 4561 y FQ(Returns)30
b(-U.)814 4755 y FJ(EXPR)47 b(PROCEDURE)e(MINUS\(U\);)957
4868 y(DIFFERENCE\(0,)g(U\);)p eop
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645 644 bop 241 299 a @beginspecial @setspecial @endspecial
FM(91.3.)72 b(FUNCTIONS)2045 b FQ(645)241 623 y FJ(PLUS)p
FQ(\([)p FN(U)p FQ(:)p FD(numb)-5 b(er)p FQ(]\):)p FD(numb)g(er)892
b(no)-5 b(eval,)34 b(nospr)-5 b(e)g(ad,)35 b(or)f(macr)-5
b(o)391 736 y FQ(F)d(orms)31 b(the)f(sum)g(of)g(all)f(its)h(argumen)m
(ts.)391 931 y FJ(MACRO)46 b(PROCEDURE)f(PLUS\(U\);)534
1043 y(EXPAND\(CDR)g(U,)i('PLUS2\);)241 1467 y(PLUS2)p
FQ(\()p FN(U)p FQ(:)p FD(numb)-5 b(er)p FQ(,)31 b FN(V)p
FQ(:)p FD(numb)-5 b(er)p FQ(\):)p FD(numb)g(er)1054 b(eval,)33
b(spr)-5 b(e)g(ad)391 1579 y FQ(Returns)29 b(the)i(sum)e(of)i(U)f(and)g
(V.)241 1969 y FJ(QUOTIENT)p FQ(\()p FN(U)p FQ(:)p FD(numb)-5
b(er)p FQ(,)30 b FN(V)p FQ(:)p FD(numb)-5 b(er)p FQ(\):)p
FD(numb)g(er)911 b(eval,)33 b(spr)-5 b(e)g(ad)391 2082
y FQ(The)27 b(quotien)m(t)i(of)f(U)g(divided)e(b)m(y)i(V)g(is)f
(returned.)39 b(Division)26 b(of)i(t)m(w)m(o)i(p)s(ositiv)m(e)391
2194 y(or)37 b(t)m(w)m(o)i(negativ)m(e)g(in)m(tegers)f(is)f(con)m(v)m
(en)m(tional.)63 b(When)38 b(b)s(oth)f(U)g(and)h(V)f(are)391
2307 y(in)m(tegers)i(and)g(exactly)h(one)g(of)g(them)f(is)f(negativ)m
(e)j(the)f(v)-5 b(alue)38 b(returned)h(is)391 2420 y(the)h(negativ)m(e)
i(truncation)e(of)g(the)h(absolute)f(v)-5 b(alue)40 b(of)h(U)f(divided)
e(b)m(y)j(the)391 2533 y(absolute)27 b(v)-5 b(alue)26
b(of)i(V.)f(An)g(error)g(o)s(ccurs)g(if)f(division)e(b)m(y)j(zero)h(is)
e(attempted:)391 2819 y FJ(*****)46 b(Attempt)g(to)h(divide)f(by)h(0)h
(in)f(QUOTIENT)241 3381 y(REMAINDER)p FQ(\()p FN(U)p
FQ(:)p FD(numb)-5 b(er)p FQ(,)29 b FN(V)p FQ(:)p FD(numb)-5
b(er)p FQ(\):)p FD(numb)g(er)864 b(eval,)33 b(spr)-5
b(e)g(ad)391 3494 y FQ(If)35 b(b)s(oth)g(U)h(and)f(V)h(are)g(in)m
(tegers)h(the)f(result)e(is)h(the)h(in)m(teger)g(remainder)f(of)391
3607 y(U)j(divided)d(b)m(y)j(V.)h(If)e(either)h(parameter)g(is)f
(\015oating)h(p)s(oin)m(t,)h(the)g(result)e(is)391 3720
y(the)27 b(di\013erence)f(b)s(et)m(w)m(een)h(U)g(and)f(V*\(U/V\))j(all)
c(in)h(\015oating)g(p)s(oin)m(t.)39 b(If)26 b(either)391
3833 y(n)m(um)m(b)s(er)g(is)h(negativ)m(e)i(the)f(remainder)e(is)h
(negativ)m(e.)41 b(If)27 b(b)s(oth)g(are)h(p)s(ositiv)m(e)f(or)391
3946 y(b)s(oth)32 b(are)g(negativ)m(e)i(the)f(remainder)e(is)g(p)s
(ositiv)m(e.)46 b(An)32 b(error)g(o)s(ccurs)h(if)e(V)i(is)391
4059 y(zero:)391 4232 y FJ(*****)46 b(Attempt)g(to)h(divide)f(by)h(0)h
(in)f(REMAINDER)391 4599 y(EXPR)f(PROCEDURE)g(REMAINDER\(U,)e(V\);)534
4712 y(DIFFERENCE\(U,)g(TIMES2\(QUOTIENT\(U,)f(V\),)k(V\)\);)p
eop
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646 645 bop 664 299 a @beginspecial @setspecial @endspecial
FQ(646)787 b FM(CHAPTER)30 b(91.)72 b(THE)30 b(ST)-8
b(AND)m(ARD)31 b(LISP)f(REPOR)-8 b(T)664 623 y FJ(SUB1)p
FQ(\()p FN(U)p FQ(:)p FD(numb)j(er)p FQ(\):)p FD(numb)g(er)1554
b(eval,)33 b(spr)-5 b(e)g(ad)814 736 y FQ(Returns)36
b(the)g(v)-5 b(alue)36 b(of)h(U)f(less)g(1.)59 b(If)36
b(U)g(is)g(a)h(FLO)m(A)-8 b(T)37 b(t)m(yp)s(e)f(n)m(um)m(b)s(er,)h(the)
814 849 y(v)-5 b(alue)30 b(returned)f(is)h(U)g(less)g(1.0.)814
1043 y FJ(EXPR)47 b(PROCEDURE)e(SUB1\(U\);)957 1156 y(DIFFERENCE\(U,)g
(1\);)664 1579 y(TIMES)p FQ(\([)p FN(U)p FQ(:)p FD(numb)-5
b(er)p FQ(]\):)p FD(numb)g(er)845 b(no)-5 b(eval,)33
b(nospr)-5 b(e)g(ad,)36 b(or)d(macr)-5 b(o)814 1692 y
FQ(Returns)30 b(the)g(pro)s(duct)f(of)i(all)e(its)h(argumen)m(ts.)814
1887 y FJ(MACRO)47 b(PROCEDURE)e(TIMES\(U\);)957 2000
y(EXPAND\(CDR)g(U,)j('TIMES2\);)664 2423 y(TIMES2)p FQ(\()p
FN(U)p FQ(:)p FD(numb)-5 b(er)p FQ(,)31 b FN(V)p FQ(:)p
FD(numb)-5 b(er)p FQ(\):)p FD(numb)g(er)1007 b(eval,)33
b(spr)-5 b(e)g(ad)814 2536 y FQ(Returns)30 b(the)g(pro)s(duct)f(of)i(U)
f(and)g(V.)664 2689 y @beginspecial @setspecial @endspecial
166 x FR(91.3.12)113 b(MAP)37 b(Comp)s(osite)f(F)-9 b(unctions)664
3294 y FJ(MAP)p FQ(\()p FN(X)p FQ(:)p FD(list)p FQ(,)31
b(F)p FN(N)p FQ(:)p FD(function)p FQ(\):)p FD(any)1379
b(eval,)33 b(spr)-5 b(e)g(ad)814 3407 y FQ(Applies)28
b(FN)j(to)g(successiv)m(e)g(CDR)f(segmen)m(ts)i(of)e(X.)h(NIL)f(is)g
(returned.)814 3602 y FJ(EXPR)47 b(PROCEDURE)e(MAP\(X,)h(FN\);)957
3714 y(WHILE)h(X)g(DO)g FL(<<)g FJ(FN)h(X;)f(X)g(:=)g(CDR)g(X)h
FL(>>)p FJ(;)664 4138 y(MAPC)p FQ(\(X:list,)29 b(FN:function\):)p
FD(any)1351 b(eval,)33 b(spr)-5 b(e)g(ad)814 4250 y FQ(FN)28
b(is)e(applied)e(to)k(successiv)m(e)f(CAR)g(segmen)m(ts)h(of)f(list)f
(X.)h(NIL)g(is)f(returned.)814 4445 y FJ(EXPR)47 b(PROCEDURE)e
(MAPC\(X,)h(FN\);)957 4558 y(WHILE)h(X)g(DO)g FL(<<)g
FJ(FN)h(CAR)f(X;)g(X)g(:=)g(CDR)g(X)h FL(>>)p FJ(;)p
eop
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647 646 bop 241 299 a @beginspecial @setspecial @endspecial
FM(91.3.)72 b(FUNCTIONS)2045 b FQ(647)241 623 y FJ(MAPCAN)p
FQ(\(X:list,)28 b(FN:function\):)p FD(any)1255 b(eval,)33
b(spr)-5 b(e)g(ad)391 736 y FQ(A)31 b(concatenated)j(list)c(of)i(FN)g
(applied)d(to)k(successiv)m(e)f(CAR)f(elemen)m(ts)h(of)g(X)391
849 y(is)d(returned.)391 1043 y FJ(EXPR)46 b(PROCEDURE)g(MAPCAN\(X,)f
(FN\);)534 1156 y(IFNULL)h(X)h(THEN)g(NIL)629 1269 y(ELSE)g(NCONC\(FN)f
(CAR)g(X,)i(MAPCAN\(CDR)d(X,)i(FN\)\);)241 1692 y(MAPCAR)p
FQ(\(X:list,)28 b(FN:function\):)p FD(any)1255 b(eval,)33
b(spr)-5 b(e)g(ad)391 1805 y FQ(Returned)29 b(is)h(a)g(constructed)h
(list)e(of)i(FN)f(applied)f(to)i(eac)m(h)g(CAR)f(of)h(list)e(X.)391
2000 y FJ(EXPR)46 b(PROCEDURE)g(MAPCAR\(X,)f(FN\);)534
2112 y(IFNULL)h(X)h(THEN)g(NIL)629 2225 y(ELSE)g(FN)g(CAR)g(X)h(.)f
(MAPCAR\(CDR)e(X,)i(FN\);)241 2648 y(MAPCON)p FQ(\(X:list,)28
b(FN:function\):)p FD(any)1255 b(eval,)33 b(spr)-5 b(e)g(ad)391
2761 y FQ(Returned)41 b(is)g(a)h(concatenated)j(list)40
b(of)i(FN)h(applied)d(to)i(successiv)m(e)h(CDR)391 2874
y(segmen)m(ts)31 b(of)g(X.)391 3069 y FJ(EXPR)46 b(PROCEDURE)g
(MAPCON\(X,)f(FN\);)534 3181 y(IFNULL)h(X)h(THEN)g(NIL)629
3294 y(ELSE)g(NCONC\(FN)f(X,)h(MAPCON\(CDR)e(X,)i(FN\)\);)241
3717 y(MAPLIST)p FQ(\(X:list,)28 b(FN:function\):)p FD(any)1207
b(eval,)33 b(spr)-5 b(e)g(ad)391 3830 y FQ(Returns)23
b(a)h(constructed)g(list)f(of)h(FN)g(applied)e(to)j(successiv)m(e)f
(CDR)g(segmen)m(ts)391 3943 y(of)30 b(X.)391 4138 y FJ(EXPR)46
b(PROCEDURE)g(MAPLIST\(X,)f(FN\);)534 4250 y(IFNULL)h(X)h(THEN)g(NIL)
629 4363 y(ELSE)g(FN)g(X)h(.)f(MAPLIST\(CDR)e(X,)i(FN\);)241
4533 y @beginspecial @setspecial @endspecial eop
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648 647 bop 664 299 a @beginspecial @setspecial @endspecial
FQ(648)787 b FM(CHAPTER)30 b(91.)72 b(THE)30 b(ST)-8
b(AND)m(ARD)31 b(LISP)f(REPOR)-8 b(T)664 555 y FR(91.3.13)113
b(Comp)s(osite)36 b(F)-9 b(unctions)664 995 y FJ(APPEND)p
FQ(\()p FN(U)p FQ(:)p FD(list)p FQ(,)31 b FN(V)p FQ(:)p
FD(list)p FQ(\):)p FD(list)1526 b(eval,)33 b(spr)-5 b(e)g(ad)814
1108 y FQ(Returns)29 b(a)h(constructed)g(list)e(in)g(whic)m(h)h(the)h
(last)f(elemen)m(t)h(of)g(U)g(is)e(follo)m(w)m(ed)814
1221 y(b)m(y)i(the)h(\014rst)f(elemen)m(t)g(of)h(V.)g(The)f(list)f(U)h
(is)g(copied,)g(V)g(is)g(not.)814 1415 y FJ(EXPR)47 b(PROCEDURE)e
(APPEND\(U,)g(V\);)957 1528 y(IFNULL)h(U)i(THEN)f(V)1053
1641 y(ELSE)f(CAR)h(U)h(.)f(APPEND\(CDR)e(U,)i(V\);)664
2064 y(ASSOC)p FQ(\()p FN(U)p FQ(:)p FD(any)p FQ(,)31
b FN(V)p FQ(:)p FD(alist)p FQ(\):)p FP(f)p FD(dotte)-5
b(d-p)g(air)p FQ(,)36 b(NIL)p FP(g)893 b FD(eval,)33
b(spr)-5 b(e)g(ad)814 2177 y FQ(If)40 b(U)g(o)s(ccurs)g(as)g(the)g(CAR)
g(p)s(ortion)f(of)h(an)g(elemen)m(t)h(of)f(the)g(alist)f(V,)i(the)814
2290 y(dotted-pair)e(in)e(whic)m(h)h(U)h(o)s(ccurred)f(is)g(returned,)i
(else)f(NIL)f(is)g(returned.)814 2403 y(ASSOC)d(migh)m(t)i(not)g
(detect)h(a)f(p)s(o)s(orly)e(formed)i(alist)f(so)h(an)f(in)m(v)-5
b(alid)72 b(con-)814 2515 y(struction)30 b(ma)m(y)h(b)s(e)e(detected)j
(b)m(y)e(CAR)g(or)h(CDR.)814 2710 y FJ(EXPR)47 b(PROCEDURE)e(ASSOC\(U,)
h(V\);)957 2823 y(IF)i(NULL)e(V)i(THEN)e(NIL)1101 2936
y(ELSE)g(IF)h(ATOM)g(CAR)g(V)g(THEN)1339 3048 y(ERROR\(000,)e(LIST\(V,)
h("is)h(a)g(poorly)f(formed)h(alist"\)\))1101 3161 y(ELSE)f(IF)h(U)h(=)
f(CAAR)g(V)g(THEN)g(CAR)g(V)1101 3274 y(ELSE)f(ASSOC\(U,)g(CDR)h(V\);)
664 3697 y(DEFLIST)p FQ(\()p FN(U)p FQ(:)p FD(d)5 b(list)p
FQ(,)30 b FN(IND)p FQ(:)p FD(id)p FQ(\):)p FD(list)1349
b(eval,)33 b(spr)-5 b(e)g(ad)814 3810 y FQ(A)29 b("dlist")f(is)g(a)i
(list)d(in)h(whic)m(h)g(eac)m(h)i(elemen)m(t)g(is)e(a)h(t)m(w)m(o)h
(elemen)m(t)g(list:)39 b(\(ID:id)814 3923 y(PR)m(OP:an)m(y\).)81
b(Eac)m(h)44 b(ID)g(in)f(U)g(has)g(the)h(indicator)f(IND)g(with)g(prop)
s(ert)m(y)814 4036 y(PR)m(OP)35 b(placed)f(on)h(its)g(prop)s(ert)m(y)f
(list)f(b)m(y)i(the)g(PUT)g(function.)53 b(The)35 b(v)-5
b(alue)814 4149 y(of)36 b(DEFLIST)f(is)g(a)h(list)e(of)i(the)g(\014rst)
f(elemen)m(ts)g(of)h(eac)m(h)h(t)m(w)m(o)g(elemen)m(t)f(list.)814
4262 y(Lik)m(e)30 b(PUT,)h(DEFLIST)e(ma)m(y)i(not)g(b)s(e)f(used)f(to)i
(de\014ne)f(functions.)814 4456 y FJ(EXPR)47 b(PROCEDURE)e(DEFLIST\(U,)
g(IND\);)957 4569 y(IF)j(NULL)e(U)i(THEN)e(NIL)1053 4682
y(ELSE)g FL(<<)i FJ(PUT\(CAAR)d(U,)i(IND,)g(CADAR)f(U\);)1481
4795 y(CAAR)g(U)i FL(>>)f FJ(.)95 b(DEFLIST\(CDR)45 b(U,)i(IND\);)p
eop
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649 648 bop 241 299 a @beginspecial @setspecial @endspecial
FM(91.3.)72 b(FUNCTIONS)2045 b FQ(649)241 623 y FJ(DELETE)p
FQ(\()p FN(U)p FQ(:)p FD(any)p FQ(,)30 b FN(V)p FQ(:)p
FD(list)p FQ(\):)p FD(list)1503 b(eval,)33 b(spr)-5 b(e)g(ad)391
736 y FQ(Returns)28 b(V)g(with)g(the)h(\014rst)e(top)i(lev)m(el)g(o)s
(ccurrence)g(of)f(U)h(remo)m(v)m(ed)h(from)e(it.)391
931 y FJ(EXPR)46 b(PROCEDURE)g(DELETE\(U,)f(V\);)534
1043 y(IF)i(NULL)g(V)g(THEN)g(NIL)629 1156 y(ELSE)g(IF)g(CAR)g(V)h(=)f
(U)g(THEN)g(CDR)g(V)629 1269 y(ELSE)g(CAR)g(V)g(.)h(DELETE\(U,)d(CDR)i
(V\);)241 1692 y(DIGIT)p FQ(\()p FN(U)p FQ(:)p FD(any)p
FQ(\):)p FD(b)-5 b(o)g(ole)g(an)1665 b(eval,)33 b(spr)-5
b(e)g(ad)391 1805 y FQ(Returns)29 b(T)h(if)g(U)g(is)f(a)i(digit,)f
(otherwise)f(NIL.)391 2000 y FJ(EXPR)46 b(PROCEDURE)g(DIGIT\(U\);)534
2112 y(IF)h(MEMQ\(U,)f('\(!0)h(!1)g(!2)g(!3)g(!4)g(!5)g(!6)h(!7)f(!8)g
(!9\)\))629 2225 y(THEN)g(T)g(ELSE)g(NIL;)241 2648 y(LENGTH)p
FQ(\()p FN(X)p FQ(:)p FD(any)p FQ(\):)p FD(inte)-5 b(ger)1631
b(eval,)33 b(spr)-5 b(e)g(ad)391 2761 y FQ(The)30 b(top)g(lev)m(el)g
(length)g(of)h(the)f(list)f(X)i(is)e(returned.)391 2956
y FJ(EXPR)46 b(PROCEDURE)g(LENGTH\(X\);)534 3069 y(IF)h(ATOM)g(X)g
(THEN)g(0)629 3181 y(ELSE)g(PLUS\(1,)f(LENGTH)g(CDR)h(X\);)241
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3143 1989 V 1196 1992 1950 4 v 1053 2071 a(IF)47 b(PAIRP)f(CAR)h(U)h
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2651 y FJ(LINELENGTH)p FQ(\()p FN(LEN)p FQ(:)p FP(f)p
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3103 y(line)36 b(length)h(is)g(returned)f(except)j(when)d(LEN)i(is)e
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1043 y FJ(EXPR)47 b(PROCEDURE)e(PRINT\(U\);)1053 1156
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1579 y(PRIN1)p FQ(\()p FN(U)p FQ(:)p FD(any)p FQ(\):)p
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b(alue)25 b(of)h(U)f(is)g(returned.)38 b(Items)26 b(are)g(displa)m(y)m
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FL(>)31 b(<)p FD(statement)j(list)p FL(>)241 1797 y(<)p
FD(expr)-5 b(ession)p FL(>)31 b FQ(::=)453 1910 y FL(<)p
FD(expr)-5 b(ession)928 1924 y FO(1)969 1910 y FL(>)30
b FN(.)40 b FL(<)p FD(expr)-5 b(ession)1614 1924 y FO(2)1655
1910 y FL(>)30 b FQ(=)-15 b FP(\))665 2023 y FQ(\(CONS)30
b FL(<)p FD(expr)-5 b(ession)1461 2037 y FO(1)1502 2023
y FL(>)30 b(<)p FD(expr)-5 b(ession)2078 2037 y FO(2)2119
2023 y FL(>)30 b FP(j)453 2136 y FL(<)p FD(expr)-5 b(ession)928
2150 y FO(1)969 2136 y FL(>)30 b FN(=)g FL(<)p FD(expr)-5
b(ession)1656 2150 y FO(2)1697 2136 y FL(>)30 b FQ(=)-15
b FP(\))665 2249 y FQ(\(EQUAL)30 b FL(<)p FD(expr)-5
b(ession)1531 2263 y FO(1)1572 2249 y FL(>)30 b(<)p FD(expr)-5
b(ession)2148 2263 y FO(2)2189 2249 y FL(>)p FQ(\))31
b FP(j)453 2362 y FL(<)p FD(expr)-5 b(ession)928 2376
y FO(1)969 2362 y FL(>)30 b FN(EQ)f FL(<)p FD(expr)-5
b(ession)1722 2376 y FO(2)1763 2362 y FL(>)30 b FQ(=)-15
b FP(\))665 2475 y FQ(\(EQ)30 b FL(<)p FD(expr)-5 b(ession)1338
2489 y FO(1)1379 2475 y FL(>)30 b(<)p FD(expr)-5 b(ession)1955
2489 y FO(2)1996 2475 y FL(>)p FQ(\))30 b FP(j)453 2588
y FQ(')p FL(<)p FD(expr)-5 b(ession)p FL(>)32 b FQ(=)-15
b FP(\))29 b FQ(\(QUOTE)h FL(<)p FD(expr)-5 b(ession)p
FL(>)p FQ(\))32 b FP(j)453 2700 y FQ(function)d FL(<)p
FD(expr)-5 b(ession)p FL(>)31 b FQ(=)-15 b FP(\))30 b
FQ(\(function)g FL(<)p FD(expr)-5 b(ession)p FL(>)p FQ(\))31
b FP(j)453 2813 y FQ(function\()p FL(<)p FD(ar)-5 b(gument)32
b(list)p FL(>)p FQ(\))f(=)-15 b FP(\))30 b FQ(\(function)f
FL(<)p FD(ar)-5 b(gument)34 b(list)p FL(>)p FQ(\))d FP(j)453
2926 y FQ(n)m(um)m(b)s(er)e(=)-15 b FP(\))30 b FQ(n)m(um)m(b)s(er)f
FP(j)453 3039 y FQ(id)g(=)-15 b FP(\))30 b FQ(id)241
3265 y FL(<)p FD(ar)-5 b(gument)33 b(list)p FL(>)e FQ(::=)f(\(\))h(=)
-15 b FP(\))30 b(j)453 3378 y FL(<)p FD(expr)-5 b(ession)p
FL(>)31 b FQ(=)-15 b FP(\))30 b FL(<)p FD(expr)-5 b(ession)p
FL(>)32 b FP(j)453 3491 y FL(<)p FD(expr)-5 b(ession)p
FL(>)p FQ(,)32 b FL(<)p FD(ar)-5 b(gument)33 b(list)p
FL(>)e FQ(=)-15 b FP(\))29 b FL(<)p FD(expr)-5 b(ession)p
FL(>)32 b(<)p FD(ar)-5 b(gument)33 b(list)p FL(>)241
3735 y FQ(Notice)e(the)g(three)f(in\014x)f(op)s(erators)h(.)41
b(EQ)30 b(and)g(=)g(whic)m(h)f(are)i(translated)f(in)m(to)g(calls)241
3848 y(on)g(CONS,)g(EQ,)g(and)g(EQUAL)g(resp)s(ectiv)m(ely)-8
b(.)40 b(Note)32 b(also)e(that)h(a)g(call)e(on)i(a)241
3961 y(function)e(whic)m(h)g(has)h(no)g(formal)g(parameters)h(m)m(ust)f
(ha)m(v)m(e)h(\(\))g(as)g(an)f(argumen)m(t)h(list.)241
4074 y(The)f(QUOTE)f(function)g(is)h(abbreviated)f(b)m(y)i('.)p
eop
%%Page: 666 666
666 665 bop 664 299 a @beginspecial @setspecial @endspecial
FQ(666)787 b FM(CHAPTER)30 b(91.)72 b(THE)30 b(ST)-8
b(AND)m(ARD)31 b(LISP)f(REPOR)-8 b(T)p eop
%%Page: 667 667
667 666 bop 241 299 a @beginspecial @setspecial @endspecial
1470 x @beginspecial @setspecial @endspecial 1406 2026
a FI(P)-5 b(art)65 b(IV)1239 2491 y FT(App)6 b(endix)1667
5187 y FQ(667)p eop
%%Page: 668 668
668 667 bop 664 299 a @beginspecial @setspecial @endspecial
eop
%%Page: 669 669
669 668 bop 241 299 a @beginspecial @setspecial @endspecial
165 x @beginspecial @setspecial @endspecial 764 x FI(App)5
b(endix)65 b(A)241 1693 y FT(Reserv)-6 b(ed)76 b(Iden)-6
b(ti\014ers)241 2187 y FQ(W)e(e)31 b(list)e(here)i(all)e(iden)m
(ti\014ers)f(that)j(are)g(normally)e(reserv)m(ed)h(in)f(REDUCE)241
2300 y(including)e(names)j(of)h(commands,)f(op)s(erators)g(and)g(switc)
m(hes)g(initially)d(in)i(the)241 2413 y(system.)41 b(Excluded)28
b(are)j(w)m(ords)f(that)h(are)g(reserv)m(ed)f(in)f(sp)s(eci\014c)g
(implemen)m(tations)241 2526 y(of)h(the)h(system.)241
2896 y(Commands)479 b FJ(ALGEBRAIC)28 b(ANTISYMMETRIC)f(ARRAY)i(BYE)g
(CLEAR)1166 3009 y(CLEARRULES)f(COMMENT)g(CONT)h(DECOMPOSE)f(DEFINE)
1166 3122 y(DEPEND)h(DISPLAY)f(ED)i(EDITDEF)e(END)i(EVEN)f(FACTOR)g
(FOR)1166 3235 y(FORALL)g(FOREACH)f(GO)i(GOTO)f(IF)h(IN)g(INDEX)f
(INFIX)g(INPUT)1166 3348 y(INTEGER)g(KORDER)f(LET)i(LINEAR)e(LISP)i
(LISTARGP)e(LOAD)1166 3461 y(LOAD)p 1364 3461 29 4 v
34 w(PACKAGE)g(MASS)h(MATCH)g(MATRIX)g(MSHELL)1166 3574
y(NODEPEND)f(NONCOM)h(NONZERO)f(NOSPUR)h(ODD)h(OFF)f(ON)1166
3687 y(OPERATOR)f(ORDER)h(OUT)h(PAUSE)f(PRECEDENCE)1166
3800 y(PRINT)p 1412 3800 V 33 w(PRECISION)f(PROCEDURE)g(QUIT)h(REAL)g
(REMFAC)1166 3913 y(REMIND)g(RETRY)g(RETURN)g(SAVEAS)f(SCALAR)h(SETMOD)
1166 4026 y(SHARE)g(SHOWTIME)f(SHUT)i(SPUR)f(SYMBOLIC)f(SYMMETRIC)1166
4138 y(VECDIM)h(VECTOR)g(WEIGHT)f(WRITE)h(WTLEVEL)241
4326 y FQ(Bo)s(olean)i(Op)s(erators)177 b FJ(EVENP)29
b(FIXP)g(FREEOF)g(NUMBERP)f(ORDP)i(PRIMEP)241 4514 y
FQ(In\014x)f(Op)s(erators)315 b FJ(:=)30 b(=)g(>=)g(>)g(<=)g(<)g(=>)f
(+)h(*)g(/)g(^)h(**)e(.)h(WHERE)f(SETQ)g(OR)h(AND)1166
4627 y(MEMBER)f(MEMQ)g(EQUAL)g(NEQ)h(EQ)f(GEQ)h(GREATERP)e(LEQ)1166
4740 y(LESSP)h(PLUS)g(DIFFERENCE)f(MINUS)h(TIMES)g(QUOTIENT)1166
4852 y(EXPT)g(CONS)1667 5187 y FQ(669)p eop
%%Page: 670 670
670 669 bop 664 299 a @beginspecial @setspecial @endspecial
FQ(670)1047 b FM(APPENDIX)31 b(A.)61 b(RESER)-10 b(VED)30
b(IDENTIFIERS)664 555 y FQ(Numerical)f(Op)s(erators)91
b FJ(ABS)29 b(ACOS)g(ACOSH)g(ACOT)h(ACOTH)e(ACSC)i(ACSCH)f(ASEC)1590
668 y(ASECH)g(ASIN)g(ASINH)g(ATAN)g(ATANH)g(ATAN2)g(COS)g(COSH)h(COT)
1590 781 y(COTH)f(CSC)g(CSCH)h(EXP)f(FACTORIAL)f(FIX)h(FLOOR)g(HYPOT)g
(LN)1590 894 y(LOG)g(LOGB)g(LOG10)g(NEXTPRIME)f(ROUND)h(SEC)h(SECH)f
(SIN)1590 1007 y(SINH)g(SQRT)g(TAN)h(TANH)664 1194 y
FQ(Pre\014x)g(Op)s(erators)261 b FJ(APPEND)28 b(ARGLENGTH)g(CEILING)h
(COEFF)g(COEFFN)1590 1307 y(COFACTOR)f(CONJ)h(DEG)g(DEN)h(DET)f(DF)h
(DILOG)f(EI)h(EPS)f(ERF)1590 1420 y(FACTORIZE)f(FIRST)g(GCD)i(G)g
(IMPART)f(INT)g(INTERPOL)f(LCM)1590 1533 y(LCOF)h(LENGTH)g(LHS)g
(LINELENGTH)f(LTERM)h(MAINVAR)f(MAT)1590 1646 y(MATEIGEN)g(MAX)h(MIN)h
(MKID)f(NULLSPACE)f(NUM)h(PART)h(PF)1590 1759 y(PRECISION)e(RANDOM)g
(RANDOM)p 2660 1759 29 4 v 33 w(NEW)p 2837 1759 V 33
w(SEED)i(RANK)f(REDERR)1590 1872 y(REDUCT)f(REMAINDER)g(REPART)h(REST)g
(RESULTANT)1590 1985 y(REVERSE)f(RHS)i(SECOND)e(SET)i(SHOWRULES)e(SIGN)
h(SOLVE)1590 2098 y(STRUCTR)f(SUB)i(SUM)f(THIRD)g(TP)h(TRACE)f(VARNAME)
664 2285 y FQ(Reserv)m(ed)i(V)-8 b(ariables)175 b FJ(CARD)p
1788 2285 V 33 w(NO)30 b(E)g(EVAL)p 2217 2285 V 33 w(MODE)f(FORT)p
2663 2285 V 33 w(WIDTH)g(HIGH)p 3157 2285 V 34 w(POW)g(I)1590
2398 y(INFINITY)f(K!*)h(LOW)p 2325 2398 V 34 w(POW)g(NIL)h(PI)g(ROOT)p
3024 2398 V 33 w(MULTIPLICITY)1590 2511 y(T)664 2699
y FQ(Switc)m(hes)584 b FJ(ADJPREC)28 b(ALGINT)h(ALLBRANCH)f(ALLFAC)g
(BFSPACE)1590 2812 y(COMBINEEXPT)f(COMBINELOGS)g(COMP)i(COMPLEX)g
(CRAMER)1590 2925 y(CREF)e(DEFN)h(DEMO)g(DIV)g(ECHO)g(ERRCONT)f
(EVALLHSEQP)f(EXP)1590 3038 y(EXPANDLOGS)h(EZGCD)i(FACTOR)g(FORT)g
(FULLROOTS)f(GCD)1590 3150 y(IFACTOR)g(INT)i(INTSTR)e(LCM)i(LIST)f
(LISTARGS)f(MCD)1590 3263 y(MODULAR)g(MSG)i(MULTIPLICITIES)c(NAT)k
(NERO)f(NOSPLIT)1590 3376 y(OUTPUT)f(PERIOD)h(PRECISE)f(PRET)i(PRI)f
(RAT)h(RATARG)1590 3489 y(RATIONAL)e(RATIONALIZE)f(RATPRI)i(REVPRI)f
(RLISP88)1590 3602 y(ROUNDALL)g(ROUNDBF)g(ROUNDED)h(SAVESTRUCTR)1590
3715 y(SOLVESINGULAR)d(TIME)k(TRA)f(TRFAC)g(TRIGFORM)f(TRINT)664
3903 y FQ(Other)i(Reserv)m(ed)h(Ids)157 b FJ(BEGIN)29
b(DO)g(EXPR)h(FEXPR)f(INPUT)f(LAMBDA)h(LISP)g(MACRO)1590
4016 y(PRODUCT)f(REPEAT)h(SMACRO)f(SUM)i(UNTIL)f(WHEN)g(WHILE)g(WS)p
eop
%%Page: 671 671
671 670 bop 241 299 a @beginspecial @setspecial @endspecial
970 x FT(Bibliograph)-6 b(y)241 1641 y @beginspecial
@setspecial @endspecial 286 1752 a FQ([1])47 b(George)32
b(A.)e(Bak)m(er\(Jr.\))i(and)e(P)m(eter)h(Gra)m(v)m(es-Morris.)42
b FD(Pad)n(\023)-44 b(e)33 b(Appr)-5 b(oximants,)428
1864 y(Part)33 b(I:)f(Basic)h(The)-5 b(ory)p FQ(.)42
b(Addison-W)-8 b(esley)30 b(Publishing)c(Compan)m(y)-8
b(,)31 b(Reading,)428 1977 y(Massac)m(h)m(usetts,)h(1981.)241
2032 y @beginspecial @setspecial @endspecial 286 2165
a([2])47 b(Computation)29 b(Cen)m(ter.)41 b FD(LISP)33
b(R)-5 b(efer)g(enc)g(e)33 b(Manual,)g(CDC-6000)p FQ(.)41
b(The)428 2278 y(Univ)m(ersit)m(y)29 b(of)i(T)-8 b(exas)31
b(at)g(Austin.)241 2333 y @beginspecial @setspecial @endspecial
286 2466 a([3])47 b(S.-C.)30 b(Chou.)40 b(Pro)m(ving)29
b(elemen)m(tary)i(geometry)h(theorems)f(using)e(W)-8
b(u's)428 2578 y(algorithm.)39 b(In)30 b FD(Contemp.)k(Math.)p
FQ(,)d(v)m(olume)f(19,)h(pages)g(243)h({)f(286.)h(AMS,)428
2691 y(Pro)m(vidence,)e(Rho)s(de)g(Island,)f(1984.)241
2746 y @beginspecial @setspecial @endspecial 286 2879
a([4])47 b(S.-C.)30 b(Chou.)40 b FD(Me)-5 b(chanic)g(al)33
b(ge)-5 b(ometry)34 b(the)-5 b(or)g(em)35 b(pr)-5 b(oving)p
FQ(.)42 b(Reidel,)29 b(Dortrec)m(h)m(t,)428 2992 y(1988.)241
3029 y @beginspecial @setspecial @endspecial 286 3180
a([5])47 b(S.-C.)30 b(Chou.)40 b(Automated)31 b(reasoning)f(in)f
(geometries)i(using)e(the)428 3292 y(c)m(haracteristic)i(set)g(metho)s
(d)e(and)h(Gr\177)-45 b(obner)30 b(basis)f(metho)s(d.)40
b(In)30 b FD(Pr)-5 b(o)g(c.)428 3405 y(ISSA)n(C-90)p
FQ(,)30 b(pages)h(255{260.)j(A)m(CM)d(Press,)f(1990.)241
3460 y @beginspecial @setspecial @endspecial 286 3593
a([6])47 b(Andreas)29 b(Dolzmann)i(and)e(Thomas)h(Sturm.)40
b(Redlog:)g(Computer)30 b(algebra)428 3706 y(meets)h(computer)f(logic.)
40 b FD(A)n(CM)32 b(SIGSAM)g(Bul)5 b(letin)p FQ(,)30
b(31\(2\):2{9,)35 b(June)29 b(1997.)241 3766 y @beginspecial
@setspecial @endspecial 286 3894 a([7])47 b(Andreas)29
b(Dolzmann)i(and)e(Thomas)h(Sturm.)40 b(Simpli\014cation)26
b(of)428 4006 y(quan)m(ti\014er-free)j(form)m(ulae)h(o)m(v)m(er)i
(ordered)e(\014elds.)39 b FD(Journal)34 b(of)f(Symb)-5
b(olic)428 4119 y(Computation)p FQ(,)33 b(24\(2\):209{231,)j(August)30
b(1997.)241 4179 y @beginspecial @setspecial @endspecial
286 4307 a([8])47 b(Andreas)29 b(Dolzmann)i(and)e(Thomas)h(Sturm.)40
b FD(R)-5 b(e)g(d)5 b(lo)-5 b(g)34 b(User)e(Manual)p
FQ(.)41 b(FMI,)428 4420 y(Univ)m(ersit\177)-45 b(at)30
b(P)m(assau,)h(D-94030)i(P)m(assau,)e(German)m(y)-8 b(,)31
b(April)e(1999.)42 b(Edition)428 4533 y(2.0)31 b(for)f(V)-8
b(ersion)30 b(2.0.)241 4570 y @beginspecial @setspecial
@endspecial 286 4720 a([9])47 b(Stanford)29 b(Cen)m(ter)i(for)f
(Information)f(Pro)s(cessing.)40 b FD(LISP/360)34 b(R)-5
b(efer)g(enc)g(e)428 4833 y(Manual)p FQ(.)41 b(Stanford)29
b(Univ)m(ersit)m(y)-8 b(.)1667 5187 y(671)p eop
%%Page: 672 672
672 671 bop 664 299 a @beginspecial @setspecial @endspecial
FQ(672)2127 b FM(BIBLIOGRAPHY)664 464 y @beginspecial
@setspecial @endspecial 91 x FQ([10])47 b(M.)31 b(L.)f(Griss)g(and)f
(A.)i(C.)f(Hearn.)41 b(A)30 b(p)s(ortable)g(LISP)f(compiler.)851
668 y FD(Softwar)-5 b(e|Pr)g(actic)g(e)35 b(and)f(Exp)-5
b(erienc)g(e)p FQ(,)31 b(11:541{605,)k(June)29 b(1981.)664
723 y @beginspecial @setspecial @endspecial 133 x([11])47
b(A.)31 b(C.)f(Hearn.)41 b(REDUCE)30 b(user's)g(man)m(ual:)40
b(V)-8 b(ersion)30 b(3.3.)42 b(Publication)28 b(CP78)851
969 y(\(Rev)j(1/88\),)i(RAND,)e(1988.)664 1029 y @beginspecial
@setspecial @endspecial 127 x([12])47 b(A.)31 b(C.)f(Hearn,)h(P)-8
b(.)31 b(K.)f(Kuo,)g(and)g(D.)h(R.)f(Y)-8 b(ennie.)41
b(Radiativ)m(e)30 b(corrections)g(to)851 1269 y(an)g(electron-p)s
(ositron)g(scattering)h(exp)s(erimen)m(t.)39 b FD(Phys.)33
b(R)-5 b(ev.)p FQ(,)851 1382 y(187:2088{2096,)36 b(1969.)664
1437 y @beginspecial @setspecial @endspecial 133 x([13])47
b(W)-8 b(olfram)31 b(Ko)s(epf.)39 b(REDUCE)31 b(pac)m(k)-5
b(age)32 b(for)e(the)h(inde\014nite)d(and)i(de\014nite)851
1683 y(summation.)40 b FD(SIGSAM)32 b(Bul)5 b(letin)p
FQ(,)30 b(29\(1\):14{30,)35 b(Jan)m(uary)30 b(1995.)664
1743 y @beginspecial @setspecial @endspecial 127 x([14])47
b(T.)30 b(H.)h(Ko)s(orn)m(winder.)38 b(On)30 b(Zeilb)s(erger's)e
(algorithm)i(and)f(its)h FL(q)s FQ(-analogue:)41 b(a)851
1983 y(rigorous)30 b(description.)38 b FD(J.)32 b(of)h(Comput.)h(and)f
(Appl.)h(Math.)p FQ(,)d(48:91{111,)j(1993.)664 2038 y
@beginspecial @setspecial @endspecial 133 x([15])47 b
FD(MA)n(CLISP)31 b(R)-5 b(efer)g(enc)g(e)34 b(Manual)p
FQ(,)d(Marc)m(h)g(1976.)664 2231 y @beginspecial @setspecial
@endspecial 127 x([16])47 b(John)30 b(McCarth)m(y)-8
b(,)31 b(P)m(aul)f(W.)h(Abrahams,)f(Daniel)g(J.)g(Edw)m(ards,)f(Timoth)
m(y)h(P)-8 b(.)851 2471 y(Hart,)31 b(and)f(Mic)m(hael)g(I.)h(Levin.)39
b FD(LISP)33 b(1.5)g(Pr)-5 b(o)g(gr)g(ammers)36 b(Manual)p
FQ(.)41 b(The)851 2584 y(M.I.T.)31 b(Press,)f(Cam)m(bridge,)g(Massac)m
(h)m(usettes,)j(1965.)664 2639 y @beginspecial @setspecial
@endspecial 133 x([17])47 b(Mats)31 b(Nordstrom,)g(Erik)e(Sandew)m
(all,)g(and)g(Diz)i(Breslo)m(w.)41 b FD(LISP)32 b(F1:)42
b(A)851 2885 y(F)n(OR)-7 b(TRAN)32 b(Implementation)j(of)e(LISP)f(1.5)p
FQ(.)42 b(Uppsala)29 b(Univ)m(ersit)m(y)-8 b(,)851 2998
y(Departmen)m(t)32 b(of)e(Computer)g(Sciences.)664 3053
y @beginspecial @setspecial @endspecial 132 x([18])47
b(Lynn)29 b(H.)i(Quam)f(and)f(Whit\014eld)g(Di\016e.)40
b FD(Stanfor)-5 b(d)35 b(LISP)e(1.6)g(Manual)p FQ(.)851
3298 y(Stanford)26 b(Arti\014cial)f(In)m(telligence)h(Lab)s(oratory)-8
b(,)29 b(op)s(erating)d(note)i(28.7)g(edition.)664 3353
y @beginspecial @setspecial @endspecial 133 x([19])47
b(W)-8 b(arren)31 b(T)-8 b(eitelman.)40 b FD(INTERLISP)32
b(R)-5 b(efer)g(enc)g(e)33 b(Manual)p FQ(.)41 b(XER)m(O)m(X,)32
b(P)m(alo)851 3599 y(Alto)f(Researc)m(h)g(Cen)m(ters,)g(3333)h(Co)m(y)m
(ote)g(Road,)f(P)m(alo)g(Alto,)g(California)851 3712
y(94304,)i(1978.)664 3767 y @beginspecial @setspecial
@endspecial 132 x([20])47 b(V)-8 b(olk)m(er)31 b(W)-8
b(eispfenning.)39 b(Comprehensiv)m(e)29 b(Gr\177)-45
b(obner)30 b(bases.)40 b FD(Journal)34 b(of)851 4012
y(Symb)-5 b(olic)34 b(Computation)p FQ(,)f(14:1{29,)g(July)c(1992.)664
4067 y @beginspecial @setspecial @endspecial 133 x([21])47
b(W.-T.)31 b(W)-8 b(u.)41 b(On)30 b(the)g(decision)f(problem)g(and)h
(the)g(mec)m(hanization)h(of)851 4313 y(theorem-pro)m(ving)f(in)f
(elemen)m(tary)i(geometry)-8 b(.)43 b(In)29 b FD(Contemp.)34
b(Math.)p FQ(,)851 4426 y(v)m(olume)c(19,)i(pages)f(213)g({)g(234.)h
(AMS,)f(Pro)m(vidence,)f(Rho)s(de)g(Island,)f(1984.)664
4481 y @beginspecial @setspecial @endspecial 132 x([22])47
b(W.-T.)31 b(W)-8 b(u.)41 b(Some)31 b(recen)m(t)g(adv)-5
b(ances)31 b(in)e(mec)m(hanical)h(theorem)h(pro)m(ving)e(of)851
4726 y(geometry)-8 b(.)42 b(In)30 b FD(Contemp.)k(Math.)p
FQ(,)d(v)m(olume)f(19,)i(pages)f(235)g({)g(241.)h(AMS,)851
4839 y(Pro)m(vidence,)e(Rho)s(de)g(Island,)f(1984.)p
eop
%%Page: 673 673
673 672 bop 241 299 a @beginspecial @setspecial @endspecial
FM(BIBLIOGRAPHY)2126 b FQ(673)241 464 y @beginspecial
@setspecial @endspecial 91 x([23])47 b(W.-T.)31 b(W)-8
b(u.)41 b FD(Me)-5 b(chanic)g(al)34 b(The)-5 b(or)g(em)34
b(Pr)-5 b(oving)33 b(in)g(Ge)-5 b(ometries)p FQ(.)42
b(Num)m(b)s(er)29 b(1)i(in)428 668 y(T)-8 b(exts)31 b(and)e(Monographs)
i(in)e(Sym)m(b)s(olic)f(Computation.)i(Springer,)e(Wien,)428
781 y(1994.)p eop
%%Page: 674 674
674 673 bop 664 299 a @beginspecial @setspecial @endspecial
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@beginspecial @setspecial @endspecial(455)664 2010 y
FP(j)p 694 2010 28 4 v 63 w FQ(op)s(erator,)i @beginspecial
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FJ(.)95 b(\(CONS\))p FQ(,)29 b @beginspecial @setspecial
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1672 y(v)m(ector,)i @beginspecial @setspecial @endspecial(270)2304
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2010 y(::=:,)g @beginspecial @setspecial @endspecial(355)2304
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2309 3817 V 2337 3817 a FP(j)i FQ(op)s(erator,)h @beginspecial
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y FJ(ACOS)p FQ(,)e @beginspecial @setspecial @endspecial(83)q(,)i
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eop
%%Page: 675 675
675 674 bop 241 299 a @beginspecial @setspecial @endspecial
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29 4 v 33 w(COLUMNS)p FQ(,)d @beginspecial @setspecial
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1346 y FJ(ADD)p 391 1346 V 33 w(ROWS)p FQ(,)f @beginspecial
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V 33 w(TO)p 520 1458 V 34 w(COLUMNS)p FQ(,)f @beginspecial
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@endspecial(405)241 1571 y FJ(ADD)p 391 1571 V 33 w(TO)p
520 1571 V 34 w(ROWS)p FQ(,)f @beginspecial @setspecial
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1684 y FJ(ADJ)p FQ(,)e @beginspecial @setspecial @endspecial(467)241
1797 y FJ(ADJPREC)p FQ(,)f @beginspecial @setspecial
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2023 V 33 w(Ai)p FQ(,)h @beginspecial @setspecial @endspecial(543)241
2136 y FJ(Airy)p 439 2136 V 33 w(Aiprime)p FQ(,)f @beginspecial
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2249 V 33 w(Bi)p FQ(,)h @beginspecial @setspecial @endspecial(543)241
2362 y FJ(Airy)p 439 2362 V 33 w(Biprime)p FQ(,)f @beginspecial
@setspecial @endspecial(543)241 2475 y FJ(ALATOMP)p FQ(,)f
@beginspecial @setspecial @endspecial(255)241 2588 y
FJ(ALG)p 391 2588 V 33 w(TO)p 520 2588 V 34 w(SYMB)p
FQ(,)i @beginspecial @setspecial @endspecial(256)241
2700 y FJ(ALGEBRAIC)p FQ(,)e @beginspecial @setspecial
@endspecial(197)241 2813 y(Algebraic)i(mo)s(de,)g @beginspecial
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@endspecial(203)q(,)g @beginspecial @setspecial @endspecial(204)241
2926 y FJ(ALGINT)p FQ(,)e @beginspecial @setspecial @endspecial(193)q
(,)i @beginspecial @setspecial @endspecial(231)241 3039
y(alist,)e @beginspecial @setspecial @endspecial(620)241
3152 y(alist)407 3265 y(in)g(ASSOC,)g @beginspecial @setspecial
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@setspecial @endspecial(651)407 3491 y(in)h(SUBLIS,)h
@beginspecial @setspecial @endspecial(652)241 3604 y
FJ(ALKERNP)p FQ(,)e @beginspecial @setspecial @endspecial(255)241
3717 y FJ(ALL)p FQ(,)h @beginspecial @setspecial @endspecial(497)241
3830 y FJ(ALL!*)p FQ(,)g @beginspecial @setspecial @endspecial(352)241
3942 y FJ(ALLBRANCH)p FQ(,)f @beginspecial @setspecial
@endspecial(99)241 4055 y FJ(ALLFAC)p FQ(,)h @beginspecial
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@endspecial(119)241 4168 y FJ(allsymmetrybases)p FQ(,)26
b @beginspecial @setspecial @endspecial(558)241 4281
y FJ(ALTITUDE)p FQ(,)i @beginspecial @setspecial @endspecial(364)241
4394 y(AND,)j @beginspecial @setspecial @endspecial(640)241
4507 y FJ(AND)p FQ(,)e @beginspecial @setspecial @endspecial(497)241
4620 y FJ(ANGLE)p 487 4620 V 33 w(SUM)p FQ(,)g @beginspecial
@setspecial @endspecial(364)241 4733 y(an)m(teceden)m(t)j
(\(cond-form\),)f @beginspecial @setspecial @endspecial(620)241
4846 y FJ(ANTICOM)p FQ(,)d @beginspecial @setspecial
@endspecial(320)r(,)i @beginspecial @setspecial @endspecial(466)241
4959 y FJ(ANTICOMM)p FQ(,)e @beginspecial @setspecial
@endspecial(466)1880 555 y FJ(ANTICOMMUTE)p FQ(,)g @beginspecial
@setspecial @endspecial(467)1880 668 y FJ(ANTISYMMETRIC)p
FQ(,)f @beginspecial @setspecial @endspecial(107)r(,)j
@beginspecial @setspecial @endspecial(320)1880 781 y(an)m(y)-8
b(,)32 b @beginspecial @setspecial @endspecial(619)1880
894 y(APPEND,)f @beginspecial @setspecial @endspecial(648)1880
1007 y FJ(APPEND)p FQ(,)e @beginspecial @setspecial @endspecial(61)1880
1120 y FJ(APPENDN)p FQ(,)g @beginspecial @setspecial
@endspecial(245)1880 1233 y(APPL)-8 b(Y,)31 b @beginspecial
@setspecial @endspecial(653)1880 1346 y FJ(APPLYSYM)p
FQ(,)e @beginspecial @setspecial @endspecial(194)q(,)i
@beginspecial @setspecial @endspecial(235)1880 1458 y(ARBCONST)f(op)s
(erator,)h @beginspecial @setspecial @endspecial(450)1880
1571 y FJ(ARBVARS)p FQ(,)e @beginspecial @setspecial
@endspecial(99)1880 1684 y FJ(ARGLENGTH)p FQ(,)g @beginspecial
@setspecial @endspecial(131)1880 1797 y FJ(ARNUM)p FQ(,)h
@beginspecial @setspecial @endspecial(194)q(,)h @beginspecial
@setspecial @endspecial(239)1880 1910 y FJ(ARRAY)p FQ(,)f
@beginspecial @setspecial @endspecial(75)1880 2023 y
FJ(ARRAY)p 2126 2023 V 33 w(TO)p 2255 2023 V 34 w(LIST)p
FQ(,)g @beginspecial @setspecial @endspecial(259)1880
2136 y FJ(ASEC)p FQ(,)g @beginspecial @setspecial @endspecial(83)q(,)g
@beginspecial @setspecial @endspecial(86)1880 2249 y
FJ(ASECH)p FQ(,)g @beginspecial @setspecial @endspecial(83)q(,)g
@beginspecial @setspecial @endspecial(86)1880 2362 y
FJ(ASFIRST)p FQ(,)f @beginspecial @setspecial @endspecial(246)1880
2475 y FJ(ASFLIST)p FQ(,)g @beginspecial @setspecial
@endspecial(246)1880 2588 y FJ(ASIN)p FQ(,)h @beginspecial
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@endspecial(86)1880 2813 y FJ(ASLAST)p FQ(,)f @beginspecial
@setspecial @endspecial(246)1880 2926 y FJ(ASREST)p FQ(,)g
@beginspecial @setspecial @endspecial(246)1880 3039 y(Assignmen)m(t,)i
@beginspecial @setspecial @endspecial(64)q(,)f @beginspecial
@setspecial @endspecial(65)q(,)h @beginspecial @setspecial
@endspecial(67,)g @beginspecial @setspecial @endspecial(72)q(,)f
@beginspecial @setspecial @endspecial(202)r(,)2213 3152
y @beginspecial @setspecial @endspecial(204)1880 3265
y FJ(ASSIST)p FQ(,)f @beginspecial @setspecial @endspecial(194)r(,)h
@beginspecial @setspecial @endspecial(243)1880 3378 y
FJ(ASSLIST)p FQ(,)f @beginspecial @setspecial @endspecial(246)1880
3491 y(ASSOC,)h @beginspecial @setspecial @endspecial(648)1880
3604 y FJ(ASSOC)p FQ(,)g @beginspecial @setspecial @endspecial(498)1880
3717 y(asso)s(ciation)h(list,)e @beginspecial @setspecial
@endspecial(620)1880 3830 y FJ(assumptions)p FQ(,)f @beginspecial
@setspecial @endspecial(101)1880 3942 y(Asymptotic)j(command,)f
@beginspecial @setspecial @endspecial(153)r(,)g @beginspecial
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@endspecial(90)1880 4168 y FJ(ATAN2)p FQ(,)f @beginspecial
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b @beginspecial @setspecial @endspecial(623)1880 4620
y(atom,)h @beginspecial @setspecial @endspecial(619)1880
4733 y FJ(AUGMENT)p FQ(,)d @beginspecial @setspecial
@endspecial(328)1880 4846 y FJ(AUGMENT)p 2222 4846 V
33 w(COLUMNS)p FQ(,)g @beginspecial @setspecial @endspecial(403)q(,)h
@beginspecial @setspecial @endspecial(407)1880 4959 y(A)-10
b(VEC)31 b(function,)e @beginspecial @setspecial @endspecial(270)p
eop
%%Page: 676 676
676 675 bop 664 299 a @beginspecial @setspecial @endspecial
FQ(676)2553 b FM(INDEX)664 555 y FJ(AVECTOR)p FQ(,)29
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@beginspecial @setspecial @endspecial(552)664 1203 y
FJ(B)p 718 1203 29 4 v 34 w(PART)p FQ(,)g @beginspecial
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1542 y FJ(BAGLMAT)p FQ(,)g @beginspecial @setspecial
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1054 1767 V 32 w(MOD)p FQ(,)g @beginspecial @setspecial
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FQ(,)f @beginspecial @setspecial @endspecial(404)r(,)h
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FJ(BEGIN)47 b(...END)p FQ(,)28 b @beginspecial @setspecial
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2106 y FJ(BELAST)p FQ(,)h @beginspecial @setspecial @endspecial(245)664
2219 y FJ(Bernoulli)p FQ(,)f @beginspecial @setspecial
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@beginspecial @setspecial @endspecial(542)664 2445 y(Bernoulli)f(p)s
(olynomials,)g @beginspecial @setspecial @endspecial(543)664
2558 y FJ(BernoulliP)p FQ(,)g @beginspecial @setspecial
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32 w(base)p FQ(,)i @beginspecial @setspecial @endspecial(446)664
2784 y(Bessel)h(functions,)e @beginspecial @setspecial
@endspecial(542)664 2896 y FJ(BesselI)p FQ(,)g @beginspecial
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@beginspecial @setspecial @endspecial(542)664 3122 y
FJ(BesselK)p FQ(,)g @beginspecial @setspecial @endspecial(542)664
3235 y FJ(BesselY)p FQ(,)g @beginspecial @setspecial
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@beginspecial @setspecial @endspecial(542)664 3574 y
FJ(Bezout)p FQ(,)g @beginspecial @setspecial @endspecial(140)664
3687 y FJ(BF)p 766 3687 V 34 w(PART)p FQ(,)g @beginspecial
@setspecial @endspecial(554)664 3800 y FJ(BFSPACE)p FQ(,)g
@beginspecial @setspecial @endspecial(148)664 3913 y
FJ(Binomial)p FQ(,)g @beginspecial @setspecial @endspecial(542)664
4026 y(Binomial)g(co)s(e\016cien)m(ts,)i @beginspecial
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@beginspecial @setspecial @endspecial(71)q(,)g @beginspecial
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4251 V 33 w(MATRIX)p FQ(,)e @beginspecial @setspecial
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4364 y FJ(BNDEQ!*)p FQ(,)e @beginspecial @setspecial
@endspecial(339)664 4477 y FJ(BOOLEAN)p FQ(,)g @beginspecial
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@endspecial(277)664 4590 y(Bo)s(olean,)g @beginspecial
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@beginspecial @setspecial @endspecial(619)664 4816 y
FJ(BOS)p FQ(,)g @beginspecial @setspecial @endspecial(552)664
4929 y FJ(BOTH)p FQ(,)g @beginspecial @setspecial @endspecial(416)2304
555 y FJ(BOUNDS)p FQ(,)f @beginspecial @setspecial @endspecial(437)q(,)
i @beginspecial @setspecial @endspecial(443)2304 668
y FJ(BPART)p FQ(,)e @beginspecial @setspecial @endspecial(554)2304
781 y(Buc)m(h)m(b)s(erger's)i(Algorithm,)e @beginspecial
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@beginspecial @setspecial @endspecial(77)2304 1090 y
FJ(C1)p 2406 1090 V 34 w(CIRCLE)p FQ(,)f @beginspecial
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@beginspecial @setspecial @endspecial(194)r(,)h @beginspecial
@setspecial @endspecial(283)2304 1316 y(Call)f(b)m(y)h(v)-5
b(alue,)30 b @beginspecial @setspecial @endspecial(187)r(,)g
@beginspecial @setspecial @endspecial(189)2304 1429 y(CAMAL,)h
@beginspecial @setspecial @endspecial(285)2304 1542 y
FJ(CAMAL)p FQ(,)e @beginspecial @setspecial @endspecial(194)q(,)i
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(form,)h @beginspecial @setspecial @endspecial(111)2304
1767 y FJ(canonicaldecomposition)p FQ(,)24 b @beginspecial
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@setspecial @endspecial(626)2304 1993 y(CAR)2470 2106
y(comp)s(osite)g(forms,)g @beginspecial @setspecial @endspecial(626)
2304 2219 y FJ(CARD)p 2502 2219 V 33 w(NO)p FQ(,)g @beginspecial
@setspecial @endspecial(123)2304 2332 y FJ(CARTAN)p 2598
2332 V 33 w(SYSTEM)p FQ(,)f @beginspecial @setspecial
@endspecial(329)2304 2445 y(cartesian)h(co)s(ordinates,)h
@beginspecial @setspecial @endspecial(453)2304 2558 y
FJ(Catalan)p FQ(,)e @beginspecial @setspecial @endspecial(541)2304
2671 y FJ(CAUCHY)p 2598 2671 V 33 w(SYSTEM)p FQ(,)g @beginspecial
@setspecial @endspecial(329)2304 2784 y FJ(CC)p 2406
2784 V 34 w(TANGENT)p FQ(,)f @beginspecial @setspecial
@endspecial(364)2304 2896 y(CDR,)i @beginspecial @setspecial
@endspecial(626)2304 3009 y(CDR)2470 3122 y(comp)s(osite)g(forms,)g
@beginspecial @setspecial @endspecial(626)2304 3235 y
FJ(CEILING)p FQ(,)f @beginspecial @setspecial @endspecial(80)2304
3348 y(Celestial)g(Mec)m(hanics,)i @beginspecial @setspecial
@endspecial(285)2304 3461 y FJ(CFRAC)p FQ(,)e @beginspecial
@setspecial @endspecial(489)2304 3574 y FJ(CGB)p FQ(,)h
@beginspecial @setspecial @endspecial(290)2304 3687 y
FJ(CGBFULLRED)p FQ(,)e @beginspecial @setspecial @endspecial(294)2304
3800 y FJ(CGBGEN)p FQ(,)h @beginspecial @setspecial @endspecial(292)
2304 3913 y FJ(CGBGS)p FQ(,)g @beginspecial @setspecial
@endspecial(294)2304 4026 y FJ(CGBREAL)p FQ(,)g @beginspecial
@setspecial @endspecial(293)2304 4138 y FJ(CGBSTAT)p
FQ(,)g @beginspecial @setspecial @endspecial(294)2304
4251 y(c)m(hain)h(rule,)f @beginspecial @setspecial @endspecial(337)
2304 4364 y FJ(CHAN)p FQ(,)g @beginspecial @setspecial
@endspecial(554)2304 4477 y FJ(CHANGEVAR)p FQ(,)f @beginspecial
@setspecial @endspecial(295)2304 4590 y FJ(CHANGEVR)p
FQ(,)g @beginspecial @setspecial @endspecial(194)2304
4703 y FJ(CHAR)p 2502 4703 V 33 w(MATRIX)p FQ(,)h @beginspecial
@setspecial @endspecial(404)q(,)i @beginspecial @setspecial
@endspecial(408)2304 4816 y FJ(CHAR)p 2502 4816 V 33
w(POLY)p FQ(,)f @beginspecial @setspecial @endspecial(403)q(,)h
@beginspecial @setspecial @endspecial(404)q(,)f @beginspecial
@setspecial @endspecial(408)2304 4929 y FJ(character)p
FQ(,)e @beginspecial @setspecial @endspecial(558)p eop
%%Page: 677 677
677 676 bop 241 299 a @beginspecial @setspecial @endspecial
FM(INDEX)2552 b FQ(677)241 555 y(Character)31 b(set,)g
@beginspecial @setspecial @endspecial(43)241 668 y FJ(CHARACTERISTIC)p
919 668 29 4 v 30 w(VARIETY)p FQ(,)e @beginspecial @setspecial
@endspecial(330)241 781 y FJ(CHARACTERS)p FQ(,)f @beginspecial
@setspecial @endspecial(329)241 894 y(Cheb)m(yshev)h(\014t,)i
@beginspecial @setspecial @endspecial(437)241 1007 y(Cheb)m(yshev)e(p)s
(olynomials,)f @beginspecial @setspecial @endspecial(543)241
1120 y FJ(Chebyshev)p 679 1120 V 32 w(base)p 903 1120
V 33 w(T)p FQ(,)i @beginspecial @setspecial @endspecial(446)241
1233 y FJ(Chebyshev)p 679 1233 V 32 w(base)p 903 1233
V 33 w(U)p FQ(,)g @beginspecial @setspecial @endspecial(446)241
1346 y FJ(Chebyshev)p 679 1346 V 32 w(df)p FQ(,)g @beginspecial
@setspecial @endspecial(443)241 1458 y FJ(Chebyshev)p
679 1458 V 32 w(eval)p FQ(,)f @beginspecial @setspecial
@endspecial(444)241 1571 y FJ(Chebyshev)p 679 1571 V
32 w(fit)p FQ(,)g @beginspecial @setspecial @endspecial(443)241
1684 y FJ(Chebyshev)p 679 1684 V 32 w(int)p FQ(,)g @beginspecial
@setspecial @endspecial(443)241 1797 y FJ(ChebyshevT)p
FQ(,)f @beginspecial @setspecial @endspecial(543)241
1910 y FJ(ChebyshevU)p FQ(,)g @beginspecial @setspecial
@endspecial(543)241 2023 y FJ(CHECKPROLIST)p FQ(,)f @beginspecial
@setspecial @endspecial(253)241 2136 y FJ(Chi)p FQ(,)i
@beginspecial @setspecial @endspecial(544)241 2249 y
FJ(CHIRAL)p FQ(,)g @beginspecial @setspecial @endspecial(555)241
2362 y FJ(CHIRAL1)p FQ(,)f @beginspecial @setspecial
@endspecial(555)241 2475 y FJ(CHOLESKY)p FQ(,)g @beginspecial
@setspecial @endspecial(404)241 2588 y FJ(CHOOSE)p 535
2588 V 32 w(PC)p FQ(,)i @beginspecial @setspecial @endspecial(364)241
2700 y FJ(CHOOSE)p 535 2700 V 32 w(PL)p FQ(,)g @beginspecial
@setspecial @endspecial(365)241 2813 y FJ(Ci)p FQ(,)g
@beginspecial @setspecial @endspecial(544)241 2926 y
FJ(CIRCLE)p FQ(,)f @beginspecial @setspecial @endspecial(365)241
3039 y FJ(CIRCLE1)p FQ(,)f @beginspecial @setspecial
@endspecial(365)241 3152 y FJ(CIRCLE)p 535 3152 V 32
w(CENTER)p FQ(,)h @beginspecial @setspecial @endspecial(365)241
3265 y FJ(CIRCLE)p 535 3265 V 32 w(SQRADIUS)p FQ(,)g
@beginspecial @setspecial @endspecial(365)241 3378 y
FJ(CL)p 343 3378 V 34 w(TANGENT)p FQ(,)f @beginspecial
@setspecial @endspecial(365)241 3491 y FJ(CLEANUP)p FQ(,)g
@beginspecial @setspecial @endspecial(329)r(,)i @beginspecial
@setspecial @endspecial(330)241 3604 y FJ(CLEAR)p FQ(,)f
@beginspecial @setspecial @endspecial(156)q(,)i @beginspecial
@setspecial @endspecial(160)q(,)g @beginspecial @setspecial
@endspecial(256)241 3717 y FJ(CLEARBAG)p FQ(,)d @beginspecial
@setspecial @endspecial(247)241 3830 y FJ(CLEARFLAG)p
FQ(,)g @beginspecial @setspecial @endspecial(253)241
3942 y FJ(CLEARFUNCTIONS)p FQ(,)e @beginspecial @setspecial
@endspecial(256)241 4055 y FJ(CLEAROP)p FQ(,)i @beginspecial
@setspecial @endspecial(256)241 4168 y FJ(CLEARPHYSOP)p
FQ(,)f @beginspecial @setspecial @endspecial(463)241
4281 y FJ(CLEARRULES)p FQ(,)h @beginspecial @setspecial
@endspecial(161)241 4394 y(Clebsc)m(h)h(Gordan)h(co)s(e\016cien)m(ts,)i
@beginspecial @setspecial @endspecial(543)241 4507 y
FJ(Clebsch)p 583 4507 V 32 w(Gordan)p FQ(,)d @beginspecial
@setspecial @endspecial(543)241 4620 y(CLOSE,)g @beginspecial
@setspecial @endspecial(656)241 4733 y FJ(CLOSED)p FQ(,)g
@beginspecial @setspecial @endspecial(330)241 4846 y
FJ(CLOSURE)p FQ(,)f @beginspecial @setspecial @endspecial(329)241
4959 y FJ(COBASIS)p FQ(,)g @beginspecial @setspecial
@endspecial(327)1880 555 y(co)s(de)j(templates,)g @beginspecial
@setspecial @endspecial(358)1880 668 y(CODEP)-8 b(,)31
b @beginspecial @setspecial @endspecial(618)q(,)g @beginspecial
@setspecial @endspecial(623)1880 781 y FJ(COEFF)p FQ(,)f
@beginspecial @setspecial @endspecial(128)1880 894 y
FJ(COEFF)p 2126 894 V 33 w(MATRIX)p FQ(,)f @beginspecial
@setspecial @endspecial(404)1880 1007 y(Co)s(e\016cien)m(t,)i
@beginspecial @setspecial @endspecial(147)r({)p @beginspecial
@setspecial @endspecial(150)1880 1120 y FJ(COEFFN)p FQ(,)e
@beginspecial @setspecial @endspecial(129)1880 1233 y
FJ(COERCEMAT)p FQ(,)g @beginspecial @setspecial @endspecial(261)1880
1346 y FJ(COFACTOR)p FQ(,)g @beginspecial @setspecial
@endspecial(181)1880 1458 y(coframe,)j @beginspecial
@setspecial @endspecial(338)q(,)f @beginspecial @setspecial
@endspecial(341)1880 1571 y(COFRAME)2046 1684 y(WITH)g(METRIC,)f
@beginspecial @setspecial @endspecial(341)2046 1797 y(WITH)h(SIGNA)-8
b(TURE,)31 b @beginspecial @setspecial @endspecial(341)1880
1910 y FJ(COFRAMING)p FQ(,)e @beginspecial @setspecial
@endspecial(326)q(,)h @beginspecial @setspecial @endspecial(327)1880
2023 y FJ(COLLECT)p FQ(,)f @beginspecial @setspecial
@endspecial(67)1880 2136 y FJ(COLLINEAR)p FQ(,)g @beginspecial
@setspecial @endspecial(365)1880 2249 y FJ(COLUMN)p 2174
2249 V 33 w(DIM)p FQ(,)h @beginspecial @setspecial @endspecial(403)q(,)
h @beginspecial @setspecial @endspecial(405)1880 2362
y FJ(COMBINATIONS)p FQ(,)d @beginspecial @setspecial
@endspecial(251)1880 2475 y FJ(COMBINEEXPT)p FQ(,)g @beginspecial
@setspecial @endspecial(86)1880 2588 y FJ(COMBINELOGS)p
FQ(,)g @beginspecial @setspecial @endspecial(85)1880
2700 y FJ(COMBNUM)p FQ(,)h @beginspecial @setspecial
@endspecial(250)1880 2813 y FJ(COMM)p FQ(,)h @beginspecial
@setspecial @endspecial(466)q(,)h @beginspecial @setspecial
@endspecial(536)1880 2926 y(Command,)f @beginspecial
@setspecial @endspecial(75)1880 3039 y(Command)g(terminator,)g
@beginspecial @setspecial @endspecial(169)1880 3152 y
FJ(COMMENT)p FQ(,)f @beginspecial @setspecial @endspecial(48)1880
3265 y(commen)m(ts,)j @beginspecial @setspecial @endspecial(622)1880
3378 y FJ(COMMUTE)p FQ(,)d @beginspecial @setspecial
@endspecial(467)1880 3491 y FJ(COMP)p FQ(,)h @beginspecial
@setspecial @endspecial(219)1880 3604 y FJ(COMPACT)p
FQ(,)f @beginspecial @setspecial @endspecial(194)q(,)i
@beginspecial @setspecial @endspecial(297)1880 3717 y(COMP)-8
b(A)m(CT)31 b(op)s(erator,)g @beginspecial @setspecial
@endspecial(297)1880 3830 y(COMP)-8 b(A)m(CT)31 b(pac)m(k)-5
b(age,)32 b @beginspecial @setspecial @endspecial(297)1880
3942 y FJ(COMPANION)p FQ(,)d @beginspecial @setspecial
@endspecial(404)1880 4055 y(Compiler,)g @beginspecial
@setspecial @endspecial(219)1880 4168 y FJ(COMPLEX)p
FQ(,)g @beginspecial @setspecial @endspecial(150)1880
4281 y(Complex)h(co)s(e\016cien)m(t,)h @beginspecial
@setspecial @endspecial(150)1880 4394 y(Comp)s(ound)e(statemen)m(t,)j
@beginspecial @setspecial @endspecial(70)q(,)f @beginspecial
@setspecial @endspecial(72)1880 4507 y(COMPRESS,)e @beginspecial
@setspecial @endspecial(618)r(,)h @beginspecial @setspecial
@endspecial(628)1880 4620 y FJ(CONCURRENT)p FQ(,)e @beginspecial
@setspecial @endspecial(365)1880 4733 y(COND,)j @beginspecial
@setspecial @endspecial(640)1880 4846 y(cond-form,)g
@beginspecial @setspecial @endspecial(620)1880 4959 y(Conditional)d
(statemen)m(t,)33 b @beginspecial @setspecial @endspecial(66)p
eop
%%Page: 678 678
678 677 bop 664 299 a @beginspecial @setspecial @endspecial
FQ(678)2553 b FM(INDEX)664 555 y FJ(CONJ)p FQ(,)30 b
@beginspecial @setspecial @endspecial(80)664 668 y(CONS,)g
@beginspecial @setspecial @endspecial(626)664 781 y FJ(CONS)p
FQ(,)g @beginspecial @setspecial @endspecial(245)664
894 y(consequen)m(t)h(\(cond-form\),)g @beginspecial
@setspecial @endspecial(620)664 1007 y(constan)m(t,)h
@beginspecial @setspecial @endspecial(619)664 1120 y(CONST)-8
b(ANTP)g(,)30 b @beginspecial @setspecial @endspecial(623)664
1233 y(Constructor,)g @beginspecial @setspecial @endspecial(205)664
1346 y FJ(CONT)p FQ(,)g @beginspecial @setspecial @endspecial(176)664
1458 y FJ(CONTACT)p FQ(,)f @beginspecial @setspecial
@endspecial(326)664 1571 y FJ(CONTFR)p FQ(,)g @beginspecial
@setspecial @endspecial(194)664 1684 y FJ(CONTFRAC)p
FQ(,)g @beginspecial @setspecial @endspecial(489)664
1797 y(con)m(tin)m(uation)h(lines,)f @beginspecial @setspecial
@endspecial(357)664 1910 y FJ(contour)p FQ(,)g @beginspecial
@setspecial @endspecial(372)664 2023 y FJ(CONTRACT)p
FQ(,)g @beginspecial @setspecial @endspecial(465)664
2136 y FJ(CONVERT)p FQ(,)g @beginspecial @setspecial
@endspecial(411)664 2249 y FJ(COORDINATES)p FQ(,)f @beginspecial
@setspecial @endspecial(327)q(,)j @beginspecial @setspecial
@endspecial(330)664 2362 y(COORDINA)-8 b(TES)30 b(op)s(erator,)g
@beginspecial @setspecial @endspecial(272)664 2475 y(COORDS)f(v)m
(ector,)k @beginspecial @setspecial @endspecial(272)664
2588 y FJ(COPY)p 862 2588 29 4 v 33 w(INTO)p FQ(,)d @beginspecial
@setspecial @endspecial(403)q(,)h @beginspecial @setspecial
@endspecial(405)664 2700 y FJ(COS)p FQ(,)f @beginspecial
@setspecial @endspecial(83)q(,)g @beginspecial @setspecial
@endspecial(86)664 2813 y FJ(COSH)p FQ(,)g @beginspecial
@setspecial @endspecial(83)q(,)g @beginspecial @setspecial
@endspecial(86)664 2926 y FJ(COT)p FQ(,)g @beginspecial
@setspecial @endspecial(83)q(,)g @beginspecial @setspecial
@endspecial(86)664 3039 y FJ(COTH)p FQ(,)g @beginspecial
@setspecial @endspecial(83)q(,)g @beginspecial @setspecial
@endspecial(86)664 3152 y FJ(CP)p FQ(,)g @beginspecial
@setspecial @endspecial(554)664 3265 y FJ(CRACK)p FQ(,)f
@beginspecial @setspecial @endspecial(194)r(,)h @beginspecial
@setspecial @endspecial(299)664 3378 y FJ(CRAMER)p FQ(,)f
@beginspecial @setspecial @endspecial(95)q(,)i @beginspecial
@setspecial @endspecial(179)664 3491 y FJ(CREF)p FQ(,)f
@beginspecial @setspecial @endspecial(221)q(,)h @beginspecial
@setspecial @endspecial(222)664 3604 y FJ(CRESYS)p FQ(,)e
@beginspecial @setspecial @endspecial(536)664 3717 y
FJ(CROSS)p FQ(,)g @beginspecial @setspecial @endspecial(328)664
3830 y(CR)m(OSS)830 3942 y(v)m(ector,)j @beginspecial
@setspecial @endspecial(270)664 4055 y(cross)f(pro)s(duct,)e
@beginspecial @setspecial @endspecial(270)q(,)i @beginspecial
@setspecial @endspecial(455)664 4168 y(Cross)f(reference,)h
@beginspecial @setspecial @endspecial(221)664 4281 y
FJ(CROSSVECT)p FQ(,)d @beginspecial @setspecial @endspecial(259)664
4394 y FJ(CSC)p FQ(,)i @beginspecial @setspecial @endspecial(83)q(,)g
@beginspecial @setspecial @endspecial(86)664 4507 y FJ(CSCH)p
FQ(,)g @beginspecial @setspecial @endspecial(83)q(,)g
@beginspecial @setspecial @endspecial(86)664 4620 y(CURL)830
4733 y(op)s(erator,)h @beginspecial @setspecial @endspecial(271)664
4846 y(curl)830 4959 y(v)m(ector)h(\014eld,)d @beginspecial
@setspecial @endspecial(271)2304 555 y(curl)g(op)s(erator,)i
@beginspecial @setspecial @endspecial(456)2304 668 y
FJ(CVIT)p FQ(,)e @beginspecial @setspecial @endspecial(194)r(,)h
@beginspecial @setspecial @endspecial(303)2304 781 y
FJ(CVITBTR)p FQ(,)f @beginspecial @setspecial @endspecial(303)2304
894 y FJ(CVITOP)p FQ(,)g @beginspecial @setspecial @endspecial(303)2304
1007 y FJ(CVITRACE)p FQ(,)f @beginspecial @setspecial
@endspecial(303)2304 1120 y FJ(CYCLICPERMLIST)p FQ(,)f
@beginspecial @setspecial @endspecial(250)2304 1233 y(cylindrical)g(co)
s(ordinates,)j @beginspecial @setspecial @endspecial(453)2304
1429 y FJ(D)p FQ(,)g @beginspecial @setspecial @endspecial(552)2304
1542 y FJ(D)p 2358 1542 V 34 w(PART)p FQ(,)f @beginspecial
@setspecial @endspecial(554)2304 1654 y(data)i(structures,)f
@beginspecial @setspecial @endspecial(619)2304 1767 y(DE,)h
@beginspecial @setspecial @endspecial(631)2304 1880 y(Declaration,)g
@beginspecial @setspecial @endspecial(75)2304 1993 y(DECLARE)f
(function,)f @beginspecial @setspecial @endspecial(356)2304
2106 y FJ(DECOMPOSE)p FQ(,)f @beginspecial @setspecial
@endspecial(141)2304 2219 y(default)2470 2332 y(term)i(order,)g
@beginspecial @setspecial @endspecial(376)2304 2445 y
FJ(defid)p FQ(,)f @beginspecial @setspecial @endspecial(510)2304
2558 y FJ(defindex)p FQ(,)f @beginspecial @setspecial
@endspecial(510)2304 2671 y FJ(DEFINE)p FQ(,)h @beginspecial
@setspecial @endspecial(78)2304 2784 y(de\014nite)g(in)m(tegration)h
(\(simple\),)g @beginspecial @setspecial @endspecial(274)2304
2896 y FJ(DEFINT)p FQ(,)f @beginspecial @setspecial @endspecial(194)q
(,)i @beginspecial @setspecial @endspecial(305)2304 3009
y(DEFINT)f(function,)g @beginspecial @setspecial @endspecial(274)2304
3122 y(DEFLINEINT)g(function,)f @beginspecial @setspecial
@endspecial(275)2304 3235 y(DEFLIST,)h @beginspecial
@setspecial @endspecial(648)2304 3348 y FJ(DEFN)p FQ(,)f
@beginspecial @setspecial @endspecial(203)r(,)h @beginspecial
@setspecial @endspecial(223)r(,)g @beginspecial @setspecial
@endspecial(224)2304 3461 y FJ(DEFPOLY)p FQ(,)f @beginspecial
@setspecial @endspecial(239)2304 3574 y FJ(DEG)p FQ(,)h
@beginspecial @setspecial @endspecial(143)2304 3687 y(Degree,)i
@beginspecial @setspecial @endspecial(143)2304 3800 y
FJ(DEL)p FQ(,)e @beginspecial @setspecial @endspecial(552)2304
3913 y(DELETE,)g @beginspecial @setspecial @endspecial(649)2304
4026 y FJ(DELETE)p FQ(,)f @beginspecial @setspecial @endspecial(244)
2304 4138 y FJ(DELETE)p 2598 4138 V 33 w(ALL)p FQ(,)g
@beginspecial @setspecial @endspecial(244)2304 4251 y
FJ(DELLASTDIGIT)p FQ(,)e @beginspecial @setspecial @endspecial(249)2304
4364 y FJ(DELPAIR)p FQ(,)i @beginspecial @setspecial
@endspecial(244)2304 4477 y(DELSQ)2470 4590 y(op)s(erator,)i
@beginspecial @setspecial @endspecial(271)2304 4703 y(delsq)e(op)s
(erator,)i @beginspecial @setspecial @endspecial(456)2304
4816 y FJ(DEMO)p FQ(,)e @beginspecial @setspecial @endspecial(76)2304
4929 y FJ(DEN)p FQ(,)h @beginspecial @setspecial @endspecial(134)q(,)h
@beginspecial @setspecial @endspecial(143)p eop
%%Page: 679 679
679 678 bop 241 299 a @beginspecial @setspecial @endspecial
FM(INDEX)2552 b FQ(679)241 555 y FJ(DEPATOM)p FQ(,)28
b @beginspecial @setspecial @endspecial(252)241 668 y
FJ(DEPEND)p FQ(,)h @beginspecial @setspecial @endspecial(109)241
781 y(dep)s(end,)g @beginspecial @setspecial @endspecial(103)241
894 y(DEPEND)i(statemen)m(t,)h @beginspecial @setspecial
@endspecial(457)241 1007 y FJ(DEPTH)p FQ(,)d @beginspecial
@setspecial @endspecial(245)241 1120 y FJ(DEPVARP)p FQ(,)f
@beginspecial @setspecial @endspecial(255)241 1233 y
FJ(DER)p FQ(,)h @beginspecial @setspecial @endspecial(552)241
1346 y(deriv)-5 b(ativ)m(e)407 1458 y(v)g(ariational,)29
b @beginspecial @setspecial @endspecial(339)241 1571
y(deriv)-5 b(ativ)m(es,)30 b @beginspecial @setspecial
@endspecial(313)241 1684 y FJ(DERIVED)p 583 1684 29 4
v 32 w(SYSTEMS)p FQ(,)f @beginspecial @setspecial @endspecial(329)241
1797 y FJ(DESIR)p FQ(,)g @beginspecial @setspecial @endspecial(194)q(,)
i @beginspecial @setspecial @endspecial(309)241 1910
y FJ(DET)p FQ(,)e @beginspecial @setspecial @endspecial(112)r(,)h
@beginspecial @setspecial @endspecial(179)241 2023 y
FJ(DETIDNUM)p FQ(,)e @beginspecial @setspecial @endspecial(249)241
2136 y FJ(DETRAFO)p FQ(,)g @beginspecial @setspecial
@endspecial(237)241 2249 y(DF,)j @beginspecial @setspecial
@endspecial(631)241 2362 y FJ(DF)p FQ(,)f @beginspecial
@setspecial @endspecial(87)q(,)g @beginspecial @setspecial
@endspecial(88)241 2475 y FJ(DFP)p FQ(,)f @beginspecial
@setspecial @endspecial(314)241 2588 y FJ(DFP)p 391 2588
V 33 w(COMMUTE)p FQ(,)g @beginspecial @setspecial @endspecial(316)241
2700 y FJ(DFPART)p FQ(,)g @beginspecial @setspecial @endspecial(194)q
(,)i @beginspecial @setspecial @endspecial(313)241 2813
y FJ(DIAGONAL)p FQ(,)d @beginspecial @setspecial @endspecial(403)q(,)j
@beginspecial @setspecial @endspecial(405)241 2926 y
FJ(diagonalize)p FQ(,)c @beginspecial @setspecial @endspecial(558)241
3039 y(DIFFERENCE,)k @beginspecial @setspecial @endspecial(642)241
3152 y(Di\013eren)m(tiation,)f @beginspecial @setspecial
@endspecial(87)q(,)h @beginspecial @setspecial @endspecial(88,)g
@beginspecial @setspecial @endspecial(109)241 3265 y(di\013eren)m
(tiation)407 3378 y(partial,)e @beginspecial @setspecial
@endspecial(336)407 3491 y(v)m(ector,)j @beginspecial
@setspecial @endspecial(271)241 3604 y FJ(DIFFSET)p FQ(,)c
@beginspecial @setspecial @endspecial(249)241 3717 y(DIGIT,)i
@beginspecial @setspecial @endspecial(649)241 3830 y
FJ(DILOG)p FQ(,)f @beginspecial @setspecial @endspecial(83)q(,)h
@beginspecial @setspecial @endspecial(90)241 3942 y FJ(dilog)p
FQ(,)f @beginspecial @setspecial @endspecial(544)241
4055 y(Dilogarithm)g(function,)g @beginspecial @setspecial
@endspecial(544)241 4168 y FJ(DIM)p FQ(,)g @beginspecial
@setspecial @endspecial(329)241 4281 y FJ(DIM)p 391 4281
V 33 w(GRASSMANN)p 856 4281 V 32 w(VARIETY)p FQ(,)g @beginspecial
@setspecial @endspecial(329)241 4394 y(dimension,)f @beginspecial
@setspecial @endspecial(335)241 4507 y(Dirac)i FL(\015)36
b FQ(matrix,)30 b @beginspecial @setspecial @endspecial(212)241
4620 y(direct)g(pro)s(duct,)f @beginspecial @setspecial
@endspecial(410)241 4733 y FJ(DISJOIN)p FQ(,)f @beginspecial
@setspecial @endspecial(330)241 4846 y FJ(DISPJACOBIAN)p
FQ(,)f @beginspecial @setspecial @endspecial(296)241
4959 y FJ(DISPLAY)p FQ(,)h @beginspecial @setspecial
@endspecial(174)1880 555 y(Displa)m(y)-8 b(,)31 b @beginspecial
@setspecial @endspecial(111)1880 668 y FJ(DISPLAYFLAG)p
FQ(,)d @beginspecial @setspecial @endspecial(253)1880
781 y(DISPLA)-8 b(YFRAME)32 b(command,)e @beginspecial
@setspecial @endspecial(342)1880 894 y(Displa)m(ying)f(structure,)h
@beginspecial @setspecial @endspecial(126)1880 1007 y
FJ(DISTRIBUTE)p FQ(,)e @beginspecial @setspecial @endspecial(257)1880
1120 y FJ(DIV)p FQ(,)i @beginspecial @setspecial @endspecial(117)r(,)g
@beginspecial @setspecial @endspecial(147)q(,)h @beginspecial
@setspecial @endspecial(498)1880 1233 y(DIV)2046 1346
y(op)s(erator,)g @beginspecial @setspecial @endspecial(271)1880
1458 y(div)e(op)s(erator,)i @beginspecial @setspecial
@endspecial(456)1880 1571 y(div)m(ergence)2046 1684 y(v)m(ector)h
(\014eld,)e @beginspecial @setspecial @endspecial(271)1880
1797 y(DIVIDE,)i @beginspecial @setspecial @endspecial(642)1880
1910 y(division)c(b)m(y)i(zero,)h @beginspecial @setspecial
@endspecial(642)r(,)f @beginspecial @setspecial @endspecial(645)1880
2023 y FJ(DIVPOL)p FQ(,)f @beginspecial @setspecial @endspecial(258)
1880 2136 y FJ(DLINEINT)p FQ(,)g @beginspecial @setspecial
@endspecial(458)1880 2249 y(dlist,)g @beginspecial @setspecial
@endspecial(648)1880 2362 y(DM,)j @beginspecial @setspecial
@endspecial(631)1880 2475 y FJ(DO)p FQ(,)e @beginspecial
@setspecial @endspecial(67)q(,)h @beginspecial @setspecial
@endspecial(69)1880 2588 y(Dollar)f(sign,)g @beginspecial
@setspecial @endspecial(63)1880 2700 y FJ(DOT)p FQ(,)g
@beginspecial @setspecial @endspecial(464)1880 2813 y(DOT)2046
2926 y(v)m(ector,)j @beginspecial @setspecial @endspecial(270)1880
3039 y(Dot)f(pro)s(duct,)d @beginspecial @setspecial
@endspecial(211)r(,)h @beginspecial @setspecial @endspecial(270)1880
3152 y(dot)h(pro)s(duct,)e @beginspecial @setspecial
@endspecial(456)1880 3265 y(dot-notation,)j @beginspecial
@setspecial @endspecial(617)q(,)f @beginspecial @setspecial
@endspecial(619)1880 3378 y FJ(DOT)p 2030 3378 V 34 w(HAM)p
FQ(,)f @beginspecial @setspecial @endspecial(554)1880
3491 y(dotgrad)h(op)s(erator,)g @beginspecial @setspecial
@endspecial(456)1880 3604 y(dotted-pair,)g @beginspecial
@setspecial @endspecial(617)q(,)g @beginspecial @setspecial
@endspecial(625)q(,)g @beginspecial @setspecial @endspecial(626)1880
3717 y(DOUBLE)g(switc)m(h,)f @beginspecial @setspecial
@endspecial(353)1880 3830 y FJ(DR)p FQ(,)g @beginspecial
@setspecial @endspecial(552)1880 3942 y FJ(DRR)p FQ(,)g
@beginspecial @setspecial @endspecial(555)1880 4055 y
FJ(DUMMY)p FQ(,)g @beginspecial @setspecial @endspecial(194)q(,)h
@beginspecial @setspecial @endspecial(319)1880 4168 y
FJ(DUMMY)p 2126 4168 V 33 w(BASE)p FQ(,)f @beginspecial
@setspecial @endspecial(319)1880 4281 y FJ(dummy)p 2126
4281 V 33 w(names)p FQ(,)g @beginspecial @setspecial
@endspecial(320)1880 4394 y FJ(DUMMYPRI)p FQ(,)f @beginspecial
@setspecial @endspecial(267)1880 4507 y FJ(DVFSF)p FQ(,)h
@beginspecial @setspecial @endspecial(497)q(,)h @beginspecial
@setspecial @endspecial(498)1880 4620 y FJ(DVINT)p FQ(,)f
@beginspecial @setspecial @endspecial(458)1880 4733 y
FJ(DVOLINT)p FQ(,)f @beginspecial @setspecial @endspecial(458)1880
4846 y FJ(DYW)p FQ(,)h @beginspecial @setspecial @endspecial(554)p
eop
%%Page: 680 680
680 679 bop 664 299 a @beginspecial @setspecial @endspecial
FQ(680)2553 b FM(INDEX)664 555 y FJ(E)p FQ(,)30 b @beginspecial
@setspecial @endspecial(46)664 668 y FJ(ECHO)p FQ(,)g
@beginspecial @setspecial @endspecial(169)664 781 y FJ(ED)p
FQ(,)g @beginspecial @setspecial @endspecial(173)r(,)g
@beginspecial @setspecial @endspecial(174)664 894 y FJ(EDITDEF)p
FQ(,)f @beginspecial @setspecial @endspecial(175)664
1007 y FJ(EDS)p FQ(,)h @beginspecial @setspecial @endspecial(323)q(,)h
@beginspecial @setspecial @endspecial(326)664 1120 y
FJ(EDS:)47 b(Exterior)e(differential)996 1233 y(dystems)p
FQ(,)29 b @beginspecial @setspecial @endspecial(323)664
1346 y FJ(EDSDEBUG)p FQ(,)g @beginspecial @setspecial
@endspecial(330)664 1458 y FJ(EDSDISJOINT)p FQ(,)f @beginspecial
@setspecial @endspecial(330)664 1571 y FJ(EDSSLOPPY)p
FQ(,)g @beginspecial @setspecial @endspecial(330)664
1684 y FJ(EDSVERBOSE)p FQ(,)g @beginspecial @setspecial
@endspecial(330)664 1797 y FJ(Ei)p FQ(,)i @beginspecial
@setspecial @endspecial(83)q(,)h @beginspecial @setspecial
@endspecial(544)664 1910 y(EJECT,)e @beginspecial @setspecial
@endspecial(656)r(,)h @beginspecial @setspecial @endspecial(657)664
2023 y FJ(EllipticE)p FQ(,)e @beginspecial @setspecial
@endspecial(544)664 2136 y FJ(EllipticF)p FQ(,)g @beginspecial
@setspecial @endspecial(544)664 2249 y FJ(EllipticK)p
FQ(,)g @beginspecial @setspecial @endspecial(544)664
2362 y FJ(EllipticTheta)p FQ(,)f @beginspecial @setspecial
@endspecial(544)664 2475 y FJ(ELMULT)p FQ(,)i @beginspecial
@setspecial @endspecial(244)664 2588 y(EMSG*)i(\(global\),)g
@beginspecial @setspecial @endspecial(638)q(,)g @beginspecial
@setspecial @endspecial(661)664 2700 y FJ(END)p FQ(,)f
@beginspecial @setspecial @endspecial(77)664 2813 y(end)g(of)g(\014le,)
g @beginspecial @setspecial @endspecial(661)664 2926
y(end)g(of)g(line,)f @beginspecial @setspecial @endspecial(661)664
3039 y FJ(EPS)p FQ(,)h @beginspecial @setspecial @endspecial(213)q(,)h
@beginspecial @setspecial @endspecial(343)664 3152 y(EQ,)f
@beginspecial @setspecial @endspecial(623)664 3265 y(EQ)830
3378 y(in)f(MEMQ,)i @beginspecial @setspecial @endspecial(650)830
3491 y(of)g(dotted-pairs,)f @beginspecial @setspecial
@endspecial(626)830 3604 y(of)h(function-p)s(oin)m(ters,)d
@beginspecial @setspecial @endspecial(618)r(,)i @beginspecial
@setspecial @endspecial(623)830 3717 y(of)h(GENSYMs,)g
@beginspecial @setspecial @endspecial(629)830 3830 y(of)g(iden)m
(ti\014ers,)d @beginspecial @setspecial @endspecial(627)664
3942 y(EQN,)i @beginspecial @setspecial @endspecial(623)664
4055 y(EQUAL,)g @beginspecial @setspecial @endspecial(623)664
4168 y FJ(EQUAL)p FQ(,)f @beginspecial @setspecial @endspecial(498)r(,)
h @beginspecial @setspecial @endspecial(499)664 4281
y(EQUAL)830 4394 y(in)f(ASSOC,)g @beginspecial @setspecial
@endspecial(648)830 4507 y(in)g(DELETE,)h @beginspecial
@setspecial @endspecial(649)830 4620 y(in)f(MEMBER,)j
@beginspecial @setspecial @endspecial(650)830 4733 y(in)d(SASSOC,)g
@beginspecial @setspecial @endspecial(651)830 4846 y(in)g(SUBST,)h
@beginspecial @setspecial @endspecial(652)664 4959 y(Equation,)g
@beginspecial @setspecial @endspecial(57)2304 555 y FJ(EQUIV)p
FQ(,)f @beginspecial @setspecial @endspecial(330)q(,)i
@beginspecial @setspecial @endspecial(497)2304 668 y
FJ(ERF)p FQ(,)f @beginspecial @setspecial @endspecial(90)2304
781 y FJ(erf)p FQ(,)g @beginspecial @setspecial @endspecial(544)2304
894 y FJ(erfc)p FQ(,)f @beginspecial @setspecial @endspecial(544)2304
1007 y FJ(ERRCONT)p FQ(,)g @beginspecial @setspecial
@endspecial(173)2304 1120 y(ERR)m(OR,)h @beginspecial
@setspecial @endspecial(622)r(,)g @beginspecial @setspecial
@endspecial(638)r(,)g @beginspecial @setspecial @endspecial(661)2304
1233 y(error)2470 1346 y(t)m(yp)s(e)g(mismatc)m(h)h(error,)f
@beginspecial @setspecial @endspecial(622)2304 1458 y(error)g
(messages,)h @beginspecial @setspecial @endspecial(622)2304
1571 y(ERR)m(ORSET,)e @beginspecial @setspecial @endspecial(638)2304
1684 y(escap)s(e)i(c)m(haracter,)h @beginspecial @setspecial
@endspecial(622)2304 1797 y(Euclidean)c(metric,)j @beginspecial
@setspecial @endspecial(341)2304 1910 y FJ(Euler)p FQ(,)e
@beginspecial @setspecial @endspecial(542)2304 2023 y(Euler)g(p)s
(olynomials,)f @beginspecial @setspecial @endspecial(542)2304
2136 y FJ(Euler)p 2550 2136 29 4 v 33 w(Gamma)p FQ(,)h
@beginspecial @setspecial @endspecial(541)2304 2249 y
FJ(EulerP)p FQ(,)g @beginspecial @setspecial @endspecial(543)2304
2362 y(EV)-10 b(AL,)30 b @beginspecial @setspecial @endspecial(654)2304
2475 y FJ(EVAL)p FQ(,)f @beginspecial @setspecial @endspecial(353)2304
2588 y(EV)-10 b(AL)2470 2700 y(function,)29 b @beginspecial
@setspecial @endspecial(620)2470 2813 y(function)g(t)m(yp)s(e,)i
@beginspecial @setspecial @endspecial(621)2470 2926 y(lam)m(b)s(da)e
(expressions,)g @beginspecial @setspecial @endspecial(620)2470
3039 y(MA)m(CR)m(O)i(functions,)e @beginspecial @setspecial
@endspecial(621)2470 3152 y(of)h(constan)m(ts,)i @beginspecial
@setspecial @endspecial(619)2304 3265 y FJ(EVAL)p 2502
3265 V 33 w(MODE)p FQ(,)e @beginspecial @setspecial @endspecial(197)
2304 3378 y FJ(evalb)p FQ(,)f @beginspecial @setspecial
@endspecial(527)2304 3491 y FJ(EVALLHSEQP)p FQ(,)f @beginspecial
@setspecial @endspecial(57)2304 3604 y FJ(EVEN)p FQ(,)h
@beginspecial @setspecial @endspecial(104)2304 3717 y(Ev)m(en)h(op)s
(erator,)h @beginspecial @setspecial @endspecial(104)2304
3830 y FJ(EVENP)p FQ(,)e @beginspecial @setspecial @endspecial(56)2304
3942 y(EVLIS,)h @beginspecial @setspecial @endspecial(654)2304
4055 y FJ(EX)p FQ(,)g @beginspecial @setspecial @endspecial(497)2304
4168 y FJ(EXCALC)p FQ(,)f @beginspecial @setspecial @endspecial(194)q
(,)i @beginspecial @setspecial @endspecial(325)q(,)g
@beginspecial @setspecial @endspecial(333)2304 4281 y(EX)m(CALC)f(pac)m
(k)-5 b(age)2470 4394 y(example,)30 b @beginspecial @setspecial
@endspecial(336)r(,)g @beginspecial @setspecial @endspecial(337)r(,)g
@beginspecial @setspecial @endspecial(339)q(,)h @beginspecial
@setspecial @endspecial(340)q(,)2636 4507 y @beginspecial
@setspecial @endspecial(342)2304 4620 y(Exclamation)f(mark,)g
@beginspecial @setspecial @endspecial(43)2304 4733 y
FJ(EXCLUDE)p FQ(,)f @beginspecial @setspecial @endspecial(514)2304
4846 y(EXDEGREE)i(command,)f @beginspecial @setspecial
@endspecial(334)2304 4959 y FJ(EXFACTORS)p FQ(,)e @beginspecial
@setspecial @endspecial(330)p eop
%%Page: 681 681
681 680 bop 241 299 a @beginspecial @setspecial @endspecial
FM(INDEX)2552 b FQ(681)241 555 y FJ(EXP)p FQ(,)29 b @beginspecial
@setspecial @endspecial(83)q(,)i @beginspecial @setspecial
@endspecial(86)q(,)f @beginspecial @setspecial @endspecial(90)q(,)h
@beginspecial @setspecial @endspecial(134)q(,)g @beginspecial
@setspecial @endspecial(137)241 668 y(EXP)-8 b(AND,)31
b @beginspecial @setspecial @endspecial(655)241 781 y
FJ(EXPAND)p 535 781 29 4 v 32 w(CASES)p FQ(,)f @beginspecial
@setspecial @endspecial(96)241 894 y FJ(EXPANDLOGS)p
FQ(,)e @beginspecial @setspecial @endspecial(85)241 1007
y FJ(EXPLICIT)p FQ(,)g @beginspecial @setspecial @endspecial(252)241
1120 y(EXPLODE,)i @beginspecial @setspecial @endspecial(618)q(,)h
@beginspecial @setspecial @endspecial(628)q(,)g @beginspecial
@setspecial @endspecial(639)241 1233 y(EXPR,)f @beginspecial
@setspecial @endspecial(618)r(,)g @beginspecial @setspecial
@endspecial(619)q(,)h @beginspecial @setspecial @endspecial(631)241
1346 y FJ(EXPR)p FQ(,)e @beginspecial @setspecial @endspecial(203)241
1458 y(Expression,)g @beginspecial @setspecial @endspecial(53)241
1571 y(EXPT,)h @beginspecial @setspecial @endspecial(643)241
1684 y FJ(EXTEND)p FQ(,)f @beginspecial @setspecial @endspecial(403)q
(,)i @beginspecial @setspecial @endspecial(405)241 1797
y FJ(extended)p 631 1797 V 32 w(gosper)p FQ(,)e @beginspecial
@setspecial @endspecial(600)241 1910 y(exterior)h(calculus,)f
@beginspecial @setspecial @endspecial(333)241 2023 y(exterior)h
(di\013eren)m(tiation,)f @beginspecial @setspecial @endspecial(336)241
2136 y(exterior)h(form)407 2249 y(declaration,)g @beginspecial
@setspecial @endspecial(334)407 2362 y(v)m(ector,)i @beginspecial
@setspecial @endspecial(334)407 2475 y(with)d(indices,)g
@beginspecial @setspecial @endspecial(340)241 2588 y(exterior)h(pro)s
(duct,)g @beginspecial @setspecial @endspecial(335)q(,)g
@beginspecial @setspecial @endspecial(343)241 2700 y(extra-b)s(o)s
(olean,)h @beginspecial @setspecial @endspecial(619)241
2813 y FJ(EXTRACTLIST)p FQ(,)c @beginspecial @setspecial
@endspecial(253)241 2926 y FJ(EXTRACTMAT)p FQ(,)h @beginspecial
@setspecial @endspecial(367)241 3039 y FJ(EXTREMUM)p
FQ(,)g @beginspecial @setspecial @endspecial(252)241
3152 y FJ(EZGCD)p FQ(,)h @beginspecial @setspecial @endspecial(137)241
3348 y FJ(FACTOR)p FQ(,)g @beginspecial @setspecial @endspecial(115)q
(,)i @beginspecial @setspecial @endspecial(135)241 3461
y FJ(FACTORIAL)p FQ(,)d @beginspecial @setspecial @endspecial(80)q(,)i
@beginspecial @setspecial @endspecial(190)241 3574 y(F)-8
b(actorization,)32 b @beginspecial @setspecial @endspecial(134)241
3687 y FJ(FACTORIZE)p FQ(,)c @beginspecial @setspecial
@endspecial(135)q(,)j @beginspecial @setspecial @endspecial(136)241
3800 y FJ(FALSE)p FQ(,)e @beginspecial @setspecial @endspecial(497)241
3913 y(F)-8 b(ast)32 b(loading)d(of)h(co)s(de,)h @beginspecial
@setspecial @endspecial(220)241 4026 y FJ(FAST)p 439
4026 V 33 w(LA)p FQ(,)f @beginspecial @setspecial @endspecial(413)241
4138 y FJ(FCOMB)p FQ(,)f @beginspecial @setspecial @endspecial(554)241
4251 y(FDOMAIN)i(command,)f @beginspecial @setspecial
@endspecial(336)241 4364 y FJ(FER)p FQ(,)f @beginspecial
@setspecial @endspecial(552)241 4477 y(FEXPR,)i @beginspecial
@setspecial @endspecial(618)q(,)f @beginspecial @setspecial
@endspecial(619)r(,)g @beginspecial @setspecial @endspecial(621)r(,)g
@beginspecial @setspecial @endspecial(631)241 4590 y
FJ(FEXPR)p FQ(,)f @beginspecial @setspecial @endspecial(203)241
4703 y(Fib)s(onacci,)g @beginspecial @setspecial @endspecial(542)241
4816 y FJ(Fibonacci)p FQ(,)f @beginspecial @setspecial
@endspecial(542)241 4929 y(Fib)s(onacci)h(p)s(olynomials,)f
@beginspecial @setspecial @endspecial(543)1880 555 y
FJ(FibonacciP)p FQ(,)g @beginspecial @setspecial @endspecial(543)1880
668 y FJ(FIDE)p FQ(,)i @beginspecial @setspecial @endspecial(194)q(,)h
@beginspecial @setspecial @endspecial(345)1880 781 y(\014le)f(handle,)f
@beginspecial @setspecial @endspecial(656)q({)p @beginspecial
@setspecial @endspecial(659)1880 894 y(File)h(handling,)e
@beginspecial @setspecial @endspecial(169)1880 1007 y(\014les,)i
@beginspecial @setspecial @endspecial(656)q(,)h @beginspecial
@setspecial @endspecial(657)1880 1120 y FJ(FIND)p 2078
1120 V 34 w(COMPANION)p FQ(,)d @beginspecial @setspecial
@endspecial(403)q(,)j @beginspecial @setspecial @endspecial(408)1880
1233 y FJ(FIRST)p FQ(,)f @beginspecial @setspecial @endspecial(60)1880
1346 y FJ(FIRSTROOT)p FQ(,)f @beginspecial @setspecial
@endspecial(515)1880 1458 y(FIX,)i @beginspecial @setspecial
@endspecial(641)r(,)f @beginspecial @setspecial @endspecial(643)1880
1571 y FJ(FIX)p FQ(,)g @beginspecial @setspecial @endspecial(81)1880
1684 y(FIXP)-8 b(,)32 b @beginspecial @setspecial @endspecial(624)1880
1797 y FJ(FIXP)p FQ(,)e @beginspecial @setspecial @endspecial(56)1880
1910 y FJ(FJACOB)p FQ(,)f @beginspecial @setspecial @endspecial(554)
1880 2023 y(FLA)m(G,)j @beginspecial @setspecial @endspecial(616)r(,)e
@beginspecial @setspecial @endspecial(630)1880 2136 y(FLA)m(GP)-8
b(,)32 b @beginspecial @setspecial @endspecial(616)r(,)e
@beginspecial @setspecial @endspecial(630)1880 2249 y(\015ags,)h
@beginspecial @setspecial @endspecial(629)1880 2362 y(FLO)m(A)-8
b(T,)32 b @beginspecial @setspecial @endspecial(641)q(,)f
@beginspecial @setspecial @endspecial(643)1880 2475 y(\015oating)2046
2588 y(input,)e @beginspecial @setspecial @endspecial(616)2046
2700 y(output,)i @beginspecial @setspecial @endspecial(628)1880
2813 y(FLO)m(A)-8 b(TP)g(,)32 b @beginspecial @setspecial
@endspecial(624)1880 2926 y FJ(FLOOR)p FQ(,)e @beginspecial
@setspecial @endspecial(81)1880 3039 y(FLUID,)i @beginspecial
@setspecial @endspecial(616)q(,)f @beginspecial @setspecial
@endspecial(633)1880 3152 y(\015uid)2046 3265 y(in)f(tracebac)m(k,)i
@beginspecial @setspecial @endspecial(638)2046 3378 y(un)m(binding)27
b(b)m(y)k(ERR)m(OR,)f @beginspecial @setspecial @endspecial(638)1880
3491 y(\015uid)f(binding,)e @beginspecial @setspecial
@endspecial(633)1880 3604 y(\015uid)i(binding)2046 3717
y(as)i(default,)f @beginspecial @setspecial @endspecial(633)1880
3830 y(FLUIDP)-8 b(,)32 b @beginspecial @setspecial @endspecial(634)
1880 3942 y FJ(FOLLOWLINE)p FQ(,)c @beginspecial @setspecial
@endspecial(250)1880 4055 y FJ(FOR)p FQ(,)i @beginspecial
@setspecial @endspecial(74)1880 4168 y FJ(FOR)47 b(ALL)p
FQ(,)30 b @beginspecial @setspecial @endspecial(155)q(,)h
@beginspecial @setspecial @endspecial(156)1880 4281 y
FJ(FOR)47 b(EACH)p FQ(,)30 b @beginspecial @setspecial
@endspecial(67)q(,)g @beginspecial @setspecial @endspecial(68)q(,)h
@beginspecial @setspecial @endspecial(202)1880 4394 y(F)m(ORDER)g
(command,)g @beginspecial @setspecial @endspecial(343)1880
4507 y(formal)f(parameter)h(limit,)d @beginspecial @setspecial
@endspecial(621)1880 4620 y FJ(FORT)p FQ(,)i @beginspecial
@setspecial @endspecial(123)1880 4733 y FJ(FORT)p 2078
4733 V 34 w(WIDTH)p FQ(,)f @beginspecial @setspecial
@endspecial(125)1880 4846 y(F)m(OR)-8 b(TRAN,)32 b @beginspecial
@setspecial @endspecial(123)q(,)f @beginspecial @setspecial
@endspecial(124)1880 4959 y FJ(FORTUPPER)p FQ(,)e @beginspecial
@setspecial @endspecial(125)p eop
%%Page: 682 682
682 681 bop 664 299 a @beginspecial @setspecial @endspecial
FQ(682)2553 b FM(INDEX)664 555 y FJ(FOURIER)p FQ(,)29
b @beginspecial @setspecial @endspecial(286)664 668 y(F)-8
b(ourier)30 b(cosine)g(transform,)g @beginspecial @setspecial
@endspecial(307)664 781 y(F)-8 b(ourier)30 b(Series,)g
@beginspecial @setspecial @endspecial(285)664 894 y(F)-8
b(ourier)30 b(sine)f(transform,)h @beginspecial @setspecial
@endspecial(307)664 1007 y FJ(FPART)p FQ(,)f @beginspecial
@setspecial @endspecial(554)664 1120 y FJ(FPS)p FQ(,)h
@beginspecial @setspecial @endspecial(194)q(,)h @beginspecial
@setspecial @endspecial(349)664 1233 y FJ(fps)p 814 1233
29 4 v 34 w(search)p 1136 1233 V 32 w(depth)p FQ(,)f
@beginspecial @setspecial @endspecial(350)664 1346 y(FRAME)h(command,)g
@beginspecial @setspecial @endspecial(342)664 1458 y
FJ(FREEOF)p FQ(,)e @beginspecial @setspecial @endspecial(56)664
1571 y FJ(FREQUENCY)p FQ(,)f @beginspecial @setspecial
@endspecial(244)664 1684 y FJ(Fresnel)p 1006 1684 V 33
w(C)p FQ(,)i @beginspecial @setspecial @endspecial(544)664
1797 y FJ(Fresnel)p 1006 1797 V 33 w(S)p FQ(,)g @beginspecial
@setspecial @endspecial(544)664 1910 y FJ(frobenius)p
FQ(,)e @beginspecial @setspecial @endspecial(432)664
2023 y(ft)m(yp)s(e,)j @beginspecial @setspecial @endspecial(619)664
2136 y(FUIDP)-8 b(,)32 b @beginspecial @setspecial @endspecial(616)664
2249 y FJ(FULLROOTS)p FQ(,)c @beginspecial @setspecial
@endspecial(97)664 2362 y FJ(FUN)p FQ(,)i @beginspecial
@setspecial @endspecial(552)664 2475 y(FUNAR)m(Gs)i(not)f(supp)s
(orted,)d @beginspecial @setspecial @endspecial(655)664
2588 y(FUNCTION,)i @beginspecial @setspecial @endspecial(357)r(,)g
@beginspecial @setspecial @endspecial(655)664 2700 y(F)-8
b(unction,)30 b @beginspecial @setspecial @endspecial(191)664
2813 y(function,)f @beginspecial @setspecial @endspecial(620)664
2926 y(function)830 3039 y(as)i(GLOBAL,)g @beginspecial
@setspecial @endspecial(631)830 3152 y(as)g(global,)f
@beginspecial @setspecial @endspecial(632)664 3265 y(function-p)s(oin)m
(ter,)f @beginspecial @setspecial @endspecial(618)664
3378 y(function-p)s(oin)m(ter)830 3491 y(output,)h @beginspecial
@setspecial @endspecial(628)664 3604 y(functions,)f @beginspecial
@setspecial @endspecial(616)664 3717 y FJ(FUNCVAR)p FQ(,)g
@beginspecial @setspecial @endspecial(252)664 3913 y
FJ(G)p FQ(,)h @beginspecial @setspecial @endspecial(212)664
4026 y FJ(G3)p FQ(,)g @beginspecial @setspecial @endspecial(589)664
4138 y FJ(Gamma)p FQ(,)f @beginspecial @setspecial @endspecial(542)664
4251 y(Gamma)i(function,)f @beginspecial @setspecial
@endspecial(542)664 4364 y FJ(gammatofactorial)p FQ(,)c
@beginspecial @setspecial @endspecial(604)664 4477 y(garbage)32
b(collector,)f @beginspecial @setspecial @endspecial(661)664
4590 y FJ(GCD)p FQ(,)f @beginspecial @setspecial @endspecial(137)664
4703 y FJ(GDIMENSION)p FQ(,)e @beginspecial @setspecial
@endspecial(378)664 4816 y(Gegen)m(bauer)k(p)s(olynomials,)27
b @beginspecial @setspecial @endspecial(543)664 4929
y FJ(GegenbauerP)p FQ(,)h @beginspecial @setspecial @endspecial(543)
2304 555 y(Generalised)h(Hyp)s(ergeometric)2636 668 y(functions,)g
@beginspecial @setspecial @endspecial(545)2304 781 y(generic)h
(function,)g @beginspecial @setspecial @endspecial(313)2304
894 y FJ(GENERIC)p 2646 894 V 32 w(FUNCTION)p FQ(,)f
@beginspecial @setspecial @endspecial(313)2304 1007 y
FJ(GENPOS)p FQ(,)g @beginspecial @setspecial @endspecial(330)2304
1120 y(GENSYM,)i @beginspecial @setspecial @endspecial(629)2304
1233 y FJ(GENTRAN)p FQ(,)e @beginspecial @setspecial
@endspecial(194)q(,)h @beginspecial @setspecial @endspecial(351)r(,)g
@beginspecial @setspecial @endspecial(521)2304 1346 y(GENTRAN)2470
1458 y(\014le)f(output,)i @beginspecial @setspecial @endspecial(361)
2470 1571 y(preev)-5 b(aluation,)30 b @beginspecial @setspecial
@endspecial(354)q(,)g @beginspecial @setspecial @endspecial(359)2470
1684 y(templates,)h @beginspecial @setspecial @endspecial(358)2304
1797 y(GENTRAN)f(pac)m(k)-5 b(age)2470 1910 y(example,)30
b @beginspecial @setspecial @endspecial(352)2304 2023
y(GENTRANIN)h(command,)f @beginspecial @setspecial @endspecial(358)2304
2136 y FJ(GENTRANOPT)p FQ(,)e @beginspecial @setspecial
@endspecial(521)2304 2249 y(GENTRANOUT)i(command,)g @beginspecial
@setspecial @endspecial(361)2304 2362 y(GENTRANSEG)g(switc)m(h,)g
@beginspecial @setspecial @endspecial(357)2304 2475 y(GENTRANSHUT)g
(command,)g @beginspecial @setspecial @endspecial(361)2304
2588 y FJ(GEOMETRY)p FQ(,)e @beginspecial @setspecial
@endspecial(363)2304 2700 y FJ(GEQ)p FQ(,)i @beginspecial
@setspecial @endspecial(498)2304 2813 y(GET,)g @beginspecial
@setspecial @endspecial(616)r(,)g @beginspecial @setspecial
@endspecial(630)2304 2926 y(GET)2470 3039 y(not)h(for)f(functions,)f
@beginspecial @setspecial @endspecial(630)2304 3152 y
FJ(GET)p 2454 3152 V 33 w(COLUMNS)p FQ(,)g @beginspecial
@setspecial @endspecial(403)q(,)i @beginspecial @setspecial
@endspecial(405)2304 3265 y FJ(GET)p 2454 3265 V 33 w(ROWS)p
FQ(,)f @beginspecial @setspecial @endspecial(403)q(,)h
@beginspecial @setspecial @endspecial(406)2304 3378 y(GETCSYSTEM)e
(command,)h @beginspecial @setspecial @endspecial(272)2304
3491 y(GETD,)h @beginspecial @setspecial @endspecial(616)q(,)g
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@setspecial @endspecial(632)2304 3604 y FJ(GETROOT)p
FQ(,)e @beginspecial @setspecial @endspecial(515)2304
3717 y(GETV,)h @beginspecial @setspecial @endspecial(639)2304
3830 y FJ(GHOSTFACTOR)p FQ(,)d @beginspecial @setspecial
@endspecial(260)2304 3942 y FJ(GINDEPENDENT)p 2886 3942
V 31 w(SETS)p FQ(,)i @beginspecial @setspecial @endspecial(378)2304
4055 y FJ(GLEXCONVERT)p FQ(,)e @beginspecial @setspecial
@endspecial(379)2304 4168 y(GLOBAL,)k @beginspecial @setspecial
@endspecial(616)q(,)g @beginspecial @setspecial @endspecial(634)2304
4281 y(global)f(binding,)d @beginspecial @setspecial
@endspecial(633)2304 4394 y(GLOBALP)-8 b(,)31 b @beginspecial
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@endspecial(632)q(,)g @beginspecial @setspecial @endspecial(634)2304
4507 y FJ(GLTBASIS)p FQ(,)d @beginspecial @setspecial
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4620 y FJ(GNUPLOT)p FQ(,)f @beginspecial @setspecial
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4733 y(GO,)g @beginspecial @setspecial @endspecial(620)r(,)g
@beginspecial @setspecial @endspecial(636)2304 4846 y(GO)2470
4959 y(in)f(COND,)i @beginspecial @setspecial @endspecial(636)q(,)f
@beginspecial @setspecial @endspecial(640)p eop
%%Page: 683 683
683 682 bop 241 299 a @beginspecial @setspecial @endspecial
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b @beginspecial @setspecial @endspecial(72)q(,)g @beginspecial
@setspecial @endspecial(73)241 668 y FJ(Golden)p 535
668 29 4 v 32 w(Ratio)p FQ(,)g @beginspecial @setspecial
@endspecial(541)241 781 y FJ(gosper)p FQ(,)f @beginspecial
@setspecial @endspecial(599)241 894 y(Gosp)s(er's)h(Algorithm,)f
@beginspecial @setspecial @endspecial(547)241 1007 y
FJ(GRA)p FQ(,)g @beginspecial @setspecial @endspecial(554)241
1120 y(GRAD)407 1233 y(op)s(erator,)i @beginspecial @setspecial
@endspecial(271)241 1346 y(grad)f(op)s(erator,)h @beginspecial
@setspecial @endspecial(456)241 1458 y(gradien)m(t)407
1571 y(v)m(ector)h(\014eld,)d @beginspecial @setspecial
@endspecial(271)241 1684 y FJ(GRADLEX)p FQ(,)f @beginspecial
@setspecial @endspecial(389)241 1797 y(GRADLEX)407 1910
y(term)i(order,)g @beginspecial @setspecial @endspecial(376)241
2023 y FJ(GRAM)p 439 2023 V 33 w(SCHMIDT)p FQ(,)f @beginspecial
@setspecial @endspecial(404)q(,)i @beginspecial @setspecial
@endspecial(411)241 2136 y FJ(GRAS)p FQ(,)e @beginspecial
@setspecial @endspecial(552)241 2249 y(Grassmann)g(Op)s(erators,)h
@beginspecial @setspecial @endspecial(259)241 2362 y
FJ(GRASSMANN)p 679 2362 V 32 w(VARIETY)p FQ(,)e @beginspecial
@setspecial @endspecial(329)241 2475 y FJ(GRASSP)p FQ(,)h
@beginspecial @setspecial @endspecial(260)241 2588 y
FJ(GRASSPARITY)p FQ(,)e @beginspecial @setspecial @endspecial(260)241
2700 y(GREA)-8 b(TERP)g(,)31 b @beginspecial @setspecial
@endspecial(643)241 2813 y FJ(GREATERP)p FQ(,)d @beginspecial
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@beginspecial @setspecial @endspecial(383)241 3039 y
FJ(GROEBFULLREDUCTION)p FQ(,)d @beginspecial @setspecial
@endspecial(378)r(,)30 b @beginspecial @setspecial @endspecial(382)241
3152 y FJ(GROEBNER)p FQ(,)e @beginspecial @setspecial
@endspecial(195)q(,)j @beginspecial @setspecial @endspecial(375)q(,)g
@beginspecial @setspecial @endspecial(377)241 3265 y(Gro)s(ebner,)f
@beginspecial @setspecial @endspecial(95)241 3378 y(Gro)s(ebner)f
(Bases,)j @beginspecial @setspecial @endspecial(425)241
3491 y(GR)m(OEBNER)f(pac)m(k)-5 b(age,)32 b @beginspecial
@setspecial @endspecial(375)241 3604 y(GR)m(OEBNER)f(pac)m(k)-5
b(age)407 3717 y(example,)30 b @beginspecial @setspecial
@endspecial(377)241 3830 y FJ(GROEBNERF)p FQ(,)e @beginspecial
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@endspecial(384)241 3942 y FJ(GROEBOPT)p FQ(,)d @beginspecial
@setspecial @endspecial(378)q(,)j @beginspecial @setspecial
@endspecial(382)241 4055 y FJ(GROEBRESTRICTION)p FQ(,)26
b @beginspecial @setspecial @endspecial(382)241 4168
y FJ(GROEBSTAT)p FQ(,)i @beginspecial @setspecial @endspecial(382)241
4281 y FJ(GROESOLVE)p FQ(,)g @beginspecial @setspecial
@endspecial(384)241 4394 y(Group)h(statemen)m(t,)k @beginspecial
@setspecial @endspecial(65)q(,)d @beginspecial @setspecial
@endspecial(66)q(,)h @beginspecial @setspecial @endspecial(70)241
4507 y FJ(GSYS)p FQ(,)e @beginspecial @setspecial @endspecial(291)241
4620 y FJ(GSYS2CGB)p FQ(,)f @beginspecial @setspecial
@endspecial(292)241 4733 y FJ(GVARS)p FQ(,)h @beginspecial
@setspecial @endspecial(377)241 4846 y FJ(GVARSLAST)p
FQ(,)f @beginspecial @setspecial @endspecial(378)241
4959 y FJ(gvarslast)p FQ(,)g @beginspecial @setspecial
@endspecial(377)1880 555 y FJ(GZERODIM?)p FQ(,)h @beginspecial
@setspecial @endspecial(378)1880 751 y(Hank)m(el)i(functions,)e
@beginspecial @setspecial @endspecial(542)1880 864 y(Hank)m(el)i
(transform,)f @beginspecial @setspecial @endspecial(307)1880
977 y FJ(Hankel1)p FQ(,)f @beginspecial @setspecial @endspecial(542)
1880 1090 y FJ(Hankel2)p FQ(,)g @beginspecial @setspecial
@endspecial(542)1880 1203 y FJ(HARMONIC)p FQ(,)g @beginspecial
@setspecial @endspecial(285)1880 1316 y FJ(HCONCMAT)p
FQ(,)g @beginspecial @setspecial @endspecial(262)1880
1429 y FJ(HDIFF)p FQ(,)h @beginspecial @setspecial @endspecial(286)1880
1542 y FJ(HERMAT)p FQ(,)f @beginspecial @setspecial @endspecial(262)
1880 1654 y(Hermite)i(p)s(olynomials,)d @beginspecial
@setspecial @endspecial(543)1880 1767 y FJ(Hermite)p
2222 1767 V 33 w(base)p FQ(,)h @beginspecial @setspecial
@endspecial(446)1880 1880 y FJ(HermiteP)p FQ(,)g @beginspecial
@setspecial @endspecial(543)1880 1993 y FJ(HERMITIAN)p
2318 1993 V 32 w(TP)p FQ(,)h @beginspecial @setspecial
@endspecial(403)r(,)g @beginspecial @setspecial @endspecial(406)1880
2106 y FJ(HESSIAN)p FQ(,)f @beginspecial @setspecial
@endspecial(404)q(,)i @beginspecial @setspecial @endspecial(408)1880
2219 y(HF)-10 b(A)m(CTORS)30 b(scale)h(factors,)g @beginspecial
@setspecial @endspecial(272)1880 2332 y FJ(hidden3d)p
FQ(,)e @beginspecial @setspecial @endspecial(372)1880
2445 y(High)h(energy)h(trace,)h @beginspecial @setspecial
@endspecial(215)1880 2558 y(High)e(energy)h(v)m(ector)h(expression,)
2213 2671 y @beginspecial @setspecial @endspecial(211)q(,)e
@beginspecial @setspecial @endspecial(214)1880 2784 y
FJ(HIGH)p 2078 2784 V 34 w(POW)p FQ(,)f @beginspecial
@setspecial @endspecial(129)1880 2896 y FJ(HIGHESTDERIV)p
FQ(,)f @beginspecial @setspecial @endspecial(450)1880
3009 y FJ(HILBERT)p FQ(,)h @beginspecial @setspecial
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3122 y FJ(HINT)p FQ(,)f @beginspecial @setspecial @endspecial(286)1880
3235 y(History)-8 b(,)31 b @beginspecial @setspecial
@endspecial(174)1880 3348 y(Ho)s(dge-*)h(dualit)m(y)d(op)s(erator,)i
@beginspecial @setspecial @endspecial(338)q(,)2213 3461
y @beginspecial @setspecial @endspecial(343)1880 3574
y FJ(HSUB)p FQ(,)f @beginspecial @setspecial @endspecial(286)1880
3687 y FJ(hyperrecursion)p FQ(,)d @beginspecial @setspecial
@endspecial(602)1880 3800 y FJ(hypersum)p FQ(,)i @beginspecial
@setspecial @endspecial(602)1880 3913 y FJ(hyperterm)p
FQ(,)g @beginspecial @setspecial @endspecial(602)1880
4026 y FJ(HYPEXPAND)p FQ(,)g @beginspecial @setspecial
@endspecial(258)1880 4138 y FJ(HYPOT)p FQ(,)h @beginspecial
@setspecial @endspecial(83)q(,)g @beginspecial @setspecial
@endspecial(86)1880 4251 y FJ(HYPREDUCE)p FQ(,)f @beginspecial
@setspecial @endspecial(258)1880 4447 y FJ(I)p FQ(,)i
@beginspecial @setspecial @endspecial(46)1880 4560 y(i,)f
@beginspecial @setspecial @endspecial(239)1880 4673 y
FJ(I)p 1934 4673 V 35 w(SOLVE)p FQ(,)f @beginspecial
@setspecial @endspecial(519)1880 4786 y FJ(iBeta)p FQ(,)h
@beginspecial @setspecial @endspecial(542)1880 4899 y(id)p
eop
%%Page: 684 684
684 683 bop 664 299 a @beginspecial @setspecial @endspecial
FQ(684)2553 b FM(INDEX)830 555 y FQ(escap)s(e)31 b(c)m(haracter,)h
@beginspecial @setspecial @endspecial(617)830 668 y(input,)d
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(length,)h @beginspecial @setspecial @endspecial(617)830
894 y(minim)m(um)e(size,)i @beginspecial @setspecial
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@endspecial(628)664 1120 y(id-list,)f @beginspecial @setspecial
@endspecial(619)664 1233 y FJ(ideal)47 b(dimension)p
FQ(,)28 b @beginspecial @setspecial @endspecial(378)664
1346 y FJ(IDEALQUOTIENT)p FQ(,)f @beginspecial @setspecial
@endspecial(384)664 1458 y FJ(IDEALS)p FQ(,)i @beginspecial
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@endspecial(385)664 1571 y(Iden)m(ti\014er,)f @beginspecial
@setspecial @endspecial(45)664 1684 y(iden)m(ti\014er)f(\(see)i(id\),)f
@beginspecial @setspecial @endspecial(616)664 1797 y(IDP)-8
b(,)31 b @beginspecial @setspecial @endspecial(624)664
1910 y FJ(IF)p FQ(,)f @beginspecial @setspecial @endspecial(65)q(,)h
@beginspecial @setspecial @endspecial(66)664 2023 y FJ(IFACTOR)p
FQ(,)e @beginspecial @setspecial @endspecial(135)664
2136 y FJ(iGamma)p FQ(,)g @beginspecial @setspecial @endspecial(542)664
2249 y FJ(IMAGINARY)p FQ(,)f @beginspecial @setspecial
@endspecial(409)664 2362 y(imaginary)h(unit,)g @beginspecial
@setspecial @endspecial(239)664 2475 y FJ(IMPART)p FQ(,)g
@beginspecial @setspecial @endspecial(80)q(,)i @beginspecial
@setspecial @endspecial(81,)g @beginspecial @setspecial
@endspecial(83)664 2588 y FJ(IMPL)p FQ(,)f @beginspecial
@setspecial @endspecial(497)664 2700 y FJ(IMPLICIT)p
FQ(,)f @beginspecial @setspecial @endspecial(252)664
2813 y(IMPLICIT)g(option,)h @beginspecial @setspecial
@endspecial(357)664 2926 y(IMPLICIT)p 1102 2926 28 4
v 32 w(T)-8 b(A)g(YLOR)30 b(op)s(erator,)996 3039 y @beginspecial
@setspecial @endspecial(562)664 3152 y FJ(IN)p FQ(,)g
@beginspecial @setspecial @endspecial(169)664 3265 y(incomplete)g(Beta)
i(function,)d @beginspecial @setspecial @endspecial(542)664
3378 y(incomplete)h(Gamma)h(function,)e @beginspecial
@setspecial @endspecial(542)664 3491 y(Inde\014nite)g(in)m(tegration,)h
@beginspecial @setspecial @endspecial(88)664 3604 y FJ(INDEPENDENCE)p
FQ(,)d @beginspecial @setspecial @endspecial(327)664
3717 y FJ(independent)45 b(sets)p FQ(,)29 b @beginspecial
@setspecial @endspecial(378)664 3830 y FJ(INDEX)p FQ(,)g
@beginspecial @setspecial @endspecial(212)664 3942 y
FJ(INDEX)p 910 3942 29 4 v 33 w(EXPAND)p FQ(,)g @beginspecial
@setspecial @endspecial(330)664 4055 y(INDEXSYMMETRIES)996
4168 y(command,)i @beginspecial @setspecial @endspecial(340)664
4281 y FJ(INEQ)p FQ(,)f @beginspecial @setspecial @endspecial(195)q(,)h
@beginspecial @setspecial @endspecial(387)664 4394 y
FJ(INFINITY)p FQ(,)e @beginspecial @setspecial @endspecial(46,)i
@beginspecial @setspecial @endspecial(514)664 4507 y
FJ(INFIX)p FQ(,)e @beginspecial @setspecial @endspecial(108)664
4620 y(In\014x)g(op)s(erator,)i @beginspecial @setspecial
@endspecial(48)q({)p @beginspecial @setspecial @endspecial(51)664
4733 y(inner)e(pro)s(duct,)g @beginspecial @setspecial
@endspecial(456)664 4846 y(inner)g(pro)s(duct)830 4959
y(exterior)i(form,)f @beginspecial @setspecial @endspecial(337)2304
555 y(INPUT,)g @beginspecial @setspecial @endspecial(657)2304
668 y FJ(INPUT)p FQ(,)f @beginspecial @setspecial @endspecial(174)2304
781 y(Input,)g @beginspecial @setspecial @endspecial(169)2304
894 y FJ(INSERT)p FQ(,)g @beginspecial @setspecial @endspecial(244)2304
1007 y FJ(INSERT)p 2598 1007 V 33 w(KEEP)p 2823 1007
V 33 w(ORDER)p FQ(,)g @beginspecial @setspecial @endspecial(244)2304
1120 y(Instan)m(t)h(ev)-5 b(aluation,)31 b @beginspecial
@setspecial @endspecial(76)q(,)f @beginspecial @setspecial
@endspecial(131)q(,)h @beginspecial @setspecial @endspecial(154)q(,)
2636 1233 y @beginspecial @setspecial @endspecial(178)q(,)g
@beginspecial @setspecial @endspecial(180)2304 1346 y
FJ(INT)p FQ(,)f @beginspecial @setspecial @endspecial(88)q(,)g
@beginspecial @setspecial @endspecial(176)q(,)h @beginspecial
@setspecial @endspecial(231)q(,)g @beginspecial @setspecial
@endspecial(305)2304 1458 y FJ(INTEGER)p FQ(,)e @beginspecial
@setspecial @endspecial(71)2304 1571 y(In)m(teger,)i
@beginspecial @setspecial @endspecial(54)2304 1684 y(in)m(teger)2470
1797 y(input,)e @beginspecial @setspecial @endspecial(615)2470
1910 y(magnitude,)h @beginspecial @setspecial @endspecial(615)q(,)h
@beginspecial @setspecial @endspecial(641)2470 2023 y(output,)f
@beginspecial @setspecial @endspecial(628)2304 2136 y(in)m(teger-list,)
g @beginspecial @setspecial @endspecial(619)2304 2249
y FJ(INTEGRAL)p 2694 2249 V 32 w(ELEMENT)p FQ(,)f @beginspecial
@setspecial @endspecial(329)2304 2362 y(In)m(tegration,)i
@beginspecial @setspecial @endspecial(88)q(,)g @beginspecial
@setspecial @endspecial(106)2304 2475 y(in)m(tegration)2470
2588 y(de\014nite)e(\(simple\),)g @beginspecial @setspecial
@endspecial(274)2470 2700 y(line,)g @beginspecial @setspecial
@endspecial(275)2470 2813 y(v)m(olume,)h @beginspecial
@setspecial @endspecial(274)2304 2926 y(In)m(teractiv)m(e)i(use,)e
@beginspecial @setspecial @endspecial(173)q(,)h @beginspecial
@setspecial @endspecial(176)2304 3039 y(INTERN,)f @beginspecial
@setspecial @endspecial(616)q(,)h @beginspecial @setspecial
@endspecial(629)q(,)g @beginspecial @setspecial @endspecial(659)2304
3152 y FJ(INTERPOL)p FQ(,)d @beginspecial @setspecial
@endspecial(142)2304 3265 y FJ(INTERSECT)p FQ(,)g @beginspecial
@setspecial @endspecial(249)2304 3378 y FJ(intersect)p
FQ(,)g @beginspecial @setspecial @endspecial(526)2304
3491 y FJ(INTERSECTION)p 2886 3491 V 31 w(POINT)p FQ(,)h
@beginspecial @setspecial @endspecial(365)2304 3604 y(In)m(terv)-5
b(al,)30 b @beginspecial @setspecial @endspecial(437)2304
3717 y(In)m(tro)s(duction,)f @beginspecial @setspecial
@endspecial(37)2304 3830 y FJ(INTSTR)p FQ(,)g @beginspecial
@setspecial @endspecial(112)2304 3942 y FJ(INVARIANTS)p
FQ(,)f @beginspecial @setspecial @endspecial(330)2304
4055 y FJ(INVBASE)p FQ(,)h @beginspecial @setspecial
@endspecial(195)q(,)h @beginspecial @setspecial @endspecial(389)r(,)g
@beginspecial @setspecial @endspecial(390)2304 4168 y
FJ(INVERSE)p FQ(,)f @beginspecial @setspecial @endspecial(555)2304
4281 y(INVERSE)p 2720 4281 28 4 v 32 w(T)-8 b(A)g(YLOR,)31
b @beginspecial @setspecial @endspecial(562)2304 4394
y FJ(INVERT)p FQ(,)e @beginspecial @setspecial @endspecial(330)2304
4507 y FJ(INVLAP)p FQ(,)g @beginspecial @setspecial @endspecial(393)
2304 4620 y FJ(INVOLUTION)p FQ(,)f @beginspecial @setspecial
@endspecial(329)2304 4733 y FJ(INVOLUTIVE)p FQ(,)g @beginspecial
@setspecial @endspecial(330)2304 4846 y FJ(INVTORDER)p
FQ(,)g @beginspecial @setspecial @endspecial(390)2304
4959 y FJ(invztrans)p FQ(,)g @beginspecial @setspecial
@endspecial(609)p eop
%%Page: 685 685
685 684 bop 241 299 a @beginspecial @setspecial @endspecial
FM(INDEX)2552 b FQ(685)241 555 y FJ(ISOLATER)p FQ(,)28
b @beginspecial @setspecial @endspecial(514)241 743 y
FJ(JACOB)p FQ(,)h @beginspecial @setspecial @endspecial(554)241
856 y(Jacobi)h(Elliptic)d(F)-8 b(unctions)30 b(and)573
969 y(In)m(tegrals,)h @beginspecial @setspecial @endspecial(544)241
1082 y(Jacobi's)f(p)s(olynomials,)e @beginspecial @setspecial
@endspecial(543)241 1195 y FJ(JACOBIAN)p FQ(,)g @beginspecial
@setspecial @endspecial(404)q(,)j @beginspecial @setspecial
@endspecial(409)q(,)g @beginspecial @setspecial @endspecial(440)241
1308 y FJ(Jacobicd)p FQ(,)d @beginspecial @setspecial
@endspecial(544)241 1421 y FJ(Jacobicn)p FQ(,)g @beginspecial
@setspecial @endspecial(544)241 1534 y FJ(Jacobics)p
FQ(,)g @beginspecial @setspecial @endspecial(544)241
1647 y FJ(Jacobidc)p FQ(,)g @beginspecial @setspecial
@endspecial(544)241 1760 y FJ(Jacobidn)p FQ(,)g @beginspecial
@setspecial @endspecial(544)241 1872 y FJ(Jacobids)p
FQ(,)g @beginspecial @setspecial @endspecial(544)241
1985 y FJ(Jacobinc)p FQ(,)g @beginspecial @setspecial
@endspecial(544)241 2098 y FJ(Jacobind)p FQ(,)g @beginspecial
@setspecial @endspecial(544)241 2211 y FJ(Jacobins)p
FQ(,)g @beginspecial @setspecial @endspecial(544)241
2324 y FJ(JacobiP)p FQ(,)g @beginspecial @setspecial
@endspecial(543)241 2437 y FJ(Jacobisc)p FQ(,)g @beginspecial
@setspecial @endspecial(544)241 2550 y FJ(Jacobisd)p
FQ(,)g @beginspecial @setspecial @endspecial(544)241
2663 y FJ(Jacobisn)p FQ(,)g @beginspecial @setspecial
@endspecial(544)241 2776 y FJ(JOIN)p FQ(,)h @beginspecial
@setspecial @endspecial(67)241 2889 y FJ(jordan)p FQ(,)g
@beginspecial @setspecial @endspecial(434)241 3002 y
FJ(JORDAN)p 535 3002 29 4 v 32 w(BLOCK)p FQ(,)h @beginspecial
@setspecial @endspecial(404)q(,)h @beginspecial @setspecial
@endspecial(409)241 3114 y FJ(jordansymbolic)p FQ(,)26
b @beginspecial @setspecial @endspecial(433)241 3303
y(K-transform,)k @beginspecial @setspecial @endspecial(307)241
3416 y FJ(KBASIS)p FQ(,)f @beginspecial @setspecial @endspecial(266)241
3528 y(KEEP)g(command,)i @beginspecial @setspecial @endspecial(343)241
3641 y(Kernel,)e @beginspecial @setspecial @endspecial(111)r(,)h
@beginspecial @setspecial @endspecial(112)q(,)h @beginspecial
@setspecial @endspecial(115)q(,)g @beginspecial @setspecial
@endspecial(128)241 3754 y(k)m(ernel)f(form,)g @beginspecial
@setspecial @endspecial(112)241 3867 y FJ(KERNLIST)p
FQ(,)e @beginspecial @setspecial @endspecial(244)241
3980 y FJ(Khinchin)p FQ(,)g @beginspecial @setspecial
@endspecial(541)241 4093 y FJ(KORDER)p FQ(,)h @beginspecial
@setspecial @endspecial(128)q(,)i @beginspecial @setspecial
@endspecial(464)241 4206 y FJ(KORDERLIST)p FQ(,)d @beginspecial
@setspecial @endspecial(252)241 4319 y FJ(KRONECKER)p
679 4319 V 32 w(PRODUCT)p FQ(,)g @beginspecial @setspecial
@endspecial(404)r(,)i @beginspecial @setspecial @endspecial(410)241
4432 y(Kummer)f(functions,)g @beginspecial @setspecial
@endspecial(543)241 4545 y FJ(KummerM)p FQ(,)f @beginspecial
@setspecial @endspecial(543)241 4658 y FJ(KummerU)p FQ(,)g
@beginspecial @setspecial @endspecial(543)241 4846 y(l'H^)-45
b(opital's)29 b(rule,)g @beginspecial @setspecial @endspecial(399)r(,)h
@beginspecial @setspecial @endspecial(458)241 4959 y
FJ(L2)p 343 4959 V 34 w(ANGLE)p FQ(,)f @beginspecial
@setspecial @endspecial(365)1880 555 y(Lab)s(el,)h @beginspecial
@setspecial @endspecial(72)q(,)g @beginspecial @setspecial
@endspecial(73)1880 668 y(Laguerre)h(p)s(olynomials,)d
@beginspecial @setspecial @endspecial(543)1880 781 y
FJ(Laguerre)p 2270 781 V 33 w(base)p FQ(,)h @beginspecial
@setspecial @endspecial(446)1880 894 y FJ(LaguerreP)p
FQ(,)g @beginspecial @setspecial @endspecial(543)1880
1007 y FJ(laline!*)p FQ(,)g @beginspecial @setspecial
@endspecial(510)1880 1120 y(LAMBD)m(A,)k @beginspecial
@setspecial @endspecial(620)1880 1233 y FJ(LAMBDA)p FQ(,)c
@beginspecial @setspecial @endspecial(201)1880 1346 y(lam)m(b)s(da)h
(expression,)f @beginspecial @setspecial @endspecial(620)1880
1458 y(Lam)m(b)s(ert)i FL(!)i FQ(function,)c @beginspecial
@setspecial @endspecial(544)1880 1571 y(Lam)m(b)s(ert's)i(W,)g
@beginspecial @setspecial @endspecial(95)1880 1684 y
FJ(Lambert)p 2222 1684 V 33 w(W)p FQ(,)f @beginspecial
@setspecial @endspecial(544)1880 1797 y FJ(LAPLACE)p
FQ(,)f @beginspecial @setspecial @endspecial(195)q(,)i
@beginspecial @setspecial @endspecial(393)1880 1910 y(Laplace)g
(transform,)f @beginspecial @setspecial @endspecial(307)1880
2023 y(Laplacian)2046 2136 y(v)m(ector)i(\014eld,)e @beginspecial
@setspecial @endspecial(271)1880 2249 y FJ(lasimp)p FQ(,)f
@beginspecial @setspecial @endspecial(509)1880 2362 y
FJ(LAST)p FQ(,)h @beginspecial @setspecial @endspecial(245)1880
2475 y FJ(latex)p FQ(,)g @beginspecial @setspecial @endspecial(509)1880
2588 y(Lauren)m(t)h(series,)f @beginspecial @setspecial
@endspecial(561)1880 2700 y(Lauren)m(t)h(series)f(expansions,)f
@beginspecial @setspecial @endspecial(567)1880 2813 y
FJ(LCM)p FQ(,)h @beginspecial @setspecial @endspecial(138)1880
2926 y FJ(LCOF)p FQ(,)g @beginspecial @setspecial @endspecial(144)1880
3039 y(Leading)g(co)s(e\016cien)m(t,)i @beginspecial
@setspecial @endspecial(144)1880 3152 y FJ(LEADTERM)p
FQ(,)d @beginspecial @setspecial @endspecial(257)1880
3265 y(Legendre)i(p)s(olynomials,)d @beginspecial @setspecial
@endspecial(187)q(,)j @beginspecial @setspecial @endspecial(543)1880
3378 y FJ(Legendre)p 2270 3378 V 33 w(base)p FQ(,)e @beginspecial
@setspecial @endspecial(446)1880 3491 y FJ(LegendreP)p
FQ(,)g @beginspecial @setspecial @endspecial(543)1880
3604 y(LENGTH,)i @beginspecial @setspecial @endspecial(649)1880
3717 y FJ(LENGTH)p FQ(,)e @beginspecial @setspecial @endspecial(59)q(,)
i @beginspecial @setspecial @endspecial(76)q(,)f @beginspecial
@setspecial @endspecial(90)q(,)h @beginspecial @setspecial
@endspecial(133)q(,)g @beginspecial @setspecial @endspecial(135)q(,)g
@beginspecial @setspecial @endspecial(179)q(,)2213 3830
y @beginspecial @setspecial @endspecial(499)1880 3942
y FJ(LEQ)p FQ(,)f @beginspecial @setspecial @endspecial(498)1880
4055 y(Lerc)m(h)h(Phi)e(function,)g @beginspecial @setspecial
@endspecial(544)1880 4168 y FJ(Lerch)p 2126 4168 V 33
w(Phi)p FQ(,)h @beginspecial @setspecial @endspecial(544)1880
4281 y(LESSP)-8 b(,)30 b @beginspecial @setspecial @endspecial(643)1880
4394 y FJ(LESSP)p FQ(,)g @beginspecial @setspecial @endspecial(498)1880
4507 y FJ(LET)p FQ(,)g @beginspecial @setspecial @endspecial(85)q(,)h
@beginspecial @setspecial @endspecial(87)q(,)f @beginspecial
@setspecial @endspecial(100)q(,)h @beginspecial @setspecial
@endspecial(106)q({)p @beginspecial @setspecial @endspecial(108)r(,)g
@beginspecial @setspecial @endspecial(152)q(,)2213 4620
y @beginspecial @setspecial @endspecial(161)q(,)f @beginspecial
@setspecial @endspecial(189)r(,)g @beginspecial @setspecial
@endspecial(190)1880 4733 y(Levi-Cevita)h(tensor,)f @beginspecial
@setspecial @endspecial(343)1880 4846 y FJ(LEX)p FQ(,)g
@beginspecial @setspecial @endspecial(389)1880 4959 y(LEX)p
eop
%%Page: 686 686
686 685 bop 664 299 a @beginspecial @setspecial @endspecial
FQ(686)2553 b FM(INDEX)830 555 y FQ(term)31 b(order,)f
@beginspecial @setspecial @endspecial(376)664 668 y FJ(LHS)p
FQ(,)g @beginspecial @setspecial @endspecial(57)664 781
y FJ(li)p FQ(,)g @beginspecial @setspecial @endspecial(544)664
894 y FJ(LIE)p FQ(,)g @beginspecial @setspecial @endspecial(195)q(,)h
@beginspecial @setspecial @endspecial(397)664 1007 y(Lie)f(Deriv)-5
b(ativ)m(e,)31 b @beginspecial @setspecial @endspecial(338)664
1120 y FJ(LIE)p 814 1120 29 4 v 34 w(LIST)p FQ(,)e @beginspecial
@setspecial @endspecial(398)664 1233 y FJ(LIECLASS)p
FQ(,)g @beginspecial @setspecial @endspecial(398)664
1346 y FJ(LIENDIMCOM1)p FQ(,)f @beginspecial @setspecial
@endspecial(397)664 1458 y FJ(LIFT)p FQ(,)i @beginspecial
@setspecial @endspecial(328)664 1571 y FJ(LIMIT)p FQ(,)f
@beginspecial @setspecial @endspecial(399)r(,)h @beginspecial
@setspecial @endspecial(458)664 1684 y FJ(LIMIT+)p FQ(,)f
@beginspecial @setspecial @endspecial(400)664 1797 y
FJ(LIMIT-)p FQ(,)g @beginspecial @setspecial @endspecial(400)664
1910 y FJ(LIMITS)p FQ(,)g @beginspecial @setspecial @endspecial(195)q
(,)i @beginspecial @setspecial @endspecial(399)664 2023
y FJ(LINALG)p FQ(,)e @beginspecial @setspecial @endspecial(195)q(,)i
@beginspecial @setspecial @endspecial(403)664 2136 y
FJ(LINE)p FQ(,)f @beginspecial @setspecial @endspecial(365)664
2249 y(line)f(in)m(tegrals,)h @beginspecial @setspecial
@endspecial(275)664 2362 y FJ(LINEAR)p FQ(,)f @beginspecial
@setspecial @endspecial(105)664 2475 y(Linear)h(op)s(erator,)g
@beginspecial @setspecial @endspecial(105)r(,)g @beginspecial
@setspecial @endspecial(106)r(,)g @beginspecial @setspecial
@endspecial(109)664 2588 y FJ(LINEAR)p 958 2588 V 33
w(DIVISORS)p FQ(,)e @beginspecial @setspecial @endspecial(330)664
2700 y FJ(LINEARISE)p FQ(,)g @beginspecial @setspecial
@endspecial(329)664 2813 y FJ(LINEINT)p FQ(,)h @beginspecial
@setspecial @endspecial(458)664 2926 y(LINEINT)h(function,)f
@beginspecial @setspecial @endspecial(275)664 3039 y(LINELENGTH,)h
@beginspecial @setspecial @endspecial(656)664 3152 y
FJ(LINELENGTH)p FQ(,)e @beginspecial @setspecial @endspecial(114)664
3265 y FJ(LISP)p FQ(,)i @beginspecial @setspecial @endspecial(197)664
3378 y(Lisp,)f @beginspecial @setspecial @endspecial(197)664
3491 y(LIST,)h @beginspecial @setspecial @endspecial(627)664
3604 y FJ(LIST)p FQ(,)g @beginspecial @setspecial @endspecial(117)664
3717 y(List,)g @beginspecial @setspecial @endspecial(59)664
3830 y(list,)f @beginspecial @setspecial @endspecial(619)664
3942 y FJ(list)p FQ(,)h @beginspecial @setspecial @endspecial(93)664
4055 y(List)g(op)s(eration,)g @beginspecial @setspecial
@endspecial(59)q(,)g @beginspecial @setspecial @endspecial(61)664
4168 y(list-notation,)g @beginspecial @setspecial @endspecial(619)664
4281 y FJ(LIST)p 862 4281 V 33 w(TO)p 991 4281 V 34 w(ARRAY)p
FQ(,)f @beginspecial @setspecial @endspecial(259)664
4394 y FJ(LIST)p 862 4394 V 33 w(TO)p 991 4394 V 34 w(IDS)p
FQ(,)h @beginspecial @setspecial @endspecial(249)664
4507 y FJ(LISTARGP)p FQ(,)f @beginspecial @setspecial
@endspecial(61)664 4620 y FJ(LISTARGS)p FQ(,)g @beginspecial
@setspecial @endspecial(61)664 4733 y FJ(LISTBAG)p FQ(,)g
@beginspecial @setspecial @endspecial(248)664 4846 y(LITER,)h
@beginspecial @setspecial @endspecial(649)664 4959 y
FJ(LN)p FQ(,)g @beginspecial @setspecial @endspecial(83)q(,)h
@beginspecial @setspecial @endspecial(86)2304 555 y FJ(LOAD)p
FQ(,)e @beginspecial @setspecial @endspecial(220)2304
668 y FJ(LOAD)p 2502 668 V 33 w(PACKAGE)p FQ(,)g @beginspecial
@setspecial @endspecial(193)q(,)i @beginspecial @setspecial
@endspecial(221)2304 781 y(lo)s(cal)f(binding,)d @beginspecial
@setspecial @endspecial(633)2304 894 y FJ(LOG)p FQ(,)j
@beginspecial @setspecial @endspecial(83)q(,)g @beginspecial
@setspecial @endspecial(86)q(,)h @beginspecial @setspecial
@endspecial(90)2304 1007 y FJ(LOG10)p FQ(,)e @beginspecial
@setspecial @endspecial(83)q(,)i @beginspecial @setspecial
@endspecial(86)2304 1120 y FJ(LOGB)p FQ(,)e @beginspecial
@setspecial @endspecial(83)q(,)i @beginspecial @setspecial
@endspecial(86)2304 1233 y(Lommel)f(functions,)f @beginspecial
@setspecial @endspecial(543)2304 1346 y FJ(Lommel1)p
FQ(,)g @beginspecial @setspecial @endspecial(543)2304
1458 y FJ(Lommel2)p FQ(,)g @beginspecial @setspecial
@endspecial(543)2304 1571 y(Lo)s(op,)h @beginspecial
@setspecial @endspecial(67)q(,)h @beginspecial @setspecial
@endspecial(68)2304 1684 y FJ(LOT)p FQ(,)f @beginspecial
@setspecial @endspecial(365)2304 1797 y FJ(LOW)p 2454
1797 V 33 w(POW)p FQ(,)g @beginspecial @setspecial @endspecial(129)2304
1910 y FJ(LOWER)p 2550 1910 V 33 w(MATRIX)p FQ(,)f @beginspecial
@setspecial @endspecial(409)2304 2023 y FJ(LOWESTDEG)p
FQ(,)f @beginspecial @setspecial @endspecial(258)2304
2136 y FJ(lpon)p FQ(,)h @beginspecial @setspecial @endspecial(393)2304
2249 y(LPOSN,)g @beginspecial @setspecial @endspecial(656)2304
2362 y FJ(LPOWER)p FQ(,)g @beginspecial @setspecial @endspecial(145)
2304 2475 y FJ(LRSETQ)p FQ(,)g @beginspecial @setspecial
@endspecial(356)2304 2588 y(lrsetq)h(op)s(erator,)h @beginspecial
@setspecial @endspecial(355)2304 2700 y FJ(LSETQ)p FQ(,)e
@beginspecial @setspecial @endspecial(355)2304 2813 y(lsetq)h(op)s
(erator,)h @beginspecial @setspecial @endspecial(354)2304
2926 y FJ(LTERM)p FQ(,)e @beginspecial @setspecial @endspecial(145)q(,)
i @beginspecial @setspecial @endspecial(209)2304 3039
y FJ(ltrig)p FQ(,)e @beginspecial @setspecial @endspecial(393)2304
3152 y FJ(LU)p 2406 3152 V 34 w(DECOM)p FQ(,)g @beginspecial
@setspecial @endspecial(404)q(,)i @beginspecial @setspecial
@endspecial(411)2304 3265 y FJ(LYST)p FQ(,)e @beginspecial
@setspecial @endspecial(554)2304 3378 y FJ(LYST1)p FQ(,)g
@beginspecial @setspecial @endspecial(554)2304 3491 y
FJ(LYST2)p FQ(,)g @beginspecial @setspecial @endspecial(554)2304
3687 y FJ(M)p FQ(,)h @beginspecial @setspecial @endspecial(470)2304
3800 y FJ(M)p 2358 3800 V 34 w(ROOTS)p FQ(,)f @beginspecial
@setspecial @endspecial(419)2304 3913 y FJ(M)p 2358 3913
V 34 w(SOLVE)p FQ(,)g @beginspecial @setspecial @endspecial(419)2304
4026 y FJ(MACIERZ)p FQ(,)g @beginspecial @setspecial
@endspecial(554)2304 4138 y(MA)m(CR)m(O,)i @beginspecial
@setspecial @endspecial(619)r(,)f @beginspecial @setspecial
@endspecial(621)q(,)h @beginspecial @setspecial @endspecial(631)2304
4251 y FJ(MACRO)p FQ(,)e @beginspecial @setspecial @endspecial(203)2304
4364 y FJ(MAINVAR)p FQ(,)g @beginspecial @setspecial
@endspecial(146)2304 4477 y FJ(MAKE)p 2502 4477 V 33
w(IDENTITY)p FQ(,)g @beginspecial @setspecial @endspecial(404)q(,)h
@beginspecial @setspecial @endspecial(409)2304 4590 y(MAP)-8
b(,)31 b @beginspecial @setspecial @endspecial(646)2304
4703 y FJ(MAP)p FQ(,)f @beginspecial @setspecial @endspecial(91)2304
4816 y FJ(map)p FQ(,)g @beginspecial @setspecial @endspecial(93)2304
4929 y(MAPC,)g @beginspecial @setspecial @endspecial(646)p
eop
%%Page: 687 687
687 686 bop 241 299 a @beginspecial @setspecial @endspecial
FM(INDEX)2552 b FQ(687)241 555 y(MAPCAN,)31 b @beginspecial
@setspecial @endspecial(647)241 668 y(MAPCAR,)f @beginspecial
@setspecial @endspecial(647)241 781 y(MAPCON,)g @beginspecial
@setspecial @endspecial(647)241 894 y(MAPLIST,)g @beginspecial
@setspecial @endspecial(647)241 1007 y FJ(MASS)p FQ(,)f
@beginspecial @setspecial @endspecial(214)r(,)h @beginspecial
@setspecial @endspecial(216)241 1120 y FJ(MAT)p FQ(,)f
@beginspecial @setspecial @endspecial(177)r(,)h @beginspecial
@setspecial @endspecial(178)241 1233 y FJ(MATCH)p FQ(,)f
@beginspecial @setspecial @endspecial(159)241 1346 y
FJ(MATEIGEN)p FQ(,)f @beginspecial @setspecial @endspecial(180)241
1458 y FJ(MATEXTC)p FQ(,)g @beginspecial @setspecial
@endspecial(262)241 1571 y FJ(MATEXTR)p FQ(,)g @beginspecial
@setspecial @endspecial(262)241 1684 y(Mathematical)j(function,)e
@beginspecial @setspecial @endspecial(83)241 1797 y FJ(MATHML)p
FQ(,)g @beginspecial @setspecial @endspecial(415)q(,)i
@beginspecial @setspecial @endspecial(416)241 1910 y
FJ(mathstyle)p FQ(,)d @beginspecial @setspecial @endspecial(510)241
2023 y(matrices)407 2136 y(in)h(GENTRAN,)i @beginspecial
@setspecial @endspecial(354)q(,)g @beginspecial @setspecial
@endspecial(355)q(,)g @beginspecial @setspecial @endspecial(360)241
2249 y FJ(MATRIX)p FQ(,)e @beginspecial @setspecial @endspecial(178)241
2362 y(Matrix)h(assignmen)m(t,)g @beginspecial @setspecial
@endspecial(183)241 2475 y(Matrix)g(calculations,)g @beginspecial
@setspecial @endspecial(177)241 2588 y FJ(MATRIX,)46
b(see)g(also)h(SPARSE)p FQ(,)29 b @beginspecial @setspecial
@endspecial(531)241 2700 y FJ(MATRIX)p 535 2700 29 4
v 32 w(AUGMENT)p FQ(,)g @beginspecial @setspecial @endspecial(403)q(,)i
@beginspecial @setspecial @endspecial(406)241 2813 y
FJ(MATRIX)p 535 2813 V 32 w(STACK)p FQ(,)f @beginspecial
@setspecial @endspecial(403)q(,)h @beginspecial @setspecial
@endspecial(406)241 2926 y FJ(MATRIXP)p FQ(,)d @beginspecial
@setspecial @endspecial(404)r(,)i @beginspecial @setspecial
@endspecial(533)241 3039 y FJ(MATSUBC)p FQ(,)e @beginspecial
@setspecial @endspecial(262)241 3152 y FJ(MATSUBR)p FQ(,)g
@beginspecial @setspecial @endspecial(262)241 3265 y(MAX,)j
@beginspecial @setspecial @endspecial(644)241 3378 y
FJ(MAX)p FQ(,)e @beginspecial @setspecial @endspecial(81)241
3491 y(MAX2,)i @beginspecial @setspecial @endspecial(644)241
3604 y FJ(MAXEXPPRINTLEN!*)p FQ(,)26 b @beginspecial
@setspecial @endspecial(357)241 3717 y FJ(MCD)p FQ(,)j
@beginspecial @setspecial @endspecial(137)r(,)h @beginspecial
@setspecial @endspecial(139)241 3830 y FJ(MEDIAN)p FQ(,)f
@beginspecial @setspecial @endspecial(365)241 3942 y(Meijer's)h(G)h
(function,)e @beginspecial @setspecial @endspecial(545)241
4055 y(MEMBER,)i @beginspecial @setspecial @endspecial(650)241
4168 y FJ(member)p FQ(,)e @beginspecial @setspecial @endspecial(528)241
4281 y(MEMQ,)i @beginspecial @setspecial @endspecial(650)241
4394 y FJ(MERGE)p 487 4394 V 33 w(LIST)p FQ(,)e @beginspecial
@setspecial @endspecial(244)241 4507 y(metric)h(structure,)g
@beginspecial @setspecial @endspecial(341)241 4620 y
FJ(MIDPOINT)p FQ(,)e @beginspecial @setspecial @endspecial(365)241
4733 y(MIN,)j @beginspecial @setspecial @endspecial(644)241
4846 y FJ(MIN)p FQ(,)e @beginspecial @setspecial @endspecial(81)241
4959 y(MIN2,)i @beginspecial @setspecial @endspecial(644)1880
555 y(Minim)m(um,)e @beginspecial @setspecial @endspecial(437)1880
668 y FJ(MINOR)p FQ(,)h @beginspecial @setspecial @endspecial(403)q(,)h
@beginspecial @setspecial @endspecial(406)1880 781 y(MINUS,)g
@beginspecial @setspecial @endspecial(644)1880 894 y(MINUSP)-8
b(,)31 b @beginspecial @setspecial @endspecial(624)1880
1007 y FJ(MINVECT)p FQ(,)e @beginspecial @setspecial
@endspecial(259)1880 1120 y(mixed-mo)s(de)h(arithmetic,)g
@beginspecial @setspecial @endspecial(641)1880 1233 y
FJ(MKAND)p FQ(,)g @beginspecial @setspecial @endspecial(497)1880
1346 y FJ(MKDEPEND)p FQ(,)f @beginspecial @setspecial
@endspecial(330)1880 1458 y FJ(MKID)p FQ(,)h @beginspecial
@setspecial @endspecial(92)q(,)g @beginspecial @setspecial
@endspecial(261)1880 1571 y FJ(MKIDM)p FQ(,)g @beginspecial
@setspecial @endspecial(261)1880 1684 y FJ(MKIDNEW)p
FQ(,)f @beginspecial @setspecial @endspecial(249)1880
1797 y FJ(MKLIST)p FQ(,)g @beginspecial @setspecial @endspecial(244)
1880 1910 y FJ(MKOR)p FQ(,)h @beginspecial @setspecial
@endspecial(497)1880 2023 y FJ(MKPOLY)p FQ(,)f @beginspecial
@setspecial @endspecial(515)1880 2136 y FJ(MKRANDTABL)p
FQ(,)f @beginspecial @setspecial @endspecial(250)1880
2249 y FJ(MKSET)p FQ(,)i @beginspecial @setspecial @endspecial(249)q(,)
h @beginspecial @setspecial @endspecial(526)1880 2362
y(MKVECT,)f @beginspecial @setspecial @endspecial(639)1880
2475 y FJ(MML)p FQ(,)g @beginspecial @setspecial @endspecial(416)1880
2588 y(Mo)s(de,)h @beginspecial @setspecial @endspecial(76)1880
2700 y(Mo)s(de)g(comm)m(unication,)f @beginspecial @setspecial
@endspecial(203)1880 2813 y FJ(MODSR)p FQ(,)g @beginspecial
@setspecial @endspecial(195)q(,)h @beginspecial @setspecial
@endspecial(419)1880 2926 y FJ(MODULAR)p FQ(,)e @beginspecial
@setspecial @endspecial(149)1880 3039 y(Mo)s(dular)g(co)s(e\016cien)m
(t,)j @beginspecial @setspecial @endspecial(149)1880
3152 y FJ(MONOM)p FQ(,)e @beginspecial @setspecial @endspecial(257)1880
3265 y FJ(monomial)p 2270 3265 V 33 w(base)p FQ(,)f @beginspecial
@setspecial @endspecial(446)1880 3378 y(Mo)s(ore{P)m(enrose)k(in)m(v)m
(erse,)d @beginspecial @setspecial @endspecial(411)1880
3491 y(Motzkin,)h @beginspecial @setspecial @endspecial(542)1880
3604 y FJ(Motzkin)p FQ(,)e @beginspecial @setspecial
@endspecial(542)1880 3717 y FJ(MP)p FQ(,)h @beginspecial
@setspecial @endspecial(365)1880 3830 y FJ(MPVECT)p FQ(,)f
@beginspecial @setspecial @endspecial(259)1880 3942 y
FJ(MRV)p 2030 3942 V 34 w(LIMIT)p FQ(,)g @beginspecial
@setspecial @endspecial(422)1880 4055 y FJ(MRVLIMIT)p
FQ(,)g @beginspecial @setspecial @endspecial(421)1880
4168 y FJ(MSG)p FQ(,)h @beginspecial @setspecial @endspecial(223)1880
4281 y FJ(MSHELL)p FQ(,)f @beginspecial @setspecial @endspecial(216)
1880 4394 y FJ(MULT)p 2078 4394 V 34 w(COLUMNS)p FQ(,)f
@beginspecial @setspecial @endspecial(403)r(,)i @beginspecial
@setspecial @endspecial(405)1880 4507 y FJ(MULT)p 2078
4507 V 34 w(ROW)p FQ(,)f @beginspecial @setspecial @endspecial(405)1880
4620 y FJ(MULT)p 2078 4620 V 34 w(ROWS)p FQ(,)g @beginspecial
@setspecial @endspecial(403)1880 4733 y(Multiple)g(assignmen)m(t)h
(statemen)m(t,)2213 4846 y @beginspecial @setspecial
@endspecial(64)1880 4959 y FJ(MULTIPLICITIES)p FQ(,)d
@beginspecial @setspecial @endspecial(96)p eop
%%Page: 688 688
688 687 bop 664 299 a @beginspecial @setspecial @endspecial
FQ(688)2553 b FM(INDEX)664 555 y FJ(MULTIROOT)p FQ(,)28
b @beginspecial @setspecial @endspecial(517)664 751 y
FJ(N)p 718 751 29 4 v 34 w(GAT)p FQ(,)i @beginspecial
@setspecial @endspecial(554)664 864 y FJ(NASSOC)p FQ(,)f
@beginspecial @setspecial @endspecial(498)664 977 y FJ(NAT)p
FQ(,)h @beginspecial @setspecial @endspecial(125)q(,)h
@beginspecial @setspecial @endspecial(327)664 1090 y(NA)-8
b(T)31 b(\015ag,)g @beginspecial @setspecial @endspecial(340)664
1203 y FJ(nc)p 766 1203 V 34 w(cleanup)p FQ(,)e @beginspecial
@setspecial @endspecial(427)664 1316 y FJ(nc)p 766 1316
V 34 w(compact)p FQ(,)g @beginspecial @setspecial @endspecial(430)664
1429 y FJ(nc)p 766 1429 V 34 w(divide)p FQ(,)g @beginspecial
@setspecial @endspecial(429)664 1542 y FJ(nc)p 766 1542
V 34 w(factorize)p FQ(,)f @beginspecial @setspecial @endspecial(429)664
1654 y FJ(nc)p 766 1654 V 34 w(factorize)p 1232 1654
V 32 w(all)p FQ(,)i @beginspecial @setspecial @endspecial(430)664
1767 y FJ(nc)p 766 1767 V 34 w(groebner)p FQ(,)e @beginspecial
@setspecial @endspecial(428)664 1880 y FJ(nc)p 766 1880
V 34 w(preduce)p FQ(,)h @beginspecial @setspecial @endspecial(429)664
1993 y FJ(nc)p 766 1993 V 34 w(setup)p FQ(,)g @beginspecial
@setspecial @endspecial(426)664 2106 y(NCONC,)h @beginspecial
@setspecial @endspecial(650)664 2219 y FJ(NCPOLY)p FQ(,)f
@beginspecial @setspecial @endspecial(195)q(,)i @beginspecial
@setspecial @endspecial(425)664 2332 y FJ(NEARESTROOT)p
FQ(,)d @beginspecial @setspecial @endspecial(515)664
2445 y FJ(NEARESTROOTS)p FQ(,)f @beginspecial @setspecial
@endspecial(515)664 2558 y FJ(NEGATIVE)p FQ(,)i @beginspecial
@setspecial @endspecial(514)664 2671 y FJ(NEQ)p FQ(,)h
@beginspecial @setspecial @endspecial(498)q(,)h @beginspecial
@setspecial @endspecial(499)664 2784 y FJ(NERO)p FQ(,)f
@beginspecial @setspecial @endspecial(122)664 2896 y(Newton's)h(metho)s
(d,)f @beginspecial @setspecial @endspecial(437)664 3009
y FJ(NEXTPRIME)p FQ(,)e @beginspecial @setspecial @endspecial(82)664
3122 y(NIL)830 3235 y(cannot)j(b)s(e)f(c)m(hanged,)h
@beginspecial @setspecial @endspecial(634)r(,)f @beginspecial
@setspecial @endspecial(635)q(,)996 3348 y @beginspecial
@setspecial @endspecial(661)664 3461 y(NIL)g(\(global\),)h
@beginspecial @setspecial @endspecial(619)q(,)g @beginspecial
@setspecial @endspecial(622)q(,)g @beginspecial @setspecial
@endspecial(661)664 3574 y FJ(NOCONVERT)p FQ(,)d @beginspecial
@setspecial @endspecial(148)664 3687 y FJ(NODEPEND)p
FQ(,)h @beginspecial @setspecial @endspecial(109)664
3800 y(NODEPEND)i(statemen)m(t,)i @beginspecial @setspecial
@endspecial(457)664 3913 y FJ(NODRR)p FQ(,)c @beginspecial
@setspecial @endspecial(555)664 4026 y(NOETHER)h(function,)f
@beginspecial @setspecial @endspecial(339)664 4138 y(NOEV)-10
b(AL)830 4251 y(function)29 b(t)m(yp)s(e,)i @beginspecial
@setspecial @endspecial(621)664 4364 y(Non-comm)m(uting)g(op)s(erator,)
g @beginspecial @setspecial @endspecial(106)664 4477
y FJ(NONCOM)p FQ(,)e @beginspecial @setspecial @endspecial(106)q(,)i
@beginspecial @setspecial @endspecial(320)q(,)g @beginspecial
@setspecial @endspecial(461)q(,)g @beginspecial @setspecial
@endspecial(466)664 4590 y FJ(NONZERO)p FQ(,)e @beginspecial
@setspecial @endspecial(104)664 4703 y FJ(NORDP)p FQ(,)g
@beginspecial @setspecial @endspecial(255)664 4816 y
FJ(NORMFORM)p FQ(,)g @beginspecial @setspecial @endspecial(195)q(,)h
@beginspecial @setspecial @endspecial(431)664 4929 y
FJ(NOSPLIT)p FQ(,)f @beginspecial @setspecial @endspecial(117)2304
555 y(NOSPREAD)2470 668 y(function)g(t)m(yp)s(e,)i @beginspecial
@setspecial @endspecial(621)2304 781 y FJ(NOSPUR)p FQ(,)e
@beginspecial @setspecial @endspecial(215)2304 894 y(NOSUM)h(command,)g
@beginspecial @setspecial @endspecial(340)2304 1007 y(NOSUM)g(switc)m
(h,)g @beginspecial @setspecial @endspecial(340)2304
1120 y(NOT,)g @beginspecial @setspecial @endspecial(641)2304
1233 y FJ(NOT)p FQ(,)g @beginspecial @setspecial @endspecial(497)2304
1346 y FJ(NOT)p 2454 1346 V 33 w(NEGATIVE)p FQ(,)f @beginspecial
@setspecial @endspecial(409)2304 1458 y(NO)m(XPND)2470
1571 y(@,)h @beginspecial @setspecial @endspecial(337)2470
1684 y(D,)h @beginspecial @setspecial @endspecial(337)2304
1797 y(NULL,)f @beginspecial @setspecial @endspecial(624)2304
1910 y FJ(NULLSPACE)p FQ(,)e @beginspecial @setspecial
@endspecial(182)2304 2023 y FJ(NUM)p FQ(,)i @beginspecial
@setspecial @endspecial(146)2304 2136 y FJ(NUM)p 2454
2136 V 33 w(FIT)p FQ(,)g @beginspecial @setspecial @endspecial(444)2304
2249 y FJ(NUM)p 2454 2249 V 33 w(INT)p FQ(,)g @beginspecial
@setspecial @endspecial(437)r(,)g @beginspecial @setspecial
@endspecial(440)2304 2362 y FJ(NUM)p 2454 2362 V 33 w(MIN)p
FQ(,)g @beginspecial @setspecial @endspecial(437)r(,)g
@beginspecial @setspecial @endspecial(438)2304 2475 y
FJ(NUM)p 2454 2475 V 33 w(ODESOLVE)p FQ(,)f @beginspecial
@setspecial @endspecial(437)q(,)i @beginspecial @setspecial
@endspecial(441)2304 2588 y FJ(NUM)p 2454 2588 V 33 w(SOLVE)p
FQ(,)f @beginspecial @setspecial @endspecial(437)q(,)h
@beginspecial @setspecial @endspecial(439)2304 2700 y(Num)m(b)s(er,)e
@beginspecial @setspecial @endspecial(44)q(,)i @beginspecial
@setspecial @endspecial(45)2304 2813 y(n)m(um)m(b)s(er,)e
@beginspecial @setspecial @endspecial(619)2304 2926 y(NUMBERP)-8
b(,)32 b @beginspecial @setspecial @endspecial(624)2304
3039 y FJ(NUMBERP)p FQ(,)d @beginspecial @setspecial
@endspecial(56)2304 3152 y FJ(NUMERIC)p FQ(,)g @beginspecial
@setspecial @endspecial(195)q(,)h @beginspecial @setspecial
@endspecial(437)2304 3265 y(Numerical)f(op)s(erator,)i
@beginspecial @setspecial @endspecial(79)2304 3378 y(Numerical)e
(precision,)g @beginspecial @setspecial @endspecial(46)2304
3574 y(OBLIST,)g @beginspecial @setspecial @endspecial(627)2304
3687 y(OBLIST)g(en)m(try)-8 b(,)31 b @beginspecial @setspecial
@endspecial(616)r(,)f @beginspecial @setspecial @endspecial(629)r(,)g
@beginspecial @setspecial @endspecial(659)2304 3800 y
FJ(ODD)p FQ(,)g @beginspecial @setspecial @endspecial(104)2304
3913 y(Odd)f(op)s(erator,)i @beginspecial @setspecial
@endspecial(104)2304 4026 y FJ(ODDP)p FQ(,)e @beginspecial
@setspecial @endspecial(250)2304 4138 y FJ(ODEDEGREE)p
FQ(,)f @beginspecial @setspecial @endspecial(450)2304
4251 y FJ(ODELINEARITY)p FQ(,)f @beginspecial @setspecial
@endspecial(450)2304 4364 y FJ(ODEORDER)p FQ(,)h @beginspecial
@setspecial @endspecial(450)2304 4477 y FJ(ODESOLVE)p
FQ(,)g @beginspecial @setspecial @endspecial(195)r(,)i
@beginspecial @setspecial @endspecial(449)r(,)g @beginspecial
@setspecial @endspecial(450)2304 4590 y FJ(ODWA)p FQ(,)f
@beginspecial @setspecial @endspecial(554)2304 4703 y
FJ(OFF)p FQ(,)h @beginspecial @setspecial @endspecial(76)q(,)g
@beginspecial @setspecial @endspecial(77)2304 4816 y
FJ(OFSF)p FQ(,)f @beginspecial @setspecial @endspecial(497)r(,)h
@beginspecial @setspecial @endspecial(498)2304 4929 y
FJ(ON)p FQ(,)g @beginspecial @setspecial @endspecial(76)q(,)g
@beginspecial @setspecial @endspecial(77)p eop
%%Page: 689 689
689 688 bop 241 299 a @beginspecial @setspecial @endspecial
FM(INDEX)2552 b FQ(689)241 555 y FJ(ONE)p 391 555 29
4 v 33 w(FORMS)p FQ(,)29 b @beginspecial @setspecial
@endspecial(327)241 668 y FJ(ONE)p 391 668 V 33 w(OF)p
FQ(,)h @beginspecial @setspecial @endspecial(96)241 781
y(ONEP)-8 b(,)30 b @beginspecial @setspecial @endspecial(625)241
894 y FJ(ONLY)p 439 894 V 33 w(INTEGER)p FQ(,)f @beginspecial
@setspecial @endspecial(409)241 1007 y FJ(OPAPPLY)p FQ(,)f
@beginspecial @setspecial @endspecial(467)241 1120 y(OPEN,)i
@beginspecial @setspecial @endspecial(656)q(,)h @beginspecial
@setspecial @endspecial(657)241 1233 y FJ(OPERATOR)p
FQ(,)d @beginspecial @setspecial @endspecial(208)241
1346 y(Op)s(erator,)i @beginspecial @setspecial @endspecial(48)q({)p
@beginspecial @setspecial @endspecial(51)241 1458 y(Op)s(erator)g
(precedence,)h @beginspecial @setspecial @endspecial(49)q(,)f
@beginspecial @setspecial @endspecial(51)241 1571 y FJ(OPORDER)p
FQ(,)e @beginspecial @setspecial @endspecial(464)241
1684 y FJ(OPTIMIZE)p FQ(,)g @beginspecial @setspecial
@endspecial(521)241 1797 y(OR,)i @beginspecial @setspecial
@endspecial(641)241 1910 y FJ(OR)p FQ(,)g @beginspecial
@setspecial @endspecial(497)241 2023 y FJ(ORDER)p FQ(,)f
@beginspecial @setspecial @endspecial(115)q(,)i @beginspecial
@setspecial @endspecial(128)241 2136 y(ordering)407 2249
y(exterior)f(form,)g @beginspecial @setspecial @endspecial(343)241
2362 y(ordinary)e(di\013eren)m(tial)h(equations,)573
2475 y @beginspecial @setspecial @endspecial(449)241
2588 y FJ(ORDP)p FQ(,)g @beginspecial @setspecial @endspecial(56)q(,)i
@beginspecial @setspecial @endspecial(106)241 2700 y
FJ(ORTHOGONAL)p FQ(,)d @beginspecial @setspecial @endspecial(366)241
2813 y(Orthogonal)i(p)s(olynomials,)e @beginspecial @setspecial
@endspecial(539)241 2926 y FJ(ORTHOVEC)p FQ(,)g @beginspecial
@setspecial @endspecial(195)q(,)j @beginspecial @setspecial
@endspecial(453)241 3039 y FJ(OTHER)p 487 3039 V 33 w(CC)p
616 3039 V 34 w(POINT)p FQ(,)e @beginspecial @setspecial
@endspecial(366)241 3152 y FJ(OTHER)p 487 3152 V 33 w(CL)p
616 3152 V 34 w(POINT)p FQ(,)g @beginspecial @setspecial
@endspecial(366)241 3265 y FJ(OUT)p FQ(,)g @beginspecial
@setspecial @endspecial(169)r(,)h @beginspecial @setspecial
@endspecial(170)241 3378 y(OUTPUT,)g @beginspecial @setspecial
@endspecial(657)241 3491 y FJ(OUTPUT)p FQ(,)f @beginspecial
@setspecial @endspecial(114)241 3604 y(Output,)g @beginspecial
@setspecial @endspecial(120)r(,)h @beginspecial @setspecial
@endspecial(124)241 3717 y(Output)f(declaration,)h @beginspecial
@setspecial @endspecial(114)r(,)g @beginspecial @setspecial
@endspecial(115)241 3913 y FJ(P3)p 343 3913 V 34 w(ANGLE)p
FQ(,)f @beginspecial @setspecial @endspecial(366)241
4026 y FJ(P3)p 343 4026 V 34 w(CIRCLE)p FQ(,)f @beginspecial
@setspecial @endspecial(366)241 4138 y FJ(P3)p 343 4138
V 34 w(CIRCLE1)p FQ(,)g @beginspecial @setspecial @endspecial(366)241
4251 y FJ(P4)p 343 4251 V 34 w(CIRCLE)p FQ(,)g @beginspecial
@setspecial @endspecial(366)241 4364 y FJ(PAD)385 4348
y(\023)385 4364 y(E)p FQ(,)h @beginspecial @setspecial
@endspecial(490)241 4477 y(P)-8 b(A)m(GELENGTH,)32 b
@beginspecial @setspecial @endspecial(656)q(,)e @beginspecial
@setspecial @endspecial(657)241 4590 y(P)-8 b(AIR,)31
b @beginspecial @setspecial @endspecial(651)241 4703
y FJ(PAIR)p FQ(,)e @beginspecial @setspecial @endspecial(245)241
4816 y(P)-8 b(AIRP)g(,)31 b @beginspecial @setspecial
@endspecial(625)241 4929 y FJ(PAR)p FQ(,)e @beginspecial
@setspecial @endspecial(366)1880 555 y FJ(PARALLEL)p
FQ(,)g @beginspecial @setspecial @endspecial(366)1880
668 y FJ(PARSEML)p FQ(,)g @beginspecial @setspecial @endspecial(416)
1880 781 y FJ(PART)p FQ(,)h @beginspecial @setspecial
@endspecial(59)q(,)g @beginspecial @setspecial @endspecial(127)r(,)g
@beginspecial @setspecial @endspecial(130)r(,)g @beginspecial
@setspecial @endspecial(499)1880 894 y(partial)g(deriv)-5
b(ativ)m(es,)30 b @beginspecial @setspecial @endspecial(313)1880
1007 y(partial)g(di\013eren)m(tiation,)f @beginspecial
@setspecial @endspecial(336)1880 1120 y FJ(PAUSE)p FQ(,)h
@beginspecial @setspecial @endspecial(176)1880 1233 y
FJ(PDE2EDS)p FQ(,)f @beginspecial @setspecial @endspecial(326)1880
1346 y FJ(PDE2JET)p FQ(,)g @beginspecial @setspecial
@endspecial(330)1880 1458 y FJ(PEDALPOINT)p FQ(,)f @beginspecial
@setspecial @endspecial(366)1880 1571 y(P)m(ercen)m(t)k(sign,)e
@beginspecial @setspecial @endspecial(48)1880 1684 y
FJ(PERIOD)p FQ(,)f @beginspecial @setspecial @endspecial(125)1880
1797 y FJ(PERIODIC)p FQ(,)g @beginspecial @setspecial
@endspecial(488)1880 1910 y FJ(PERIODIC2RATIONAL)p FQ(,)d
@beginspecial @setspecial @endspecial(488)1880 2023 y
FJ(PERMUTATIONS)p FQ(,)i @beginspecial @setspecial @endspecial(250)1880
2136 y FJ(PF)p FQ(,)i @beginspecial @setspecial @endspecial(93)1880
2249 y FJ(PFAFFIAN)p FQ(,)f @beginspecial @setspecial
@endspecial(330)1880 2362 y(PF)m(ORM)i(statemen)m(t,)i
@beginspecial @setspecial @endspecial(334)1880 2475 y
FJ(PG)p FQ(,)d @beginspecial @setspecial @endspecial(554)1880
2588 y FJ(PHYSINDEX)p FQ(,)f @beginspecial @setspecial
@endspecial(463)q(,)h @beginspecial @setspecial @endspecial(466)1880
2700 y FJ(PHYSOP)p FQ(,)f @beginspecial @setspecial @endspecial(195)r
(,)h @beginspecial @setspecial @endspecial(461)1880 2813
y FJ(PI)p FQ(,)g @beginspecial @setspecial @endspecial(47)1880
2926 y FJ(PIVOT)p FQ(,)g @beginspecial @setspecial @endspecial(403)q(,)
h @beginspecial @setspecial @endspecial(406)1880 3039
y FJ(PLOT)p FQ(,)f @beginspecial @setspecial @endspecial(194)q(,)h
@beginspecial @setspecial @endspecial(371)1880 3152 y
FJ(PLOT)p 2078 3152 V 34 w(XMESH)p FQ(,)e @beginspecial
@setspecial @endspecial(372)1880 3265 y FJ(PLOT)p 2078
3265 V 34 w(YMESH)p FQ(,)g @beginspecial @setspecial
@endspecial(373)1880 3378 y FJ(PLOTKEEP)p FQ(,)g @beginspecial
@setspecial @endspecial(372)1880 3491 y FJ(PLOTREFINE)p
FQ(,)f @beginspecial @setspecial @endspecial(372)1880
3604 y FJ(plotrefine)p FQ(,)g @beginspecial @setspecial
@endspecial(372)1880 3717 y FJ(PLOTRESET)p FQ(,)h @beginspecial
@setspecial @endspecial(372)1880 3830 y(PLUS,)h @beginspecial
@setspecial @endspecial(645)1880 3942 y(PLUS2,)h @beginspecial
@setspecial @endspecial(645)1880 4055 y FJ(PM)p FQ(,)f
@beginspecial @setspecial @endspecial(195)r(,)g @beginspecial
@setspecial @endspecial(469)1880 4168 y FJ(Pochhammer)p
FQ(,)e @beginspecial @setspecial @endspecial(542)1880
4281 y(P)m(o)s(c)m(hhammer's)j(sym)m(b)s(ol,)e @beginspecial
@setspecial @endspecial(542)1880 4394 y FJ(POINCARE)p
FQ(,)g @beginspecial @setspecial @endspecial(330)1880
4507 y FJ(POINT)p FQ(,)h @beginspecial @setspecial @endspecial(366)1880
4620 y FJ(POINT)p 2126 4620 V 33 w(ON)p 2255 4620 V 34
w(BISECTOR)p FQ(,)f @beginspecial @setspecial @endspecial(366)1880
4733 y FJ(POINT)p 2126 4733 V 33 w(ON)p 2255 4733 V 34
w(CIRCLE)p FQ(,)g @beginspecial @setspecial @endspecial(366)1880
4846 y FJ(POINT)p 2126 4846 V 33 w(ON)p 2255 4846 V 34
w(CIRCLE1)p FQ(,)g @beginspecial @setspecial @endspecial(366)1880
4959 y FJ(POINT)p 2126 4959 V 33 w(ON)p 2255 4959 V 34
w(LINE)p FQ(,)h @beginspecial @setspecial @endspecial(366)p
eop
%%Page: 690 690
690 689 bop 664 299 a @beginspecial @setspecial @endspecial
FQ(690)2553 b FM(INDEX)664 555 y FJ(poleorder)p FQ(,)28
b @beginspecial @setspecial @endspecial(507)664 668 y
FJ(Polygamma)p FQ(,)g @beginspecial @setspecial @endspecial(542)664
781 y(P)m(olygamma)j(functions,)f @beginspecial @setspecial
@endspecial(542)664 894 y FJ(Polylog)p FQ(,)f @beginspecial
@setspecial @endspecial(544)664 1007 y(P)m(olylogarithm)h(function,)f
@beginspecial @setspecial @endspecial(544)664 1120 y(P)m(olynomial,)g
@beginspecial @setspecial @endspecial(133)664 1233 y
FJ(POSITION)p FQ(,)g @beginspecial @setspecial @endspecial(245)664
1346 y FJ(POSITIVE)p FQ(,)g @beginspecial @setspecial
@endspecial(514)664 1458 y(POSN,)h @beginspecial @setspecial
@endspecial(657)664 1571 y(p)s(o)m(w)m(er)h(series,)f
@beginspecial @setspecial @endspecial(567)664 1684 y(p)s(o)m(w)m(er)h
(series)830 1797 y(arithmetic,)f @beginspecial @setspecial
@endspecial(574)830 1910 y(comp)s(osition,)g @beginspecial
@setspecial @endspecial(573)830 2023 y(di\013eren)m(tiation,)g
@beginspecial @setspecial @endspecial(575)830 2136 y(of)h(in)m(tegral,)
f @beginspecial @setspecial @endspecial(569)830 2249
y(of)h(user)e(de\014ned)h(function,)f @beginspecial @setspecial
@endspecial(568)664 2362 y FJ(PP)p 766 2362 29 4 v 34
w(LINE)p FQ(,)g @beginspecial @setspecial @endspecial(366)664
2475 y FJ(PR)p FQ(,)h @beginspecial @setspecial @endspecial(554)664
2588 y FJ(PRECEDENCE)p FQ(,)e @beginspecial @setspecial
@endspecial(108)664 2700 y FJ(PRECISE)p FQ(,)h @beginspecial
@setspecial @endspecial(86)664 2813 y FJ(PRECISION)p
FQ(,)f @beginspecial @setspecial @endspecial(148)664
2926 y(precision,)h @beginspecial @setspecial @endspecial(353)664
3039 y(PRECISION)g(command,)h @beginspecial @setspecial
@endspecial(353)664 3152 y FJ(PRECP)p FQ(,)f @beginspecial
@setspecial @endspecial(255)664 3265 y(predicate)h(,)h
@beginspecial @setspecial @endspecial(622)664 3378 y
FJ(PREDUCE)p FQ(,)e @beginspecial @setspecial @endspecial(384)664
3491 y(Pre\014x,)h @beginspecial @setspecial @endspecial(79)q(,)h
@beginspecial @setspecial @endspecial(107)q(,)f @beginspecial
@setspecial @endspecial(108)664 3604 y(Pre\014x)g(op)s(erator,)h
@beginspecial @setspecial @endspecial(48)q(,)f @beginspecial
@setspecial @endspecial(49)664 3717 y FJ(PRET)p FQ(,)g
@beginspecial @setspecial @endspecial(223)664 3830 y
FJ(PRETTYPRINT)p FQ(,)e @beginspecial @setspecial @endspecial(224)664
3942 y(Prett)m(yprin)m(ting,)i @beginspecial @setspecial
@endspecial(223)q(,)h @beginspecial @setspecial @endspecial(224)664
4055 y FJ(PRGEN)p FQ(,)e @beginspecial @setspecial @endspecial(536)664
4168 y FJ(PRI)p FQ(,)h @beginspecial @setspecial @endspecial(115)664
4281 y FJ(PRIMEP)p FQ(,)f @beginspecial @setspecial @endspecial(56)664
4394 y(PRIN1,)i @beginspecial @setspecial @endspecial(658)664
4507 y(PRIN2,)g @beginspecial @setspecial @endspecial(658)664
4620 y(PRINC,)f @beginspecial @setspecial @endspecial(657)r(,)g
@beginspecial @setspecial @endspecial(661)664 4733 y(PRINT,)g
@beginspecial @setspecial @endspecial(658)664 4846 y(prin)m(t)f(name,)i
@beginspecial @setspecial @endspecial(616)2304 555 y(PRINT!-PRECISION)e
(command,)2636 668 y @beginspecial @setspecial @endspecial(353)2304
781 y FJ(PRINT)p 2550 781 V 33 w(PRECISION)p FQ(,)f @beginspecial
@setspecial @endspecial(148)2304 894 y FJ(PROCEDURE)p
FQ(,)g @beginspecial @setspecial @endspecial(185)2304
1007 y(Pro)s(cedure)h(b)s(o)s(dy)-8 b(,)30 b @beginspecial
@setspecial @endspecial(187)q(,)h @beginspecial @setspecial
@endspecial(189)2304 1120 y(Pro)s(cedure)e(heading,)h
@beginspecial @setspecial @endspecial(186)2304 1233 y(PR)m(OD)h(op)s
(erator,)f @beginspecial @setspecial @endspecial(547)2304
1346 y FJ(PRODUCT)p FQ(,)f @beginspecial @setspecial
@endspecial(67,)i @beginspecial @setspecial @endspecial(68)2304
1458 y(PR)m(OG,)g @beginspecial @setspecial @endspecial(637)2304
1571 y(PR)m(OG)2470 1684 y(default)e(v)-5 b(alue,)31
b @beginspecial @setspecial @endspecial(637)2470 1797
y(v)-5 b(ariables,)29 b @beginspecial @setspecial @endspecial(637)2304
1910 y(PR)m(OG2,)i @beginspecial @setspecial @endspecial(637)2304
2023 y(PR)m(OGN,)g @beginspecial @setspecial @endspecial(637)2304
2136 y(Program,)g @beginspecial @setspecial @endspecial(48)2304
2249 y(Program)f(structure,)h @beginspecial @setspecial
@endspecial(43)2304 2362 y FJ(PROLONG)p FQ(,)e @beginspecial
@setspecial @endspecial(329)2304 2475 y(Prop)s(er)g(statemen)m(t,)k
@beginspecial @setspecial @endspecial(58)q(,)d @beginspecial
@setspecial @endspecial(63)q(,)h @beginspecial @setspecial
@endspecial(64)2304 2588 y FJ(PROPERTIES)p FQ(,)d @beginspecial
@setspecial @endspecial(327)2304 2700 y(prop)s(erties,)h
@beginspecial @setspecial @endspecial(616)q(,)i @beginspecial
@setspecial @endspecial(629)2304 2813 y(prop)s(ert)m(y)f(list,)f
@beginspecial @setspecial @endspecial(629)2304 2926 y
FJ(PRSYS)p FQ(,)g @beginspecial @setspecial @endspecial(536)2304
3039 y FJ(PS)p FQ(,)h @beginspecial @setspecial @endspecial(196)q(,)h
@beginspecial @setspecial @endspecial(567)2304 3152 y(PS)f(op)s
(erator,)g @beginspecial @setspecial @endspecial(568)2304
3265 y(PSCHANGEV)-10 b(AR)30 b(op)s(erator,)h @beginspecial
@setspecial @endspecial(571)2304 3378 y(PSCOMPOSE)d(op)s(erator,)j
@beginspecial @setspecial @endspecial(572)2304 3491 y(PSDEPV)-10
b(AR)30 b(op)s(erator,)h @beginspecial @setspecial @endspecial(571)2304
3604 y FJ(PSE)p 2454 3604 V 33 w(ELE)p FQ(,)f @beginspecial
@setspecial @endspecial(554)2304 3717 y FJ(PSEUDO)p 2598
3717 V 33 w(DIVIDE)p FQ(,)f @beginspecial @setspecial
@endspecial(139)2304 3830 y FJ(PSEUDO)p 2598 3830 V 33
w(INVERSE)p FQ(,)f @beginspecial @setspecial @endspecial(404)r(,)i
@beginspecial @setspecial @endspecial(411)2304 3942 y
FJ(PSEUDO)p 2598 3942 V 33 w(REMAINDER)p FQ(,)e @beginspecial
@setspecial @endspecial(139)2304 4055 y(PSEXP)-8 b(ANSIONPT)29
b(op)s(erator,)i @beginspecial @setspecial @endspecial(571)2304
4168 y(PSEXPLIM)e(op)s(erator,)i @beginspecial @setspecial
@endspecial(568)2304 4281 y(PSFUNCTION)e(op)s(erator,)i
@beginspecial @setspecial @endspecial(571)2304 4394 y
FJ(Psi)p FQ(,)f @beginspecial @setspecial @endspecial(542)2304
4507 y(Psi)f(function,)g @beginspecial @setspecial @endspecial(542)2304
4620 y(PSINTCONST)f(\(shared\),)j @beginspecial @setspecial
@endspecial(569)2304 4733 y(PSORDER)e(op)s(erator,)i
@beginspecial @setspecial @endspecial(570)2304 4846 y(PSORDLIM)f(op)s
(erator,)h @beginspecial @setspecial @endspecial(569)2304
4959 y(PSREVERSE)e(op)s(erator,)i @beginspecial @setspecial
@endspecial(572)p eop
%%Page: 691 691
691 690 bop 241 299 a @beginspecial @setspecial @endspecial
FM(INDEX)2552 b FQ(691)241 555 y(PSSETORDER)28 b(op)s(erator,)j
@beginspecial @setspecial @endspecial(570)241 668 y(PSSUM)e(op)s
(erator,)i @beginspecial @setspecial @endspecial(573)241
781 y(PSTERM)e(op)s(erator,)i @beginspecial @setspecial
@endspecial(570)241 894 y(Puiseux)d(expansion,)i @beginspecial
@setspecial @endspecial(572)241 1007 y FJ(PULLBACK)p
FQ(,)e @beginspecial @setspecial @endspecial(328)241
1120 y(PUT,)i @beginspecial @setspecial @endspecial(616)q(,)h
@beginspecial @setspecial @endspecial(618)q(,)g @beginspecial
@setspecial @endspecial(630)241 1233 y(PUT)407 1346 y(not)f(for)h
(functions,)e @beginspecial @setspecial @endspecial(630)241
1458 y FJ(PUTBAG)p FQ(,)g @beginspecial @setspecial @endspecial(247)241
1571 y(PUTCSYSTEM)f(command,)j @beginspecial @setspecial
@endspecial(273)241 1684 y(PUTD,)f @beginspecial @setspecial
@endspecial(616)r(,)g @beginspecial @setspecial @endspecial(618)r(,)g
@beginspecial @setspecial @endspecial(632)241 1797 y
FJ(PUTFLAG)p FQ(,)e @beginspecial @setspecial @endspecial(253)241
1910 y FJ(PUTGRASS)p FQ(,)g @beginspecial @setspecial
@endspecial(260)241 2023 y FJ(PUTPROP)p FQ(,)g @beginspecial
@setspecial @endspecial(254)241 2136 y(PUTV,)i @beginspecial
@setspecial @endspecial(639)241 2332 y FJ(QBINOMIAL)p
FQ(,)e @beginspecial @setspecial @endspecial(476)241
2445 y FJ(QBRACKETS)p FQ(,)g @beginspecial @setspecial
@endspecial(476)241 2558 y FJ(QFACTORIAL)p FQ(,)g @beginspecial
@setspecial @endspecial(476)241 2671 y FJ(QG)p FQ(,)i
@beginspecial @setspecial @endspecial(589)241 2784 y
FJ(QPHIHYPERTERM)p FQ(,)d @beginspecial @setspecial @endspecial(476)241
2896 y FJ(QPOCHHAMMER)p FQ(,)g @beginspecial @setspecial
@endspecial(476)241 3009 y FJ(QPSIHYPERTERM)p FQ(,)g
@beginspecial @setspecial @endspecial(476)241 3122 y
FJ(QSUM)p FQ(,)i @beginspecial @setspecial @endspecial(475)241
3235 y FJ(QSUMRECURSION)p FQ(,)e @beginspecial @setspecial
@endspecial(477)241 3348 y(Quadrature,)i @beginspecial
@setspecial @endspecial(437)241 3461 y FJ(QUASILINEAR)p
FQ(,)e @beginspecial @setspecial @endspecial(330)241
3574 y FJ(QUASILINPDE)p FQ(,)g @beginspecial @setspecial
@endspecial(235)241 3687 y(QUIT,)j @beginspecial @setspecial
@endspecial(660)241 3800 y FJ(QUIT)p FQ(,)f @beginspecial
@setspecial @endspecial(77)241 3913 y(QUOTE,)g @beginspecial
@setspecial @endspecial(655)241 4026 y FJ(QUOTE)p FQ(,)g
@beginspecial @setspecial @endspecial(200)241 4138 y(QUOTIENT,)g
@beginspecial @setspecial @endspecial(645)241 4334 y
FJ(R)p 295 4334 29 4 v 34 w(SOLVE)p FQ(,)g @beginspecial
@setspecial @endspecial(519)241 4447 y FJ(RANDOM)p FQ(,)g
@beginspecial @setspecial @endspecial(82)241 4560 y FJ(RANDOM)p
535 4560 V 32 w(MATRIX)p FQ(,)g @beginspecial @setspecial
@endspecial(404)r(,)h @beginspecial @setspecial @endspecial(409)241
4673 y FJ(RANDOM)p 535 4673 V 32 w(NEW)p 711 4673 V 34
w(SEED)p FQ(,)f @beginspecial @setspecial @endspecial(82)241
4786 y FJ(RANDOMLIST)p FQ(,)f @beginspecial @setspecial
@endspecial(250)241 4899 y FJ(RANDPOLY)p FQ(,)g @beginspecial
@setspecial @endspecial(195)q(,)j @beginspecial @setspecial
@endspecial(481)1880 555 y(randp)s(oly)2046 668 y FJ(coeffs)p
FQ(,)e @beginspecial @setspecial @endspecial(483)2046
781 y FJ(degree)p FQ(,)g @beginspecial @setspecial @endspecial(482)2046
894 y FJ(dense)p FQ(,)h @beginspecial @setspecial @endspecial(482)2046
1007 y FJ(expons)p FQ(,)f @beginspecial @setspecial @endspecial(483)
2046 1120 y FJ(ord)p FQ(,)h @beginspecial @setspecial
@endspecial(482)2046 1233 y FJ(sparse)p FQ(,)f @beginspecial
@setspecial @endspecial(482)2046 1346 y FJ(terms)p FQ(,)h
@beginspecial @setspecial @endspecial(482)1880 1458 y
FJ(RANK)p FQ(,)g @beginspecial @setspecial @endspecial(183)1880
1571 y FJ(RANPOS)p FQ(,)f @beginspecial @setspecial @endspecial(330)
1880 1684 y FJ(RAT)p FQ(,)h @beginspecial @setspecial
@endspecial(117)1880 1797 y FJ(RATAPRX)p FQ(,)f @beginspecial
@setspecial @endspecial(487)1880 1910 y FJ(RATARG)p FQ(,)g
@beginspecial @setspecial @endspecial(129)r(,)h @beginspecial
@setspecial @endspecial(142)1880 2023 y FJ(RATIONAL)p
FQ(,)f @beginspecial @setspecial @endspecial(147)1880
2136 y(Rational)h(co)s(e\016cien)m(t,)i @beginspecial
@setspecial @endspecial(147)1880 2249 y(Rational)e(function,)g
@beginspecial @setspecial @endspecial(133)1880 2362 y
FJ(RATIONAL2PERIODIC)p FQ(,)c @beginspecial @setspecial
@endspecial(488)1880 2475 y FJ(RATIONALIZE)p FQ(,)i @beginspecial
@setspecial @endspecial(150)1880 2588 y FJ(ratjordan)p
FQ(,)h @beginspecial @setspecial @endspecial(433)1880
2700 y FJ(RATPRI)p FQ(,)g @beginspecial @setspecial @endspecial(119)
1880 2813 y FJ(RATROOT)p FQ(,)g @beginspecial @setspecial
@endspecial(517)1880 2926 y(RDS,)i @beginspecial @setspecial
@endspecial(658)1880 3039 y FJ(REACTEQN)p FQ(,)e @beginspecial
@setspecial @endspecial(195)q(,)i @beginspecial @setspecial
@endspecial(493)1880 3152 y(reacteqn)2046 3265 y FJ(inputmat)p
FQ(,)e @beginspecial @setspecial @endspecial(494)2046
3378 y FJ(outputmat)p FQ(,)g @beginspecial @setspecial
@endspecial(494)2046 3491 y FJ(rates)p FQ(,)h @beginspecial
@setspecial @endspecial(494)2046 3604 y FJ(species)p
FQ(,)f @beginspecial @setspecial @endspecial(494)1880
3717 y(READ,)i @beginspecial @setspecial @endspecial(616)r(,)f
@beginspecial @setspecial @endspecial(622)r(,)g @beginspecial
@setspecial @endspecial(627)r(,)g @beginspecial @setspecial
@endspecial(659)1880 3830 y(READCH,)h @beginspecial @setspecial
@endspecial(622)r(,)f @beginspecial @setspecial @endspecial(659)r(,)g
@beginspecial @setspecial @endspecial(661)1880 3942 y
FJ(REAL)p FQ(,)g @beginspecial @setspecial @endspecial(71)1880
4055 y(Real,)h @beginspecial @setspecial @endspecial(44)q(,)f
@beginspecial @setspecial @endspecial(45)1880 4168 y(Real)h(co)s
(e\016cien)m(t,)g @beginspecial @setspecial @endspecial(147)r(,)f
@beginspecial @setspecial @endspecial(148)1880 4281 y
FJ(REALROOTS)p FQ(,)f @beginspecial @setspecial @endspecial(514)q(,)h
@beginspecial @setspecial @endspecial(515)1880 4394 y
FJ(RED)p 2030 4394 V 34 w(HOM)p 2208 4394 V 34 w(COORDS)p
FQ(,)e @beginspecial @setspecial @endspecial(367)1880
4507 y FJ(REDERR)p FQ(,)h @beginspecial @setspecial @endspecial(189)
1880 4620 y FJ(REDEXPR)p FQ(,)g @beginspecial @setspecial
@endspecial(257)1880 4733 y FJ(REDLOG)p FQ(,)g @beginspecial
@setspecial @endspecial(289)r(,)h @beginspecial @setspecial
@endspecial(495)1880 4846 y FJ(REDUCT)p FQ(,)f @beginspecial
@setspecial @endspecial(146)1880 4959 y(relations)p eop
%%Page: 692 692
692 691 bop 664 299 a @beginspecial @setspecial @endspecial
FQ(692)2553 b FM(INDEX)830 555 y FQ(side,)30 b @beginspecial
@setspecial @endspecial(297)664 668 y(REMAINDER,)h @beginspecial
@setspecial @endspecial(645)664 781 y FJ(REMAINDER)p
FQ(,)d @beginspecial @setspecial @endspecial(139)664
894 y(REMD,)j @beginspecial @setspecial @endspecial(616)r(,)f
@beginspecial @setspecial @endspecial(632)664 1007 y
FJ(REMEMBER)p FQ(,)f @beginspecial @setspecial @endspecial(192)664
1120 y FJ(REMFAC)p FQ(,)g @beginspecial @setspecial @endspecial(116)664
1233 y(REMFLA)m(G,)j @beginspecial @setspecial @endspecial(616)q(,)f
@beginspecial @setspecial @endspecial(630)664 1346 y(REMF)m(ORDER)g
(command,)g @beginspecial @setspecial @endspecial(343)664
1458 y FJ(REMGRASS)p FQ(,)e @beginspecial @setspecial
@endspecial(260)664 1571 y FJ(REMIND)p FQ(,)g @beginspecial
@setspecial @endspecial(212)664 1684 y(REMOB,)i @beginspecial
@setspecial @endspecial(616)q(,)g @beginspecial @setspecial
@endspecial(629)664 1797 y FJ(REMOVE)p FQ(,)e @beginspecial
@setspecial @endspecial(244)664 1910 y FJ(REMOVE)p 958
1910 29 4 v 33 w(COLUMNS)p FQ(,)g @beginspecial @setspecial
@endspecial(403)q(,)h @beginspecial @setspecial @endspecial(407)664
2023 y FJ(REMOVE)p 958 2023 V 33 w(ROWS)p FQ(,)f @beginspecial
@setspecial @endspecial(403)r(,)h @beginspecial @setspecial
@endspecial(407)664 2136 y(REMPR)m(OP)-8 b(,)31 b @beginspecial
@setspecial @endspecial(616)q(,)g @beginspecial @setspecial
@endspecial(630)664 2249 y FJ(REMSYM)p FQ(,)e @beginspecial
@setspecial @endspecial(251)664 2362 y(RENOSUM)h(command,)h
@beginspecial @setspecial @endspecial(340)664 2475 y
FJ(REORDER)p FQ(,)e @beginspecial @setspecial @endspecial(330)664
2588 y FJ(REPART)p FQ(,)g @beginspecial @setspecial @endspecial(80)q(,)
i @beginspecial @setspecial @endspecial(81,)g @beginspecial
@setspecial @endspecial(83)664 2700 y FJ(REPEAT)p FQ(,)e
@beginspecial @setspecial @endspecial(70)q({)p @beginspecial
@setspecial @endspecial(72)q(,)i @beginspecial @setspecial
@endspecial(74)664 2813 y FJ(REPL)p FQ(,)f @beginspecial
@setspecial @endspecial(497)664 2926 y FJ(REPLAST)p FQ(,)f
@beginspecial @setspecial @endspecial(245)664 3039 y
FJ(requirements)p FQ(,)e @beginspecial @setspecial @endspecial(100)664
3152 y(Reserv)m(ed)k(v)-5 b(ariable,)29 b @beginspecial
@setspecial @endspecial(46)q(,)i @beginspecial @setspecial
@endspecial(47)664 3265 y FJ(RESET)p FQ(,)e @beginspecial
@setspecial @endspecial(195)r(,)h @beginspecial @setspecial
@endspecial(243)r(,)g @beginspecial @setspecial @endspecial(505)664
3378 y FJ(RESETREDUCE)p FQ(,)e @beginspecial @setspecial
@endspecial(505)664 3491 y FJ(RESIDUE)p FQ(,)h @beginspecial
@setspecial @endspecial(195)q(,)i @beginspecial @setspecial
@endspecial(507)664 3604 y FJ(residue)p FQ(,)e @beginspecial
@setspecial @endspecial(507)664 3717 y FJ(REST)p FQ(,)h
@beginspecial @setspecial @endspecial(60)664 3830 y FJ(RESTASLIST)p
FQ(,)e @beginspecial @setspecial @endspecial(246)664
3942 y FJ(RESTRICT)p FQ(,)h @beginspecial @setspecial
@endspecial(328)664 4055 y FJ(RESTRICTIONS)p FQ(,)e @beginspecial
@setspecial @endspecial(327)664 4168 y FJ(RESULT)p FQ(,)i
@beginspecial @setspecial @endspecial(536)664 4281 y
FJ(RESULTANT)p FQ(,)f @beginspecial @setspecial @endspecial(140)664
4394 y FJ(RETRY)p FQ(,)h @beginspecial @setspecial @endspecial(174)664
4507 y(RETUNR)830 4620 y(in)g(CODE,)i @beginspecial @setspecial
@endspecial(640)664 4733 y(RETURN,)f @beginspecial @setspecial
@endspecial(620)r(,)g @beginspecial @setspecial @endspecial(637)664
4846 y FJ(RETURN)p FQ(,)f @beginspecial @setspecial @endspecial(72)q({)
p @beginspecial @setspecial @endspecial(74)664 4959 y(RETURN)2470
555 y(in)g(COND,)i @beginspecial @setspecial @endspecial(636)2304
668 y(REVERSE,)f @beginspecial @setspecial @endspecial(651)2304
781 y FJ(REVERSE)p FQ(,)f @beginspecial @setspecial @endspecial(61)2304
894 y FJ(REVGRADLEX)p FQ(,)f @beginspecial @setspecial
@endspecial(389)2304 1007 y(REV)m(GRADLEX)2470 1120 y(term)i(order,)g
@beginspecial @setspecial @endspecial(376)2304 1233 y
FJ(REVPRI)p FQ(,)f @beginspecial @setspecial @endspecial(119)2304
1346 y FJ(RHS)p FQ(,)h @beginspecial @setspecial @endspecial(57)2304
1458 y(RIEMANNCONX)g(command,)h @beginspecial @setspecial
@endspecial(343)2304 1571 y(Riemannian)d(Connections,)i
@beginspecial @setspecial @endspecial(343)2304 1684 y
FJ(RLATAB)p FQ(,)f @beginspecial @setspecial @endspecial(500)2304
1797 y FJ(RLCNF)p FQ(,)g @beginspecial @setspecial @endspecial(501)2304
1910 y FJ(RLDNF)p FQ(,)g @beginspecial @setspecial @endspecial(501)2304
2023 y FJ(RLFI)p FQ(,)g @beginspecial @setspecial @endspecial(195)r(,)h
@beginspecial @setspecial @endspecial(509)2304 2136 y
FJ(RLGQE)p FQ(,)f @beginspecial @setspecial @endspecial(502)2304
2249 y FJ(RLGQEA)p FQ(,)g @beginspecial @setspecial @endspecial(502)
2304 2362 y FJ(RLGSN)p FQ(,)g @beginspecial @setspecial
@endspecial(500)2304 2475 y(Rlisp,)f @beginspecial @setspecial
@endspecial(219)2304 2588 y FJ(RLISP88)p FQ(,)h @beginspecial
@setspecial @endspecial(210)2304 2700 y FJ(RLITAB)p FQ(,)g
@beginspecial @setspecial @endspecial(500)2304 2813 y
FJ(RLNNF)p FQ(,)g @beginspecial @setspecial @endspecial(501)2304
2926 y FJ(RLOPT)p FQ(,)g @beginspecial @setspecial @endspecial(503)2304
3039 y FJ(RLPNF)p FQ(,)g @beginspecial @setspecial @endspecial(501)2304
3152 y FJ(RLQE)p FQ(,)g @beginspecial @setspecial @endspecial(501)2304
3265 y FJ(RLQEA)p FQ(,)g @beginspecial @setspecial @endspecial(502)2304
3378 y FJ(RLREALTIME)p FQ(,)f @beginspecial @setspecial
@endspecial(499)2304 3491 y FJ(RLROOTNO)p FQ(,)g @beginspecial
@setspecial @endspecial(514)2304 3604 y FJ(RLSET)p FQ(,)h
@beginspecial @setspecial @endspecial(497)2304 3717 y
FJ(RLSIMPL)p FQ(,)g @beginspecial @setspecial @endspecial(499)2304
3830 y FJ(RLTAB)p FQ(,)g @beginspecial @setspecial @endspecial(500)2304
3942 y FJ(RLVERBOSE)p FQ(,)f @beginspecial @setspecial
@endspecial(499)2304 4055 y FJ(ROOT)p 2502 4055 V 33
w(OF)p FQ(,)i @beginspecial @setspecial @endspecial(95)q(,)h
@beginspecial @setspecial @endspecial(96)2304 4168 y
FJ(ROOT)p 2502 4168 V 33 w(VAL)p FQ(,)f @beginspecial
@setspecial @endspecial(515)2304 4281 y FJ(ROOTS)p FQ(,)f
@beginspecial @setspecial @endspecial(195)q(,)i @beginspecial
@setspecial @endspecial(513)q({)p @beginspecial @setspecial
@endspecial(515)2304 4394 y FJ(ROOTS)p 2550 4394 V 33
w(AT)p 2679 4394 V 34 w(PREC)p FQ(,)e @beginspecial @setspecial
@endspecial(515)2304 4507 y FJ(ROOTSCOMPLEX)p FQ(,)e
@beginspecial @setspecial @endspecial(515)2304 4620 y
FJ(ROOTSREAL)p FQ(,)h @beginspecial @setspecial @endspecial(515)2304
4733 y FJ(ROUND)p FQ(,)h @beginspecial @setspecial @endspecial(83)2304
4846 y FJ(ROUNDALL)p FQ(,)f @beginspecial @setspecial
@endspecial(149)2304 4959 y FJ(ROUNDBF)p FQ(,)h @beginspecial
@setspecial @endspecial(148)p eop
%%Page: 693 693
693 692 bop 241 299 a @beginspecial @setspecial @endspecial
FM(INDEX)2552 b FQ(693)241 555 y FJ(ROUNDED)p FQ(,)28
b @beginspecial @setspecial @endspecial(46)q(,)j @beginspecial
@setspecial @endspecial(54)q(,)f @beginspecial @setspecial
@endspecial(86)q(,)h @beginspecial @setspecial @endspecial(122)q(,)g
@beginspecial @setspecial @endspecial(148)241 668 y FJ(ROW)p
391 668 29 4 v 33 w(DIM)p FQ(,)f @beginspecial @setspecial
@endspecial(403)q(,)h @beginspecial @setspecial @endspecial(405)241
781 y FJ(ROWS)p 439 781 V 33 w(PIVOT)p FQ(,)e @beginspecial
@setspecial @endspecial(403)r(,)h @beginspecial @setspecial
@endspecial(406)241 894 y(RPLA)m(CA,)g @beginspecial
@setspecial @endspecial(627)241 1007 y(RPLA)m(CD,)h @beginspecial
@setspecial @endspecial(627)241 1120 y(rsetq)f(op)s(erator,)h
@beginspecial @setspecial @endspecial(354)241 1233 y
FJ(RSOLVE)p FQ(,)e @beginspecial @setspecial @endspecial(195)q(,)i
@beginspecial @setspecial @endspecial(519)241 1346 y(Rule)e(lists,)g
@beginspecial @setspecial @endspecial(160)241 1458 y
FJ(RZUT)p FQ(,)g @beginspecial @setspecial @endspecial(554)241
1654 y FJ(S)p FQ(,)h @beginspecial @setspecial @endspecial(471)241
1767 y FJ(s)p 295 1767 V 34 w(i)p FQ(,)g @beginspecial
@setspecial @endspecial(544)241 1880 y FJ(S)p 295 1880
V 34 w(INT)p FQ(,)g @beginspecial @setspecial @endspecial(554)241
1993 y FJ(S)p 295 1993 V 34 w(PART)p FQ(,)f @beginspecial
@setspecial @endspecial(554)241 2106 y(SASSOC,)f @beginspecial
@setspecial @endspecial(651)241 2219 y FJ(SAVEAS)p FQ(,)h
@beginspecial @setspecial @endspecial(113)241 2332 y
FJ(SAVESTRUCTR)p FQ(,)e @beginspecial @setspecial @endspecial(127)241
2445 y(Sa)m(ving)j(an)g(expression,)f @beginspecial @setspecial
@endspecial(125)241 2558 y FJ(SCALAR)p FQ(,)g @beginspecial
@setspecial @endspecial(71)241 2671 y(Scalar,)h @beginspecial
@setspecial @endspecial(53)241 2784 y(SCALEF)-10 b(A)m(CTORS)28
b(op)s(erator,)j @beginspecial @setspecial @endspecial(272)241
2896 y FJ(SCALOP)p FQ(,)e @beginspecial @setspecial @endspecial(463)241
3009 y FJ(SCALVECT)p FQ(,)f @beginspecial @setspecial
@endspecial(259)241 3122 y FJ(SCIENTIFIC)p 727 3122 V
31 w(NOTATION)p FQ(,)h @beginspecial @setspecial @endspecial(44)241
3235 y FJ(SCOPE)p FQ(,)g @beginspecial @setspecial @endspecial(196)241
3348 y(scop)s(e,)h @beginspecial @setspecial @endspecial(633)241
3461 y(scop)s(e)407 3574 y(\015uid,)e @beginspecial @setspecial
@endspecial(633)407 3687 y(\015uid)g(and)i(compiled,)f
@beginspecial @setspecial @endspecial(635)407 3800 y(global,)h
@beginspecial @setspecial @endspecial(633)407 3913 y(lo)s(cal,)g
@beginspecial @setspecial @endspecial(633)241 4026 y(SCOPE)f(function)
407 4138 y FJ(RESETLENGTH)p FQ(,)e @beginspecial @setspecial
@endspecial(523)407 4251 y FJ(SETLENGTH)p FQ(,)h @beginspecial
@setspecial @endspecial(522)241 4364 y(SCOPE)h(option)407
4477 y FJ(INAME)p FQ(,)g @beginspecial @setspecial @endspecial(522)241
4590 y FJ(SD)p FQ(,)h @beginspecial @setspecial @endspecial(472)241
4703 y FJ(SD)p 343 4703 V 34 w(PART)p FQ(,)f @beginspecial
@setspecial @endspecial(554)241 4816 y FJ(SDIV)p FQ(,)g
@beginspecial @setspecial @endspecial(498)241 4929 y
FJ(SEC)p FQ(,)g @beginspecial @setspecial @endspecial(83)q(,)i
@beginspecial @setspecial @endspecial(86)1880 555 y FJ(SECH)p
FQ(,)f @beginspecial @setspecial @endspecial(83)q(,)g
@beginspecial @setspecial @endspecial(86)1880 668 y FJ(SECOND)p
FQ(,)f @beginspecial @setspecial @endspecial(60)1880
781 y(segmen)m(ting)i(expressions,)e @beginspecial @setspecial
@endspecial(357)1880 894 y FJ(SELECT)p FQ(,)g @beginspecial
@setspecial @endspecial(93)1880 1007 y(Selector,)i @beginspecial
@setspecial @endspecial(205)1880 1120 y FJ(SEMANTIC)p
FQ(,)e @beginspecial @setspecial @endspecial(470)1880
1233 y(Semicolon,)h @beginspecial @setspecial @endspecial(63)1880
1346 y FJ(SEMILINEAR)p FQ(,)e @beginspecial @setspecial
@endspecial(330)1880 1458 y(SET,)i @beginspecial @setspecial
@endspecial(616)q(,)h @beginspecial @setspecial @endspecial(634)1880
1571 y FJ(SET)p FQ(,)f @beginspecial @setspecial @endspecial(65)q(,)h
@beginspecial @setspecial @endspecial(92)1880 1684 y
FJ(SET)p 2030 1684 V 34 w(COFRAMING)p FQ(,)d @beginspecial
@setspecial @endspecial(326)1880 1797 y FJ(setdiff)p
FQ(,)h @beginspecial @setspecial @endspecial(527)1880
1910 y FJ(SETMOD)p FQ(,)g @beginspecial @setspecial @endspecial(149)
1880 2023 y FJ(SETP)p FQ(,)h @beginspecial @setspecial
@endspecial(249)1880 2136 y(SETQ,)g @beginspecial @setspecial
@endspecial(616)q(,)h @beginspecial @setspecial @endspecial(618)q(,)g
@beginspecial @setspecial @endspecial(635)1880 2249 y
FJ(SETS)p FQ(,)f @beginspecial @setspecial @endspecial(196)q(,)h
@beginspecial @setspecial @endspecial(525)1880 2362 y(SGN)2046
2475 y(indeterminate)f(sign,)f @beginspecial @setspecial
@endspecial(338)1880 2588 y FJ(SHARE)p FQ(,)h @beginspecial
@setspecial @endspecial(204)1880 2700 y FJ(Shi)p FQ(,)g
@beginspecial @setspecial @endspecial(544)1880 2813 y
FJ(SHORTEST)p FQ(,)f @beginspecial @setspecial @endspecial(267)1880
2926 y FJ(SHOW)p FQ(,)h @beginspecial @setspecial @endspecial(255)1880
3039 y FJ(SHOW)p 2078 3039 V 34 w(GRID)p FQ(,)f @beginspecial
@setspecial @endspecial(373)1880 3152 y FJ(SHOWRULES)p
FQ(,)g @beginspecial @setspecial @endspecial(165)1880
3265 y FJ(SHOWTIME)p FQ(,)g @beginspecial @setspecial
@endspecial(78)1880 3378 y FJ(SHUT)p FQ(,)h @beginspecial
@setspecial @endspecial(169)q({)p @beginspecial @setspecial
@endspecial(171)1880 3491 y FJ(SI)p FQ(,)g @beginspecial
@setspecial @endspecial(471)1880 3604 y FJ(Si)p FQ(,)g
@beginspecial @setspecial @endspecial(544)1880 3717 y(Side)f(e\013ect,)
k @beginspecial @setspecial @endspecial(58)1880 3830
y(side)d(relations,)f @beginspecial @setspecial @endspecial(297)1880
3942 y FJ(SIGN)p FQ(,)h @beginspecial @setspecial @endspecial(83)1880
4055 y FJ(SIMPLEX)p FQ(,)f @beginspecial @setspecial
@endspecial(404)q(,)i @beginspecial @setspecial @endspecial(412)1880
4168 y(Simplex)d(Algorithm,)i @beginspecial @setspecial
@endspecial(412)1880 4281 y(Simpli\014cation,)d @beginspecial
@setspecial @endspecial(54)q(,)k @beginspecial @setspecial
@endspecial(111)1880 4394 y FJ(SIMPLIFY)p FQ(,)e @beginspecial
@setspecial @endspecial(253)1880 4507 y FJ(simplify)p
2270 4507 V 33 w(combinatorial)p FQ(,)e @beginspecial
@setspecial @endspecial(604)1880 4620 y FJ(simplify)p
2270 4620 V 33 w(gamma)p FQ(,)i @beginspecial @setspecial
@endspecial(604)1880 4733 y FJ(simplify)p 2270 4733 V
33 w(gamma2)p FQ(,)g @beginspecial @setspecial @endspecial(604)1880
4846 y FJ(simplify)p 2270 4846 V 33 w(gamman)p FQ(,)g
@beginspecial @setspecial @endspecial(605)1880 4959 y
FJ(SIMPSYS)p FQ(,)g @beginspecial @setspecial @endspecial(536)p
eop
%%Page: 694 694
694 693 bop 664 299 a @beginspecial @setspecial @endspecial
FQ(694)2553 b FM(INDEX)664 555 y FJ(SIN)p FQ(,)30 b @beginspecial
@setspecial @endspecial(83)q(,)g @beginspecial @setspecial
@endspecial(86)664 668 y FJ(SINH)p FQ(,)g @beginspecial
@setspecial @endspecial(83)q(,)g @beginspecial @setspecial
@endspecial(86)664 781 y FJ(SixJSymbol)p FQ(,)e @beginspecial
@setspecial @endspecial(543)664 894 y FJ(size)p FQ(,)i
@beginspecial @setspecial @endspecial(372)664 1007 y
FJ(SMACRO)p FQ(,)f @beginspecial @setspecial @endspecial(203)664
1120 y FJ(smithex)p FQ(,)g @beginspecial @setspecial
@endspecial(432)664 1233 y FJ(smithex)p 1006 1233 29
4 v 33 w(int)p FQ(,)g @beginspecial @setspecial @endspecial(432)664
1346 y FJ(SolidHarmonicY)p FQ(,)e @beginspecial @setspecial
@endspecial(543)664 1458 y FJ(SOLVE)p FQ(,)i @beginspecial
@setspecial @endspecial(94)q(,)i @beginspecial @setspecial
@endspecial(95)q(,)f @beginspecial @setspecial @endspecial(99)664
1571 y(SOL)-10 b(VE)29 b(pac)m(k)-5 b(age)830 1684 y(with)29
b(R)m(OOTS)h(pac)m(k)-5 b(age,)32 b @beginspecial @setspecial
@endspecial(513)664 1797 y FJ(SOLVESINGULAR)p FQ(,)27
b @beginspecial @setspecial @endspecial(99)664 1910 y
FJ(SORTLIST)p FQ(,)i @beginspecial @setspecial @endspecial(251)664
2023 y FJ(SORTNUMLIST)p FQ(,)f @beginspecial @setspecial
@endspecial(251)664 2136 y FJ(SORTOUTODE)p FQ(,)g @beginspecial
@setspecial @endspecial(450)664 2249 y(SP)-8 b(A)m(CEDIM)31
b(command,)f @beginspecial @setspecial @endspecial(335)664
2362 y FJ(SPADD)p 910 2362 V 33 w(COLUMNS)p FQ(,)f @beginspecial
@setspecial @endspecial(532)664 2475 y FJ(SPADD)p 910
2475 V 33 w(ROWS)p FQ(,)h @beginspecial @setspecial @endspecial(532)664
2588 y FJ(SPADD)p 910 2588 V 33 w(TO)p 1039 2588 V 34
w(COLUMNS)p FQ(,)f @beginspecial @setspecial @endspecial(532)664
2700 y FJ(SPADD)p 910 2700 V 33 w(TO)p 1039 2700 V 34
w(ROWS)p FQ(,)g @beginspecial @setspecial @endspecial(532)664
2813 y FJ(SPARSE)p FQ(,)g @beginspecial @setspecial @endspecial(531)664
2926 y FJ(SPARSE,)46 b(Sparse)g(matrices)p FQ(,)28 b
@beginspecial @setspecial @endspecial(531)664 3039 y
FJ(SPARSEMATP)p FQ(,)g @beginspecial @setspecial @endspecial(533)664
3152 y FJ(SPAUGMENT)p 1102 3152 V 32 w(COLUMNS)p FQ(,)h
@beginspecial @setspecial @endspecial(532)664 3265 y
FJ(SPBAND)p 958 3265 V 33 w(MATRIX)p FQ(,)g @beginspecial
@setspecial @endspecial(532)664 3378 y FJ(SPBLOCK)p 1006
3378 V 33 w(MATRIX)p FQ(,)g @beginspecial @setspecial
@endspecial(532)664 3491 y FJ(SPCHAR)p 958 3491 V 33
w(MATRIX)p FQ(,)g @beginspecial @setspecial @endspecial(532)664
3604 y FJ(SPCHAR)p 958 3604 V 33 w(POLY)p FQ(,)g @beginspecial
@setspecial @endspecial(532)664 3717 y FJ(SPCHOLESKY)p
FQ(,)f @beginspecial @setspecial @endspecial(532)664
3830 y FJ(SPCOEFF)p 1006 3830 V 33 w(MATRIX)p FQ(,)h
@beginspecial @setspecial @endspecial(532)664 3942 y
FJ(SPCOL)p 910 3942 V 33 w(DIM)p FQ(,)h @beginspecial
@setspecial @endspecial(532)664 4055 y FJ(SPCOMPANION)p
FQ(,)e @beginspecial @setspecial @endspecial(532)664
4168 y FJ(SPCOPY)p 958 4168 V 33 w(INTO)p FQ(,)h @beginspecial
@setspecial @endspecial(532)664 4281 y FJ(SPDE)p FQ(,)h
@beginspecial @setspecial @endspecial(196)q(,)h @beginspecial
@setspecial @endspecial(535)664 4394 y FJ(SPDIAGONAL)p
FQ(,)d @beginspecial @setspecial @endspecial(532)664
4507 y FJ(SPECFN)p FQ(,)h @beginspecial @setspecial @endspecial(85)q(,)
i @beginspecial @setspecial @endspecial(196)q(,)f @beginspecial
@setspecial @endspecial(539)664 4620 y FJ(SPECFN2)p FQ(,)f
@beginspecial @setspecial @endspecial(196)q(,)i @beginspecial
@setspecial @endspecial(545)664 4733 y FJ(SPEXTEND)p
FQ(,)e @beginspecial @setspecial @endspecial(532)664
4846 y FJ(SPFIND)p 958 4846 V 33 w(COMPANION)p FQ(,)f
@beginspecial @setspecial @endspecial(532)664 4959 y
FJ(SPGET)p 910 4959 V 33 w(COLUMNS)p FQ(,)h @beginspecial
@setspecial @endspecial(532)2304 555 y FJ(SPGET)p 2550
555 V 33 w(ROWS)p FQ(,)g @beginspecial @setspecial @endspecial(532)2304
668 y FJ(SPGRAM)p 2598 668 V 33 w(SCHMIDT)p FQ(,)f @beginspecial
@setspecial @endspecial(532)2304 781 y(spherical)g(co)s(ordinates,)j
@beginspecial @setspecial @endspecial(453)2304 894 y
FJ(SphericalHarmonicY)p FQ(,)25 b @beginspecial @setspecial
@endspecial(543)2304 1007 y FJ(SPHERMITIAN)p 2838 1007
V 31 w(TP)p FQ(,)30 b @beginspecial @setspecial @endspecial(532)2304
1120 y FJ(SPHESSIAN)p FQ(,)e @beginspecial @setspecial
@endspecial(532)2304 1233 y FJ(SPJACOBIAN)p FQ(,)g @beginspecial
@setspecial @endspecial(532)2304 1346 y FJ(SPJORDAN)p
2694 1346 V 32 w(BLOCK)p FQ(,)h @beginspecial @setspecial
@endspecial(532)2304 1458 y FJ(SPLIT)p 2550 1458 V 33
w(FIELD)p FQ(,)g @beginspecial @setspecial @endspecial(241)2304
1571 y FJ(SPLITPLUSMINUS)p FQ(,)e @beginspecial @setspecial
@endspecial(258)2304 1684 y FJ(SPLITTERMS)p FQ(,)h @beginspecial
@setspecial @endspecial(257)2304 1797 y FJ(SPLU)p 2502
1797 V 33 w(DECOM)p FQ(,)h @beginspecial @setspecial
@endspecial(532)2304 1910 y FJ(SPMAKE)p 2598 1910 V 33
w(IDENTITY)p FQ(,)f @beginspecial @setspecial @endspecial(532)2304
2023 y FJ(SPMATRIX)p 2694 2023 V 32 w(AUGMENT)p FQ(,)h
@beginspecial @setspecial @endspecial(532)2304 2136 y
FJ(SPMATRIX)p 2694 2136 V 32 w(STACK)p FQ(,)g @beginspecial
@setspecial @endspecial(532)2304 2249 y FJ(SPMINOR)p
FQ(,)g @beginspecial @setspecial @endspecial(532)2304
2362 y FJ(SPMULT)p 2598 2362 V 33 w(COLUMNS)p FQ(,)f
@beginspecial @setspecial @endspecial(532)2304 2475 y
FJ(SPMULT)p 2598 2475 V 33 w(ROWS)p FQ(,)h @beginspecial
@setspecial @endspecial(532)2304 2588 y FJ(SPPIVOT)p
FQ(,)g @beginspecial @setspecial @endspecial(532)2304
2700 y FJ(SPPSEUDO)p 2694 2700 V 32 w(INVERSE)p FQ(,)g
@beginspecial @setspecial @endspecial(532)2304 2813 y(SPREAD)2470
2926 y(function)g(t)m(yp)s(e,)i @beginspecial @setspecial
@endspecial(621)2304 3039 y FJ(SPREMOVE)p 2694 3039 V
32 w(COLUMNS)p FQ(,)e @beginspecial @setspecial @endspecial(532)2304
3152 y FJ(SPREMOVE)p 2694 3152 V 32 w(ROWS)p FQ(,)h @beginspecial
@setspecial @endspecial(532)2304 3265 y FJ(SPROW)p 2550
3265 V 33 w(DIM)p FQ(,)g @beginspecial @setspecial @endspecial(532)2304
3378 y FJ(SPROWS)p 2598 3378 V 33 w(PIVOT)p FQ(,)f @beginspecial
@setspecial @endspecial(532)2304 3491 y FJ(SPSTACK)p
2646 3491 V 32 w(ROWS)p FQ(,)h @beginspecial @setspecial
@endspecial(532)2304 3604 y FJ(SPSUB)p 2550 3604 V 33
w(MATRIX)p FQ(,)f @beginspecial @setspecial @endspecial(532)2304
3717 y FJ(SPSWAP)p 2598 3717 V 33 w(COLUMNS)p FQ(,)f
@beginspecial @setspecial @endspecial(532)2304 3830 y
FJ(SPSWAP)p 2598 3830 V 33 w(ENTRIES)p FQ(,)g @beginspecial
@setspecial @endspecial(532)2304 3942 y FJ(SPSWAP)p 2598
3942 V 33 w(ROWS)p FQ(,)h @beginspecial @setspecial @endspecial(532)
2304 4055 y FJ(SpTT)p FQ(,)g @beginspecial @setspecial
@endspecial(589)2304 4168 y FJ(SPUR)p FQ(,)g @beginspecial
@setspecial @endspecial(216)2304 4281 y FJ(SQFRF)p FQ(,)g
@beginspecial @setspecial @endspecial(517)2304 4394 y
FJ(SQRDIST)p FQ(,)g @beginspecial @setspecial @endspecial(367)2304
4507 y FJ(SQRT)p FQ(,)g @beginspecial @setspecial @endspecial(83)q(,)i
@beginspecial @setspecial @endspecial(86)2304 4620 y
FJ(SQUAREP)p FQ(,)e @beginspecial @setspecial @endspecial(404)q(,)h
@beginspecial @setspecial @endspecial(533)2304 4733 y
FJ(STACK)p 2550 4733 V 33 w(ROWS)p FQ(,)f @beginspecial
@setspecial @endspecial(403)r(,)h @beginspecial @setspecial
@endspecial(407)2304 4846 y(standard)f(devices,)i @beginspecial
@setspecial @endspecial(655)2304 4959 y(Standard)e(form,)h
@beginspecial @setspecial @endspecial(205)p eop
%%Page: 695 695
695 694 bop 241 299 a @beginspecial @setspecial @endspecial
FM(INDEX)2552 b FQ(695)241 555 y(standard)29 b(input,)g
@beginspecial @setspecial @endspecial(658)241 668 y FJ(Standard)45
b(Lisp)i(Report)p FQ(,)29 b @beginspecial @setspecial
@endspecial(613)241 781 y(standard)g(output,)i @beginspecial
@setspecial @endspecial(659)241 894 y(Standard)e(quotien)m(t,)i
@beginspecial @setspecial @endspecial(205)241 1007 y(ST)-8
b(AND)m(ARD-LISP)g(,)31 b @beginspecial @setspecial @endspecial(660)241
1120 y FJ(STATE)p FQ(,)e @beginspecial @setspecial @endspecial(463)241
1233 y(Statemen)m(t,)j @beginspecial @setspecial @endspecial(63)241
1346 y(Stirling)27 b(n)m(um)m(b)s(ers,)i @beginspecial
@setspecial @endspecial(542)241 1458 y FJ(Stirling1)p
FQ(,)f @beginspecial @setspecial @endspecial(542)241
1571 y FJ(Stirling2)p FQ(,)g @beginspecial @setspecial
@endspecial(542)241 1684 y(String,)h @beginspecial @setspecial
@endspecial(47)241 1797 y(string,)g @beginspecial @setspecial
@endspecial(617)241 1910 y(string)407 2023 y(output,)h
@beginspecial @setspecial @endspecial(628)241 2136 y(STRINGP)-8
b(,)30 b @beginspecial @setspecial @endspecial(625)241
2249 y FJ(STRUCTR)p FQ(,)e @beginspecial @setspecial
@endspecial(126)r(,)i @beginspecial @setspecial @endspecial(127)241
2362 y FJ(STRUCTURE)p 679 2362 29 4 v 32 w(EQUATIONS)p
FQ(,)e @beginspecial @setspecial @endspecial(327)q(,)j
@beginspecial @setspecial @endspecial(330)241 2475 y(structures,)f
@beginspecial @setspecial @endspecial(619)241 2588 y(Structuring,)e
@beginspecial @setspecial @endspecial(111)241 2700 y(Struv)m(e)i
(functions,)f @beginspecial @setspecial @endspecial(543)241
2813 y FJ(StruveH)p FQ(,)f @beginspecial @setspecial
@endspecial(543)241 2926 y(Struv)m(eH)i(transform,)g
@beginspecial @setspecial @endspecial(307)241 3039 y
FJ(StruveL)p FQ(,)e @beginspecial @setspecial @endspecial(543)241
3152 y FJ(SUB)p FQ(,)h @beginspecial @setspecial @endspecial(57)q(,)i
@beginspecial @setspecial @endspecial(151)q(,)g @beginspecial
@setspecial @endspecial(499)241 3265 y(SUB1,)g @beginspecial
@setspecial @endspecial(646)241 3378 y FJ(SUB)p 391 3378
V 33 w(MATRIX)p FQ(,)e @beginspecial @setspecial @endspecial(403)241
3491 y(SUBLIS,)h @beginspecial @setspecial @endspecial(652)241
3604 y FJ(SUBMAT)p FQ(,)f @beginspecial @setspecial @endspecial(262)241
3717 y(SUBR)m(OUTINE,)h @beginspecial @setspecial @endspecial(357)241
3830 y FJ(subset)p FQ(,)f @beginspecial @setspecial @endspecial(528)241
3942 y FJ(subset)p 535 3942 V 32 w(eq)p FQ(,)h @beginspecial
@setspecial @endspecial(528)241 4055 y(SUBST,)g @beginspecial
@setspecial @endspecial(652)241 4168 y(Substitution,)e
@beginspecial @setspecial @endspecial(151)241 4281 y
FJ(SUCH)46 b(THAT)p FQ(,)30 b @beginspecial @setspecial
@endspecial(156)241 4394 y FJ(SUdim)p FQ(,)f @beginspecial
@setspecial @endspecial(589)241 4507 y FJ(SUM)p FQ(,)g
@beginspecial @setspecial @endspecial(67)q(,)i @beginspecial
@setspecial @endspecial(68)q(,)f @beginspecial @setspecial
@endspecial(196)r(,)g @beginspecial @setspecial @endspecial(547)241
4620 y(SUM)g(op)s(erator,)h @beginspecial @setspecial
@endspecial(547)241 4733 y FJ(SUM-SQ)p FQ(,)e @beginspecial
@setspecial @endspecial(548)241 4846 y FJ(sumrecursion)p
FQ(,)e @beginspecial @setspecial @endspecial(601)241
4959 y FJ(sumtohyper)p FQ(,)h @beginspecial @setspecial
@endspecial(603)1880 555 y FJ(SUMVECT)p FQ(,)h @beginspecial
@setspecial @endspecial(259)1880 668 y FJ(SUPPRESS)p
FQ(,)g @beginspecial @setspecial @endspecial(255)1880
781 y FJ(surface)p FQ(,)g @beginspecial @setspecial @endspecial(372)
1880 894 y FJ(SUSY2)p FQ(,)h @beginspecial @setspecial
@endspecial(551)1880 1007 y FJ(SVD)p FQ(,)g @beginspecial
@setspecial @endspecial(404)r(,)g @beginspecial @setspecial
@endspecial(412)q(,)h @beginspecial @setspecial @endspecial(532)1880
1120 y FJ(SVEC)p FQ(,)f @beginspecial @setspecial @endspecial(454)1880
1233 y FJ(SWAP)p 2078 1233 V 34 w(COLUMNS)p FQ(,)e @beginspecial
@setspecial @endspecial(403)r(,)i @beginspecial @setspecial
@endspecial(406)1880 1346 y FJ(SWAP)p 2078 1346 V 34
w(ENTRIES)p FQ(,)e @beginspecial @setspecial @endspecial(403)r(,)i
@beginspecial @setspecial @endspecial(406)1880 1458 y
FJ(SWAP)p 2078 1458 V 34 w(ROWS)p FQ(,)f @beginspecial
@setspecial @endspecial(403)r(,)h @beginspecial @setspecial
@endspecial(406)1880 1571 y(Switc)m(h,)g @beginspecial
@setspecial @endspecial(76)q(,)h @beginspecial @setspecial
@endspecial(77)1880 1684 y FJ(SWITCHES)p FQ(,)e @beginspecial
@setspecial @endspecial(243)1880 1797 y FJ(SWITCHORG)p
FQ(,)g @beginspecial @setspecial @endspecial(243)1880
1910 y FJ(SYMB)p 2078 1910 V 34 w(TO)p 2208 1910 V 34
w(ALG)p FQ(,)g @beginspecial @setspecial @endspecial(256)1880
2023 y FJ(SYMBOL)p 2174 2023 V 33 w(MATRIX)p FQ(,)g @beginspecial
@setspecial @endspecial(330)1880 2136 y FJ(SYMBOL)p 2174
2136 V 33 w(RELATIONS)p FQ(,)f @beginspecial @setspecial
@endspecial(330)1880 2249 y FJ(SYMBOLIC)p FQ(,)h @beginspecial
@setspecial @endspecial(197)1880 2362 y(Sym)m(b)s(olic)g(mo)s(de,)h
@beginspecial @setspecial @endspecial(197)q(,)h @beginspecial
@setspecial @endspecial(199)q(,)g @beginspecial @setspecial
@endspecial(203)q(,)2213 2475 y @beginspecial @setspecial
@endspecial(204)1880 2588 y(Sym)m(b)s(olic)e(pro)s(cedure,)g
@beginspecial @setspecial @endspecial(202)1880 2700 y
FJ(SYMDIFF)p FQ(,)g @beginspecial @setspecial @endspecial(249)1880
2813 y FJ(SYMLINE)p FQ(,)g @beginspecial @setspecial
@endspecial(367)1880 2926 y FJ(SYMMETRIC)p FQ(,)g @beginspecial
@setspecial @endspecial(106)q(,)h @beginspecial @setspecial
@endspecial(320)r(,)g @beginspecial @setspecial @endspecial(409)1880
3039 y FJ(SYMMETRICP)p FQ(,)e @beginspecial @setspecial
@endspecial(404)r(,)i @beginspecial @setspecial @endspecial(533)1880
3152 y FJ(SYMMETRIZE)p FQ(,)e @beginspecial @setspecial
@endspecial(251)1880 3265 y FJ(SYMMETRY)p FQ(,)h @beginspecial
@setspecial @endspecial(196)q(,)i @beginspecial @setspecial
@endspecial(557)1880 3378 y FJ(symmetrybasis)p FQ(,)c
@beginspecial @setspecial @endspecial(558)1880 3491 y
FJ(symmetrybasispart)p FQ(,)f @beginspecial @setspecial
@endspecial(558)1880 3604 y FJ(SYMPOINT)p FQ(,)j @beginspecial
@setspecial @endspecial(367)1880 3717 y FJ(SYMTREE)p
FQ(,)g @beginspecial @setspecial @endspecial(320)1880
3830 y FJ(SYSTEM)p FQ(,)g @beginspecial @setspecial @endspecial(327)
1880 4026 y FJ(T)p FQ(,)i @beginspecial @setspecial @endspecial(47)1880
4138 y(T)2046 4251 y(cannot)g(b)s(e)f(c)m(hanged,)h @beginspecial
@setspecial @endspecial(634)r(,)f @beginspecial @setspecial
@endspecial(635)r(,)2213 4364 y @beginspecial @setspecial
@endspecial(661)1880 4477 y(T)g(\(global\),)h @beginspecial
@setspecial @endspecial(619)q(,)g @beginspecial @setspecial
@endspecial(622)q(,)g @beginspecial @setspecial @endspecial(661)1880
4590 y FJ(TABLEAU)p FQ(,)e @beginspecial @setspecial
@endspecial(329)1880 4703 y FJ(TAN)p FQ(,)h @beginspecial
@setspecial @endspecial(83)q(,)h @beginspecial @setspecial
@endspecial(86)q(,)f @beginspecial @setspecial @endspecial(90)1880
4816 y(tangen)m(t)i(v)m(ector,)g @beginspecial @setspecial
@endspecial(336)1880 4929 y FJ(TANH)p FQ(,)e @beginspecial
@setspecial @endspecial(83)q(,)g @beginspecial @setspecial
@endspecial(86)p eop
%%Page: 696 696
696 695 bop 664 299 a @beginspecial @setspecial @endspecial
FQ(696)2553 b FM(INDEX)664 555 y FJ(TAYLOR)p FQ(,)29
b @beginspecial @setspecial @endspecial(196)q(,)i @beginspecial
@setspecial @endspecial(561)664 668 y(T)-8 b(A)g(YLOR)31
b(pac)m(k)-5 b(age,)32 b @beginspecial @setspecial @endspecial(561)664
781 y(T)-8 b(a)m(ylor)31 b(Series,)e @beginspecial @setspecial
@endspecial(561)664 894 y(T)-8 b(a)m(ylor)31 b(series)830
1007 y(arithmetic,)f @beginspecial @setspecial @endspecial(563)830
1120 y(di\013eren)m(tiation,)g @beginspecial @setspecial
@endspecial(564)830 1233 y(in)m(tegration,)h @beginspecial
@setspecial @endspecial(564)830 1346 y(rev)m(ersion,)f
@beginspecial @setspecial @endspecial(564)830 1458 y(substitution,)f
@beginspecial @setspecial @endspecial(564)664 1571 y(T)-8
b(A)g(YLORA)m(UTOCOMBINE)996 1684 y(switc)m(h,)30 b @beginspecial
@setspecial @endspecial(564)664 1797 y(T)-8 b(A)g(YLORA)m(UTOEXP)g(AND)
32 b(switc)m(h,)996 1910 y @beginspecial @setspecial
@endspecial(564)r(,)e @beginspecial @setspecial @endspecial(565)664
2023 y FJ(TAYLORCOMBINE)p FQ(,)d @beginspecial @setspecial
@endspecial(563)664 2136 y FJ(TAYLORKEEPORIGINAL)p FQ(,)f
@beginspecial @setspecial @endspecial(563)664 2249 y(T)-8
b(A)g(YLORKEEPORIGINAL)996 2362 y(switc)m(h,)30 b @beginspecial
@setspecial @endspecial(562)r(,)g @beginspecial @setspecial
@endspecial(565)664 2475 y(T)-8 b(A)g(YLORPRINTORDER)30
b(switc)m(h,)996 2588 y @beginspecial @setspecial @endspecial(565)664
2700 y(T)-8 b(A)g(YLORPRINTTERMS)996 2813 y(v)j(ariable,)30
b @beginspecial @setspecial @endspecial(562)664 2926
y FJ(TAYLORSERIESP)p FQ(,)d @beginspecial @setspecial
@endspecial(563)664 3039 y FJ(TAYLORTEMPLATE)p FQ(,)g
@beginspecial @setspecial @endspecial(563)664 3152 y
FJ(TAYLORTOSTANDARD)p FQ(,)f @beginspecial @setspecial
@endspecial(563)664 3265 y FJ(TCLEAR)p FQ(,)j @beginspecial
@setspecial @endspecial(266)664 3378 y(templates,)i @beginspecial
@setspecial @endspecial(358)664 3491 y FJ(TENSOP)p FQ(,)e
@beginspecial @setspecial @endspecial(463)664 3604 y
FJ(TENSOR)p FQ(,)g @beginspecial @setspecial @endspecial(266)664
3717 y(tensor)i(pro)s(duct,)e @beginspecial @setspecial
@endspecial(410)664 3830 y FJ(terminal)p FQ(,)g @beginspecial
@setspecial @endspecial(372)664 3942 y(T)-8 b(erminator,)30
b @beginspecial @setspecial @endspecial(63)664 4055 y(TERPRI,)g
@beginspecial @setspecial @endspecial(656)q(,)h @beginspecial
@setspecial @endspecial(659)664 4168 y FJ(TESTBOOL)p
FQ(,)e @beginspecial @setspecial @endspecial(280)664
4281 y FJ(TEX)p FQ(,)h @beginspecial @setspecial @endspecial(577)664
4394 y FJ(TEXBREAK)p FQ(,)f @beginspecial @setspecial
@endspecial(577)664 4507 y FJ(TEXINDENT)p FQ(,)f @beginspecial
@setspecial @endspecial(577)664 4620 y FJ(TeXitem)p FQ(,)h
@beginspecial @setspecial @endspecial(579)664 4733 y
FJ(TeXlet)p FQ(,)g @beginspecial @setspecial @endspecial(578)664
4846 y FJ(TeXsetbreak)p FQ(,)f @beginspecial @setspecial
@endspecial(578)664 4959 y FJ(THIRD)p FQ(,)h @beginspecial
@setspecial @endspecial(60)2304 555 y FJ(ThreeJSymbol)p
FQ(,)e @beginspecial @setspecial @endspecial(543)2304
668 y FJ(TIME)p FQ(,)i @beginspecial @setspecial @endspecial(76)2304
781 y(TIMES,)h @beginspecial @setspecial @endspecial(646)2304
894 y(TIMES2,)g @beginspecial @setspecial @endspecial(646)2304
1007 y FJ(title)p FQ(,)f @beginspecial @setspecial @endspecial(372)2304
1120 y FJ(TOEPLITZ)p FQ(,)f @beginspecial @setspecial
@endspecial(404)r(,)i @beginspecial @setspecial @endspecial(410)2304
1233 y FJ(togamma)p FQ(,)f @beginspecial @setspecial
@endspecial(603)2304 1346 y FJ(TORDER)p FQ(,)g @beginspecial
@setspecial @endspecial(376)2304 1458 y FJ(TORSION)p
FQ(,)g @beginspecial @setspecial @endspecial(329)2304
1571 y FJ(TP)p FQ(,)h @beginspecial @setspecial @endspecial(181)2304
1684 y FJ(TPMAT)p FQ(,)f @beginspecial @setspecial @endspecial(262)2304
1797 y FJ(TPS)p FQ(,)h @beginspecial @setspecial @endspecial(196)q(,)h
@beginspecial @setspecial @endspecial(567)2304 1910 y
FJ(TRA)p FQ(,)f @beginspecial @setspecial @endspecial(233)2304
2023 y FJ(TRACE)p FQ(,)f @beginspecial @setspecial @endspecial(181)2304
2136 y FJ(TRACEFPS)p FQ(,)f @beginspecial @setspecial
@endspecial(350)2304 2249 y(tracing)2470 2362 y(EX)m(CALC,)i
@beginspecial @setspecial @endspecial(342)2304 2475 y
FJ(TRAD)p FQ(,)f @beginspecial @setspecial @endspecial(555)2304
2588 y FJ(TRANSFORM)p FQ(,)f @beginspecial @setspecial
@endspecial(328)2304 2700 y FJ(TRFAC)p FQ(,)h @beginspecial
@setspecial @endspecial(136)2304 2813 y FJ(TRGROEB)p
FQ(,)g @beginspecial @setspecial @endspecial(382)2304
2926 y FJ(TRGROEB1)p FQ(,)f @beginspecial @setspecial
@endspecial(382)2304 3039 y FJ(TRGROEBS)p FQ(,)g @beginspecial
@setspecial @endspecial(382)2304 3152 y FJ(TRI)p FQ(,)i
@beginspecial @setspecial @endspecial(196)q(,)h @beginspecial
@setspecial @endspecial(577)2304 3265 y(TRI)2470 3378
y(page-width,)f @beginspecial @setspecial @endspecial(578)2470
3491 y(tolerance,)h @beginspecial @setspecial @endspecial(578)2304
3604 y FJ(TRIANG)p 2598 3604 29 4 v 33 w(ADJOINT)p FQ(,)d
@beginspecial @setspecial @endspecial(404)r(,)i @beginspecial
@setspecial @endspecial(412)2304 3717 y FJ(TRIGEXPAND)p
FQ(,)e @beginspecial @setspecial @endspecial(258)2304
3830 y FJ(trigfactorize)p FQ(,)f @beginspecial @setspecial
@endspecial(585)2304 3942 y FJ(TRIGFORM)p FQ(,)h @beginspecial
@setspecial @endspecial(97)2304 4055 y FJ(triggcd)p FQ(,)h
@beginspecial @setspecial @endspecial(586)2304 4168 y
FJ(trigonometric)p 2934 4168 V 31 w(base)p FQ(,)g @beginspecial
@setspecial @endspecial(446)2304 4281 y FJ(TRIGREDUCE)p
FQ(,)f @beginspecial @setspecial @endspecial(258)2304
4394 y FJ(TRIGSIMP)p FQ(,)g @beginspecial @setspecial
@endspecial(85)q(,)j @beginspecial @setspecial @endspecial(196)q(,)g
@beginspecial @setspecial @endspecial(583)2304 4507 y
FJ(trigsimp)p FQ(,)d @beginspecial @setspecial @endspecial(584)2304
4620 y(trigsimp)2470 4733 y(com)m(bine,)i @beginspecial
@setspecial @endspecial(584)2470 4846 y(compact,)i @beginspecial
@setspecial @endspecial(584)2470 4959 y(cos,)f @beginspecial
@setspecial @endspecial(584)p eop
%%Page: 697 697
697 696 bop 241 299 a @beginspecial @setspecial @endspecial
FM(INDEX)2552 b FQ(697)407 555 y(cosh,)31 b @beginspecial
@setspecial @endspecial(584)407 668 y(expand,)f @beginspecial
@setspecial @endspecial(584)407 781 y(exp)s(on,)g @beginspecial
@setspecial @endspecial(584)407 894 y(h)m(yp,)g @beginspecial
@setspecial @endspecial(584)407 1007 y(k)m(eepalltrig,)g
@beginspecial @setspecial @endspecial(584)407 1120 y(sin,)f
@beginspecial @setspecial @endspecial(584)407 1233 y(sinh,)f
@beginspecial @setspecial @endspecial(584)407 1346 y(trig,)i
@beginspecial @setspecial @endspecial(584)241 1458 y
FJ(TRUE)p FQ(,)f @beginspecial @setspecial @endspecial(497)241
1571 y(truncated)h(p)s(o)m(w)m(er)h(series,)f @beginspecial
@setspecial @endspecial(567)241 1684 y FJ(TSYM)p FQ(,)f
@beginspecial @setspecial @endspecial(266)241 1797 y(TVECTOR)g
(command,)h @beginspecial @setspecial @endspecial(334)241
1993 y(UNFLUID,)h @beginspecial @setspecial @endspecial(616)r(,)f
@beginspecial @setspecial @endspecial(635)241 2106 y
FJ(UNION)p FQ(,)f @beginspecial @setspecial @endspecial(249)241
2219 y FJ(union)p FQ(,)g @beginspecial @setspecial @endspecial(526)241
2332 y FJ(UNITMAT)p FQ(,)f @beginspecial @setspecial
@endspecial(260)241 2445 y FJ(UNTIL)p FQ(,)h @beginspecial
@setspecial @endspecial(67)241 2558 y(UPBV,)i @beginspecial
@setspecial @endspecial(640)241 2671 y FJ(UPPER)p 487
2671 29 4 v 33 w(MATRIX)p FQ(,)e @beginspecial @setspecial
@endspecial(409)241 2784 y(User)h(pac)m(k)-5 b(ages,)33
b @beginspecial @setspecial @endspecial(193)241 2979
y(v)-5 b(alues,)30 b @beginspecial @setspecial @endspecial(616)241
3092 y FJ(VANDERMONDE)p FQ(,)d @beginspecial @setspecial
@endspecial(404)r(,)j @beginspecial @setspecial @endspecial(410)241
3205 y FJ(VARDF)p FQ(,)f @beginspecial @setspecial @endspecial(339)241
3318 y(V)-8 b(ariable,)30 b @beginspecial @setspecial
@endspecial(46)241 3431 y(v)-5 b(ariable)29 b(scop)s(e,)i
@beginspecial @setspecial @endspecial(633)241 3544 y(v)-5
b(ariational)29 b(deriv)-5 b(ativ)m(e,)30 b @beginspecial
@setspecial @endspecial(339)241 3657 y FJ(VARNAME)p FQ(,)e
@beginspecial @setspecial @endspecial(125)r(,)i @beginspecial
@setspecial @endspecial(126)241 3770 y FJ(varopt)p FQ(,)f
@beginspecial @setspecial @endspecial(102)241 3883 y
FJ(VARPOINT)p FQ(,)f @beginspecial @setspecial @endspecial(367)241
3996 y FJ(VCONCMAT)p FQ(,)g @beginspecial @setspecial
@endspecial(262)241 4109 y FJ(VDF)p FQ(,)h @beginspecial
@setspecial @endspecial(457)241 4221 y(VEC)h(command,)g
@beginspecial @setspecial @endspecial(269)241 4334 y
FJ(VECDIM)p FQ(,)f @beginspecial @setspecial @endspecial(218)241
4447 y FJ(VECOP)p FQ(,)g @beginspecial @setspecial @endspecial(463)241
4560 y FJ(VECTOR)p FQ(,)g @beginspecial @setspecial @endspecial(214)241
4673 y(v)m(ector,)j @beginspecial @setspecial @endspecial(617)q(,)f
@beginspecial @setspecial @endspecial(639)241 4786 y(v)m(ector)407
4899 y(addition,)e @beginspecial @setspecial @endspecial(455)2046
555 y(cross)i(pro)s(duct,)e @beginspecial @setspecial
@endspecial(455)2046 668 y(di\013eren)m(tiation,)h @beginspecial
@setspecial @endspecial(271)2046 781 y(division,)e @beginspecial
@setspecial @endspecial(455)2046 894 y(dot)j(pro)s(duct,)f
@beginspecial @setspecial @endspecial(456)2046 1007 y(exp)s(onen)m
(tiation,)g @beginspecial @setspecial @endspecial(456)2046
1120 y(inner)f(pro)s(duct,)g @beginspecial @setspecial
@endspecial(456)2046 1233 y(in)m(tegration,)i @beginspecial
@setspecial @endspecial(271)2046 1346 y(mo)s(dulus,)d
@beginspecial @setspecial @endspecial(456)2046 1458 y(m)m
(ultiplication,)g @beginspecial @setspecial @endspecial(455)2046
1571 y(subtraction,)i @beginspecial @setspecial @endspecial(455)1880
1684 y(v)m(ector-notation,)j @beginspecial @setspecial
@endspecial(618)1880 1797 y FJ(VECTORADD)p FQ(,)c @beginspecial
@setspecial @endspecial(455)1880 1910 y FJ(VECTORCROSS)p
FQ(,)f @beginspecial @setspecial @endspecial(455)1880
2023 y FJ(VECTORDIFFERENCE)p FQ(,)f @beginspecial @setspecial
@endspecial(455)1880 2136 y FJ(VECTOREXPT)p FQ(,)h @beginspecial
@setspecial @endspecial(456)1880 2249 y FJ(VECTORMINUS)p
FQ(,)g @beginspecial @setspecial @endspecial(455)1880
2362 y(VECTORP)-8 b(,)30 b @beginspecial @setspecial
@endspecial(625)1880 2475 y FJ(VECTORPLUS)p FQ(,)e @beginspecial
@setspecial @endspecial(455)1880 2588 y FJ(VECTORQUOTIENT)p
FQ(,)f @beginspecial @setspecial @endspecial(455)1880
2700 y FJ(VECTORRECIP)p FQ(,)h @beginspecial @setspecial
@endspecial(455)1880 2813 y FJ(VECTORTIMES)p FQ(,)g @beginspecial
@setspecial @endspecial(455)1880 2926 y FJ(VERBATIM)p
FQ(,)h @beginspecial @setspecial @endspecial(509)1880
3039 y FJ(view)p FQ(,)h @beginspecial @setspecial @endspecial(372)1880
3152 y FJ(VINT)p FQ(,)g @beginspecial @setspecial @endspecial(458)1880
3265 y FJ(VMOD)p FQ(,)g @beginspecial @setspecial @endspecial(456)1880
3378 y(VMOD)h(op)s(erator,)g @beginspecial @setspecial
@endspecial(270)1880 3491 y FJ(VOLINT)p FQ(,)e @beginspecial
@setspecial @endspecial(458)1880 3604 y(V)m(OLINTEGRAL)i(function,)e
@beginspecial @setspecial @endspecial(274)1880 3717 y(V)m(OLINTORDER)h
(v)m(ector,)j @beginspecial @setspecial @endspecial(274)1880
3830 y FJ(VORDER)p FQ(,)c @beginspecial @setspecial @endspecial(458)
1880 3942 y FJ(VOUT)p FQ(,)h @beginspecial @setspecial
@endspecial(454)1880 4055 y FJ(VSTART)p FQ(,)f @beginspecial
@setspecial @endspecial(453)1880 4168 y FJ(VTAYLOR)p
FQ(,)g @beginspecial @setspecial @endspecial(457)1880
4364 y FJ(W)p 1934 4364 V 35 w(COMB)p FQ(,)g @beginspecial
@setspecial @endspecial(554)1880 4477 y FJ(WAR)p FQ(,)h
@beginspecial @setspecial @endspecial(554)1880 4590 y(w)m(arning)g
(messages,)h @beginspecial @setspecial @endspecial(622)1880
4703 y FJ(WEB)p FQ(,)f @beginspecial @setspecial @endspecial(416)1880
4816 y FJ(WEIGHT)p FQ(,)f @beginspecial @setspecial @endspecial(167)
1880 4929 y FJ(WHEN)p FQ(,)h @beginspecial @setspecial
@endspecial(161)p eop
%%Page: 698 698
698 697 bop 664 299 a @beginspecial @setspecial @endspecial
FQ(698)2553 b FM(INDEX)664 555 y FJ(WHERE)p FQ(,)29 b
@beginspecial @setspecial @endspecial(161)664 668 y FJ(WHILE)p
FQ(,)g @beginspecial @setspecial @endspecial(69)q(,)i
@beginspecial @setspecial @endspecial(71)q(,)f @beginspecial
@setspecial @endspecial(72)q(,)h @beginspecial @setspecial
@endspecial(74)664 781 y(Whittak)m(er)g(functions,)e
@beginspecial @setspecial @endspecial(543)664 894 y FJ(WhittakerM)p
FQ(,)f @beginspecial @setspecial @endspecial(543)664
1007 y FJ(WhittakerW)p FQ(,)g @beginspecial @setspecial
@endspecial(543)664 1120 y(W)-8 b(orkspace,)32 b @beginspecial
@setspecial @endspecial(113)664 1233 y FJ(WRITE)p FQ(,)d
@beginspecial @setspecial @endspecial(120)664 1346 y(WRS,)i
@beginspecial @setspecial @endspecial(659)664 1458 y
FJ(WS)p FQ(,)f @beginspecial @setspecial @endspecial(39)q(,)h
@beginspecial @setspecial @endspecial(174)664 1571 y
FJ(WTLEVEL)p FQ(,)e @beginspecial @setspecial @endspecial(167)664
1684 y FJ(WU)p FQ(,)h @beginspecial @setspecial @endspecial(196)r(,)g
@beginspecial @setspecial @endspecial(587)664 1880 y
FJ(XCOLOR)p FQ(,)f @beginspecial @setspecial @endspecial(196)q(,)i
@beginspecial @setspecial @endspecial(589)664 1993 y
FJ(XFULLREDUCE)p FQ(,)d @beginspecial @setspecial @endspecial(595)664
2106 y FJ(XIDEAL)p FQ(,)h @beginspecial @setspecial @endspecial(196)q
(,)i @beginspecial @setspecial @endspecial(593)q(,)g
@beginspecial @setspecial @endspecial(594)664 2219 y
FJ(xlabel)p FQ(,)e @beginspecial @setspecial @endspecial(372)664
2332 y FJ(XMODULO)p FQ(,)g @beginspecial @setspecial
@endspecial(594)664 2445 y FJ(XMODULOP)p FQ(,)g @beginspecial
@setspecial @endspecial(595)664 2558 y(XPND)830 2671
y(@,)h @beginspecial @setspecial @endspecial(337)830
2784 y(D,)h @beginspecial @setspecial @endspecial(337)664
2896 y FJ(XSTATS)p FQ(,)e @beginspecial @setspecial @endspecial(595)664
3092 y(Y-transform,)i @beginspecial @setspecial @endspecial(307)664
3205 y FJ(ylabel)p FQ(,)e @beginspecial @setspecial @endspecial(372)664
3401 y FJ(ZEILBERG)p FQ(,)g @beginspecial @setspecial
@endspecial(196)q(,)h @beginspecial @setspecial @endspecial(599)664
3514 y FJ(ZERO)p 862 3514 29 4 v 33 w(FORMS)p FQ(,)g
@beginspecial @setspecial @endspecial(327)664 3627 y(ZER)m(OP)-8
b(,)31 b @beginspecial @setspecial @endspecial(625)664
3740 y FJ(Zeta)p FQ(,)f @beginspecial @setspecial @endspecial(542)664
3853 y(Zeta)h(function)e(\(Riemann's\),)h @beginspecial
@setspecial @endspecial(542)664 3966 y FJ(Zeta)p 862
3966 V 33 w(function)p FQ(,)f @beginspecial @setspecial
@endspecial(544)664 4079 y FJ(zlabel)p FQ(,)g @beginspecial
@setspecial @endspecial(372)664 4192 y FJ(ZTRANS)p FQ(,)g
@beginspecial @setspecial @endspecial(196)q(,)i @beginspecial
@setspecial @endspecial(607)664 4304 y FJ(ztrans)p FQ(,)e
@beginspecial @setspecial @endspecial(607)p eop
%%Trailer
end
userdict /end-hook known{end-hook}if
%%EOF
