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module fmprint; % Fancy output package for symbolic expressions. % using TEX as intermediate language. % Author: Herbert Melenk, using ideas of maprin.red (A.C.H, A.C.N). % Modifications: % fancy!-mode!* commented out, since it applies only to % very old versions. / % Copyright (c) 2003 Anthony C. Hearn, Konrad-Zuse-Zentrum. % All rights reserved. % 8-Sep-94 % introduced data driven formatting (print-format) % 12-Apr-94 % removed print function for dfp % removed some unused local variables % corrected output for conditional expressions and % aeval/aeval* forms % 17_Mar-94 corrected line breaks in Taylor expressions % rational exponents use / % vertical bar for SUB expressions % explicit * for product of two quotients (Taylor) % switches % % ON FANCY enable algebraic output processing by this module % % ON FANCY_TEX under ON FANCY: display TEX equivalent % % properties used in this module: % % fancy-prifn print function for an operator % % fancy-pprifn print function for an oeprator including current % operator precedence for infix printing % % fancy!-flatprifn print function for objects which require % special printing if prefix operator form % would have been used, e.g. matrix, list % % fancy-prtch string for infix printing of an operator % % fancy-special-symbol % print expression for a non-indexed item % string with TEX expression "\alpha" % or % number referring ASCII symbol code % % fancy-infix-symbol special-symbol for infix operators % % fancy-prefix-symbol special symbol for prefix operators % % fancy!-symbol!-length the number of horizontal units needed for % the symbol. A standard character has 2 units. % 94-Jan-26 - Output for Taylor series repaired. % 94-Jan-17 - printing of index for Bessel function repaired. % - New functions for local encapsulation of printing % independent of smacro fancy!-level. % - Allow printing of upper case symbols locally % controlled by *fancy-lower % 93-Dec-22 Vectors printed with sqare brackets. create!-package('(fmprint),nil); fluid '( !*list !*nat !*nosplit !*ratpri !*revpri overflowed!* p!*!* testing!-width!* tablevel!* sumlevel!* outputhandler!* outputhandler!-stack!* posn!* obrkp!* % outside-brackets-p ); global '(!*eraise charassoc!* initl!* nat!*!* spare!* ofl!*); switch list,ratpri,revpri,nosplit; % Global variables initialized in this section. fluid '( fancy!-switch!-on!* fancy!-switch!-off!* !*fancy!-mode fancy!-pos!* fancy!-line!* fancy!-page!* fancy!-bstack!* !*fancy_tex !*fancy!-lower % control of conversion to lower case % fancy!-mode!* ); switch fancy_tex; % output TEX equivalent. % fancy!-mode!* := if '!6 = car reverse explode2 getenv "reduce" then 36 % else 35; % fancy!-mode!* := 36; % This needs to be more than 35. fancy!-switch!-on!* := int2id 16$ fancy!-switch!-off!* := int2id 17$ !*fancy!-lower := t; global '(fancy_lower_digits fancy_print_df); share fancy_lower_digits; % T, NIL or ALL. if null fancy_lower_digits then fancy_lower_digits:=t; share fancy_print_df; % PARTIAL, TOTAL, INDEXED. if null fancy_print_df then fancy_print_df := 'partial; switch fancy; put('fancy,'simpfg, '((t (fmp!-switch t)) (nil (fmp!-switch nil)) )); symbolic procedure fmp!-switch mode; if mode then <<if outputhandler!* neq 'fancy!-output then <<outputhandler!-stack!* := outputhandler!* . outputhandler!-stack!*; outputhandler!* := 'fancy!-output; >> >> else <<if outputhandler!* = 'fancy!-output then <<outputhandler!* := car outputhandler!-stack!*; outputhandler!-stack!* := cdr outputhandler!-stack!*; >> else rederr "FANCY is not current output handler" >>; symbolic procedure fancy!-out!-header(); if not !*fancy_tex then prin2 fancy!-switch!-on!*; symbolic procedure fancy!-out!-trailer(); <<if not !*fancy_tex then prin2 fancy!-switch!-off!*; terpri()>>; symbolic procedure fancy!-tex s; % test output: print tex string. <<prin2 fancy!-switch!-on!*; for each x in explode2 s do prin2 x; prin2t fancy!-switch!-off!*; >>; symbolic procedure fancy!-out!-item(it); if atom it then prin2 it else if eqcar(it,'ascii) then writechar(cadr it) else if eqcar(it,'tab) then for i:=1:cdr it do prin2 "\>" else if eqcar(it,'bkt) then begin scalar m,b,l; integer n; m:=cadr it; b:=caddr it; n:=cadddr it; l := b member '( !( !{ ); % if m then prin2 if l then "\left" else "\right" % else if n> 0 then <<prin2 if n=1 then "\big" else if n=2 then "\Big" else if n=3 then "\bigg" else "\Bigg"; prin2 if l then "l" else "r"; >>; if b member '(!{ !}) then prin2 "\"; prin2 b; end else rederr "unknown print item"; symbolic procedure set!-fancymode bool; if bool neq !*fancy!-mode then <<!*fancy!-mode:=bool; fancy!-pos!*:=0; fancy!-page!*:=nil; fancy!-line!*:=nil; overflowed!* := nil; % new: with tab fancy!-line!*:= '((tab . 1)); fancy!-pos!* := 10; sumlevel!* := tablevel!* := 1; >>; symbolic procedure fancy!-output(mode,l); % Interface routine. if ofl!* or posn!*>2 or not !*nat then % not terminal handler or current output line non-empty. <<if mode = 'maprin then maprin l else terpri!*(l) >> where outputhandler!* = nil else <<set!-fancymode t; if mode = 'maprin then fancy!-maprin0 l else fancy!-flush(); >>; symbolic procedure fancy!-flush(); << fancy!-terpri!* t; for each line in reverse fancy!-page!* do if line and not eqcar(car line,'tab) then <<fancy!-out!-header(); for each it in reverse line do fancy!-out!-item it; fancy!-out!-trailer(); >>; set!-fancymode nil; >> where !*lower=nil; %---------------- primitives ----------------------------------- symbolic procedure fancy!-special!-symbol(u,n); if numberp u then <<fancy!-prin2!*("\symb{",n); fancy!-prin2!*(u,0); fancy!-prin2!*("}",0); >> else fancy!-prin2!*(u,n); symbolic procedure fancy!-prin2 u; fancy!-prin2!*(u,nil); symbolic procedure fancy!-prin2!*(u,n); if numberp u and not testing!-width!* then fancy!-prin2number u else (begin scalar str,id; integer l; str := stringp u; id := idp u and not digit u; u:= if atom u then explode2 u where !*lower=!*fancy!-lower else {u}; l := if numberp n then n else 2*length u; if id and not numberp n then u:=fancy!-lower!-digits(fancy!-esc u); for each x in u do <<if str and (x='! or x='!_) then fancy!-line!* := '!\ . fancy!-line!*; fancy!-line!* := (if id and !*fancy!-lower then red!-char!-downcase x else x) . fancy!-line!*; >>; fancy!-pos!* := fancy!-pos!* #+ l; if fancy!-pos!* #> 2 #* (linelength nil #+1 ) then overflowed!*:=t; end) where !*lower = !*lower; symbolic procedure fancy!-last!-symbol(); if fancy!-line!* then car fancy!-line!*; charassoc!* := '((!A . !a) (!B . !b) (!C . !c) (!D . !d) (!E . !e) (!F . !f) (!G . !g) (!H . !h) (!I . !i) (!J . !j) (!K . !k) (!L . !l) (!M . !m) (!N . !n) (!O . !o) (!P . !p) (!Q . !q) (!R . !r) (!S . !s) (!T . !t) (!U . !u) (!V . !v) (!W . !w) (!X . !x) (!Y . !y) (!Z . !z)); symbolic procedure red!-char!-downcase u; (if x then cdr x else u) where x = atsoc(u,charassoc!*); symbolic procedure fancy!-prin2number u; % we print a number eventually causing a line break % for very big numbers. if testing!-width!* then fancy!-prin2!*(u,t) else fancy!-prin2number1 (if atom u then explode2 u else u); symbolic procedure fancy!-prin2number1 u; begin integer c,ll; ll := 2 #* (linelength nil #+1 ); while u do <<c:=c+1; if c>10 and fancy!-pos!* #> ll then fancy!-terpri!*(t); fancy!-prin2!*(car u,2); u:=cdr u; >>; end; symbolic procedure fancy!-esc u; if not('!_ memq u) then u else (if car u eq '!_ then '!\ . w else w) where w = car u . fancy!-esc cdr u; symbolic procedure fancy!-lower!-digits u; (if null m then u else if m = 'all or fancy!-lower!-digitstrail(u,nil) then fancy!-lower!-digits1(u,nil) else u ) where m=fancy!-mode 'fancy_lower_digits; symbolic procedure fancy!-lower!-digits1(u,s); begin scalar c,q,r,w,x; loop: if u then <<c:=car u; u:=cdr u>> else c:=nil; if null s then if not digit c and c then w:=c.w else << % need to close the symbol w; w:=reversip w; q:=intern compress w; if stringp (x:=get(q,'fancy!-special!-symbol)) then w:=explode2 x; r:=nconc(r,w); if digit c then <<s:=t; w:={c}>> else w:=nil; >> else if digit c then w:=c.w else << % need to close the number w. w:='!_ . '!{ . reversip('!} . w); r:=nconc(r,w); if c then <<s:=nil; w:={c}>> else w:=nil; >>; if w then goto loop; return r; end; symbolic procedure fancy!-lower!-digitstrail(u,s); if null u then s else if not s and digit car u then fancy!-lower!-digitstrail(cdr u,t) else if s and not digit car u then nil else fancy!-lower!-digitstrail(cdr u,s); symbolic procedure fancy!-terpri!* u; << if fancy!-line!* then fancy!-page!* := fancy!-line!* . fancy!-page!*; fancy!-pos!* :=tablevel!* #* 10; fancy!-line!*:= {'tab . tablevel!*}; overflowed!* := nil >>; symbolic macro procedure fancy!-level u; % unwind-protect for special output functions. {'prog,'(pos fl w), '(setq pos fancy!-pos!*), '(setq fl fancy!-line!*), {'setq,'w,cadr u}, '(cond ((eq w 'failed) (setq fancy!-line!* fl) (setq fancy!-pos!* pos))), '(return w)}; symbolic procedure fancy!-begin(); % collect current status of fancy output. Return as a list % for later recovery. {fancy!-pos!*,fancy!-line!*}; symbolic procedure fancy!-end(r,s); % terminates a fancy print sequence. Eventually resets % the output status from status record <s> if the result <r> % signals an overflow. <<if r='failed then <<fancy!-line!*:=car s; fancy!-pos!*:=cadr s>>; r>>; symbolic procedure fancy!-mode u; begin scalar m; m:= lispeval u; if eqcar(m,'!*sq) then m:=reval m; return m; end; %---------------- central formula converter -------------------- symbolic procedure fancy!-maprin0 u; if not overflowed!* then fancy!-maprint(u,0) where !*lower=nil; symbolic procedure fancy!-maprint(l,p!*!*); % Print expression l at bracket level p!*!* without terminating % print line. Special cases are handled by: % pprifn: a print function that includes bracket level as 2nd arg. % prifn: a print function with one argument. (begin scalar p,x,w,pos,fl; p := p!*!*; % p!*!* needed for (expt a (quotient ...)) case. if null l then return nil; if atom l then return fancy!-maprint!-atom(l,p); pos := fancy!-pos!*; fl := fancy!-line!*; if not atom car l then return fancy!-maprint(car l,p); l := fancy!-convert(l,nil); if (x:=get(car l,'fancy!-reform)) then return fancy!-maprint(apply1(x,l),p); if ((x := get(car l,'fancy!-pprifn)) and not(apply2(x,l,p) eq 'failed)) or ((x := get(car l,'fancy!-prifn)) and not(apply1(x,l) eq 'failed)) or (get(car l,'print!-format) and fancy!-print!-format(l,p) neq 'failed) then return nil; if testing!-width!* and overflowed!* or w='failed then return fancy!-fail(pos,fl); % eventually convert expression to a different form % for printing. l := fancy!-convert(l,'infix); % printing operators with integer argument in index form. if flagp(car l,'print!-indexed) then << fancy!-prefix!-operator(car l); w :=fancy!-print!-indexlist cdr l >> else if x := get(car l,'infix) then << p := not(x>p); w:= if p then fancy!-in!-brackets( {'fancy!-inprint,mkquote car l,x,mkquote cdr l}, '!(,'!)) else fancy!-inprint(car l,x,cdr l); >> else if x:= get(car l,'fancy!-flatprifn) then w:=apply(x,{l}) else << w:=fancy!-prefix!-operator(car l); obrkp!* := nil; if w neq 'failed then w:=fancy!-print!-function!-arguments cdr l; >>; return if testing!-width!* and overflowed!* or w='failed then fancy!-fail(pos,fl) else nil; end ) where obrkp!*=obrkp!*; symbolic procedure fancy!-convert(l,m); % special converters. if eqcar(l,'expt) and cadr l= 'e and ( m='infix or treesizep(l,20) ) then {'exp,caddr l} else l; symbolic procedure fancy!-print!-function!-arguments u; % u is a parameter list for a function. fancy!-in!-brackets( u and {'fancy!-inprint, mkquote '!*comma!*,0,mkquote u}, '!(,'!)); symbolic procedure fancy!-maprint!-atom(l,p); fancy!-level begin scalar x; if(x:=get(l,'fancy!-special!-symbol)) then fancy!-special!-symbol(x, get(l,'fancy!-special!-symbol!-size) or 2) else if vectorp l then <<fancy!-prin2!*("[",0); l:=for i:=0:upbv l collect getv(l,i); x:=fancy!-inprint(",",0,l); fancy!-prin2!*("]",0); return x>> else if not numberp l or (not (l<0) or p<=get('minus,'infix)) then fancy!-prin2!*(l,'index) else fancy!-in!-brackets( {'fancy!-prin2!*,mkquote l,t}, '!(,'!)); return if testing!-width!* and overflowed!* then 'failed else nil; end; put('print_indexed,'psopfn,'(lambda(u)(flag u 'print!-indexed))); symbolic procedure fancy!-print!-indexlist l; fancy!-print!-indexlist1(l,'!_,nil); symbolic procedure fancy!-print!-indexlist1(l,op,sep); % print index or exponent lists, with or without separator. fancy!-level begin scalar w,testing!-width!*,obrkp!*; testing!-width!* :=t; fancy!-prin2!*(op,0); fancy!-prin2!*('!{,0); w:=fancy!-inprint(sep or 'times,0,l); fancy!-prin2!*("}",0); return w; end; symbolic procedure fancy!-print!-one!-index i; fancy!-level begin scalar w,testing!-width!*,obrkp!*; testing!-width!* :=t; fancy!-prin2!*('!_,0); fancy!-prin2!*('!{,0); w:=fancy!-inprint('times,0,{i}); fancy!-prin2!*("}",0); return w; end; symbolic procedure fancy!-in!-brackets(u,l,r); % put form into brackets (round, curly,...). % u: form to be evaluated, % l,r: left and right brackets to be inserted. fancy!-level (begin scalar fp,w,r1,r2,rec; rec := {0}; fancy!-bstack!* := rec . fancy!-bstack!*; fancy!-adjust!-bkt!-levels fancy!-bstack!*; fp := length fancy!-page!*; fancy!-prin2!* (r1:='bkt.nil.l.rec, 2); w := eval u; fancy!-prin2!* (r2:='bkt.nil.r.rec, 2); % no line break: use \left( .. \right) pair. if fp = length fancy!-page!* then <<car cdr r1:= t; car cdr r2:= t>>; return w; end) where fancy!-bstack!* = fancy!-bstack!*; symbolic procedure fancy!-adjust!-bkt!-levels u; if null u or null cdr u then nil else if caar u >= caadr u then <<car cadr u := car cadr u +1; fancy!-adjust!-bkt!-levels cdr u; >>; symbolic procedure fancy!-exptpri(l,p); % Prints expression in an exponent notation. (begin scalar !*list,pp,q,w,w1,w2,pos,fl; pos:=fancy!-pos!*; fl:=fancy!-line!*; pp := not((q:=get('expt,'infix))>p); % Need to parenthesize w1 := cadr l; w2 := caddr l; testing!-width!* := t; if eqcar(w2,'quotient) and cadr w2 = 1 and (fixp caddr w2 or liter caddr w2) then return fancy!-sqrtpri!*(w1,caddr w2); if eqcar(w2,'quotient) and eqcar(cadr w2,'minus) then w2 := list('minus,list(car w2,cadadr w2,caddr w2)) else w2 := negnumberchk w2; if fancy!-maprint(w1,q)='failed then return fancy!-fail(pos,fl); fancy!-prin2!*("^",0); if eqcar(w2,'quotient) and fixp cadr w2 and fixp caddr w2 then <<fancy!-prin2!*("{",0); w:=fancy!-inprint('!/,0,cdr w2); fancy!-prin2!*("}",0)>> else w:=fancy!-maprint!-tex!-bkt(w2,0,nil); if w='failed then return fancy!-fail(pos,fl) ; end) where !*ratpri=!*ratpri, testing!-width!*=testing!-width!*; put('expt,'fancy!-pprifn,'fancy!-exptpri); symbolic procedure fancy!-inprint(op,p,l); (begin scalar x,y,w, pos,fl; pos:=fancy!-pos!*; fl:=fancy!-line!*; % print product of quotients using *. if op = 'times and eqcar(car l,'quotient) and cdr l and eqcar(cadr l,'quotient) then op:='!*; if op eq 'plus and !*revpri then l := reverse l; if not get(op,'alt) then << if op eq 'not then << fancy!-oprin op; return fancy!-maprint(car l,get('not,'infix)); >>; if op eq 'setq and not atom (x := car reverse l) and idp car x and (y := getrtype x) and (y := get(get(y,'tag),'fancy!-setprifn)) then return apply2(y,car l,x); if not atom car l and idp caar l and ((x := get(caar l,'fancy!-prifn)) or (x := get(caar l,'fancy!-pprifn))) and (get(x,op) eq 'inbrackets) % to avoid mix up of indices and exponents. then<< fancy!-in!-brackets( {'fancy!-maprint,mkquote car l,p}, '!(,'!)); >> else if !*nosplit and not testing!-width!* then fancy!-prinfit(car l, p, nil) else w:=fancy!-maprint(car l, p); l := cdr l >>; if testing!-width!* and (overflowed!* or w='failed) then return fancy!-fail(pos,fl); if !*list and obrkp!* and memq(op,'(plus minus)) then <<sumlevel!*:=sumlevel!*+1; tablevel!* := tablevel!* #+ 1>>; if !*nosplit and not testing!-width!* then % main line: fancy!-inprint1(op,p,l) else w:=fancy!-inprint2(op,p,l); if testing!-width!* and w='failed then return fancy!-fail(pos,fl); end ) where tablevel!*=tablevel!*, sumlevel!*=sumlevel!*; symbolic procedure fancy!-inprint1(op,p,l); % main line (top level) infix printing, allow line break; begin scalar lop,space; space := flagp(op,'spaced); for each v in l do <<lop := op; if op='plus and eqcar(v,'minus) then <<lop := 'minus; v:= cadr v>>; if space then fancy!-prin2!*("\,",1); if 'failed = fancy!-oprin lop then <<fancy!-terpri!* nil; fancy!-oprin lop>>; if space then fancy!-prin2!*("\,",1); fancy!-prinfit(negnumberchk v, p, nil) >>; end; symbolic procedure fancy!-inprint2(op,p,l); % second line begin scalar lop,space,w; space := flagp(op,'spaced); for each v in l do if not testing!-width!* or w neq 'failed then <<lop:=op; if op='plus and eqcar(v,'minus) then <<lop := 'minus; v:= cadr v>>; if space then fancy!-prin2!*("\,",1); fancy!-oprin lop; if space then fancy!-prin2!*("\,",1); if w neq 'failed then w:=fancy!-maprint(negnumberchk v,p) >>; return w; end; symbolic procedure fancy!-inprintlist(op,p,l); % inside algebraic list fancy!-level begin scalar fst,w,v; loop: if null l then return w; v := car l; l:= cdr l; if fst then << fancy!-prin2!*("\,",1); w:=fancy!-oprin op; fancy!-prin2!*("\,",1); >>; if w eq 'failed and testing!-width!* then return w; w:= if w eq 'failed then fancy!-prinfit(v,0,op) else fancy!-prinfit(v,0,nil); if w eq 'failed and testing!-width!* then return w; fst := t; goto loop; end; put('times,'fancy!-prtch,"\,"); symbolic procedure fancy!-oprin op; fancy!-level begin scalar x; if (x:=get(op,'fancy!-prtch)) then fancy!-prin2!*(x,1) else if (x:=get(op,'fancy!-infix!-symbol)) then fancy!-special!-symbol(x,get(op,'fancy!-symbol!-length) or 4) else if null(x:=get(op,'prtch)) then fancy!-prin2!*(op,t) else << if !*list and obrkp!* and op memq '(plus minus) and sumlevel!*=2 then if testing!-width!* then return 'failed else fancy!-terpri!* t; fancy!-prin2!*(x,t); >>; if overflowed!* then return 'failed end; put('alpha,'fancy!-special!-symbol,"\alpha"); put('beta,'fancy!-special!-symbol,"\beta"); put('gamma,'fancy!-special!-symbol,"\gamma"); put('delta,'fancy!-special!-symbol,"\delta"); put('epsilon,'fancy!-special!-symbol,"\epsilon"); put('zeta,'fancy!-special!-symbol,"\zeta"); put('eta,'fancy!-special!-symbol,"\eta"); put('theta,'fancy!-special!-symbol,"\theta"); put('iota,'fancy!-special!-symbol,"\iota"); put('kappa,'fancy!-special!-symbol,"\kappa"); put('lambda,'fancy!-special!-symbol,"\lambda"); put('mu,'fancy!-special!-symbol,"\mu"); put('nu,'fancy!-special!-symbol,"\nu"); put('xi,'fancy!-special!-symbol,"\xi"); put('pi,'fancy!-special!-symbol,"\pi"); put('rho,'fancy!-special!-symbol,"\rho"); put('sigma,'fancy!-special!-symbol,"\sigma"); put('tau,'fancy!-special!-symbol,"\tau"); put('upsilon,'fancy!-special!-symbol,"\upsilon"); put('phi,'fancy!-special!-symbol,"\phi"); put('chi,'fancy!-special!-symbol,"\chi"); put('psi,'fancy!-special!-symbol,"\psi"); put('omega,'fancy!-special!-symbol,"\omega"); if 'a neq '!A then deflist('( (!Alpha 65) (!Beta 66) (!Chi 67) (!Delta 68) (!Epsilon 69)(!Phi 70) (!Gamma 71)(!Eta 72) (!Iota 73) (!vartheta 74)(!Kappa 75)(!Lambda 76) (!Mu 77)(!Nu 78)(!O 79)(!Pi 80)(!Theta 81) (!Rho 82)(!Sigma 83)(!Tau 84)(!Upsilon 85) (!Omega 87) (!Xi 88)(!Psi 89)(!Zeta 90) (!varphi 106) ),'fancy!-special!-symbol); put('infinity,'fancy!-special!-symbol,"\infty"); % some symbols form the upper ASCII part of the symbol font put('partial!-df,'fancy!-special!-symbol,182); put('partial!-df,'fancy!-symbol!-length,8); put('empty!-set,'fancy!-special!-symbol,198); put('not,'fancy!-special!-symbol,216); put('not,'fancy!-infix!-symbol,216); % symbols as infix opertors put('leq,'fancy!-infix!-symbol,163); put('geq,'fancy!-infix!-symbol,179); put('neq,'fancy!-infix!-symbol,185); put('intersection,'fancy!-infix!-symbol,199); put('union,'fancy!-infix!-symbol,200); put('member,'fancy!-infix!-symbol,206); put('and,'fancy!-infix!-symbol,217); put('or,'fancy!-infix!-symbol,218); put('when,'fancy!-infix!-symbol,239); put('!*wcomma!*,'fancy!-infix!-symbol,",\,"); put('replaceby,'fancy!-infix!-symbol,222); put('replaceby,'fancy!-symbol!-length,8); % symbols as prefix functions % put('gamma,'fancy!-functionsymbol,71); % big Gamma % put('!~,'fancy!-functionsymbol,34); % forall put('!~,'fancy!-symbol!-length,8); % arbint, arbcomplex. put('arbcomplex,'fancy!-functionsymbol,227); put('arbint,'fancy!-functionsymbol,226); flag('(arbcomplex arbint),'print!-indexed); % flag('(delta),'print!-indexed); % Dirac delta symbol. % David Hartley voted against.. % The following definitions allow for more natural printing of % conditional expressions within rule lists. symbolic procedure fancy!-condpri0 u; fancy!-condpri(u,0); symbolic procedure fancy!-condpri(u,p); fancy!-level begin scalar w; if p>0 then fancy!-prin2 "\bigl("; while (u := cdr u) and w neq 'failed do <<if not(caar u eq 't) then <<fancy!-prin2 'if; fancy!-prin2 " "; w:=fancy!-maprin0 caar u; fancy!-prin2 "\,"; fancy!-prin2 'then; fancy!-prin2 "\,">>; if w neq 'failed then w := fancy!-maprin0 cadar u; if cdr u then <<fancy!-prin2 "\,"; fancy!-prin2 'else; fancy!-prin2 "\,">>>>; if p>0 then fancy!-prin2 "\bigr)"; if overflowed!* or w='failed then return 'failed; end; put('cond,'fancy!-pprifn,'fancy!-condpri); put('cond,'fancy!-flatprifn,'fancy!-condpri0); symbolic procedure fancy!-revalpri u; fancy!-maprin0 fancy!-unquote cadr u; symbolic procedure fancy!-unquote u; if eqcar(u,'list) then for each x in cdr u collect fancy!-unquote x else if eqcar(u,'quote) then cadr u else u; put('aeval,'fancy!-prifn,'fancy!-revalpri); put('aeval!*,'fancy!-prifn,'fancy!-revalpri); put('reval,'fancy!-prifn,'fancy!-revalpri); put('reval!*,'fancy!-prifn,'fancy!-revalpri); put('aminusp!:,'fancy!-prifn,'fancy!-patpri); put('aminusp!:,'fancy!-pat,'(lessp !&1 0)); symbolic procedure fancy!-patpri u; begin scalar p; p:=subst(fancy!-unquote cadr u,'!&1, get(car u,'fancy!-pat)); return fancy!-maprin0 p; end; symbolic procedure fancy!-boolvalpri u; fancy!-maprin0 cadr u; put('boolvalue!*,'fancy!-prifn,'fancy!-boolvalpri); symbolic procedure fancy!-quotpri u; begin scalar n1,n2,fl,w,pos,testing!-width!*; if overflowed!* then return 'failed; testing!-width!*:=t; pos:=fancy!-pos!*; fl:=fancy!-line!*; fancy!-prin2!*("\frac",0); w:=fancy!-maprint!-tex!-bkt(cadr u,0,t); n1 := fancy!-pos!*; if w='failed then return fancy!-fail(pos,fl); fancy!-pos!* := pos; w := fancy!-maprint!-tex!-bkt(caddr u,0,nil); n2 := fancy!-pos!*; if w='failed then return fancy!-fail(pos,fl); fancy!-pos!* := max(n1,n2); return t; end; symbolic procedure fancy!-maprint!-tex!-bkt(u,p,m); % Produce expression with tex brackets {...} if % necessary. Ensure that {} unit is in same formula. % If m=t brackets will be inserted in any case. begin scalar w,pos,fl,testing!-width!*; testing!-width!*:=t; pos:=fancy!-pos!*; fl:=fancy!-line!*; if not m and (numberp u and 0<=u and u <=9 or liter u) then << fancy!-prin2!*(u,t); return if overflowed!* then fancy!-fail(pos,fl); >>; fancy!-prin2!*("{",0); w := fancy!-maprint(u,p); fancy!-prin2!*("}",0); if w='failed then return fancy!-fail(pos,fl); end; symbolic procedure fancy!-fail(pos,fl); << overflowed!* := nil; fancy!-pos!* := pos; fancy!-line!* := fl; 'failed >>; put('quotient,'fancy!-prifn,'fancy!-quotpri); symbolic procedure fancy!-prinfit(u, p, op); % Display u (as with maprint) with op in front of it, but starting % a new line before it if there would be overflow otherwise. begin scalar pos,fl,w,ll,f; if pairp u and (f:=get(car u,'fancy!-prinfit)) then return apply(f,{u,p,op}); pos:=fancy!-pos!*; fl:=fancy!-line!*; begin scalar testing!-width!*; testing!-width!*:=t; if op then w:=fancy!-oprin op; if w neq 'failed then w := fancy!-maprint(u,p); end; if w neq 'failed then return t; fancy!-line!*:=fl; fancy!-pos!*:=pos; if testing!-width!* and w eq 'failed then return w; if op='plus and eqcar(u,'minus) then <<op := 'minus; u:=cadr u>>; w:=if op then fancy!-oprin op; % if the operator causes the overflow, we break the line now. if w eq 'failed then <<fancy!-terpri!* nil; if op then fancy!-oprin op; return fancy!-maprint(u, p);>>; % if at least half the line is still free and the % object causing the overflow has been a number, % let it break. if fancy!-pos!* < (ll:=linelength(nil)) then if numberp u then return fancy!-prin2number u else if eqcar(u,'!:rd!:) then return fancy!-rdprin u; % generate a line break if we are not just behind an % opening bracket at the beginning of a line. if fancy!-pos!* > linelength nil #/ 2 or not eqcar(fancy!-last!-symbol(),'bkt) then fancy!-terpri!* nil; return fancy!-maprint(u, p); end; %----------------------------------------------------------- % % support for print format property % %----------------------------------------------------------- symbolic procedure print_format(f,pat); % Assign a print pattern p to the operator form f. put(car f, 'print!-format, (cdr f . pat) . get(car f, 'print!-format)); symbolic operator print_format; symbolic procedure fancy!-print!-format(u,p); fancy!-level begin scalar fmt,fmtl,a; fmtl:=get(car u,'print!-format); l: if null fmtl then return 'failed; fmt := car fmtl; fmtl := cdr fmtl; if length(car fmt) neq length cdr u then goto l; a:=pair(car fmt,cdr u); return fancy!-print!-format1(cdr fmt,p,a); end; symbolic procedure fancy!-print!-format1(u,p,a); begin scalar w,x,y,pl,bkt,obkt,q; if eqcar(u,'list) then u:= cdr u; while u and w neq 'failed do <<x:=car u; u:=cdr u; if eqcar(x,'list) then x:=cdr x; obkt := bkt; bkt:=nil; if obkt then fancy!-prin2!*('!{,0); w:=if pairp x then fancy!-print!-format1(x,p,a) else if memq(x,'(!( !) !, !. !|)) then <<if x eq '!( then <<pl:=p.pl; p:=0>> else if x eq '!) then <<p:=car pl; pl:=cdr pl>>; fancy!-prin2!*(x,1)>> else if x eq '!_ or x eq '!^ then <<bkt:=t;fancy!-prin2!*(x,0)>> else if q:=assoc(x,a) then fancy!-maprint(cdr q,p) else fancy!-maprint(x,p); if obkt then fancy!-prin2!*('!},0); >>; return w; end; %----------------------------------------------------------- % % some operator specific print functions % %----------------------------------------------------------- symbolic procedure fancy!-prefix!-operator(u); % Print as function, but with a special character. begin scalar sy; sy := get(u,'fancy!-functionsymbol) or get(u,'fancy!-special!-symbol); if sy then fancy!-special!-symbol(sy,get(u,'fancy!-symbol!-length) or 2) else fancy!-prin2!*(u,t); end; put('sqrt,'fancy!-prifn,'fancy!-sqrtpri); symbolic procedure fancy!-sqrtpri(u); fancy!-sqrtpri!*(cadr u,2); symbolic procedure fancy!-sqrtpri!*(u,n); fancy!-level begin if not numberp n and not liter n then return 'failed; fancy!-prin2!*("\sqrt",0); if n neq 2 then <<fancy!-prin2!*("[",0); fancy!-prin2!*("\,",1); fancy!-prin2!*(n,t); fancy!-prin2!*("]",0); >>; return fancy!-maprint!-tex!-bkt(u,0,t); end; symbolic procedure fancy!-sub(l,p); % Prints expression in an exponent notation. if get('expt,'infix)<=p then fancy!-in!-brackets({'fancy!-sub,mkquote l,0},'!(,'!)) else fancy!-level begin scalar eqs,w; l:=cdr l; while cdr l do <<eqs:=append(eqs,{car l}); l:=cdr l>>; l:=car l; testing!-width!* := t; w := fancy!-maprint(l,get('expt,'infix)); if w='failed then return w; fancy!-prin2!*("\bigl",0); fancy!-prin2!*("|",1); fancy!-prin2!*('!_,0); fancy!-prin2!*("{",0); w:=fancy!-inprint('!*comma!*,0,eqs); fancy!-prin2!*("}",0); return w; end; put('sub,'fancy!-pprifn,'fancy!-sub); put('factorial,'fancy!-pprifn,'fancy!-factorial); symbolic procedure fancy!-factorial(u,n); fancy!-level begin scalar w; w := (if atom cadr u then fancy!-maprint(cadr u,9999) else fancy!-in!-brackets({'fancy!-maprint,mkquote cadr u,0}, '!(,'!)) ); fancy!-prin2!*("!",2); return w; end; put('binomial,'fancy!-prifn,'fancy!-binomial); symbolic procedure fancy!-binomial(u,n); fancy!-level begin scalar w1,w2; fancy!-prin2!*("\left(\begin{array}{c}",2); w1 := fancy!-maprint(cadr u,0); fancy!-prin2!*("\\",0); w2 := fancy!-maprint(caddr u,0); fancy!-prin2!*("\end{array}\right)",2); if w1='failed or w2='failed then return 'failed; end; symbolic procedure fancy!-intpri(u,p); if p>get('times,'infix) then fancy!-in!-brackets({'fancy!-intpri,mkquote u,0},'!(,'!)) else fancy!-level begin scalar w1,w2; % if fancy!-mode!*>35 and fancy!-height(cadr u,1.0) > 3 then if fancy!-height(cadr u,1.0) > 3 then fancy!-prin2!*("\Int",0) else fancy!-prin2!*("\int",0); w1:=fancy!-maprint(cadr u,0); fancy!-prin2!*("\,d\,",2); w2:=fancy!-maprint(caddr u,0); if w1='failed or w2='failed then return 'failed; end; symbolic procedure fancy!-height(u,h); % estimate the height of an expression. if atom u then h else if car u = 'minus then fancy!-height(cadr u,h) else if car u = 'plus or car u = 'times then eval('max. for each w in cdr u collect fancy!-height(w,h)) else if car u = 'expt then fancy!-height(cadr u,h) + fancy!-height(caddr u,h*0.8) else if car u = 'quotient then fancy!-height(cadr u,h) + fancy!-height(caddr u,h) else if get(car u,'simpfn) then fancy!-height(cadr u,h) else h; put('int,'fancy!-pprifn,'fancy!-intpri); symbolic procedure fancy!-sumpri!*(u,p,mode); if p>get('minus,'infix) then fancy!-in!-brackets({'fancy!-sumpri!*,mkquote u,0,mkquote mode}, '!(,'!)) else fancy!-level begin scalar w,w0,w1,lo,hi,var; var := caddr u; if cdddr u then lo:=cadddr u; if lo and cddddr u then hi := car cddddr u; w:=if lo then {'equal,var,lo} else var; if mode = 'sum then fancy!-prin2!*("\sum",0) % big SIGMA else if mode = 'prod then fancy!-prin2!*("\prod",0); % big PI fancy!-prin2!*('!_,0); fancy!-prin2!*('!{,0); if w then w0:=fancy!-maprint(w,0); fancy!-prin2!*('!},0); if hi then <<fancy!-prin2!*('!^,0); fancy!-maprint!-tex!-bkt(hi,0,nil); >>; fancy!-prin2!*('!\!, ,1); w1:=fancy!-maprint(cadr u,0); if w0='failed or w1='failed then return 'failed; end; symbolic procedure fancy!-sumpri(u,p); fancy!-sumpri!*(u,p,'sum); put('sum,'fancy!-pprifn,'fancy!-sumpri); put('infsum,'fancy!-pprifn,'fancy!-sumpri); symbolic procedure fancy!-prodpri(u,p); fancy!-sumpri!*(u,p,'prod); put('prod,'fancy!-pprifn,'fancy!-prodpri); symbolic procedure fancy!-limpri(u,p); if p>get('minus,'infix) then fancy!-in!-brackets({'fancy!-sumpri,mkquote u,0},'!(,'!)) else fancy!-level begin scalar w,lo,var; var := caddr u; if cdddr u then lo:=cadddr u; fancy!-prin2!*("\lim",6); fancy!-prin2!*('!_,0); fancy!-prin2!*('!{,0); fancy!-maprint(var,0); fancy!-prin2!*("\to",0); fancy!-maprint(lo,0); fancy!-prin2!*('!},0); w:=fancy!-maprint(cadr u,0); return w; end; put('limit,'fancy!-pprifn,'fancy!-limpri); symbolic procedure fancy!-listpri(u); fancy!-level (if null cdr u then fancy!-maprint('empty!-set,0) else fancy!-in!-brackets( {'fancy!-inprintlist,mkquote '!*wcomma!*,0,mkquote cdr u}, '!{,'!}) ); put('list,'fancy!-prifn,'fancy!-listpri); put('list,'fancy!-flatprifn,'fancy!-listpri); put('!*sq,'fancy!-reform,'fancy!-sqreform); symbolic procedure fancy!-sqreform u; prepsq!* sqhorner!* cadr u; put('df,'fancy!-pprifn,'fancy!-dfpri); % 9-Dec-93: 'total repaired symbolic procedure fancy!-dfpri(u,l); (if flagp(cadr u,'print!-indexed) or pairp cadr u and flagp(caadr u,'print!-indexed) then fancy!-dfpriindexed(u,l) else if m = 'partial then fancy!-dfpri0(u,l,'partial!-df) else if m = 'total then fancy!-dfpri0(u,l,'!d) else if m = 'indexed then fancy!-dfpriindexed(u,l) else rederr "unknown print mode for DF") where m=fancy!-mode('fancy_print_df); symbolic procedure fancy!-partialdfpri(u,l); fancy!-dfpri0(u,l,'partial!-df); symbolic procedure fancy!-dfpri0(u,l,symb); if null cddr u then fancy!-maprin0{'times,symb,cadr u} else if l >= get('expt,'infix) then % brackets if exponented fancy!-in!-brackets({'fancy!-dfpri0,mkquote u,0,mkquote symb}, '!(,'!)) else fancy!-level begin scalar x,d,q; integer n,m; u:=cdr u; q:=car u; u:=cdr u; while u do <<x:=car u; u:=cdr u; if u and numberp car u then <<m:=car u; u := cdr u>> else m:=1; n:=n+m; d:= append(d,{symb,if m=1 then x else {'expt,x,m}}); >>; return fancy!-maprin0 {'quotient, {'times,if n=1 then symb else {'expt,symb,n},q}, 'times. d}; end; symbolic procedure fancy!-dfpriindexed(u,l); if null cddr u then fancy!-maprin0{'times,'partial!-df,cadr u} else begin scalar w; w:=fancy!-maprin0 cadr u; if testing!-width!* and w='failed then return w; w :=fancy!-print!-indexlist fancy!-dfpriindexedx(cddr u,nil); return w; end; symbolic procedure fancy!-dfpriindexedx(u,p); if null u then nil else if numberp car u then append(for i:=2:car u collect p,fancy!-dfpriindexedx(cdr u,p)) else car u . fancy!-dfpriindexedx(cdr u,car u); put('!:rd!:,'fancy!-prifn,'fancy!-rdprin); put('!:rd!:,'fancy!-flatprifn,'fancy!-rdprin); symbolic procedure fancy!-rdprin u; fancy!-level begin scalar digits; integer dotpos,xp; u:=rd!:explode u; digits := car u; xp := cadr u; dotpos := caddr u; return fancy!-rdprin1(digits,xp,dotpos); end; symbolic procedure fancy!-rdprin1(digits,xp,dotpos); begin scalar str; if xp>0 and dotpos+xp<length digits-1 then <<dotpos := dotpos+xp; xp:=0>>; % build character string from number. for i:=1:dotpos do <<str := car digits . str; digits := cdr digits; if null digits then digits:='(!0); >>; str := '!. . str; for each c in digits do str :=c.str; if not(xp=0) then <<str:='!e.str; for each c in explode2 xp do str:=c.str>>; if testing!-width!* and fancy!-pos!* + 2#*length str > 2 #* linelength nil then return 'failed; fancy!-prin2number1 reversip str; end; put('!:cr!:,'fancy!-pprifn,'fancy!-cmpxprin); put('!:cr!:,'fancy!-pprifn,'fancy!-cmpxprin); symbolic procedure fancy!-cmpxprin(u,l); begin scalar rp,ip; rp:=reval {'repart,u}; ip:=reval {'impart,u}; return fancy!-maprint( if ip=0 then rp else if rp=0 then {'times,ip,'!i} else {'plus,rp,{'times,ip,'!i}},l); end; symbolic procedure fancy!-dn!:prin u; begin scalar lst; integer dotpos,ex; lst := bfexplode0x (cadr u, cddr u); ex := cadr lst; dotpos := caddr lst; lst := car lst; return fancy!-rdprin1 (lst,ex,dotpos) end; put ('!:dn!:, 'fancy!-prifn, 'fancy!-dn!:prin); fmp!-switch t; endmodule; %------------------------------------------------------- module f; % Matrix printing routines. fluid '(!*nat); fluid '(obrkp!*); symbolic procedure fancy!-setmatpri(u,v); fancy!-matpri1(cdr v,u); put('mat,'fancy!-setprifn,'fancy!-setmatpri); symbolic procedure fancy!-matpri u; fancy!-matpri1(cdr u,nil); put('mat,'fancy!-prifn,'fancy!-matpri); symbolic procedure fancy!-matpri1(u,x); % Prints a matrix canonical form U with name X. % Tries to do fancy display if nat flag is on. begin scalar w; w := fancy!-matpri2(u,x,nil); if w neq 'failed or testing!-width!* then return w; fancy!-matpri3(u,x); end; symbolic procedure fancy!-matpri2(u,x,bkt); % Tries to print matrix as compact block. fancy!-level begin scalar w,testing!-width!*,fl,fp,fmat,row,elt,fail; integer cols,rows,rw,maxpos; testing!-width!*:=t; rows := length u; cols := length car u; if cols*rows>400 then return 'failed; if x then << fancy!-maprint(x,0); fancy!-prin2!*(":=",4) >>; fl := fancy!-line!*; fp := fancy!-pos!*; % remaining room for the columns. rw := linelength(nil)-2 -(fancy!-pos!*+2); rw := rw/cols; fmat := for each row in u collect for each elt in row collect if not fail then <<fancy!-line!*:=nil; fancy!-pos!*:=0; w:=fancy!-maprint(elt,0); if fancy!-pos!*>maxpos then maxpos:=fancy!-pos!*; if w='failed or fancy!-pos!*>rw then fail:=t else (fancy!-line!*.fancy!-pos!*) >>; if fail then return 'failed; testing!-width!* := nil; % restore output line. fancy!-pos!* := fp; fancy!-line!* := fl; % TEX header fancy!-prin2!*(bldmsg("\left%w\begin{array}{", if bkt then car bkt else "("),0); for i:=1:cols do fancy!-prin2!*("c",0); fancy!-prin2!*("}",0); % join elements. while fmat do <<row := car fmat; fmat:=cdr fmat; while row do <<elt:=car row; row:=cdr row; fancy!-line!* := append(car elt,fancy!-line!*); if row then fancy!-line!* :='!& . fancy!-line!* else if fmat then fancy!-line!* := "\\". fancy!-line!*; >>; >>; fancy!-prin2!*(bldmsg("\end{array}\right%w", if bkt then cdr bkt else ")"),0); % compute total horizontal extent of matrix fancy!-pos!* := fp + maxpos*(cols+1); return t; end; symbolic procedure fancy!-matpri3(u,x); if null x then fancy!-matpriflat('mat.u) else begin scalar obrkp!*,!*list; integer r,c; obrkp!* := nil; if null x then x:='mat; fancy!-terpri!*; for each row in u do <<r:=r+1; c:=0; for each elt in row do << c:=c+1; if not !*nero then << fancy!-prin2!*(x,t); fancy!-print!-indexlist {r,c}; fancy!-prin2!*(":=",t); fancy!-maprint(elt,0); fancy!-terpri!* t; >>; >>; >>; end; symbolic procedure fancy!-matpriflat(u); begin fancy!-oprin 'mat; fancy!-in!-brackets( {'fancy!-matpriflat1,mkquote '!*wcomma!*,0,mkquote cdr u}, '!(,'!)); end; symbolic procedure fancy!-matpriflat1(op,p,l); % inside algebraic list begin scalar fst,w; for each v in l do <<if fst then << fancy!-prin2!*("\,",1); fancy!-oprin op; fancy!-prin2!*("\,",1); >>; % if the next row does not fit on the current print line % we move it completely to a new line. if fst then w:= fancy!-level fancy!-in!-brackets( {'fancy!-inprintlist,mkquote '!*wcomma!*,0,mkquote v}, '!(,'!)) where testing!-width!*=t; if w eq 'failed then fancy!-terpri!* t; if not fst or w eq 'failed then fancy!-in!-brackets( {'fancy!-inprintlist,mkquote '!*wcomma!*,0,mkquote v}, '!(,'!)); fst := t; >>; end; put('mat,'fancy!-flatprifn,'fancy!-matpriflat); symbolic procedure fancy!-matfit(u,p,op); % Prinfit routine for matrix. % a new line before it if there would be overflow otherwise. fancy!-level begin scalar pos,fl,fp,w,ll; pos:=fancy!-pos!*; fl:=fancy!-line!*; begin scalar testing!-width!*; testing!-width!*:=t; if op then w:=fancy!-oprin op; if w neq 'failed then w := fancy!-matpri(u); end; if w neq 'failed or (w eq 'failed and testing!-width!*) then return w; fancy!-line!*:=fl; fancy!-pos!*:=pos; w:=nil; fp := fancy!-page!*; % matrix: give us a second chance with a fresh line begin scalar testing!-width!*; testing!-width!*:=t; if op then w:=fancy!-oprin op; fancy!-terpri!* nil; if w neq 'failed then w := fancy!-matpri u; end; if w neq 'failed then return t; fancy!-line!*:=fl; fancy!-pos!*:=pos; fancy!-page!*:=fp; ll:=linelength nil; if op then fancy!-oprin op; if atom u or fancy!-pos!* > ll #/ 2 then fancy!-terpri!* nil; return fancy!-matpriflat(u); end; put('mat,'fancy!-prinfit,'fancy!-matfit); put('taylor!*,'fancy!-reform,'Taylor!*print1); endmodule; module fancy_specfn; put('besseli,'fancy!-prifn,'fancy!-bessel); put('besselj,'fancy!-prifn,'fancy!-bessel); put('bessely,'fancy!-prifn,'fancy!-bessel); put('besselk,'fancy!-prifn,'fancy!-bessel); put('besseli,'fancy!-functionsymbol,'(ascii 73)); put('besselj,'fancy!-functionsymbol,'(ascii 74)); put('bessely,'fancy!-functionsymbol,'(ascii 89)); put('besselk,'fancy!-functionsymbol,'(ascii 75)); symbolic procedure fancy!-bessel(u); fancy!-level begin scalar w; fancy!-prefix!-operator car u; w:=fancy!-print!-one!-index cadr u; if testing!-width!* and w eq 'failed then return w; return fancy!-print!-function!-arguments cddr u; end; % Hypergeometric functions. put('empty!*,'fancy!-special!-symbol,32); put('hypergeometric,'fancy!-prifn,'fancy!-hypergeometric); symbolic procedure fancy!-hypergeometric u; fancy!-level begin scalar w,a1,a2,a3; a1 :=cdr cadr u; a2 := cdr caddr u; a3 := cadddr u; fancy!-special!-symbol(get('empty!*,'fancy!-special!-symbol),nil); w:=fancy!-print!-one!-index length a1; if testing!-width!* and w eq 'failed then return w; fancy!-prin2!*("F",nil); w:=fancy!-print!-one!-index length a2; if testing!-width!* and w eq 'failed then return w; fancy!-prin2!*("(",nil); w := w eq 'failed or fancy!-print!-indexlist1(a1,'!^,'!*comma!*); w := w eq 'failed or fancy!-print!-indexlist1(a2,'!_,'!*comma!*); fancy!-prin2!*("\,",1); w := w eq 'failed or fancy!-special!-symbol(124,1); % vertical bar fancy!-prin2!*("\,",1); w := w eq 'failed or fancy!-prinfit(a3,0,nil); fancy!-prin2!*(")",nil); return w; end; % hypergeometric({1,2,u/w,v},{5,6},sqrt x); put('meijerg,'fancy!-prifn,'fancy!-meijerG); symbolic procedure fancy!-meijerG u; fancy!-level begin scalar w,a1,a2,a3; integer n,m,p,q; a1 :=cdr cadr u; a2 := cdr caddr u; a3 := cadddr u; m:=length cdar a2; n:=length cdar a1; a1 := append(cdar a1 , cdr a1); a2 := append(cdar a2 , cdr a2); p:=length a1; q:=length a2; fancy!-prin2!*("G",nil); w := w eq 'failed or fancy!-print!-indexlist1({m,n},'!^,nil); w := w eq 'failed or fancy!-print!-indexlist1({p,q},'!_,nil); fancy!-prin2!*("(",nil); w := w eq 'failed or fancy!-prinfit(a3,0,nil); w := w eq 'failed or fancy!-special!-symbol(124,1); % vertical bar w := w eq 'failed or fancy!-print!-indexlist1(a1,'!^,'!*comma!*); w := w eq 'failed or fancy!-print!-indexlist1(a2,'!_,'!*comma!*); fancy!-prin2!*(")",nil); return w; end; % meijerg({{},1},{{0}},x); endmodule; end;