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r38/packages/mathml/mathml_1.red
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2011-09-02 18:13:33
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module mathml; % Version 5 August 1999 % Modified by FJW, 22 May 2000 % Modified by Winfried Neun , 1 August 2000 fluid '(atts ch cha char count file!* pvar rdci!* rdelems!* rdlist!* rdreln!* space safe_atts temp2 unary!* !*mathprint consts_compl consts_int flagg found_compl found_int consts_mat_int consts_mat_compl found_mat_compl found_mat_int indent); %Declaration of some switches. %_mathml_ allows all output to be printed in mathml. %_both_ allows all output to be printed in mathml and in normal reduce %output. load assist; load matrix; global '(f); global '(!*mathml); switch mathml; global '(!*both); switch both; global '(!*web); switch web; LISP (FILE!*:=nil); !*mathml:=nil; !*both:=nil; !*web:=nil; off both; off mathml; off web; %Declaration of a series of lists which contain the function to be executed %when the token (cadr) is found. %Tokens to be found between <ci></ci> tags. RDci!*:=' ((!&imaginaryi!; . (consts 'i)) (!&ii!; . (consts 'i)) (!&exponential!; . (consts 'e)) (!&ee!; . (consts 'e)) (!&pi!; . (consts 'p)) (!&differentiald!; . (const 'd)) (!&dd!; . (consts 'd))); %Tokens to be found between <reln></reln> tags. RDreln!*:= '((tendsto . (tendstoRD )) (eq!/ . (relationRD 'eq)) (neq!/ . (relationRD 'neq)) (lt!/ . (relationRD 'lt)) (gt!/ . (relationRD 'gt)) (geq!/ . (relationRD 'geq)) (leq!/ . (relationRD 'leq)) (in!/ . (inRD )) (notin!/ . (notinRD )) (subset!/ . (relationRD 'subset)) (prsubset!/ . (relationRD 'prsubset)) (notprsubset!/ . (notprsubsetRD )) (notsubset!/ . (notsubsetRD ))); %Tokens to be found between <apply></apply> tags. RDlist!*:= '((divide!/ . (divideRD)) (setdiff!/ . ( setdiffRD)) (select!/ . (selectRD)) (transpose!/ . ( transposeRD)) (determinant!/ . ( determinantRD)) (fn . ( applyfnRD)) (union!/ . (unionRD)) (intersect!/ . (intersectionRD)) (implies!/ . ( impliesRD)) (not!/ . ( notRD)) (xor!/ . (xorRD)) (or!/ . (orRD)) (and!/ . (andRD)) (mean!/ . ( meanRD)) (var!/ . ( varRD)) (sdev!/ . ( sdevRD)) (moment!/ . ( momentRD)) (median!/ . ( medianRD)) (sin!/ . ( sinRD)) (sec!/ . ( secRD)) (sinh!/ . ( sinhRD)) (sech!/ . ( sechRD)) (arcsin!/ . ( arcsinRD)) (cos!/ . ( cosRD)) (csc!/ . ( cscRD)) (cosh!/ . ( coshRD)) (csch!/ . ( cschRD)) (arccos!/ . ( arccosRD)) (tan!/ . ( tanRD)) (cot!/ . ( cotRD)) (tanh!/ . ( tanhRD)) (coth!/ . ( cothRD)) (arctan!/ . ( arctanRD)) (abs!/ . ( absRD)) (ln!/ . ( lnRD)) (plus!/ . ( plusRD)) (times!/ . ( timesRD)) (power!/ . ( powerRD)) (exp!/ . ( expRD)) (factorial!/ . ( factorialRD)) (quotient!/ . ( quotientRD)) (max!/ . ( maxRD)) (min!/ . ( minRD)) (minus!/ . ( minusRD)) (rem!/ . (remRD)) (conjugate!/ . ( conjugateRD)) (root!/ . ( rootRD)) (gcd!/ . ( gcdRD)) (log!/ . (logRD)) (int!/ . (intRD)) (sum!/ . ( sumRD)) (limit!/ . (limitRD)) (condition . (conditionRD)) (product!/ . (productRD)) (diff!/ . (diffRD)) (partialdiff!/ . (partialdiffRD))); RDelems!* := '((reln . (relnRD !/reln "</reln>")) (set . ( setRD !/set "</set>")) (fn . ( fnRD !/fn "</fn>")) (declare . ( declareRD !/declare "</declare>")) (list . ( listRD !/list "</list>")) (matrix . ( matrixRD !/matrix "</matrix>")) (cn . ( cnML !/cn "</cn>")) (ci . ( ciML !/ci "</ci>")) (lambda . ( lambdaRD !/lambda "</lambda>"))); unary!* := '((determinant . (unary determinant)) (transpose . (unary transpose)) (sum . (sum_prodML sum)) (prod . (sum_prodML product)) (df . (dfML nil)) % FJW: (df.(dfML df)) (impart . (complpart impart)) (repart . (complpart repart)) (abs . (unary abs)) (gcd . (n_nary gcd)) (set . (setML set)) (factorial . (unary factorial)) (max . (n_nary max)) (min . (n_nary min)) (cos . (unary cos)) (sin . (unary sin)) (sec . (unary sec)) (cosh . (unary cosh)) (cot . (unary cot)) (coth . (unary coth)) (csch . (unary csch)) (acos . (trigML acos)) (asin . (trigML asin)) (atan . (trigML atan)) (sech . (unary sech)) (sinh . (unary sinh)) (tan . (unary tan)) (tanh . (unary tanh)) (csc . (unary csc)) (quotient . (quotientML nil)) (plus . (n_nary plus)) (times . (n_nary times)) (expt . (n_nary power)) (sqrt . (sqrtML sqrt)) (log . (unary log)) (logb . (log_baseML logb)) (log10 . (log_baseML log10)) (ln . (unary ln)) (eq . (reln eq)) (neq . (reln neq)) (gt . (reln gt)) (lt . (reln lt)) (geq . (reln geq)) (leq . (reln leq)) (union . (sets union)) (intersection . (sets intersection)) (in . (reln in)) (notin . (reln notin)) (subset . (reln subset)) (prsubset . (reln prsubset)) (notsubset . (reln notsubset)) (notprsubset . (reln notprsubset)) (setdf . (sets setdf)) (arbcomplex . (printsub2cadr arbcomplex)) (arbint . (printsub2cadr arbint)) (mat . (matrixML nil)) (minus . (minusML nil)) (int . (integralML nil)) (equal . (equalML nil)) (list . (listML nil))); %The next three functions are the lexer. When called they returns the next %mathml token in the input stream. symbolic procedure lex(); begin scalar token; token:=nil; if atts neq nil then safe_atts:=atts; atts:=nil; if ch neq !$EOF!$ then << if ch=space then while (ch:=readch())=space do else if ch='!< then char:=get_token() else char:=get_content(); if char neq nil then << count:=count+1; token:=reverse char; char:=butes(token); %By decomenting the following line, the tokens read in are one by one %printed onto the output stream. % print char; attributes(char,token)>> else lex(); >> end; symbolic procedure get_token(); begin scalar d; d:=(); while (ch:=readch()) neq '!> do d:=cons(ch,d); return cons('!$,d); end; symbolic procedure get_content(); begin scalar d; d:=(); while (ch:=readch()) neq '!< AND ch neq !$EOF!$ do if ch neq space AND id2int(ch)>10 then d:=cons(ch,d); if d neq nil then d:=cons('!$,d); return d; end; %This function will search the list of attributes _att_ for the attribute %named _key_ symbolic procedure search_att( att, key); begin scalar l, stop,d; l:=nil; d:=(); stop:=0; att:= find(att, key); if att neq '(stop) then << while (car att='! ) do att:=cdr att; if (car att = '!=) then << att:=cdr att; while (car att='! ) do att:=cdr att; if (car att='!") then << att:=cdr att; while (stop=0) do << d:=cons(car att, d); att:=cdr att; if (car att='! ) OR (car att='!$) then stop:=1 >> >> else while (stop=0) do << d:=cons(car att, d); att:=cdr att; if (car att='! ) OR (car att='!$) then stop:=1 >> >> else errorML(compress key,1); if car d='!" then d:=cdr d; return reverse d >> end; symbolic procedure find(fatt, fkey); begin; return if fkey= '() then if fatt neq nil then cdr fatt else '(stop) else find(member(car fkey, fatt), cdr fkey); end; symbolic procedure attributes(a,b); begin scalar l; l:=length a; for a:=1:l do b:=cdr b; while (car b='! ) do b:=cdr b; if b neq '(!$) then atts:=b; end; symbolic procedure butes( str ); %Removes all attributes to a token. begin cha; cha:=car str; return if (cha='! OR cha='!$) then <<'(); >> else cons(car str, butes cdr str); end; %This is the MAIN function. It is given the name of a file which contains %the mathml input. It launches the program by calling parseML(). symbolic procedure mml(ff); begin; FILE!*:=t; ff:= open(ff, 'input); ff:= rds(ff); parseML(); close rds ff; FILE!*:=nil; end; %This function starts the parsing mechanism, which is a recursive descent %parsing. symbolic procedure parseML(); begin scalar res, vswitch; res:=nil; vswitch:=nil; % FLUID '(safe_atts char ch atts count temp space temp2); space:=int2id(32); count:=0; ch:=readch(); temp2:=nil; lex(); if char='(m a t h) then res:=mathML() else errorML("<math>",2); lex(); if char='(!/ m a t h) then terpri() else errorML("</math>",19); return algebraic res; end; %The two next functions differ in that one of them parses from the next %token onwards, and the other one from the actual token onwards. symbolic procedure mathML(); begin scalar a; a:=nil; lex(); return sub_math(); end; symbolic procedure mathML2(); begin scalar a; a:=nil; return sub_math(); end; %Parses all tokens which legally follow a mathml token. symbolic procedure sub_math(); begin scalar a,aa; if char='(a p p l y) then <<a := applyML(); if char neq '(!/ a p p l y) then errorML("</apply>",3)>> else if char='(v e c t o r) then <<a := vectorRD(); if char neq '(!/ v e c t o r) then errorML("</vector>",2)>> else if (aa := assoc(compress!* char, RDelems!*)) then <<a := apply(cadr aa, '() ); if compress!* char neq third aa then errorML(third cdr aa, 2)>>; return a end; symbolic procedure compress!* u; begin scalar x; if digit car u then return compress u; for each j in u do if j eq '!/ or j eq '!- or j eq '!; or j eq '!. then x := j . '!! . x else x := j . x; return intern compress reversip x end; %The next two functions parse the <cn> and <ci> tokens and extracts its %content to be used by the function calling it. It will have different %behaviours according to the type of the <cn> data. symbolic procedure cnML(); begin scalar type, sep, tt,aa; %Must check that what is being returned is an int. type:=nil; sep:=nil; type:=search_att(atts, '(t y p e)); lex(); tt := char; lex(); if type='(c o n s t a n t) then << if (aa:=assoc(intern compress tt, RDci!*)) then return apply(first cdr aa, rest cdr aa) >>; if IDP compress tt then errorML(compress tt, 16); if type=nil then return compress tt; if member(type, '((r e a l) (i n t e g e r))) neq nil then return compress tt; if member(type, '((r a t i o n a l) (c o m p l e x !- c a r t e s i a n) (c o m p l e x !- p o l a r))) neq nil then << sep:=sepRD(); if type='(r a t i o n a l) then <<lex();return alg_quotient(compress tt, sep)>> else if type='(c o m p l e x !- c a r t e s i a n) then << lex();return comp2(compress tt, sep) >>else if type='(c o m p l e x !- p o l a r) then <<sep:= po2ca(compress tt, sep); <<lex();return comp2(car sep, cadr sep)>> >> >>; end; symbolic procedure ciML(); begin scalar test, type,aa, tt; aa:=nil; type:=nil; test:=nil; type:=search_att(atts, '(t y p e)); lex(); tt := char; lex(); << test:=compress tt; if NUMBERP test then errorML(test, 4); test:=intern test; return test>> end; %returns the algebraic value of the constant values. algebraic procedure consts(c); begin; if c=i then return i; if c=d then return d; if c=e then return e; if c=p then return pi; end; %Constructs a complex number. algebraic procedure comp2(a,b); begin; return a+b*i; end; %Returns the two values separated by a <sep/> tag. symbolic procedure sepRD(); begin scalar p1, p2; p1:=nil; p2:=nil; if char neq '(s e p !/) then errorML("<sep/>",2); lex(); p2:=compress char; return p2; end; %Creates a vector by using function matrix_row. symbolic procedure vectorRD(); begin scalar a; a:=nil; a:=matrixrowRD(); a:=lisp aeval list('mat, a); return a; end; %The following functions construct the matrix from the mathml information. symbolic procedure matrixRD(); begin scalar b1, b2, stop; stop:=0; b1:='(); b2:=nil; while stop=0 do << lex(); if char='(m a t r i x r o w) then <<b2:=matrixrowRD(); if b1 neq nil then b1:=append(b1, list b2) else b1:=list b2; if char neq '(!/ m a t r i x r o w) then errorML("</matrixrow>",2)>> else stop:=1 >>; return aeval cons ('mat ,b1); end; symbolic procedure matrixrowRD(); begin scalar a; a:=nil; a:=mathML(); return if a=nil then nil else cons(a, matrixrowRD()); end; %returns a lambda function constructed from the information supplied. symbolic procedure lambdaRD(); begin scalar b1, b2; lex(); b1:=bvarRD(); b1:=car b1; b2:=mathML(); lex(); return algebraic( (lambda b1; b2) b1 ); end; %returns a set constructed from the information supplied. symbolic procedure setRD(); begin scalar setvars; atts:='(t y p e != s e t !$); setvars:= cons('list,stats_getargs()); setvars:=cons(car setvars, norepeat(cdr setvars)); return setvars; end; %This function will keep one copy only of any repeating elements symbolic procedure norepeat(args); begin; return if args=nil then nil else if length args=1 then list car args else append(list car args, norepeat(delall(car args, cdr args))); end; %This function will delete all occurences of element x in list l symbolic procedure delall(x,l); if l=nil then nil else if x=car l then delall(x, cdr l) else append(list car l ,delall(x, cdr l)); %returns a list constructed from the information supplied. symbolic procedure listRD(); begin scalar setvars, lorder, tmp; lorder:=search_att(atts, '(o r d e r)); atts:='(t y p e != l i s t !$); setvars:= cons('list,stats_getargs()); tmp := setvars; if lorder='(l e x i c o g r a p h i c) then setvars:=algebraic sortlist (setvars, lexog); if lorder='(n u m e r i c) then setvars:=algebraic sortlist (setvars, numer) else setvars:=algebraic sortlist (setvars, pred); if setvars = nil then setvars:= tmp; return setvars; end; %Defines the predicate function used by function _sortlist_. Sortlist comes %from package assist, and its documentation can be found in assist's %documentation %This one will sort all elements in numerical and alphanumerical order symbolic procedure pred(u,v); begin; return if NUMBERP u and NUMBERP v then <<if u<v then t>> else if IDP u and IDP v then <<if id2int(u) < id2int(v) then t>> else if NUMBERP u and IDP v then <<if u<id2int(v) then t>> else if IDP u and NUMBERP v then <<if id2int(u)<v then t>>; end; %This one sorts in alphanumerical order symbolic procedure lexog(u,v); begin; return if IDP u and IDP v then <<if id2int(u) < id2int(v) then t>> else t; end; %This one sorts in numerical order symbolic procedure numer(u,v); begin; return if NUMBERP u and NUMBERP v then <<if u<v then t>> else t; end; %Makes the next token in the inputstream an operator. symbolic procedure fnRD(); begin scalar b1; lex(); if char neq '(c i) then errorML(compress char,20) else b1:= mathML2(); if ATOM b1 then algebraic operator b1; lex(); return b1; end; %Reads the declare construct and sets the value of the given variable to %the given value. symbolic procedure declareRD(); begin scalar b1, b2, flagg, at; at:=atts; flagg := nil; b1:=mathML(); clear b1; clear reval b1; lex(); if at neq nil then put(b1, 'type, search_att(at,'(t y p e))); if search_att(at, '(t y p e)) = '(v e c t o r) then flagg:=t; if char='(!/ d e c l a r e) then return nil; b2 :=mathML2(); if get(b1, 'type)='(f n) then << algebraic operator b1>>; if flagg = t then setk(b1, b2) else algebraic set(b1, b2); lex(); return nil; end; %This function will determine if the next token is a valid token following %an apply token. It then calls the appropriate function if succesful. symbolic procedure applyML(); begin scalar aa; lex(); if (aa := assoc(compress!* char, RDlist!*)) then return apply(first cdr aa, rest cdr aa) else if char='(i d e n t !/) or char='(c o m p o s e !/) then return nil else if char='(i n v e r s e !/) then return t else errorML(compress!* char, 17) end; %Reads the next two elements and returns their setdifference. symbolic procedure setdiffRD(); begin scalar b1, b2; b1:=mathML(); b2:=mathML(); lex(); if b1=reval b1 and b2=reval b2 then return list('setdiff,b1, b2) else if b1=reval b1 then return list('setdiff, b1, reval b2) else if b2=reval b2 then return list('setdiff, reval b1, b2) else return append(list('set), setdiff(reval b1, reval b2)); end; %Reads through a select construct and acts accordingly. symbolic procedure selectRD(); begin scalar a1, res; a1:=stats_getargs(); if caar a1='mat then res:=mat_select(a1); if caar a1='list then res:=list_select(a1); if ATOM res then return res; return cons('list, res); end; symbolic procedure mat_select(a1); begin if length car a1=2 then return nth(cadar a1, cadr a1) else if length a1=2 then return nth(cdar a1, cadr a1); if length a1=3 then return nth(nth(cdar a1, caddr a1), cadr a1); end; symbolic procedure list_select(a1); begin scalar b1; b1:=cdar a1; return nth(b1, cadr a1); end; %Returns the transpose of the element contained in the transpose tags. symbolic procedure transposeRD(); begin scalar a, res; a:=mathML(); res:=algebraic(tp a); lex(); return res; end; %Returns the determinant of the given element. symbolic procedure determinantRD(); begin scalar a, res; a:=mathML(); res:=alg_det a; lex(); return res; end; algebraic procedure alg_det(a); begin; return det a; end; %Takes the given function name, makes it an operator, and then %applies it to the arguments specified in the mathml input. symbolic procedure applyfnRD(); begin scalar b1, b2, c1; b1:=nil; b2:=nil; c1:=nil; b1:=fnRD(); b2:=stats_getargs(); b2:=cons(b1, b2); c1:=algebraic b2; return c1; end; %Returns the union of the elements specified. symbolic procedure unionRD(); begin scalar b1, a1, a2,type,res; b1:=stats_getargs(); a1:=car b1; a2:=cadr b1; if PAIRP a1 AND PAIRP a2 then << type := car a1; a1:=cons('list, eval_list cdr a1); a2:=cons('list, eval_list cdr a2); res:=algebraic union(a1,a2); >> else << type := 'list; res := cons('list,cons(a1,list a2)); >>; return cons(type, cdr res); end; %Returns the intersection of the elements specified. symbolic procedure intersectionRD(); begin scalar b1, a1, a2,type,res; b1:=stats_getargs(); a1:=car b1; a2:=cadr b1; if PAIRP a1 AND PAIRP a2 then << type := car a1; a1:=cons('list, eval_list cdr a1); a2:=cons('list, eval_list cdr a2); res:=algebraic intersect(a1,a2); >> else << type := 'list; res := cons('list,cons(a1,list a2)); >>; return cons(type, cdr res); end; %Takes all the arguments in a list, and forces an evaluation on them if they can be %evaluated. symbolic procedure eval_list(args); begin; return if args=nil then nil else cons(reval car args, eval_list(cdr args)); end; %Takes all the arguments in a list of sets, and evaluates them if they can %be evaluated. symbolic procedure eval_list_sets(args); begin scalar ab; return if args=nil then nil else <<if PAIRP reval car args then << if car reval car args='list then ab:=cons('set, cdr reval car args)>> else ab:=reval car args; cons(ab, eval_list_sets(cdr args))>>; end; %Sets global variable temp2 to 'stop if an evaluatable element is found in %list args. symbolic procedure constants(args); begin scalar b1; if args neq nil then b1:=car args; return if args=nil then nil else <<if b1=reval b1 AND IDP b1 OR PAIRP b1 then temp2:='stop else constants(cdr args)>>; end; %Return boolean values of the arguments given. symbolic procedure notRD(); begin scalar a; a:=mathML(); lex(); return not(reval a); end; symbolic procedure impliesRD(); begin scalar a1,b1,c1; a1:=mathML(); b1:=mathML(); if b1='false then b1:=nil; if a1='false then a1:=nil; if reval a1 AND not reval b1 then c1:=nil else c1:=t; lex(); return c1; end; symbolic procedure andRD(); begin scalar a; a:=stats_getargs(); a:=subst(nil, 'false, a); a:=and2RD(a); return a; end; symbolic procedure and2RD(args); begin return if length args=1 then reval car args else and(reval car args, and2RD(cdr args)); end; symbolic procedure orRD(); begin scalar a; a:=stats_getargs(); a:=subst(nil, 'false, a); a:=or2RD(a); return a; end; symbolic procedure or2RD(args); begin return if length args=1 then reval car args else or(reval car args, or2RD(cdr args)); end; symbolic procedure xorRD(); begin scalar a; a:=stats_getargs(); a:=subst(nil, 'false, a); a:=xor2RD(a); return a; end; symbolic procedure xor2RD(args); begin return if args=() then nil else alg_xor(reval car args, xor2RD(cdr args)); end; symbolic procedure alg_xor(a,b); begin; return and(or(a,b),not(and(a,b))); end; %All defined trigonometric functions. algebraic procedure sinRD(); begin scalar a; a:=symbolic mathML(); symbolic lex(); return sin(a); end; algebraic procedure secRD(); begin scalar a; a:=symbolic mathML(); symbolic lex(); return sec(a); end; algebraic procedure sinhRD(); begin scalar a; a:=symbolic mathML(); symbolic lex(); return sinh(a); end; algebraic procedure sechRD(); begin scalar a; a:=symbolic mathML(); symbolic lex(); return sech(a); end; algebraic procedure arcsinRD(); begin scalar a; a:=symbolic mathML(); symbolic lex(); return asin(a); end; algebraic procedure cosRD(); begin scalar a; a:=symbolic mathML(); symbolic lex(); return cos(a); end; algebraic procedure cscRD(); begin scalar a; a:=symbolic mathML(); symbolic lex(); return csc(a); end; algebraic procedure coshRD(); begin scalar a; a:=symbolic mathML(); symbolic lex(); return cosh(a); end; algebraic procedure cschRD(); begin scalar a; a:=symbolic mathML(); symbolic lex(); return csch(a); end; algebraic procedure arccosRD(); begin scalar a; a:=symbolic mathML(); symbolic lex(); return acos(a); end; algebraic procedure tanRD(); begin scalar a; a:=symbolic mathML(); symbolic lex(); return tan(a); end; algebraic procedure cotRD(); begin scalar a; a:=symbolic mathML(); symbolic lex(); return cot(a); end; algebraic procedure tanhRD(); begin scalar a; a:=symbolic mathML(); symbolic lex(); return tanh(a); end; algebraic procedure cothRD(); begin scalar a; a:=symbolic mathML(); symbolic lex(); return coth(a); end; algebraic procedure arctanRD(); begin scalar a; a:=symbolic mathML(); symbolic lex(); return atan(a); end; %Reads the condition tag. symbolic procedure conditionRD(); begin scalar a; lex(); if char='(r e l n) then a:=relnRD() else a:=mathML(); lex(); return a; end; %This function will read all legal tags following the <reln> tag. symbolic procedure relnRD(); begin scalar a,aa; lex(); if (aa := assoc(compress!* char, RDreln!*)) then a := apply(first cdr aa, rest cdr aa) else errorML(compress!* char, 18); return if a=t then t else if null a then 'false else a; end; symbolic procedure relationRD( type ); begin scalar args,a; args:=stats_getargs(); if type='(quote eq) then <<a:= alg_eq(args)>> else if type='(quote neq) then <<a:= alg_neq(args)>> else if type='(quote lt) then <<a:= alg_lt(args)>> else if type='(quote gt) then <<a:= alg_gt(args)>> else if type='(quote subset) then <<a:=subsetRD(args)>> else if type='(quote prsubset) then <<a:=prsubsetRD(args)>> else if type='(quote geq) then <<a:= alg_geq(args)>> else if type='(quote leq) then <<a:= alg_leq(args)>>; return if a=t then t else if a=nil then 'false else a; end; %The following functions do all the necessay actions in order to evaluate %what should be by the tags. symbolic procedure notsubsetRD(); begin scalar b1, b2; b1:=mathML(); b2:=mathML(); lex(); if b1=reval b1 AND b2=reval b2 then return list('notsubset, b1, b2); if b1= reval b1 then return list('notsubset, b1,cons ('set, cdr reval b2)); if b2= reval b2 then return list('notsubset, cons('set,cdr reval b1), b2); if intersection(cdr reval b1,cdr reval b2)=nil then return t else return nil; end; symbolic procedure notprsubsetRD(); begin scalar b1, b2; b1:=mathML(); b2:=mathML(); lex(); if b1=reval b1 AND b2=reval b2 then return list('notprsubset, b1, b2); if b1= reval b1 then return list('notprsubset, b1,cons('set, cdr reval b2)); if b2= reval b2 then return list('notprsubset, cons('set,cdr reval b1), b2); if reval b1 = reval b2 then return t; if intersection(cdr reval b1,cdr reval b2)=nil then return t else return nil; end; symbolic procedure subsetRD(sets); begin scalar args,val; args:=sets; val:=t; while (length args > 1) do << if NUMBERP reval car args then errorML(reval car args,5); if car args = reval car args OR cadr args = reval cadr args then << args:='(); val:=cons('subset, eval_list_sets(sets))>> else << val:=AND(val, alg_subset(reval car args, reval cadr args)); args:=cdr args >> >>; return val; end; symbolic procedure alg_subset(a,b); begin; if a=b then return t else if setdiff(a,b)=nil then return t else return nil; end; symbolic procedure prsubsetRD(sets); begin scalar args, val; val:=t; while (length args > 1) do << if car args = reval car args OR cadr args = reval cadr args then << args:='(); val:=cons('prsubset, eval_list_sets(sets))>> else << val:=AND(val, alg_prsubset(reval car args, reval cadr args)); args:=cdr args >> >>; return val; end; symbolic procedure alg_prsubset(a,b); begin; if setdiff(a,b)=nil then return t else return nil; end; symbolic procedure inRD(); begin scalar b1,b2; b1:= mathML(); b2:= mathML(); lex(); if b2 = reval b2 AND ATOM b2 then << if b2='n then <<if FIXP b1 then return t else return nil>>; if b2='r then <<if NUMBERP b1 then return t else return nil>>; return list('in, reval b1, b2) >>; if MEMBER(reval b1,reval b2) neq nil then return t else return nil; end; symbolic procedure notinRD(); begin scalar b1,b2; b1:= mathML(); b2:= mathML(); lex(); if b2 = reval b2 AND ATOM b2 then << if b2='N then if FIXP b1 then return nil else return nil; if b2='R then if NUMBERP b1 then return nil else return nil; return list('notin, reval b1, b2)>>; if MEMBER(reval b1,reval b2) neq nil then return nil else return t; end; symbolic procedure alg_eq(args); begin; constants(args); return alg_eq2 eval_list args; end; symbolic procedure alg_eq2(args); begin; return if length args=1 then t else if (reval car args eq reval cadr args) then alg_eq2(cdr args); end; symbolic procedure alg_neq(args); begin; constants(args); return alg_neq2(eval_list(args)); end; symbolic procedure alg_neq2(args); begin; return if length args=1 then t else if (reval car args neq reval cadr args) then alg_neq2(cdr args); end; symbolic procedure alg_lt(args); begin; constants(args); if temp2='stop then <<temp2:=nil; return append(list 'lt, eval_list(args))>> else return alg_lt2(eval_list(args)); end; symbolic procedure alg_lt2(args); begin; return if length args=1 then t else if (NUMBERP reval car args AND NUMBERP reval cadr args )then <<if (reval car args < reval cadr args) then alg_lt2(cdr args) else nil>> else errorML("",6); end; symbolic procedure alg_gt(args); begin; constants(args); if temp2='stop then <<temp2:=nil; return append(list 'gt, eval_list(args))>> else return alg_gt2(eval_list(args)); end; symbolic procedure alg_gt2(args); begin; return if length args=1 then t else if (NUMBERP reval car args AND NUMBERP reval cadr args )then <<if (reval car args > reval cadr args) then alg_gt2(cdr args) else nil>> else errorML("",6); end; symbolic procedure alg_geq(args); begin; constants(args); if temp2='stop then <<temp2:=nil; return append(list 'g_eq, eval_list(args))>> else return alg_geq2(eval_list(args)); end; symbolic procedure alg_geq2(args); begin; return if length args=1 then t else if (NUMBERP reval car args AND NUMBERP reval cadr args )then <<if (reval car args >= reval cadr args) then alg_geq2(cdr args) else nil>> else errorML("",6); end; symbolic procedure alg_leq(args); begin; constants(args); if temp2='stop then <<temp2:=nil; return append(list 'l_eq, eval_list(args))>> else return alg_leq2(eval_list(args)); end; symbolic procedure alg_leq2(args); begin; return if length args=1 then t else if (NUMBERP reval car args AND NUMBERP reval cadr args )then <<if (reval car args <= reval cadr args) then alg_leq2(cdr args) else nil>> else errorML("",6); end; %Interprets the <tendsto> tag when used in the <limit> tag. symbolic procedure tendstoRD(); begin scalar attr, arg1 ,arg2; if intersection(atts, '(t y p e)) neq nil then attr:=search_att(atts, '(t y p e)) else attr:=nil; arg1:=mathML(); arg2:=mathML(); lex(); return list (attr,arg2); end; %Returns the limit of the information given. Uses the Reduce package %LIMITS. symbolic procedure limitRD(); begin scalar var, condi, low, exp; lex(); if char='(b v a r) then << var:=bvarRD(); if eqn(cadr var,1) then var:=car var else errorML("<degree>",8); lex()>> else var:=nil; if char='(l o w l i m i t) then << low:=lowlimitRD(); lex()>> else if char='(c o n d i t i o n) then << condi:=conditionRD(); if char neq '(!/ c o n d i t i o n) then errorML("</condition>",2); lex()>> else condi:=nil; exp:=mathML2(); lex(); if condi=nil then return alg_limit(exp, var, low, 'norm); if low=nil then if car condi='(a b o v e) then return alg_limit(exp, var, cadr condi, 'plus) else return alg_limit(exp, var, cadr condi, 'min); end; algebraic procedure alg_limit(exp, var, tendto, type); begin; if type='norm then return limit(exp, var, tendto); if type='plus then return limit!+(exp,var,tendto); if type='min then return limit!-(exp,var,tendto); end; %Returns the sum. symbolic procedure sumRD(); begin scalar svar, low, upper, express, res; svar:=nil; low:=nil; upper:=nil; express:=nil; res:=nil; lex(); if char='(b v a r) then <<svar:=bvarRD(); if eqn(cadr svar,1) then svar:=car svar else errorML("<degree>",7); lex()>> else errorML("<bvar>",9); if char='(l o w l i m i t) then << low:=lowlimitRD(); lex(); if char='(u p l i m i t) then << upper:=upperlimitRD(); lex()>> else errorML("<uplimit>",10) >> else if char='(i n t e r v a l) then << res:=intervalRD(); lex(); low:=car res; upper:=cadr res >> else errorML("<lowlimit> or <interval>",11); express:=mathML2(); lex(); return algebraic sum(express, svar, low, upper); end; algebraic procedure alg_sum( low, upper, formu); begin scalar temp,var2; algebraic; temp:=0; var2:=symbolic svar; for tt:=low:upper do << set(var2,tt); temp:=temp+formu; clear symbolic svar; var2:=symbolic svar>>; symbolic; return temp; end; %Returns the product. symbolic procedure productRD(); begin scalar pvar, low, upper, pexpress, res; lex(); if char='(b v a r) then <<pvar:=bvarRD(); if eqn(cadr pvar,1) then pvar:=car pvar else errorML("<degree>",12); lex()>> else errorML("<bvar>",9); if char='(l o w l i m i t) then << low:=lowlimitRD(); lex(); if char='(u p l i m i t) then << upper:=upperlimitRD(); lex()>> else errorML("<uplimit>",10)>> else if char='(i n t e r v a l) then << res:=intervalRD(); lex(); low:=car res; upper:=cadr res >> else errorML("<lowlimit> or <interval>",11); pexpress:=mathML2(); lex(); return algebraic prod(pexpress, pvar, low, upper); end; algebraic procedure alg_prod( low, upper, formu); begin scalar temp,var2; algebraic; temp:=1; var2:=symbolic pvar; for tt:=low:upper do << set(var2,tt); temp:=temp*formu; clear symbolic pvar; var2:=symbolic pvar>>; symbolic; return temp; end; %Returns the partial derivative. symbolic procedure partialdiffRD(); begin scalar res, bvar, express; lex(); bvar:=getargsRD(); express:=mathML2(); lex(); res:=differentiate(express, bvar); return res; end; symbolic procedure differentiate(express, bvar); begin scalar temp,diffed; return if eqn(length bvar,0) then express else <<temp:=car bvar; diffed:=alg_df(express, car temp, cadr temp); differentiate(diffed, cdr bvar)>>; end; %This function reads through the a series of <bvar> tags and extracts the %variables. symbolic procedure getargsRD(); begin scalar a; %Dont forget. This function leaves the file pointer on %the next token after the last bvar. So you need to use mathML2 after. if char='(b v a r) then <<a:=bvarRD(); lex(); return cons (a,getargsRD())>>; end; %Returns the derivative. symbolic procedure diffRD(); begin scalar bvar, degree, express, res; lex(); if char='(b v a r) then <<bvar:=bvarRD(); degree:=cadr bvar; bvar:=car bvar; lex()>> else <<bvar:=nil; degree:=nil>>; express:=mathML2(); lex(); res:=alg_df(express, bvar, degree); return res; end; algebraic procedure alg_df(a,b,c); begin; return df(a,b,c); end; %This function will calculate the integral. Takes in the expression, then %the bound variable, and finally the limits if they exist. symbolic procedure intRD(); begin scalar bvar, low, upper, int, exp; lex(); if char='(b v a r) then <<bvar:=bvarRD(); if eqn(cadr bvar,1) then bvar:=car bvar else errorML("",13); lex()>> else errorML("<bvar>",14); if char='(l o w l i m i t) then <<low:=lowlimitRD(); lex()>> else low:=nil; if char='(u p l i m i t) then <<upper:=upperlimitRD(); lex()>> else upper:=nil; if char='(i n t e r v a l) then <<int:=intervalRD(); low:=car int; upper:=cadr int; lex()>> else int:=nil; exp:=mathML2(); lex(); return alg_int(exp, bvar, low, upper); end; algebraic procedure alg_int(exp, bvar, low, upper); begin scalar res; if (low='nil) AND (upper=nil) then res:= int(exp, bvar) else res:= int(exp,bvar,low,upper); return res; end; %Here we parse bound variables. The function reads the variable as well as %the degree if there is one. symbolic procedure bvarRD(); begin scalar var, deg; lex(); if char='(d e g r e e) then errorML("<bvar>",15); var:=mathML2(); lex(); if char='(d e g r e e) then << deg:=mathML(); lex(); if char neq '(!/ d e g r e e) then error("</degree>",2); lex()>> else deg:=1; if char='(!/ b v a r) then return list(var, deg) else errorML("</bvar>", 2); end; %Functions used to parse the limits of an integral, sum, or product. symbolic procedure lowlimitRD(); begin scalar lowlimit; lowlimit:=mathML(); lex(); if char='(!/ l o w l i m i t) then return lowlimit else errorML("</lowlimit>", 2); end; symbolic procedure upperlimitRD(); begin scalar upperlimit; upperlimit:=mathML(); lex(); if char='(!/ u p l i m i t) then return upperlimit else errorML("</uplimit>", 2); end; symbolic procedure intervalRD(); begin scalar l,u; l:=mathML(); u:=mathML(); lex(); if char='(!/ i n t e r v a l) then return list(l,u) else errorML("</interval>", 2); end; %Following functions just evaluate calculus functions. symbolic procedure lnRD(); begin scalar a; a:=alg_ln(mathML()); lex(); return a; end; algebraic procedure alg_ln(a); begin; return ln(a); end; symbolic procedure logRD(); begin scalar a, a1, base; base:=nil; lex(); if char='(l o g b a s e) then <<base:=logbaseRD(); lex()>>; a1:=mathML2(); lex(); a:=alg_log(a1, base); return a; end; algebraic procedure alg_log(a, base); begin; if base=nil then return log(a) else return logb(a, base); end; symbolic procedure logbaseRD(); begin scalar a; a:=mathML(); lex(); if char='(!/ l o g b a s e) then return a else errorML("</logbase>",2); end; symbolic procedure conjugateRD(); begin scalar a; a:= alg_conj(mathML()); lex(); return a; end; algebraic procedure alg_conj(a); begin; return conj(a); end; symbolic procedure minusRD(); begin scalar c,b; c:=mathML(); b:=mathML(); if b=nil then c:=alg_minus(c) else << c:=alg_difference(c,b); lex()>>; return c; end; algebraic procedure alg_minus(a); begin; return -a; end; algebraic procedure alg_difference(a,b); begin; return difference(a,b); end; symbolic procedure absRD(); begin scalar a; a:=alg_abs(mathML()); lex(); return a; end; algebraic procedure alg_abs(a); begin; return abs(a); end; symbolic procedure rootRD(); begin scalar b,deg; lex(); if char='(d e g r e e) then << deg:=mathML(); lex(); if char neq '(!/ d e g r e e) then error("</degree>","Syntax ERROR: Missing end tag"); lex()>> else deg:=2; b:=mathML2(); lex(); return alg_root(b,deg); end; algebraic procedure alg_root(b,a); begin; return b**(1/a); end; symbolic procedure remRD(); begin scalar a, a1, a2; a1:=mathml(); a2:=mathml(); a:=alg_remainder(a1, a2); lex(); return a; end; algebraic procedure alg_remainder(a,b); begin; return remainder(a,b); end; symbolic procedure factorialRD(); begin scalar a; a:=alg_factorial(mathML()); lex(); return a; end; algebraic procedure alg_factorial(a); begin; return factorial(a); end; symbolic procedure expRD(); begin scalar a; a:= alg_exp(mathML()); lex(); return a; end; algebraic procedure alg_exp(a); begin; return exp(a); end; symbolic procedure quotientRD(); begin scalar a, a1, a2; a1:=mathML(); a2:=mathML(); if IDP reval a1 OR IDP reval a2 then a:=alg_quotient(a1,a2) else a:= (reval a1)/(reval a2); lex(); return a; end; algebraic procedure alg_quotient(a,b); begin; return a/b; end; symbolic procedure divideRD(); begin scalar a, a1, a2; a1:=mathML(); a2:=mathML(); if a2 = 0 then errorML("", 21); a:=alg_divide(a1,a2); lex(); return a; end; algebraic procedure alg_divide(a,b); begin; return quotient(a,b); end; symbolic procedure gcdRD(); begin scalar c1; c1:=stats_getargs(); constants(c1); if temp2='stop then << temp2:=nil; return cons('gcd, eval_list(c1))>> else return gcdRD2(c1); end; symbolic procedure gcdRD2(args); begin scalar a; a:=reval car args; return if length args=1 then car args else alg_gcd2(a, gcdRD2(cdr args)); end; algebraic procedure alg_gcd2(a , b); begin; return gcd(a,b); end; symbolic procedure minRD(); begin scalar a; a:=mathML(); return if a=nil then nil else alg_min(a,minRD()); end; algebraic procedure alg_min(a,b); begin; return min(b,a); end; symbolic procedure maxRD(); begin scalar a; a:=mathML(); return if a=nil then nil else alg_max(a,maxRD()); end; algebraic procedure alg_max(a,b); begin; return max(a,b) end; lisp operator plusRD; symbolic procedure plusRD(); begin scalar abc1; abc1:=nil; abc1:=mathML(); return if abc1 = nil then 0 else alg_plus(abc1, plusRD()); end; algebraic procedure alg_plus(acb1,b); begin; return acb1+b; end; symbolic procedure timesRD(); begin scalar a; a:=nil; a:=mathML(); return if a=nil then 1 else alg_times(a, timesRD()); end; algebraic procedure alg_times(a,b); begin; if b=i then return a*i; return a*b; end; symbolic procedure powerRD(); begin scalar var,power; var:=mathML(); power:=mathML(); lex(); return alg_expt(var,power); end; algebraic procedure alg_expt(a,b); begin; return expt(a,b); end; %The following function is in charge of providing the correct error message %as well as closing the input/output stream, and exiting the program %correctly. symbolic procedure errorML( str, msg ); begin; terpri(); princ "***** Error in token number "; princ count; princ " (<"; princ compress char; princ ">)"; terpri(); if msg=1 then << princ "Needed attribute"; princ str; princ " and none was found.">> else if msg=2 then << princ "Missing tag: "; princ str >> else if msg=3 then << princ "Undefined error!"; princ " Token number "; princ sub1 count; princ " probably mispelled or an"; princ "ambiguous or erroneous use of <apply></apply>.">> else if msg=4 then << princ "Numerical constant "; princ str; princ " was enclosed between <ci></ci> tags."; terpri(); princ "Correct syntax: <cn>"; princ str; princ "</cn>.">> else if msg=5 then << princ "All arguments must be sets"; terpri(); princ str; princ " does not represent a set.">> else if msg=6 then << princ "Non-numeric argument in arithmetic.">> else if msg=7 then << princ "The degree quantifier is of no use in the sumation"; princ "operator.">> else if msg=8 then << princ "The degree quantifier is of no use in the limit"; princ " operator.">> else if msg=9 then << princ "The index of sumation has not been specified."; terpri(); princ "Please use <bvar></bvar> tags to specify an index.">> else if msg=10 then << princ "Upperlimit not specified.">> else if msg=11 then << princ "Upper and lower limits have not been specified.">> else if msg=12 then << princ "The degree quantifier is of no use in the product"; princ " operator.">> else if msg=13 then << princ "The degree quantifier is not allowed in the integral"; princ " operator.">> else if msg=14 then << princ "Variable of integration not specified."; princ "Please use <bvar></bvar> tags to specify variable.">> else if msg=15 then << princ "Incorrect use of <bvar></bvar> tags."; princ " Correct use:"; terpri(); princ "<bvar> bound_var </bvar> [<degree> degree </degree>] </bvar>">> else if msg=16 then << princ "Symbolic constant "; princ str; princ " was enclosed between <cn></cn> tags."; terpri(); princ "Correct syntax: <ci> "; princ str; princ " </ci>"; terpri(); princ "or <cn type=""constant""> </cn>"; princ "if using constants ⅈ, ⅈ, ⅇ, ⅇ or π." >> else if msg=17 then << princ "Unknown tag: <"; princ str;princ ">."; terpri(); princ "Token not allowed within <apply></apply> tags."; terpri(); princ "Might be: <"; princ str; princ "/>.">> else if msg=18 then << princ "Unknown tag: <"; princ str;princ ">."; terpri(); princ "Not allowed within <reln></reln> tags.">> else if msg=19 then << princ "Undefined error!"; princ " Token "; princ sub1 count; princ " is probably mispelled"; terpri(); princ "or unknown, "; princ "or the </math> tag is missing">> else if msg=20 then << princ "Function "; princ str; princ "()"; princ " was not enclosed in <ci></ci> tags."; terpri(); princ "Correct syntax: <fn><ci>"; princ str; princ "</ci></fn>.">> else if msg=21 then << princ "Error, division by 0">>; terpri(); if FILE!*=t then close rds f; FILE!*:=nil; rederr(""); rederr(""); terpri(); end; %Following function are in charge of parsing statistics related mathml. symbolic procedure meanRD(); begin scalar b, size, args; args:=stats_getargs(); b:=0; size:=length( args ); while (args neq ()) do << b:=alg_plus(b, car args); args:= cdr args >>; return alg_quotient(b,size); end; symbolic procedure sdevRD( ); begin scalar args,mean,b,size; args:=stats_getargs(); mean:=alg_mean( args ); size:=length(args); while(args neq ()) do << b:=alg_plus(b, alg_expt(alg_difference(car args, mean),2)); args:=cdr args; >>; return b; end; symbolic procedure varRD( ); begin scalar args; args:=stats_getargs(); return alg_expt(sdev( args ), 2); end; symbolic procedure medianRD( ); begin scalar args, siz, si; args:=stats_getargs(); args:=cons('list, args); args:=sortl(args); args:=cdr args; si:=length args; siz:=si/2; if remainder(si,2)=0 then return alg_quotient(alg_plus(nth(args,siz),nth(args,(siz+1))),2) else return nth(args, siz); end; algebraic procedure sortl(args); begin scalar rr; rr:=sortlist(args, pred); if rr=nil then return sortnumlist(args) else return rr; end; symbolic procedure momentRD( ); begin scalar args,size,d,i; args:=stats_getargs(); if char='(d e g r e e) then <<i:=mathML(); lex(); if char='(!/ d e g r e e) then lex() else errorML("</degree>",2)>> else i:=1; d:=(); size:=length args; while args neq () do << d:=cons(alg_expt(car args, i),d); args:=cdr args>>; return alg_mean(d); end; symbolic procedure alg_mean ( args ); begin scalar b, size, args; b:=0; size:=length( args ); while (args neq ()) do << b:=alg_plus(b, car args); args:= cdr args >>; return alg_quotient(b,size); end; symbolic procedure sdev( args ); begin scalar mean,b,size; mean:=alg_mean( args ); size:=length(args); while(args neq ()) do << b:=alg_plus(b, alg_expt(alg_difference(car args, mean),2)); args:=cdr args; >>; return b; end; %The following function gets all arguments from the mathml input. symbolic procedure stats_getargs(); begin scalar ww; ww:=nil; ww:=mathML(); if ww neq nil then << return cons (ww,stats_getargs())>>; end; %Transforms polar-complex to cartesian-complex. symbolic procedure po2ca(r,p); begin scalar theta,x,y; theta:=rad p; x:=r*cos(theta); y:=r*sin(theta); return(list(x,y)) end; symbolic procedure rad(mu); %note approx. pi begin scalar b; b:=mu*3.141529/180; return b end; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %Here start the functions in charge of pasing reduce's output and printing% %it out in mathml. % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %This the mathml printer which reads reduce output and translates it to %mathml. symbolic procedure math_ml_printer (mode,u); << if !*both=t then (<< if u=t then else maprin(u); terpri!* nil>>) where outputhandler!* := nil; if mode neq 'terpri then << % FLUID '(indent, flagg,found_int, found_compl, consts_compl, consts_int); % FLUID '(found_mat_int, found_mat_compl, consts_mat_int, consts_mat_compl); found_mat_int=0$; found_mat_compl=0$; indent:=0$ consts_compl:=()$ consts_mat_compl:=()$ consts_int:=()$ consts_mat_int:=()$ found_int:=0$ found_compl:=0$ flagg:=0$ if (PAIRP u) then << if !*web=t then printout("<EMBED TYPE=""text/mathml"" MMLDATA="""); printout("<math>"); indent:=3; if ((car u)='setq) then <<if (PAIRP caddr u) then if (issq(caddr u)=1) then arbitrary_c( PREPSQ cadr caddr u ) else if (caaddr u='mat) then arbitrary_c(caddr u) else if (caaddr u='list) then arbitrary_c( !*a2k caddr u); setqML( u )>> else if ((car u)='list) then << arbitrary_c( !*a2k u ); listML(cdr u)>> else if ((car u)='mat) then << arbitrary_c( u ); matrixML(cdr u)>> else if ((car u)='!*sq) then << arbitrary_c(PREPSQ (cadr u)); expression(PREPSQ (cadr u))>> else expression(u); indent:=indent-3; close_forall(); indent:=0; printout( "</math>" ); if !*web=t then princ(""" HEIGHT=300 WIDTH=500>"); terpri() >> else if (ATOM u) then << if !*web=t then printout("<EMBED TYPE=""text/mathml"" MMLDATA="" "); printout( "<math>" ); indent:=3; expression( u ); indent:=0; printout( "</math>" ); if !*web=t then princ(" "" HEIGHT=300 WIDTH=500>"); terpri() >> else ; >> >>; %Prints out vectors. symbolic procedure vectorML( elem ); begin; printout("<vector>"); indent:=indent+3; multi_elem(car elem); indent:=indent-3; printout("</vector>") end; %Following functions print out matrices. symbolic procedure matrixML( elem ); begin; if length elem=1 then vectorML( elem ) else << printout("<matrix>"); indent:=indent+3; matrix_rows(elem); indent:=indent-3; printout("</matrix>") >>; end; symbolic procedure matrix_rows( elem ); begin; if (elem neq()) then << printout("<matrixrow>"); indent:=indent+3; row(car elem); indent:=indent-3; printout("</matrixrow>"); matrix_rows( cdr elem ); >> end; symbolic procedure row( elem ); begin; if (elem neq()) then << expression(car elem); row(cdr elem);>> end; %This function searches for arbitrary integers, or complex in the reduce %output. If so, it declares these variables in a forall statement. symbolic procedure arbitrary_c( elem ); begin; found_int:=nil; found_mat_int:=nil; found_compl:=nil; found_mat_compl:=nil; if (PAIRP elem) then << if (car elem='mat) then << isarb_mat_compl(cdr elem); isarb_mat_int(cdr elem)>> else << isarb_compl(elem); isarb_int(elem)>>; if ((found_compl=1) OR (found_int=1)) then << flagg:=1; printout( "<apply><forall/>" ); indent:=indent+3; print_arb_compl(elem); print_arb_int(elem); printout( "<condition>"); indent:=indent+3; if ((found_compl=1) AND (found_int=1)) then << printout( "<apply><and/>" ); indent:=indent+3>> else if ((length consts_compl) > 1) then << printout( "<apply><and/>" ); indent:=indent+3>> else if ((length consts_int) > 1) then << printout( "<apply><and/>" ); indent:=indent+3>>; if (found_compl=1) then in_complexML( consts_compl ); if (found_int=1) then in_integerML( consts_int ); if ((found_compl=1) AND (found_int=1)) then << indent:=indent-3; printout( "</apply>" )>> else if ((length consts_compl) > 1) then << indent:=indent-3; printout( "</apply>" )>> else if ((length consts_int) > 1) then << indent:=indent-3; printout( "</apply>" )>>; indent:=indent-3; printout( "</condition>" )>>; if ((found_mat_compl=1) OR (found_mat_int=1)) then << flagg:=1; printout( "<apply><forall/>" ); indent:=indent+3; printarb_mat_compl(cdr elem); printarb_mat_int(cdr elem); printout( "<condition>"); indent:=indent+3; if ((found_mat_compl=1) AND (found_mat_int=1)) then << printout( "<apply><and/>" ); indent:=indent+3>> else if ((length consts_mat_compl) > 1) then << printout( "<apply><and/>" ); indent:=indent+3>> else if ((length consts_mat_int) > 1) then << printout( "<apply><and/>" ); indent:=indent+3>>; if (found_mat_compl=1) then in_complexML( consts_mat_compl ); if (found_mat_int=1) then in_integerML( consts_mat_int ); if ((found_mat_compl=1) AND (found_mat_int=1)) then << indent:=indent-3; printout( "</apply>" )>> else if ((length consts_mat_compl) > 1) then << indent:=indent-3; printout( "</apply>" )>> else if ((length consts_mat_int) > 1) then << indent:=indent-3; printout( "</apply>" )>>; indent:=indent-3; printout( "</condition>" )>>; >> end; symbolic procedure in_complexML( elem ); begin; if (elem neq ()) then << printout("<reln><in/>"); indent:=indent+3; printsub2( car elem, 'compl ); printout("<ci type=""set""> C </ci>"); indent:=indent-3; printout("</reln>"); in_complexML( cdr elem )>>; end; symbolic procedure in_integerML( elem ); begin; if (elem neq ()) then << printout("<reln><in/>"); indent:=indent+3; printsub2( car elem, 'int ); printout("<ci type=""set""> N </ci>"); indent:=indent-3; printout("</reln>"); in_integerML( cdr elem )>>; end; symbolic procedure close_forall(); begin; if (flagg=1) then printout("</apply>"); end; %Prints out setq statements as <declare> statements. symbolic procedure setqML( elem ); begin; printout( "<declare>" ); indent:=indent+3; expression(cadr elem); expression( caddr elem); indent:=indent-3; printout( "</declare>" ); end; %Prints out lists. symbolic procedure listML( elem ); begin; printout( "<list>" ); indent:=indent+3; multilists( elem ); indent:=indent-3; printout( "</list>" ); end; symbolic procedure multilists( elem ); begin; if elem neq nil then if ((LENGTH elem)=1) then expression (car elem) else <<expression(car elem); multilists(cdr elem);>> end; %This function takes in a reduce expression, and parses it. It also takes %expressions created by the above program. symbolic procedure expression( elem ); begin scalar aa; if (ATOM elem) then f4( elem ) else if car elem='!:RD!: then <<printout elem>> else << if (aa:=assoc(car elem, unary!*)) then << if caddr aa = nil then apply(cadr aa, list cdr elem) else apply(cadr aa, list(cdr elem, caddr aa)) >> else if ((car elem)= '!*sq) then expression (PREPSQ (cadr elem)) else operator_fn(elem);>>; end; %Prints out sum, or products. symbolic procedure sum_prodML( elem, tty ); begin; printout("<apply>"); princ "<"; princ tty; princ "/>"; indent:=indent+3; printout("<bvar>"); indent:=indent+3; expression( cadr elem ); indent:=indent-3; printout("</bvar>"); printout("<lowlimit>"); indent:=indent+3; expression( caddr elem ); indent:=indent-3; printout("</lowlimit>"); printout("<uplimit>"); indent:=indent+3; expression( cadddr elem ); indent:=indent-3; printout("</uplimit>"); expression car elem; indent:=indent-3; printout("</apply>"); end; %Prints out derivatives. symbolic procedure dfml( elem ); begin scalar test; test:=cdr elem; if length test=1 OR (length test=2 AND NUMBERP cadr test) then printout("<apply><diff/>") else printout("<apply><partialdiff/>"); indent:=indent+3; dfargs(cdr elem); % FJW: two statements swapped expression(car elem); indent:=indent-3; printout("</apply>"); end; symbolic procedure dfargs( elem ); begin; if elem neq nil then << if length elem>1 then << if NUMBERP cadr elem then <<printout("<bvar>"); indent:=indent+3; expression car elem; degreeML(cadr elem); indent:=indent-3; printout("</bvar>"); dfargs(cddr elem)>> else <<printout("<bvar>"); indent:=indent+3; expression car elem; indent:=indent-3; printout("</bvar>"); dfargs(cdr elem)>>; >> else << printout("<bvar>"); indent:=indent+3; expression car elem; indent:=indent-3; printout("</bvar>"); dfargs(cdr elem)>> >>; end; %Prints out degree statements. symbolic procedure degreeML( elem ); begin; printout("<degree>"); indent:=indent+3; expression( elem ); indent:=indent-3; printout("</degree>"); end; symbolic procedure complpart( elem, tty); begin; printout("<apply><fn><"); princ tty; princ "></fn>"; indent:=indent+3; expression(car elem); indent:=indent-3; printout("<apply>"); end; %Prints out set theory related functions. symbolic procedure sets(elem, tty); begin; printout("<apply>"); princ "<"; princ tty; princ "/>"; indent:=indent+3; multi_elem( elem ); indent:=indent-3; printout("</apply>"); end; %Prints out relns. symbolic procedure reln(elem, tty); begin; printout("<reln>"); princ "<"; princ tty; princ "/>"; indent:=indent+3; multi_elem( elem ); indent:=indent-3; printout("</reln>"); end; %Prints out a set. symbolic procedure setML( elem ); begin; printout("<set>"); indent:=indent+3; multi_elem( elem ); indent:=indent-3; printout("</set>"); end; %Prints out unknown functions as a function. It prints out all variables %declared a soperators. symbolic procedure operator_fn( elem ); begin; printout("<apply><fn><ci>"); princ car elem; princ "</ci></fn>"; indent:=indent+3; multi_args(cdr elem); indent:=indent-3; printout("</apply>"); end; %Reads through a list and prints out each component. symbolic procedure multi_args( elem ); begin; if (elem neq ()) then <<expression(car elem); multi_args( cdr elem );>> end; %Prints out all trigonometric functions which have not the same tag name, %as reduce function. symbolic procedure trigML(elem, type); begin; printout("<apply>"); if ((type='acos) OR (type='asin) OR (type='atan)) then << if (type='acos) then princ "<arccos/>"; if (type='asin) then princ "<arcsin/>"; if (type='atan) then princ "<arctan/>">>; indent:=indent+3; expression(car elem); indent:=indent-3; printout("</apply>"); end; %Prints out all unary functions such as log, or many trig functions. symbolic procedure unary( elem, type ); begin; printout("<apply>"); princ "<"; princ type; princ "/>"; indent:=indent+3; expression(car elem ); indent:=indent-3; printout("</apply>"); end; %Prints out logs with a base. symbolic procedure log_baseML(elem, type); begin; printout("<apply><log/>"); indent:=indent+3; printout("<logbase>"); indent:=indent+3; if (type='logb) then expression(cadr elem); if (type='log10) then f4(10); indent:=indent-3; printout("</logbase>"); expression(car elem); indent:=indent-3; printout("<apply>"); end; %Prints out equal relns. symbolic procedure equalML( elem ); begin; printout( "<reln><eq/>" ); indent:=indent+3; expression(car elem); expression(cadr elem); indent:=indent-3; printout( "</reln>" ); end; %Prints out square roots. symbolic procedure sqrtML( elem , type); begin; printout( "<apply><root/>" ); indent:=indent+3; printout( "<degree><cn> 2 </cn></degree>" ); expression( car elem ); indent:=indent-3; printout( "</apply>" ); end; %Prints out integrals. symbolic procedure integralML( elem ); begin; printout( "<apply><int/>" ); indent:=indent+3; printout( "<bvar>" ); indent:=indent+3; expression (cadr elem); indent:=indent-3; printout( "</bvar>" ); if (length cdr elem >1) then << printout("<lowlimit>"); indent:=indent+3; expression( caddr elem ); indent:=indent-3; printout("</lowlimit>"); printout("<uplimit>"); indent:=indent+3; expression( cadddr elem ); indent:=indent-3; printout("</uplimit>")>>; expression( car elem ); indent:=indent-3; printout( "</apply>" ); end; %Prints out quotients. symbolic procedure quotientML( elem ); begin; if (NUMBERP car elem) AND (NUMBERP cadr elem) then << if !*web=nil then printout("<cn type=""rational""> ") else printout("<cn type="rational"> "); princ car elem; princ " <sep/> "; princ cadr elem; princ " </cn>">> else << printout( "<apply><divide/>" ); indent:=indent+3; expression( car elem ); expression( cadr elem ); indent:=indent-3; printout( "</apply>" )>>; end; %Prints out all n_nary functions. symbolic procedure n_nary( elem, type ); begin; if car elem = 'e AND type = 'power then unary(cdr elem, 'exp) else << printout( "<apply>" ); princ "<"; princ type; princ "/>"; indent:=indent+3; multi_elem( elem ); indent:=indent-3; printout( "</apply>" )>> end; symbolic procedure multi_elem( elem ); begin; if ((length elem)=1) then expression( car elem ) else <<expression( car elem ); multi_elem( cdr elem );>> end; symbolic procedure minusML( elem ); begin; printout( "<apply><minus/>" ); indent:=indent+3; multiminus( elem ); indent:=indent-3; printout( "</apply>" ); end; symbolic procedure multiminus( elem ); begin; expression(car elem); if ((length elem)=2) then expression (cadr elem); end; %Prints out all pieces of data: i.e terminal symbols. %They can be numbers, identifiers, or constants. symbolic procedure f4(exp); begin; if (exp='infinity) then << if !*web=nil then printout("<cn type=""constant"">") else printout("<cn type="constant">"); princ "∞"; princ "</cn>">> else << if (exp='e) then << if !*web=nil then printout("<cn type=""constant"">") else printout("<cn type="constant">"); princ "ⅇ"; princ "</cn>">> else << if (exp='i) then << if !*web=nil then printout("<cn type=""constant"">") else printout("<cn type="constant">"); princ "ⅈ"; princ "</cn>">> else << if (NUMBERP exp) then << printout "<cn"; if (FLOATP exp) then <<if !*web=nil then princ " type=""real"">" else princ " type="real">" >> else if (FIXP exp) then <<if !*web=nil then princ " type=""integer"">" else princ " type="integer">" >> else princ ">"; princ exp; princ "</cn>">>; if (IDP exp) then << printout "<ci"; if (listp exp) then <<if !*web=nil then princ " type=""list"">" else princ " type="list">">> else if (vectorp exp) then <<if !*web=nil then princ " type=""vector"">" else princ " type="vector">">> else princ ">"; princ exp; princ "</ci>">>; >> >> >> end; %Functions used to print out variables with a subscript. symbolic procedure printsub( subscript, type ); begin; printout("<bvar>"); indent:=indent+3; printout("<ci>"); indent:=indent+3; printout( "<msub>" ); indent:=indent+3; if (type='compl) then printout( "<mi>c</mi>" ); if (type='int) then printout( "<mi>d</mi>" ); printout( "<mn>" ); princ subscript; princ "</mn>"; indent:=indent-3; printout( "</msub>" ); indent:=indent-3; printout("</ci>"); indent:=indent-3; printout("</bvar>"); end; symbolic procedure printsub2( subscript, type ); begin; printout("<ci>"); indent:=indent+3; printout( "<msub>" ); indent:=indent+3; if (type='compl) then printout( "<mi>c</mi>" ); if (type='int) then printout( "<mi>d</mi>" ); printout( "<mn>" ); princ subscript; princ "</mn>"; indent:=indent-3; printout( "</msub>" ); indent:=indent-3; printout("</ci>"); end; %Prints out expressions in math form. Plagiarised from reduce code of %mathprint symbolic procedure ma_print l; begin scalar temp; temp:=outputhandler!*; outputhandler!*:=nil; terpri!* nil; if !*web=nil then maprin "<cn type=""real"">" else maprin "<cn type="real">"; maprin l; maprin "</cn>"; terpri!* nil; outputhandler!*:=temp; end; %Function in charge of doing all printing in order to make sure the %indentation is always correct. symbolic procedure printout( str ); begin; if !*web = nil then terpri(); if !*web = nil then for i := 1:indent do << princ " " >>; if PAIRP str then <<if car str='!:rd!: OR car str='!:rn!: then ma_print str else princ str>> else princ str; end; %Following functions are quite obscure. They find arbitrary constants in %expressions and matrices. Then record them, and everytime they appear, are %replaced with a fancy subscripts C, or D. symbolic procedure issq( elem ); begin scalar value; value:=0; if (ATOM elem) then value:=0 else <<if ((car elem)='!*sq) then value:=1 else value:=0>>; return value; end; symbolic procedure isarb_compl( elem ); begin; if (PAIRP elem) then << if ((car elem)= 'arbcomplex) then found_compl:=1 else multi_isarb_compl(cdr elem);>> end; symbolic procedure multi_isarb_compl( elem ); begin; if (PAIRP elem) then << if (elem=()) then else <<isarb_compl(car elem); multi_isarb_compl( cdr elem);>> >> end; symbolic procedure isarb_int( elem ); begin; if (PAIRP elem) then << if ((car elem)= 'arbint) then found_int:=1 else multi_isarb_int(cdr elem);>> end; symbolic procedure multi_isarb_int( elem ); begin; if (PAIRP elem) then << if (elem=()) then else <<isarb_int(car elem); multi_isarb_int( cdr elem);>> >> end; symbolic procedure print_arb_compl( elem ); begin; if (PAIRP elem) then << if ((car elem)= 'arbcomplex) then << if (xnp(list (cadr elem),consts_compl) eq nil) then << printsub(cadr elem, 'compl); consts_compl:=cons(cadr elem, consts_compl)>> >> else multi_compl(cdr elem);>> end; symbolic procedure multi_compl( elem ); begin; if (elem=()) then else <<print_arb_compl(car elem); multi_compl( cdr elem);>> end; symbolic procedure print_arb_int( elem ); begin; if (PAIRP elem) then << if ((car elem)= 'arbint) then << if (xnp(list (cadr elem),consts_int) eq nil) then << printsub(cadr elem, 'int); consts_int:=cons(cadr elem, consts_int)>> >> else multi_int(cdr elem);>> end; symbolic procedure multi_int( elem ); begin; if (elem=()) then else <<print_arb_int(car elem); multi_int( cdr elem);>> end; symbolic procedure isarb_mat_int( elem ); begin; if (elem neq()) then << isarb_row_int(car elem); isarb_mat_int( cdr elem ); >> end; symbolic procedure isarb_row_int( elem ); begin; if (elem neq()) then << if (issq(car elem)=1) then if (PAIRP (PREPSQ cadr (car elem))) then if (car (PREPSQ cadr (car elem))='arbint) then found_mat_int:=1; isarb_row_int(cdr elem);>> end; symbolic procedure isarb_mat_compl( elem ); begin; if (elem neq()) then << isarb_row_compl(car elem); isarb_mat_compl( cdr elem ); >> end; symbolic procedure isarb_row_compl( elem ); begin; if (elem neq()) then << if (issq(car elem)=1) then if (PAIRP (PREPSQ cadr (car elem))) then if (car (PREPSQ cadr (car elem))='arbcomplex) then found_mat_compl:=1; isarb_row_compl(cdr elem);>> end; symbolic procedure printarb_mat_compl( elem ); begin; if (elem neq()) then << printarb_row_compl(car elem); printarb_mat_compl( cdr elem ); >> end; symbolic procedure printarb_row_compl( elem ); begin scalar value; if (elem neq()) then << if (issq(car elem)=1) then if (PAIRP (PREPSQ cadr (car elem))) then << value:=cadr PREPSQ cadr car elem; if (car (PREPSQ cadr (car elem)))='arbcomplex then if (xnp(list (value), consts_mat_compl) eq nil) then << printsub(value, 'compl); consts_mat_compl:=cons(value, consts_mat_compl)>> >>; printarb_row_compl(cdr elem);>> end; symbolic procedure printarb_mat_int( elem ); begin; if (elem neq()) then << printarb_row_int(car elem); printarb_mat_int( cdr elem ); >> end; symbolic procedure printarb_row_int( elem ); begin scalar value; if (elem neq()) then << if (issq(car elem)=1) then if (PAIRP (PREPSQ cadr (car elem))) then << value:=cadr PREPSQ cadr car elem; if (car (PREPSQ cadr (car elem)))='arbint then if (xnp(list (value), consts_mat_int) eq nil) then << printsub(value, 'int); consts_mat_int:=cons(value, consts_mat_int)>> >>; printarb_row_int(cdr elem);>> end; %Following function is the same as math_ml_printer, just that it prints out %input given from mml, which reads from files, and not form the reduce %normal output stream. symbolic procedure math_ml (u); << % FLUID '(indent flagg found_int found_compl consts_compl % consts_int !*mathprint); % FLUID '(found_mat_int found_mat_compl consts_mat_int % consts_mat_compl); !*mathprint:=0; found_mat_int=0$; found_mat_compl=0$; indent:=0$ consts_compl:=()$ consts_mat_compl:=()$ consts_int:=()$ consts_mat_int:=()$ found_int:=0$ found_compl:=0$ flagg:=0$ if (PAIRP u) then << printout("<math>"); indent:=3; if ((car u)='setq) then <<if (PAIRP caddr u) then if (issq(caddr u)=1) then arbitrary_c( PREPSQ cadr caddr u ) else if (caaddr u='mat) then arbitrary_c(caddr u) else if (caaddr u='list) then arbitrary_c( !*a2k caddr u); setqML( u )>> else if ((car u)='list) then << arbitrary_c( !*a2k u ); listML(cdr u)>> else if ((car u)='mat) then << arbitrary_c( u ); matrixML(cdr u)>> else if ((car u)='!*sq) then << arbitrary_c(PREPSQ (cadr u)); expression(PREPSQ (cadr u))>> else expression(u); indent:=indent-3; close_forall(); indent:=0; printout( "</math>" ) >> else if (ATOM u) then << printout( "<math>" ); indent:=3; expression( u ); indent:=0; printout( "</math>" )>> else ; >>; %This function executes certain commands when switches state are changed. %It will change the outputhandler!* when mathml is set to on or both is set %to on. And then modify it accroding to the switches states. symbolic procedure onoff(u,bool); begin scalar x,y; if not idp u then typerr(u,"switch") else if not flagp(u,'switch) then rerror(rlisp,25,list(u,"not defined as switch")); x := intern compress append(explode '!*,explode u); if !*switchcheck and lispeval x eq bool then return nil else if y := atsoc(bool,get(u,'simpfg)) then lispeval('progn . append(cdr y,list nil)); if bool and x eq '!*!r!a!i!s!e then x := '!*raise; % Special case. if x='!*web AND bool=t then outputhandler!*:='math_ml_printer; if x='!*web AND bool=nil then if !*mathml neq t then outputhandler!*:=nil; if x='!*mathml AND bool=t then outputhandler!*:='math_ml_printer; if x='!*mathml AND bool=nil then if !*both=nil then outputhandler!*:=nil; if x='!*both AND bool=t then outputhandler!*:='math_ml_printer; if x='!*both AND bool=nil then if !*mathml=nil then outputhandler!*:=nil else outputhandler!*:='math_ml_printer; set(x,bool); end; lisp operator mml; lisp operator parseml; endmodule; end;