diff options
Diffstat (limited to 'texmf-dist/scripts/ketpic/ketlib/oshima')
-rw-r--r-- | texmf-dist/scripts/ketpic/ketlib/oshima/os_muldif.pdf | bin | 2214196 -> 0 bytes | |||
-rw-r--r-- | texmf-dist/scripts/ketpic/ketlib/oshima/os_muldif.rr | 18855 |
2 files changed, 0 insertions, 18855 deletions
diff --git a/texmf-dist/scripts/ketpic/ketlib/oshima/os_muldif.pdf b/texmf-dist/scripts/ketpic/ketlib/oshima/os_muldif.pdf Binary files differdeleted file mode 100644 index d3d06401..00000000 --- a/texmf-dist/scripts/ketpic/ketlib/oshima/os_muldif.pdf +++ /dev/null diff --git a/texmf-dist/scripts/ketpic/ketlib/oshima/os_muldif.rr b/texmf-dist/scripts/ketpic/ketlib/oshima/os_muldif.rr deleted file mode 100644 index badddccb..00000000 --- a/texmf-dist/scripts/ketpic/ketlib/oshima/os_muldif.rr +++ /dev/null @@ -1,18855 +0,0 @@ -/* The latest version will be at ftp://akagi.ms.u-tokyo.ac.jp/pub/math/muldif - scp os_muldif.[dp]* ${USER}@lemon.math.kobe-u.ac.jp:/home/web/OpenXM/Current/doc/other-docs -*/ -#define USEMODULE 1 -/* #undef USEMODULE */ - -/* os_muldif.rr (Library for Risa/Asir) - * Toshio Oshima (Nov. 2007 - June 2017) - * - * For polynomials and differential operators with coefficients - * in rational funtions (See os_muldif.pdf) - * - * "Tab = 4 column" is best - */ - -ord([zz,dz,dy,dx])$ - -#ifdef USEMODULE -module os_md; -static Muldif.rr$ -static TeXEq$ -static TeXLim$ -static DIROUT$ -static DIROUTD$ -static DVIOUTL$ -static DVIOUTA$ -static DVIOUTB$ -static DVIOUTH$ -static DVIOUTF$ -static LCOPT$ -static COLOPT$ -static LPOPT$ -static LFOPT$ -static ErMsg$ -static FLIST$ -static IsYes$ -static XYPrec$ -static XYcm$ -static TikZ$ -static XYLim$ -static Canvas$ -static ID_PLOT$ -static Rand$ -static LQS$ -localf spType2$ -localf erno$ -localf chkfun$ -localf makev$ -localf shortv$ -localf makenewv$ -localf vweyl$ -localf mycat$ -localf mycat0$ -localf fcat$ -localf findin$ -localf countin$ -localf mycoef$ -localf mydiff$ -localf myediff$ -localf m2l$ -localf m2ll$ -localf mydeg$ -localf pfctr$ -localf mymindeg$ -localf m1div$ -localf mulsubst$ -localf cmpsimple$ -localf simplify$ -localf monotos$ -localf minustos$ -localf monototex$ -localf vnext$ -localf ldict$ -localf ndict$ -localf nextsub$ -localf nextpart$ -localf transpart$ -localf trpos$ -localf sprod$ -localf sinv$ -localf slen$ -localf sord$ -localf vprod$ -localf dvangle$ -localf dvprod$ -localf dnorm$ -localf mulseries$ -localf pluspower$ -localf vtozv$ -localf dupmat$ -localf matrtop$ -localf mytrace$ -localf mydet$ -localf mperm$ -localf mtranspose$ -localf mtoupper$ -localf mydet2$ -localf myrank$ -localf meigen$ -localf transm$ -localf vgen$ -localf mmc$ -localf lpgcd$ -localf mdivisor$ -localf mdsimplify$ -localf m2mc$ -localf easierpol$ -localf paracmpl$ -localf mykernel$ -localf myimage$ -localf mymod$ -localf mmod$ -localf ladd$ -localf lchange$ -localf llsize$ -localf llbase$ -localf lsort$ -localf lmax$ -localf lmin$ -localf lgcd$ -localf llcm$ -localf ldev$ -localf lsol$ -localf lnsol$ -localf l2p$ -localf m2v$ -localf lv2m$ -localf m2lv$ -localf s2m$ -localf c2m$ -localf m2diag$ -localf myinv$ -localf madjust$ -localf mpower$ -localf mrot$ -localf texlen$ -localf isdif$ -localf fctrtos$ -localf texlim$ -localf fmult$ -localf radd$ -localf getel$ -localf ptol$ -localf rmul$ -localf mtransbys$ -localf drawopt$ -localf execdraw$ -localf execproc$ -localf myswap$ -localf mysubst$ -localf evals$ -localf myval$ -localf myeval$ -localf mydeval$ -localf myfeval$ -localf myf2eval$ -localf myf3eval$ -localf myfdeval$ -localf myf2deval$ -localf myf3deval$ -localf myexp$ -localf mycos$ -localf mysin$ -localf mytan$ -localf myarg$ -localf myasin$ -localf myacos$ -localf myatan$ -localf mylog$ -localf mypow$ -localf scale$ -localf arg$ -localf sqrt$ -localf gamma$ -localf lngamma$ -localf digamma$ -localf dilog$ -localf zeta$ -localf eta$ -localf jell$ -localf frac$ -localf erfc$ -localf fouriers$ -localf todf$ -localf f2df$ -localf df2big$ -localf compdf$ -localf fzero$ -localf fmmx$ -localf flim$ -localf fcont$ -localf fresidue$ -localf mmulbys$ -localf appldo$ -localf appledo$ -localf muldo$ -localf jacobian$ -localf hessian$ -localf wronskian$ -localf adj$ -localf laplace1$ -localf laplace$ -localf mce$ -localf mc$ -localf rede$ -localf ad$ -localf add$ -localf vadd$ -localf addl$ -localf cotr$ -localf rcotr$ -localf muledo$ -localf mulpdo$ -localf transpdosub$ -localf transpdo$ -localf translpdo$ -localf rpdiv$ -localf mygcd$ -localf mylcm$ -localf sftpexp$ -localf applpdo$ -localf tranlpdo$ -localf divdo$ -localf qdo$ -localf sqrtdo$ -localf ghg$ -localf ev4s$ -localf b2e$ -localf sftpow$ -localf sftpowext$ -localf polinsft$ -localf pol2sft$ -localf polroots$ -localf fctri$ -localf binom$ -localf expower$ -localf seriesHG$ -localf seriesMc$ -localf seriesTaylor$ -localf evalred$ -localf toeul$ -localf fromeul$ -localf sftexp$ -localf fractrans$ -localf soldif$ -localf chkexp$ -localf sqrtrat$ -localf getroot$ -localf expat$ -localf polbyroot$ -localf polbyvalue$ -localf pcoef$ -localf prehombf$ -localf prehombfold$ -localf sub3e$ -localf fuchs3e$ -localf okubo3e$ -localf eosub$ -localf even4e$ -localf odd5e$ -localf extra6e$ -localf rigid211$ -localf solpokuboe$ -localf stoe$ -localf dform$ -localf polinvsym$ -localf polinsym$ -localf tohomog$ -localf substblock$ -localf okuboetos$ -localf heun$ -localf fspt$ -localf abs$ -localf calc$ -localf isint$ -localf israt$ -localf iscrat$ -localf isalpha$ -localf isnum$ -localf isalphanum$ -localf isdecimal$ -localf isvar$ -localf isyes$ -localf isall$ -localf iscoef$ -localf iscombox$ -localf sproot$ -localf spgen$ -localf chkspt$ -localf cterm$ -localf terms$ -localf polcut$ -localf redgrs$ -localf cutgrs$ -localf mcgrs$ -localf mc2grs$ -localf mcmgrs$ -localf anal2sp$ -localf delopt$ -localf str_char$ -localf str_pair$ -localf str_cut$ -localf str_str$ -localf str_subst$ -localf str_times$ -localf str_tb$ -localf strip$ -localf i2hex$ -localf sjis2jis$ -localf jis2sjis$ -localf s2os$ -localf l2os$ -localf r2os$ -localf s2euc$ -localf s2sjis$ -localf r2ma$ -localf evalma$ -localf ssubgrs$ -localf verb_tex_form$ -localf tex_cuteq$ -localf my_tex_form$ -localf texket$ -localf smallmattex$ -localf divmattex$ -localf dviout0$ -localf myhelp$ -localf isMs$ -localf showbyshell$ -localf readcsv$ -localf tocsv$ -localf getbyshell$ -localf show$ -localf dviout$ -localf rtotex$ -localf mtotex$ -localf ltotex$ -localf texbegin$ -localf texcr$ -localf texsp$ -localf getbygrs$ -localf mcop$ -localf shiftop$ -localf conf1sp$ -localf pgen$ -localf diagm$ -localf mgen$ -localf madj$ -localf newbmat$ -localf unim$ -localf pfrac$ -localf cfrac$ -localf cfrac2n$ -localf sqrt2rat$ -localf s2sp$ -localf sp2grs$ -localf fimag$ -localf trig2exp$ -localf intpoly$ -localf integrate$ -localf simplog$ -localf fshorter$ -localf isshortneg$ -localf intrat$ -localf powsum$ -localf bernoulli$ -localf lft01$ -localf linfrac01$ -localf nthmodp$ -localf issquaremodp$ -localf rootmodp$ -localf rabin$ -localf primroot$ -localf varargs$ -localf ptype$ -localf pfargs$ -localf average$ -localf sint$ -localf frac2n$ -localf xyproc$ -localf xypos$ -localf xyput$ -localf xybox$ -localf xyline$ -localf xylines$ -localf xycirc$ -localf xybezier$ -localf lbezier$ -localf draw_bezier$ -localf tobezier$ -localf velbezier$ -localf ptbezier$ -localf cutf$ -localf fsum$ -localf fint$ -localf periodicf$ -localf cmpf$ -localf areabezier$ -localf saveproc$ -localf xygraph$ -localf xy2graph$ -localf xyarrow$ -localf xyarrows$ -localf xyang$ -localf xyoval$ -localf ptcommon$ -localf ptcopy$ -localf ptaffine$ -localf ptlattice$ -localf ptpolygon$ -localf ptwindow$ -localf ptbbox$ -localf lninbox$ -localf ptcombezier$ -localf ptcombz$ -localf lchange$ -localf init$ -localf powprimroot$ -localf distpoint$ -localf ntable$ -localf keyin$ -localf mqsub$ -localf msort$ -#else -extern Muldif.rr$ -extern TeXEq$ -extern TeXLim$ -extern DIROUT$ -extern DIROUTD$ -extern DVIOUTL$ -extern DVIOUTA$ -extern DVIOUTB$ -extern DVIOUTH$ -extern DVIOUTF$ -static LCOPT$ -static COLOPT$ -static LPOPT$ -static LFOPT$ -extern TikZ$ -extern ErMsg$ -extern FLIST$ -extern IsYes$ -extern XYPrec$ -extern XYcm$ -extern TikZ$ -extern XYLim$ -extern Canvas$ -extern ID_PLOT$ -extern Rand$ -extern LQS$ -#endif -static S_Fc,S_Dc,S_Ic,S_Ec,S_EC,S_Lc$ -static S_FDot$ -extern AMSTeX$ -Muldif.rr="00170612"$ -AMSTeX=1$ -TeXEq=5$ -TeXLim=80$ -TikZ=0$ -XYcm=0$ -XYPrec=3$ -XYLim=4$ -Rand=0$ -DIROUT="%HOME%\\tex"$ -DVIOUTL="%ASIRROOT%\\bin\\risatex0.bat"$ -DVIOUTA="%ASIRROOT%\\bin\\risatex.bat"$ -DVIOUTB="%ASIRROOT%\\bin\\risatex1%TikZ%.bat"$ -DVIOUTH="start dviout -2 -hyper=0x90 \"%ASIRROOT%\\help\\os_muldif.dvi\" #%LABEL%"$ -DVIOUTF=0$ -LCOPT=["red","green","blue","yellow","cyan","magenta","black","white","gray"]$ -COLOPT=[0xff,0xff00,0xff0000,0xffff,0xffff00,0xff00ff,0,0xffffff,0xc0c0c0]$ -LPOPT=["above","below","left","right"]$ -LFOPT=["very thin","thin","dotted","dashed"]$ -Canvas=[400,400]$ -LQS=[[1,0]]$ - -ErMsg = newvect(3,[ - "irregal argument", /* 0 */ - "too big size", /* 1 */ - "irregal option" /* 2 */ -])$ -FLIST=0$ -IsYes=[]$ -ID_PLOT=-1$ - -def erno(N) -{ - /* extern ErMsg; */ - print(ErMsg[N]); -} - -def chkfun(Fu, Fi) -{ - /* extern FLIST; */ - /* extern Muldif.rr; */ - - if(type(Fu) <= 1){ - if(Fu==1) - mycat(["Loaded os_muldif Ver.", Muldif.rr, "(Toshio Oshima)"]); - else - mycat(["Risa/Asir Ver.", version()]); - return 1; - } - if(type(FLIST) < 4) - FLIST = flist(); - if(type(Fu) == 4){ - for(; Fu != [] ;Fu = cdr(Fu)) - if(chkfun(car(Fu),Fi) == 0) return 0; - return 1; - } - if(findin(Fu, FLIST) >= 0) - return 1; - FLIST = flist(); - if(findin(Fu, FLIST) >= 0) - return 1; - if(type(Fi)==7){ - mycat0(["load(\"", Fi,"\") -> try again!\n"],1); - load(Fi); - } - return 0; -/* - if(type(Fi) == 7) - Fi = [Fi]; - for( ; Fi != []; Fi = cdr(Fi)) - load(car(Fi)); - FLIST = flist(); - return (findin(Fu,FLIST)>=0)?1:0; -*/ -} - -def makev(L) -{ - S = ""; - Num=getopt(num); - while(length(L) > 0){ - VL = car(L); L = cdr(L); - if(type(VL) == 7) - S = S+VL; - else if(type(VL) == 2 || VL < 10) - S = S+rtostr(VL); - else if(VL<46 && Num!=1) - S = S+asciitostr([VL+87]); - else - S = S+rtostr(VL); - } - return strtov(S); -} - -def makenewv(L) -{ - if((V=getopt(var))<2) V="z_"; - else if(isvar(V)) V=rtostr(V); - if(type(N=getopt(num))!=1) N=0; - Var=vars(L); - for(Va=Var;Va!=[];Va=cdr(Va)) - if(vtype(car(Va))==2) Var=append(vars(args(car(Va))),Var); - for(XX=[],I=J=0;;I++){ - X=strtov(V+rtostr(I)); - if(findin(X,Var)<0){ - XX=cons(X,XX); - if(++J>N) return X; - else if(J==N) return reverse(XX); - } - } -} - -def shortv(P,L) -{ - V=vars(P); - if(type(T=getopt(top))==2) T=strtoascii(rtostr(T))[0]-87; - else T=10; - for(;L!=[];L=cdr(L)){ - for(J=0;J<36;J++){ - if(findin(X=makev([car(L),J]|num=1),V)>=0){ - while(findin(Y=makev([T]),V)>=0) T++; - if(T>35) return P; - P=subst(P,X,Y); - T++; - }else if(J>0) break; - } - } - return P; -} - -def vweyl(L) -{ - if(type(L) == 4){ - if(length(L) == 2) - return L; - else - return [L[0],makev(["d",L[0]])]; - } - /* else if(type(L)<2) return L; */ - return [L,makev(["d", L])]; -} - -def mycat(L) -{ - if(type(L) != 4){ - print(L); - return; - } - Opt = getopt(delim); - Del = (type(Opt) >= 0)?Opt:" "; - Opt = getopt(cr); - CR = (type(Opt) >= 0)?0:1; - while(L != []){ - if(Do==1) - print(Del,0); - print(car(L),0); - L=cdr(L); - Do = 1; - } - if(CR) print(""); -} - -def fcat(S,X) -{ - if(type(S)!=7){ - T="fcat"; - if(S>=2&&S<=9) T+=rtostr(S); - T=DIROUTD+T+".txt"; - if(S==-1) return T; - if(S!=0&&access(T)) remove_file(T); - S=T; - } - output(S); - print(X); - output(); - if(getopt(exe)==1) shell("\""+S+"\""); -} - -def mycat0(L,T) -{ - Opt = getopt(delim); - Del = (type(Opt) >= 0)?Opt:""; - while(L != []){ - if(Do==1) - print(Del,0); - print(car(L),0); - L=cdr(L); - Do = 1; - } - if(T) print(""); -} - -def findin(M,L) -{ - if(type(L)==4){ - for(I = 0; L != []; L = cdr(L), I++) - if(car(L) == M) return I; - }else if(type(L)==5){ - K=length(L); - for(I = 0; I < K; I++) - if(L[I] == M) return I; - }else return -2; - return -1; -} - -def countin(S,M,L) -{ - Step=getopt(step); - if(type(Step)==1){ - N=(Step>0)?Step:-Step; - if(type(L)==5) L=vtol(L); - L=qsort(L); - while(car(L)<S&&L!=[]) L=cdr(L); - S+=M; - for(R=[],C=I=0;L!=[];){ - if(car(L)<S||(Step>0&&car(L)==S)){ - C++; - L=cdr(L); - }else{ - R=cons(C,R);C=0;S+=M; - if(N>1&&++I>=N) break; - } - } - if(C>0) R=cons(C,R); - if(N>1&&(N-=length(R))>0) while(N-->0) R=cons(0,R); - return reverse(R); - } - if(type(L)==4){ - for(N=0; L!=[]; L=cdr(L)) - if(car(L)>=S && car(L)<=M) N++; - }else if(type(L)==5){ - K=length(L); - for(I = 0; I < K; I++) - if(L[I]>=S && L[I]<=M) N++; - }else return -2; - return N; -} - -def mycoef(P,N,X) -{ - if(type(P)<3 && type(N)<3) - return coef(P,N,X); - if(type(P) >= 4) -#ifdef USEMODULE - return map(os_md.mycoef,P,N,X); -#else - return map(mycoef,P,N,X); -#endif - if(type(N)==4){ - for(;N!=[];N=cdr(N),X=cdr(X)) - P=mycoef(P,car(N),car(X)); - return P; - } - if(deg(dn(P), X) > 0){ - P = red(P); - if(deg(dn(P), X) > 0) - return 0; - } - return red(coef(nm(P),N,X)/dn(P)); -} - -def mydiff(P,X) -{ - if(X == 0) - return 0; - if(type(P)<3 && type(X)<3) - return diff(P,X); - if(type(P) >= 4) -#ifdef USEMODULE - return map(os_md.mydiff,P,X); -#else - return map(mydiff,P,X); -#endif - if(type(X)==4){ - for(;X!=[];X=cdr(X)) P=mydiff(P,car(X)); - return P; - } - if(deg(dn(P),X) == 0) - return red(diff(nm(P),X)/dn(P)); - return red(diff(P,X)); -} - -def myediff(P,X) -{ - if(X == 0) - return 0; - if(type(P) < 3) - return ediff(P,X); - if(type(P) >= 4) -#ifdef USEMODULE - return map(os_md.myediff,P,X); -#else - return map(myediff,P,X); -#endif - if(deg(dn(P),X) == 0) - return red(ediff(nm(P),X)/dn(P)); - return red(X*diff(P,X)); -} - -def m2l(M) -{ - if(type(M) < 4) - return [M]; - if(type(M) == 4){ - if(type(car(M))==4 && getopt(flat)==1){ - for(MM = []; M!=[]; M=cdr(M)) - MM = append(MM,car(M)); - return MM; - } - return M; - } - if(type(M) == 5) - return vtol(M); - S = size(M); - for(MM = [], I = S[0]-1; I >= 0; I--) - MM = append(vtol(M[I]), MM); - return MM; -} - -def mydeg(P,X) -{ - if(type(P) < 3) - return deg(P,X); - II = -1; - Opt = getopt(opt); - if(type(P) >= 4){ - S=(type(P) == 6)?size(P)[0]:0; - P = m2l(P); - for(I = 0, Deg = -3; P != []; P = cdr(P), I++){ - if( (DT = mydeg(car(P),X)) == -2) - return -2; - if(DT > Deg){ - Deg = DT; - II = I; - } - } - return (Opt==1)?([Deg,(S==0)?II:[idiv(II,S),irem(II,S)]]):Deg; - } - P = red(P); - if(deg(dn(P),X) == 0) - return deg(nm(P),X); - return -2; -} - -def pfctr(P,X) -{ - P=red(P); - if((T=ptype(P,X))>3) return []; - if(T==3){ - G=pfctr(dn(P),X); - F=pfctr(nm(P),X); - R=[[car(F)[0]/car(G)[0],1]]; - for(F=cdr(F);F!=[];F=cdr(F)) R=cons(car(F),R); - for(G=cdr(G);G!=[];G=cdr(G)) R=cons([car(G)[0],-car(G)[1]],R); - return reverse(R); - } - F=fctr(nm(P)); - for(R=[],C=1/dn(P);F!=[];F=cdr(F)) - if(mydeg(car(F)[0],X)>0) R=cons(car(F),R); - else C*=car(F)[0]^car(F)[1]; - return cons([C,1],reverse(R)); -} - -def mymindeg(P,X) -{ - if(type(P) < 3) - return mindeg(P,X); - II = -1;T=60; - Opt = getopt(opt); - if(type(P) >= 4){ - S=(type(P) == 6)?size(P)[0]:0; - P = m2l(P); - for(I = 0, Deg = -3; P != []; P = cdr(P), I++){ - if(car(P) == 0) - continue; - if( (DT = mydeg(car(P),X)) == -2) - return -2; - if(DT < Deg || Deg == -3){ - if(DT==0){ - if(type(car(P))>=T) continue; - T=type(car(P)); - } - Deg = DT; - II = I; - } - } - return (Opt==1)?([Deg,(S==0)?II:[idiv(II,S),irem(II,S)]]):Deg; - } - P = red(P); - if(deg(dn(P),X) == 0) - return mindeg(nm(P),X); - return -2; -} - -def m1div(M,N,L) -{ - L = (type(L) <= 3)?[0,L]:vweyl[L]; - DX = L[1]; X = L[0]; - if(mydeg(N,DX) != 0) - return 0; - DD = mydeg(M,DX); - MM = M; - while( (Deg=mydeg(MM,DX)) > 0){ - MC = mycoef(MM,Deg,DX)*DX^(Deg-1); - MS = radd(MC, MS); - MM = radd(MM, muldo(MC,radd(-DX,N),L)); - } - return [MM, MS]; -} - - -def mulsubst(F,L) -{ - N = length(L); - if(N == 0) - return F; - if(type(L[0])!=4) L=[L]; - if(getopt(inv)==1){ - for(R=[];L!=[];L=cdr(L)) R=cons([car(L)[1],car(L)[0]],R); - L=reverse(R); - } - if(length(L)==1) return mysubst(F,L); - L1 = newvect(N); - for(J = 0; J < N ; J++) - L1[J] = uc(); - L2 = newvect(N); - for(J = 0; J < N; J++){ - S = L[J][1]; - for(I = 0; I < N; I++) - S = mysubst(S,[L[I][0],L1[I]]); - L2[J] = S; - } - for(J = 0; J < N; J++) - F = mysubst(F, [L[J][0],L2[J]]); - for(J = 0; J < N; J++) - F = mysubst(F, [L1[J],L[J][0]]); - return F; -} - -def cmpsimple(P,Q) -{ - T = getopt(comp); - if(P == Q) - return 0; - D = 0; - if(type(T) < 0) - T = 7; - if(iand(T,1)) - D = length(vars(P)) - length(vars(Q)); - if(!D && iand(T,2)) - D = nmono(P) - nmono(Q); - if(!D && iand(T,4)) - D = str_len(rtostr(P)) - str_len(rtostr(Q)); - if(!D){ - if(P > Q) D++; - else D--; - } - return D; -} - -def simplify(P,L,T) -{ - if(type(P) > 3) -#ifdef USEMODULE - return map(os_md.simplify,P,L,T); -#else - return map(simplify,P,L,T); -#endif - if(type(L[0]) == 4){ - if(length(L[0]) > 1) -#if USEMODULE - return fmult(os_md.simplify,P,L,[T]); -#else - return fmult(simplify,P,L,[T]); -#endif - L = L[0]; - } - if(type(Var=getopt(var)) == 4 && Var!=[]){ - if(type(P) == 3) - return simplify(nm(P),P,L,T|var=Var)/simplify(dn(P),P,L,T|var=Var); - V = car(Var); - if((I = mydeg(P,V)) > 0){ - Var = cdr(Var); - for(Q=0; I>=0 ; I--) - Q += simplify(mycoef(P,I,V), L, T|var=Var)*V^I; - return Q; - } - } - if(length(L) == 1){ - L = car(L); - for(V = vars(L); V != []; V = cdr(V)){ - VT = car(V); - if(deg(L,VT) != 1) continue; - P = simplify(P, [VT, -red(coef(L,0,VT)/coef(L,1,VT))], T); - } - return P; - } - Q = mysubst(P,[L[0],L[1]]); - return (cmpsimple(P,Q|comp=T) <= 0)?P:Q; -} - -def monotos(P) -{ - if(nmono(P) <= 1) - return rtostr(P); - return "("+rtostr(P)+")"; -} - - -def monototex(P) -{ - Q=my_tex_form(P); - if(nmono(P)<2 && (getopt(minus)!=1 || str_str(Q,"-"|top=0,end=0)<0)) - return Q; - return "("+Q+")"; -} - -def minustos(S) -{ - if(str_str(S,"-"|top=0,end=0)<0) return S; - return "("+S+")"; -} - -def vnext(V) -{ - S = length(V); - for(I = S-1; I > 0; I--){ - if(V[I-1] < V[I]){ - V0 = V[I-1]; - for(J = I+1; J < S; J++) - if(V0 >= V[J]) break; - V[I-1] = V[--J]; - V[J] = V0; - for(J = S-1; I < J; I++, J--){ - V0 = V[I]; - V[I] = V[J]; - V[J] = V0; - } - return 1; - } - } - return 0; -} - -def ldict(N, M) -{ - Opt = getopt(opt); - R = S = []; - for(I = 2; N > 0; I++){ - R = cons(irem(N,I), R); - N = idiv(N,I); - } - L = LL = length(R); - T=newvect(LL+1); - while(L-- > 0){ - V = car(R); R = cdr(R); - for(I = J = 0; J <= V ; I++){ - if(T[I] == 0) - J++; - } - T[I-1] = 1; - S = cons(LL-I+1, S); - } - for(I = 0; I <= LL; I++){ - if(T[I] == 0){ - S = cons(LL-I, S); - break; - } - } - if(M == 0) - return S; - if(M <= LL){ - print("too small size"); - return 0; - } - T = []; - for(I = --M; I > LL; I--) - T = cons(I,T); - S = append(S,T); - if(Opt == 2 || Opt == 3) - S = reverse(S); - if(Opt != 1 && Opt != 3) - return S; - for(T = []; S != []; S = cdr(S)) - T = cons(M-car(S),T); - return T; -} - -def ndict(L) -{ - Opt = getopt(opt); - R = []; - if(Opt != 1 && Opt != 2) - L = reverse(L); - T = (Opt == 1 || Opt == 3)?1:0; - for( ; L != []; L = cdr(L)){ - for(I = 0, V = car(L), LT = cdr(L); LT != []; LT = cdr(LT)) - if(T == 0){ - if(V < car(LT)) I++; - }else if (V > car(LT)) I++; - R = cons(I, R); - } - R = reverse(R); - for(V = 0, I = length(R); I > 0; R = cdr(R), I--) - V = V*I + car(R); - return V; -} - -def nextsub(L,N) -{ - if(type(L) == 1){ - for(LL = [], I = L-1; I >= 0; I--) - LL = cons(I,LL); - return LL; - } - M = length(L = ltov(L)); - K = N-M; - for(I = M-1; I >= 0; I--) - if(L[I] < I+K) break; - if(I < 0) - return 0; - for(J = L[I]+1; I < M; I++, J++) - L[I] = J; - return vtol(L); -} - -def nextpart(L) -{ - if(car(L) <= 1) - return 0; - for(I = 0, L = reverse(L); car(L) == 1; L=cdr(L)) - I++; - I += (K = car(L)); - R = irem(I,--K); - R = (R==0)?[]:[R]; - for(J = idiv(I,K); J > 0; J--) - R = cons(K,R); - L = cdr(L); - while(L!=[]){ - R = cons(car(L), R); - L = cdr(L); - } - return R; -} - -def transpart(L) -{ - L = reverse(L); - for(I=1, R=[]; L!= []; I++){ - R = cons(length(L), R); - while(L != [] && car(L) <= I) - L = cdr(L); - } - return reverse(R); -} - -def trpos(A,B,N) -{ - S = newvect(N); - for(I = 0; I < N; I++) - S[I]=(I==A)?B:((I==B)?A:I); - return S; -} - -def sprod(S,T) -{ - L = length(S); - V = newvect(L); - while(--L >= 0) - V[L] = S[T[L]]; - return V; -} - -def sinv(S) -{ - L = length(S); - V = newvect(L); - while(--L >= 0) - V[S[L]] = L; - return V; -} - -def slen(S) -{ - L = length(S); - for(V = 0, J = 2; J < L; i++){ - for(I = 0; I < J; I++) - if(S[I] > S[J]) V++; - } - return V; -} - -def sord(W,V) -{ - L = length(W); - W0 = nevect(L); - V0 = newvect(L); - for(I = F = C = 0; I < L; I++){ - C = 0; - if( (W1 = W[I]) > (V1 = V[I]) ){ - if(F < 0) C = 1; - else if(F==0) F = 1; - }else if(W1 < V1){ - if(F > 0) C = 1; - else if(F==0) F = -1; - } - for(J = I;--J >= 0 && W0[J] > W1; ) W0[J+1] = W0[J]; - W0[J+1] = W1; - for(J = I;--J >= 0 && V0[J] > V1; ) V0[J+1] = V0[J]; - V0[J+1] = V1; - if(C){ - for(J = I; J >= 0; J--){ - if((W1=W0[J]) == (V1=V0[J])) continue; - if(W1 > V1){ - if(F < 0) return 2; - } - else if(F > 0) return 2; - } - } - } - return F; -} - -def vprod(V1,V2) -{ - for(R = 0, I = length(V1)-1; I >= 0; I--) - R = radd(R, rmul(V1[I], V2[I])); - return R; -} - -def dnorm(V) -{ - if(type(V)<2) return dabs(V); - R=0; - if(type(V)!=4) - for (I = length(V)-1; I >= 0; I--) R+= V[I]^2; - else{ - if(type(V[0])>3){ - V=ltov(V[0])-ltov(V[1]); - return dnorm(V); - } - for(;V!=[]; V=cdr(V)) R+=car(V)^2; - } - return dsqrt(R); -} - -def dvprod(V1,V2) -{ - if(type(V1)<2) return V1*V2; - R=0; - if(type(V1)!=4) - for(I = length(V1)-1; I >= 0; I--) - R += V1[I]*V2[I]; - else{ - for(; V1!=[]; V1=cdr(V1),V2=cdr(V2)) - R+=car(V1)*car(V2); - } - return R; -} - -def dvangle(V1,V2) -{ - if(V2==0 && type(V1)==4 && length(V1)==3 && - (type(V1[0])==4 || type(V1[0])==5 || type(V1[1])==4 || type(V1[1])==5 || - type(V1[2])==4 || type(V1[2])==5) ){ - if(V1[0]==0 || V1[1]==0 || V1[2]==0) return 1; - PV2=V1[1]; - if(type(PV2)==4){ - PV2=ltov(PV2); - return dvangle(PV2-ltov(V1[0]),ltov(V1[2])-PV2); - }else - return dvangle(PV2-V1[0],V1[2]-PV2); - } - if((L1=dnorm(V1))==0 || (L2=dnorm(V2))==0) return 1; - return dvprod(V1,V2)/(L1*L2); -} - -def mulseries(V1,V2) -{ - L = length(V1); - if(size(V2) < L) - L = size(V2); - VV = newvect(L); - for(J = 0; J < L; J++){ - for(K = R = 0; K <= J; K++) - R = radd(R,rmul(V1[K],V2[J-K])); - VV[J] = R; - } - return VV; -} - -def scale(L) -{ - T=0;LS=1; - if(type(L)!=4){ - if(L==2){ - L=[[[1,2,1/20],[2,5,1/10],[5,10,1/5], [10,20,1/2],[20,50,1],[50,100,2]], - [[1,2,1/10],[2,5,1/2], [10,20,1],[20,50,5]], - [[1,2,1/2],[2,10,1], [10,20,5],[20,100,10]]]; - LS=2; - }else if(L==3){ - L=[[[1,2,1/20],[2,5,1/10],[5,10,1/5], [10,20,1/2],[20,50,1],[50,100,2], - [100,200,5],[200,500,10],[500,1000,20]], - [[1,2,1/10],[2,5,1/2], [10,20,1],[20,50,5], [100,200,10],[200,500,50]], - [[1,2,1/2],[2,10,1], [10,20,5],[20,100,10], [100,200,50],[200,1000,100]]]; - LS=3; - }else{ - L=[[[1,2,1/50],[5,10,1/2],[5,10,1/10]],[[1,5,1/10],[5,10,1/2]], - [[1,5,1/2],[5,10,1]]]; - } - }else if(type(L[0])!=4){ - L=[L]; - if(length(L)!=3||L[0]+L[2]>L[1]) T=L; - } - if(T==0){ - if(type(L[0][0])!=4) L=[L]; - for(R=[];L!=[];L=cdr(L)){ - for(RR=[],LT=car(L);LT!=[];LT=cdr(LT)) - for(I=car(LT)[0];I<=car(LT)[1];I+=car(LT)[2]) RR=cons(I,RR); - RR=lsort(RR,[],1); - R=cons(RR,R); - } - R=reverse(R); - for(T=[];R!=[];R=cdr(R)){ - if(length(R)>1) T=cons(lsort(R[0],R[1],"setminus"),T); - else T=cons(R[0],T); - } - } - V0=dlog(10); - S0=S1=1;D0=D1=0; - SC=getopt(scale); - if(type(SC)==4){ - S0=SC[0];S1=SC[1]; - }else if(type(S)==1){ - S0=S;S1=0; - }else return T; - if(type(D=getopt(shift))==4){ - D0=D[0];D1=D[1]; - } - if(type(F=getopt(f))>1) F=f2df(F); - else F=0; - for(M=[],I=length(T);T!=[];T=cdr(T),I--){ - for(S=car(T);S!=[];S=cdr(S)){ - V=((!F)?dlog(car(S))/dlog(10)/LS:myfdeval(F,car(S)))*S0; - if(S1!=0){ - M=cons([V+D0,D1],M); - M=cons([V+D0,I*((length(SC)>2)?SC[I]:S1)+D1],M); - M=cons(0,M); - }else M=cons(V+D0,M); - } - } - if(S1!=0) M=cdr(M); - M=reverse(M); - if(getopt(TeX)==1){ - if(type(U=getopt(line))==4) - M=cons([U[0]+D0,D1],cons([U[1]+D0,D1],cons(0,M))); - S=xylines(M); - if(type(Mes=getopt(mes))==4){ - S3=car(Mes); - V=car(scale(cdr(Mes))); - if(!F) Mes=scale(cdr(Mes)|scale=[S0/LS,0],shift=[D0,D1]); - else Mes=scale(cdr(Mes)|f=F,scale=[S0,0],shift=[D0,D1]); - for(M=Mes;M!=[];M=cdr(M),V=cdr(V)) - S+=xyput([car(M),S3,deval(car(V))]); - } - return S; - } - return M; -} - -def pluspower(P,V,N,M) -{ - RR = 1; - for(K = R = 1; K < M-1; I++){ - R = R*(N-K+1)*P/K; - RR = radd(RR,R); - } - VV = newvect(M); - for(K = 0; K < M-1; K++) - VV[K] = red(mycoef(RR,K,V)); -} - -def vtozv(V) -{ - if(type(V)<4) V=newvect(1,[V]); - S = length(V); - VV = newvect(S); - Lcm = 1; - for(K = 0; K < S; K++){ - VV[K] = red(V[K]); - Lcm = lcm(Lcm,dn(VV[K])); - C = ptozp(nm(VV[K])|factor=0); - if(K == 0){ - Dn = dn(C[1]); - Nm = nm(C[1]); - PNm = nm(C[0]); - }else{ - Dn = ilcm(Dn,dn(C[1])); - Nm = igcd(Nm,nm(C[1])); - PNm = gcd(PNm,nm(C[0])); - } - } - if(!(M=Nm*PNm)) return [VV,0]; - Mul = (Lcm*Dn)/M; - for(K = 0; K < S; K++) - VV[K] = rmul(VV[K],Mul); - return [VV,Mul]; -} - -def dupmat(M) -{ - if(type(M) == 6){ - Size = size(M); - MM = newmat(Size[0],Size[1]); - for(I = 0; I < Size[0]; I++){ - for(J = 0; J < Size[1]; J++) - MM[I][J] = M[I][J]; - } - return MM; - } - if(type(M) == 5) - return ltov(vtol(M)); - return M; -} - -def matrtop(M) -{ - S = size(M); - MM = dupmat(M); - Lcm = newvect(S[0]); - for(J = 0; J < S[0]; J++){ - U = vtozv(M[J]); - for(K = -1, I = 0; I < S[1]; I++) - MM[J][I] = U[0][I]; - Lcm[J] = U[1]; - } - return [MM,Lcm]; -} - -def mytrace(M) -{ - S=size(M); - if(S[0]!=S[1]) return 0; - for(I=V=0; I<S[0]; I++){ - V+=M[I][I]; - } - return V; -} - -def mydet(M) -{ - MM = matrtop(M); - if(type(MM[0]) == 6){ - S = size(M); - for(Dn = 1, I = 0; I < S[0]; I++) - Dn *= MM[1][I]; - return (!Dn)?0:red(det(MM[0])/Dn); - } -} - -def mperm(M,P,Q) -{ - if(type(M) == 6){ - S = size(M); - if(type(P) <= 1) - P=(P==1)?Q:trpos(0,0,S[0]); - if(type(P) > 3 && type(P[0]) >= 4) - P = trpos(P[0][0],P[0][1],S[0]); - else if(type(P) == 4){ - if(length(P)==2 && type(P[1])==4){ - P0=P[0];P1=car(P[1]);P=newvect(P1); - for(I=0;I<P1;I++) P[I]=P0+I; - }else P = ltov(P); - } - if(type(Q) <= 1) - Q=(Q==1)?P:trpos(0,0,S[1]); - if(type(Q) > 3 && type(Q[0]) >= 4) - Q = trpos(Q[0][0],Q[0][1],S[1]); - if(type(Q) == 4){ - if(length(Q)==2 && type(Q[1])==4){ - P0=Q[0];P1=car(Q[1]);Q=newvect(P1); - for(I=0;I<P1;I++) Q[I]=P0+I; - }else Q = ltov(Q); - } - MM = newmat(S0=length(P),S1=length(Q)); - for(I = 0; I < S0; I++){ - MMI = MM[I]; MPI = M[P[I]]; - for(J = 0; J < S1; J++) - MMI[J] = MPI[Q[J]]; - } - return MM; - } - if((type(M) == 5 || type(M) == 4) && type(P) >= 4){ - if(length(P) == 1 && type(car(P)) == 4) - P = trpos(car(P)[0],car(P)[1],length(M)); - MM = newvect(S = length(P)); - for(I = 0; I < S; I++) - MM[I] = M[P[I]]; - if(type(M) == 4) - MM = vtol(MM); - return MM; - } - return M; -} - -def mtranspose(M) -{ - if(type(M)==4){ - MV=ltov(M); - II=length(MV); - for(I=L=0; I<II; I++){ - if(type(MV[I])!=4) return M; - MV[I]=ltov(MV[I]); - } - for(R=[],J=0; ;J++){ - for(T=[],I=F=0; I<II; I++){ - if(length(MV[I])>J){ - F=1; - T=cons(MV[I][J],T); - } - } - if(F==0) return reverse(R); - if(F==1) R=cons(reverse(T),R); - } - } - if(type(M) != 6) - return M; - S = size(M); - MM = newmat(S[1],S[0]); - for(I = 0; I < S[0]; I++){ - for(J = 0; J < S[1]; J++) - MM[J][I] = M[I][J]; - } - return MM; -} - -def mtoupper(MM, F) -{ - TeXs=["\\ -=\\ ","\\ +=\\ "]; - Lins=[" -= line"," += line"]; - Assume=["If","Assume"]; - if(type(St = getopt(step))!=1) St=0; - Opt = getopt(opt); - if(type(Opt)!=1) Opt=0; - TeX=getopt(dviout); - if(type(Tab=getopt(tab))!=1 && Tab!=0) Tab=2; - Line="\\text{line}"; - if(type(TeX)!=1 || !St) TeX=0; - Size = size(MM); - if(F==-1){ - M = newmat(Size[0], Size[1]+1); - for(I = 0; I < Size[0]; I++){ - for(J = 0; J < Size[1]; J++) - M[I][J] = MM[I][J]; - M[I][Size[1]] = zz^I; - } - Size = size(M); - F = 1; - }else if(F<0){ - F=Size[0]; - M = newbmat(1,2,[[MM,mgen(F,0,[1],0)]]); - Size=[Size[0],F+Size[1]]; - }else - M = dupmat(MM); - if(St){ - if(TeX) Lout=[[dupmat(M)]]; - else mycat0([M,"\n\n"],0); - } - Top=""; - if(Opt>3){ - for(I=Opt; I>4; I--) - Top+=(TeX)?"\\ ":" "; - } - PC=IF=1; - for(K = JJ = 0; K < Size[1] - F; K++){ - for(J = JJ; J < Size[0]; J++){ - if(M[J][K] != 0){ /* search simpler element */ - if(Opt>2 && (Mul=M[J][K])!=1){ - for(FF=0,JT=J; JT<Size[0]; JT++){ - if((Val=M[JT][K])==1){ /* 1 */ - Mul=1;J=JT; break; - } - if(Val==0 || type(Val)>type(Mul)) continue; - if(type(Val)<type(Mul) || (Val==-1 && Mul!=-1)){ - Mul=Val; J=JT; /* smaller type */ - } - else if(Opt>3){ - if(isint(Val)==1){ /* integer elememt */ - if(isint(Mul)!=1){ - Mul=Val; J=JT; /* integer */ - } - if(FF<3||(FF==3&&Val>0)){ - for(JK=K+1;;){ - if(JK>=Size[1]-F){ - J=JT; - FF=((Mul=Val)>0)?4:3; - break; /* divisible int => 4: pos_int 3: neg_int */ - } - if(isint(M[JT][JK++]/Val)!=1) break; - } - } - }else if(!FF){ - for(JK=K+1; JK<Size[1]-F; JK++){ - if(isint(M[JT][JK]/Val)!=1) break; - J=JT; FF=1; /* divisible => 1: non integer */ - } - } - } - } - if(FF==0 && Opt>3 && Mul!=1 && Mul!=-1){ /* FF > 0 => divisible */ - for(FF=0,J0=J; J0<Size[0]-1 && FF!=9; J0++){ - VV0=M[J0][K]; - if(VV0==0 || isint(VV0)==0) continue; - for(J1=J0+1;J1<Size[0] && FF!=9; J1++){ - VV1=M[J1][K]; - if(VV1==0 || isint(VV1)==0) continue; - for(C=FT=0,V0=VV0,V1=VV1; C<2 && FF!=10; C++,V1=V0,V0=VV1){ - for(CC=0,RC=ceil(V0/V1);CC<2;CC++,RC--){ - if((CD=V0-RC*V1)==0 && (RC==1 || RC==-1)){ - FT=1; FF=10; /* 10: vanish by +- */ - }else if(CD==1){ - FV=(vars(M[J0])==[]&&vars(M[J1])==[])?1:0; - if((RC==1 || RC==-1) && FF<8+FV){ - FT=1; FF=8+FV; /* 8/9: 1 by +- */ - }else if(FF<6+VF){ - FT=1; FF=6+FV; /* 6/7: 1 by times */ - } - }else if(CD==-1){ - FV=(vars(M[J0])==[]&&vars(M[J1])==[])?1:0; - if((RC==1 || RC==-1) && FF<4+FV){ - FT=1; FF=4+FV; /* 4/5: 1 by +- */ - }else if(FF<2+VF){ - FT=1; FF=2+FV; /* 2/3: 1 by times */ - } - } - if(FT==1){ - FT=0; KRC=RC; - if(C==0){ - KJ0=J0; KJ1=J1; - }else{ - KJ0=J1; KJ1=J0; - } - } - } - } - } - } - if(FF>0){ - for(I=K;I<Size[1];I++) - M[KJ0][I]=radd(M[KJ0][I],rmul(M[KJ1][I],-KRC)); - if(KRC<0){ - KRC=-KRC;Sgn=1; - }else - Sgn=0; - if(St){ - if(TeX){ - if(KRC==1) - Lout=cons([Top+"\\xrightarrow{", Line,KJ0+1,TeXs[Sgn], - Line,KJ1+1,"}",dupmat(M)],Lout); - else - Lout=cons([Top+"\\xrightarrow{", Line,KJ0+1,TeXs[Sgn], - Line,KJ1+1,"\\times\\left(",KRC,"\\right)}", - dupmat(M)],Lout); - - }else{ - if(KRC==1) - mycat([Top+"line",KJ0+1,Lins[Sgn],KJ1+1,"\n",M,"\n"]); else - mycat([Top+"line",KJ0+1,Lins[Sgn],KJ1+1," * (",KRC,")\n",M,"\n"]); - } - } - Mul=M[KJ0][K]; J=KJ0; - if(FF==10){ - J--; continue; - } - } - } - } - /* a parameter Var */ - Var=0; - if(St && Opt>4 && length(Var=vars(nm(M[J][K])))==1){ - J0=J;Jv=mydeg(nm(M[J0][K]),car(Var)); - for(I=JJ;I<Size[0]; I++){ - if((MIK=M[I][K])==0) continue; - if((T=vars(MIK=nm(MIK)))==[]){ /* 1/poly */ - J=I;Var=[]; break; - } - if(length(T)>1) continue; - if(mydeg(MIK,T[0])<Jv){ - J0=I;Jv=mydeg(MIK);Var=T; /* search minimal degree */ - } - } - if(length(Var)==1){ - Var=car(Var); - Q=nm(M[J0][K]); - for(I=JJ; I<Size[0]; I++){ - if(I==J0 || mydeg(nm(M[I][K]),Var)<0) continue; - T=rpdiv(nm(M[I][K]),Q,Var); - if(T[0]!=0 && (vars(T)==[] || vars(T)==[Var])) break; /* dec. deg */ - } - } - } - if(type(Var)==2){ /* 1 variable */ - if(I==Size[0]){ - for(QF=0,Q0=1,QR=getroot(Q,Var|mult=1);QR!=[];QR=cdr(QR)){ - if(deg(T=QR[0][1],Var)>0){ - QF=1;Q0*=T; continue; - } - if(subst(PC,Var,T)==0) continue; - Q0*=(Var-(T=QR[0][1])); - if(type(T)<2){ - M0=subst(M,Var,T); - if(TeX){ - Lout=cons(["\\hspace{",Tab*(St-3)-1,"mm}\\text{If }", - Var,"=",T,","] ,Lout); - Lout=append(mtoupper(M0,F|step=St+1,opt=Opt,dviout=-2,tab=Tab),Lout); - }else{ - mycat([str_times(" ",St-1)+"If",Var,"=",T,","]); - mtoupper(M0,F|step=St+1,opt=Opt); - } - } - } - if(Q0!=1){ - if(TeX) - Lout=cons(["\\hspace{",Tab*(St-3)-1,"mm}\\text{"+Assume[QF]+" }", - Q0/=fctr(Q0)[0][0],"\\ne0,"],Lout); - else - mycat([str_times(" ",St-1)+Assume[QF],Q0,"!=0,"]); - PC*=Q0; - } - IF=0;St++; - }else{ - KRC=-red((T[2]*dn(M[J0][K]))/(T[1]*dn(M[I][K]))); - for(II=K;II<Size[1];II++) - M[I][II]=radd(M[I][II],rmul(M[J0][II],KRC)); - if(TeX) - Lout=cons([Top+"\\xrightarrow{", Line,I+1,"\\ +=\\ ",Line, - J0+1,"\\times\\left(",KRC,"\\right)}",dupmat(M)],Lout); - else - mycat([Top+"line",I+1,"+=",Line,J0+1," * (",KRC,")\n",M,"\n"]); - J=JJ-1; - continue; - } - } - if(J != JJ){ - for(I = K; I < Size[1]; I++){ - Temp = M[JJ][I]; - M[JJ][I] = M[J][I]; - M[J][I] = (Opt>=2)?Temp:-Temp; - } - if(St){ - if(TeX) - Lout=cons([Top+"\\xrightarrow{",Line,JJ+1,"\\ \\leftrightarrow\\ ", - Line,J+1,"}",dupmat(M)],Lout); - else - mycat0([Top+"line",JJ+1," <-> line",J+1,"\n",M,"\n\n"],0); - } - } - /* Assume PC != 0 */ - if(Opt>1){ - Mul = M[JJ][K]; - if(Opt > 5 && St && IF && (Var=vars(MIK=nm(Mul)))!=[]){ - TF=fctr(MIK); - for(FF=0,Q0=1,TP=cdr(TF);TP!=[];TP=cdr(TP)){ - if(type(dn(red(PC/(TP0=car(car(TP))))))<2) continue; /* divisible */ - Q0*=TP0; - for(Var=vars(TP0);Var!=[];Var=cdr(Var)){ - if(mydeg(TP0,X=car(Var))==1 && type(dn(red(PC/mycoef(TP0,1,X))))<2){ - /* TP0=A*X+B with non-vanishing A */ - T=red(-mycoef(TP0,0,X)/mycoef(TP0,1,X)); - M0=mysubst(M,[X,T]); - if(TeX){ - Lout=cons(["\\hspace{",Tab*(St-3)-1,"mm}\\text{If }", - X,"=",T,","] ,Lout); - Lout=append(mtoupper(M0,F|step=St+1,opt=Opt,dviout=-2,tab=Tab), - Lout); - }else{ - mycat([str_times(" ",St-1)+"If",X,"=",T,","]); - mtoupper(M0,F|step=St+1,opt=Opt); - } - break; - } - } - if(Var==[] && Opt>6){ - for(Var=vars(TP0);Var!=[];Var=cdr(Var)){ - if(mydeg(TP0,X=car(Var))==1){ - /* TP0=A*X+B, A is a poly of X0 with rational funct */ - T=nm(mycoef(TP0,1,X)); - for(Var0=vars(T);Var0!=[]; Var0=cdr(Var0)){ - X0=car(Var0); - if(type(dn(red(PC/type(mycoef(T,mydeg(T,X0),X0)))))>1) continue; - TR=getroot(T,X0|mult=1); - if(findin(X0,vars(TR))<0) break; - } - if(Var0==[]) continue; - for(;TR!=[0];TR=cdr(TR)){ - if(TR==[]){ - TR=[0,0]; - T0=-mycoef(TP0,0,X)/mycoef(TP0,1,X); - X0=X; - }else T0=car(TR)[1]; - M0=mysubst(M,[X0,T0]); - if(TeX){ - Lout=cons(["\\hspace{",Tab*(St-3)-1,"mm}\\text{If }", - X0,"=",T0,","] ,Lout); - Lout=append(mtoupper(M0,F|step=St+1,opt=Opt,dviout=-2,tab=Tab), - Lout); - }else{ - mycat([str_times(" ",St-1)+"If",X0,"=",T0,","]); - mtoupper(M0,F|step=St+1,opt=Opt); - } - } - - } - break; - } - } - if(Var==[]){ - FF=1; - } - } - if(Q0!=1){ - if(FF) FF=1; - if(TeX) Lout=cons(["\\hspace{",Tab*(St-3)-1,"mm}\\text{"+Assume[FF]+" }",Q0/=fctr(Q0)[0][0],"\\ne0,"], - Lout); - else mycat([str_times(" ",St-1)+Assume[FF],Q0,"!=0,"]); - PC*=Q0;St++; - } - } - IF=M[JJ][K]=1; - if(Mul!=1){ - for(L=K+1; L<Size[1]; L++) - M[JJ][L]=red(M[JJ][L]/Mul); - if(St){ - if(TeX) - Lout=cons([Top+"\\xrightarrow{",Line,JJ+1, - "\\ \\times=\\ \\left(",red(1/Mul),"\\right)}", - dupmat(M)],Lout); - else - mycat0([Top+"line",JJ+1, " *= (",red(1/Mul), ")\n",M,"\n\n"],0); - } - } - - } - for(J = (Opt>0)?0:(JJ+1); J < Size[0]; J++){ - if(J == JJ) - continue; - Mul = -M[J][K]; - if(Mul!=0){ - if(Opt!=2) Mul=rmul(Mul,1/M[JJ][K]); - for(I = K+1; I < Size[1]; I++) - M[J][I] = radd(M[J][I],rmul(M[JJ][I],Mul)); - M[J][K] = 0; - if(St){ - if(Mul<0){ - Mul=-Mul;Sgn=0; - }else Sgn=1; - if(TeX){ - if(Mul==1) - Lout=cons([Top+"\\xrightarrow{", Line,J+1,TeXs[Sgn],Line,JJ+1, - "}",dupmat(M)],Lout); - else Lout=cons([Top+"\\xrightarrow{", Line,J+1,TeXs[Sgn],Line,JJ+1, - "\\times\\left(",Mul,"\\right)}",dupmat(M)],Lout); - }else{ - if(Mul==1) - mycat0([Top+"line",J+1, Lins[Sgn],JJ+1,"\n",M,"\n\n"],0); - else - mycat0([Top+"line",J+1, Lins[Sgn],JJ+1," * (",Mul,")\n",M,"\n\n"],0); - } - } - } - } - JJ++; - } - } - } - if(TeX){ - if(TeX==-2) return Lout; - Lout=reverse(Lout); - Br="\\allowdisplaybreaks"; - Cr="\\\\\n &"; - if(getopt(pages)==1) Cr=Br+Cr; - if(type(S=getopt(cr))==7) Cr=S; - if(type(Lim=getopt(lim))==1){ - if(Lim>0){ - if(Lim<30) Lim=TeXLim; - Lim*=2; - } - }else Lim=0; - Out = ltotex(Lout|opt=["cr","spts0"],str=1,cr=Cr,lim=Lim); - if(TeX<0) return Out; - dviout(Out|eq=(str_str(Cr,Br)>=0)?6:5,keep=(TeX==1)?0:1); - } - return M; -} - -def mydet2(M) -{ - S = size(M); - Det = 1; - MM = mtoupper(M,0); - for(I = 0; I < S[0]; I++) - Det = rmul(Det,MM[I][I]); - return Det; -} - -def myrank(MM) -{ - S = size(MM); - M = dupmat(MM); - M = mtoupper(M,0); - C = 0; - for(I = K = 0; I < S[0]; I++){ - for(J = K; J < S[1]; J++){ - if(M[I][J] != 0){ - C++; K++; - break; - } - } - } - return C; -} - -def meigen(M) -{ - F = getopt(mult); - if(type(M)==4 || type(M)==5){ - II=length(M); - for(R=[],I=II-1; I>=0; I--){ - if(F==1) - R=cons(meigen(M[I]|mult=1),R); - else - R=cons(meigen(M[I]),R); - } - return R; - } - S = size(M)[0]; - P = mydet2(mgen(S,0,[zz],0)-M); - return (F==1)?getroot(P,zz|mult=1):getroot(P,zz); -} - -def transm(M) -{ - if(type(M)!=6) M=s2m(M); - if(type(M)!=6){ - errno(0); - return 0; - } - L=[M];TeX=""; - Line=["\\text{line}","\\text{col}"]; - if((DVI=getopt(dviout)) !=1) DVI=0; - else dviout(M); - for(;;){ - print(L0=dupmat(car(L))); - Sz=size(L0); - S=keyin("? "); - N=0; - if(str_len(S)<=1){ - if(S=="q") return L; - if(S=="t"){ - N=mtranspose(L0); - TeX=["\\text{transpose}"]; - } - else if(S=="f"){ - if(length(L)>1){ - if(LF!=0) TeX=""; - L=cdr(L);LF=L0; - if(DVI){ - dviout0(-1); - dviout(" "); - } - } - }else if(S=="g"){ - if(LF!=0) N=LF; - }else if(S=="0"){ - N=M;L=[];TeX=[]; - }else if(S=="a"||S=="A"){ - if(DVI&&S=="A") mtoupper(L0,0|step=1,opt=10,dviout=1); - else mtoupper(L0,0|step=1,opt=10); - }else{ - mycat0([ - "2,5 : line2 <-> line5", - "2,5,-2 ; line2 += (-2)*line5", - "2,2,-2 : line2 *= -2", - "2,5,0 : line2 += (?)*line5 for reduction", - "r,2,5 : raw2 <-> raw5 (r,2,5,-2 etc.)", - "s,x,2 : subst(*,x,2)", - "t : transpose", - "0 : first matrix", - "f : previous matrix", - "g : next matrix (only after f)", - "A : auto (a : without TeX)", - "q : quit" - ],1|delim="\n"); - } - }else{ - FR=0; - S=evals(S|del=","); - if(S[0]==r){ - FR=1; S=cdr(S); - } - if((LL=length(S))>=2){ - S0=S[0]-1;S1=S[1]-1; - if(S[0]==s){ - if(length(S)==3) N=subst(L0,S[1],S[2]); - if(DVI) TeX=[S[1],"\\mapsto",S[2]]; - }else if(FR==0){ - if(S0<0 || S0>=Sz[0] || S1<0 || S1>=Sz[0]) continue; - if(LL==2){ - N=rowx(L0,S0,S1); - if(DVI) TeX=[Line[0],S[0],"\\ \\leftrightarrow\\ ",Line[0],S[1]]; - }else{ - S2=S[2]; - if(S0==S1){ - N=rowm(L0,S0,S2); - if(DVI) TeX=[Line[0],S[0],"\\ \\times=\\ ",S2]; - }else{ - if(S2==0){ - for(J=0;J<Sz[1] && L0[S1][J]==0;J++); - if(J<Sz[1]) S2=-L0[S0][J]/L0[S1][J]; - } - if(S2!=0){ - N=rowa(L0,S0,S1,S2); - if(DVI) TeX=[Line[0],S[0],"\\ +=\\ ",Line[0], - S[1],"\\ \\times\\ (",S2,")"]; - } - } - } - }else{ - if(S0<0 || S0>=Sz[1] || S1<0 && S1>=Sz[1]) continue; - if(LL==2){ - N=colx(L0,S0,S1); - if(DVI) TeX=[Line[1],S[0],"\\ \\leftrightarrow\\ ",Line[1],S[1]]; - }else{ - S2=S[2]; - if(S0==S1){ - N=colm(L0,S0,S2); - if(DVI) TeX=[Line[1],S[0],"\\ \\times=\\ ",S[2]]; - }else{ - if(S2!=0){ - for(J=0; I1<Sz[0] && L0[I1][J]==0; J++); - if(J<Sz[0]) S2=-L0[J][S0]/L0[J][S1]; - }if(S2!=0){ - N=cola(L0,S0,S1,S2); - if(DVI) TeX=[Line[1],S[0],"\\ +=\\ ",Line[1], - S[1],"\\ \\times\\ (",S2,")"]; - } - } - } - } - } - } - if(N!=0){ - LF=0;L=cons(N,L); - if(DVI) dviout("\\xrightarrow{"+ltotex(TeX|opt="spts0",str=1)+"}"+mtotex(N)|eq=8); - } - } -} - -def vgen(V,W,S) -{ - IM=length(V); - I=(getopt(opt)==0)?IM:0; - for(SS=0; I<IM && (SS==0 || V[I]<=W[I]); I++) - SS += W[I]; - if(I<IM){ - W[I]++; - SS--; - }else - SS=S; - for(J=0;J<I;J++){ - W[J] = (SS<=V[J])?SS:V[J]; - SS -= W[J]; - } - if(SS>0) - return -1; - return(I==IM)?0:I; -} - -def mmc(M,X) -{ - Mt=getopt(mult); - if(type(M)==7) M=os_md.s2sp(M); - if(type(M)!=4||type(M[0])!=6) return 0; - if(type(M[0])!=6){ /* spectre type -> GRS */ - G=s2sp(M|std=1); - L=length(G); - for(V=[],I=L-2;I>=0;I--) V=cons(makev([I+10]),V); - V=cons(makev([L+9]),V); - G=sp2grs(G,V,[1,length(G[0]),-1]|mat=1); - if(getopt(short)!=0){ - V=append(cdr(V),[V[0]]); - G=shortv(G,V); - } - R=chkspt(G|mat=1); - if(Mt!=1) Mt=0; - if(R[2]!=2 || R[3]!=0 || !(R=getbygrs(G,1|mat=1))) return 0; - MZ=newmat(1,1); - SS=length(G); - if(Mt==1) SS=SS*(SS-1)/2; - for(M=[],I=0;I<SS;I++) M=cons(MZ,M); - for(RR=R; RR!=[]; RR=cdr(RR)){ - RT=car(RR)[0]; - if(type(RT)==4){ - if(RT[0]!=0) M=mmc(M,[RT[0]]|simplify=Simp); - M=mmc(M,[cdr(RT)]); - } - } -/* for(R=cdr(R);R!=[];R=cdr(R)) M=mmc(M,[car(R)[0]]|mult=Mt); */ - } - if(X==0) return M; - L=length(M); - if((L>=6 && Mt!=0)||(L==3&&Mt==1)){ - for(SS=2,I=3; I<L; I+=(++SS)); - if(I!=L) return -1; - Mt=1; - }else{ - SS=L;Mt=0; - } - if(length(X)==SS+1){ - if(car(X)!=0&&(M=mmc(M,[car(X)]|mult=Mt))==0) return M; - return mmc(M,cdr(X)|mult=Mt); - } - for(I=X;I!=[];I=cdr(I)) if(I[0]!=0) break; - if(I==[]) return M; - Simp=getopt(simplify); - if(Simp!=0 && type(Simp)!=1) Simp=2; - N=newvect(L); - for(I=0;I<L;I++) N[I]=dupmat(M[I]); - S=size(N[0])[0]; - if(type(X)==4&&length(X)>SS){ /* addition */ - for(I=0;I<SS;I++,X=cdr(X)) if(X[I] != 0) N[I] = radd(N[I],car(X)); - } - if(length(X)!=1) return 0; - X=X[0]; - MZ = newmat(S,S); - MM = newvect(L); - for(M1=J=0; J<SS; J++){ - for(R=[],I=SS-1; I>=0; I--){ - if(I==J){ - for(RR=[],K=SS-1; K>=0; K--) - RR=cons((K==I)?N[K]+diagm(S,[X]):N[K],RR); - R=cons(RR,R); - }else R=cons([MZ],R); - } - MM[J]=newbmat(SS,SS,R); - if(J==0) M1=MM[0]; - else M1=radd(M1,MM[J]); - } - /* middle convolution */ - for(P=0,Q=1;J<L;J++){ /* A_{P,Q} */ - for(R=[],I=SS-1; I>=0; I--){ - for(RR=[],K=SS-1;K>=0;K--){ - MT=MZ; - if(I==K){ - MT=N[J]; - if(I==P) MT-=N[Q]; - else if(I==Q) MT-=N[P]; - }else if(I==P && K==Q) MT=N[Q]; - else if(I==Q && K==P) MT=N[P]; - RR=cons(MT,RR); - } - R=cons(RR,R); - } - MM[J]=newbmat(SS,SS,R); - if(++Q==SS){ - P++;Q=P+1; - } - } - for(R=[],I=SS-1; I>=0; I--){ - for(RR=[N[I]],J=0; J<I; J++) RR=cons(MZ,RR); - R=cons(RR,R); - } - M0 = newbmat(SS,SS,R); - KE = append(mykernel(M0|opt=1),mykernel(M1|opt=1)); - if(length(KE) == 0) return MM; - KK = mtoupper(lv2m(KE),0); - for(I=0;I<L;I++) MM[I] = mmod(MM[I],KK); - if(Simp!=0) MM = mdsimplify(MM|type=Simp); - return MM; -} - -def lpgcd(L) -{ - for(F=[]; L!=[]; L=cdr(L)){ - if((P=car(L))==0) continue; - if(F==[]){ - F=fctr(P); - S=length(F); - S--; - V=newvect(S); - M=newvect(S); - for(I=0; I<S; I++){ - M[I] = F[I+1][1]; - V[I] = F[I+1][0]; - } - N=nm(ptozp(P|factor=1)[1]); - continue; - } - N=igcd(ptozp(P|factor=1)[1],N); - for(I=0; I<S; I++){ - for(Q=P,CT=0; CT<M[I]; CT++) - if((Q=tdiv(Q,V[I])) == 0) break; - if(CT<M[I]) M[I]=CT; - } - } - if(F==[]) return 0; - for(Q=N,I=0;I<S; I++){ - while(M[I]>0){ - Q *= V[I]; - M[I]--; - } - } - return Q; -} - -def mdivisor(M,X) -{ - S=size(M=dupmat(M)); - XX=(type(X)==4||X==0)?X:[0,X]; - S0=S[0]; S1=S[1]; - if((Tr=getopt(trans))==1||Tr==2){ - Tr0=1; - GR=mgen(S0,0,1,0); GC=mgen(S1,0,1,0); - }else Tr=Tr0=0; - /* 0,a,b : (a,b)->(1,1) - 1 : (1,1) invertible - 2,i,M : line 0,i by M - 3,j,M : col 0,j by M - 4,j : col 1 += col j - 5,j,T : line j by T - 6,j,T : col 1 += col j by T (non-com) - 7,j : line 2<->j (non-com) - */ - if(type(V=getopt(dviout))==1){ - if(type(XX)==4 && type(XX[0])>1) Var=[XX[1],"\\partial"]; - else Var=0; - Tr=(abs(V)==3)?0:1; - MM=dupmat(M); - II=((S[0]>S[1])?S[1]:S[0])+1; - if(abs(V)>1){ - Is1=Js1=S[0]+S[1]; - Is=Js=[0,[Is1]]; - }else{ - Is=[0,[Is1=S[0]]];Js=[0,[Js1=S[1]]]; - } - VV=V; - V=newvect(II); - for(I=0;I<II;I++) V[I]=[]; - N=newbmat(2,2,[[M,mgen(S[0],0,[1],0)],[mgen(S[1],0,[1],0)]]); - mdivisor(M,X|step=1,dviout=V); - L=S[0]+S[1]; - if(Tr){ - NN=mperm(N,Is1,Js1); - for(K=S[0];K<Is1;K++){ - for(L=S[1];L<Js1;L++) - NN[K][L]=" "; - } - Out=[[mperm(NN,Is,Js)]]; - } - for(I=1;I<II;I++){ - I0=I-1; - if(V[I]==[]) continue; - for(T=reverse(V[I]);T!=[];T=cdr(T)){ - St=[]; - C=car(R=car(T)); - if(C==0){ - N=mperm(N,(R[1]==0)?0:[[R[1]+I0,I0]],(R[2]==0)?0:[[R[2]+I0,I0]]); - - if(Tr){ - if(R[2]!=0) St=append(["C",I,"\\leftrightarrow C",R[2]+I],St); - if(R[1]!=0){ - if(R[2]!=0) St=cons(",\\ ",St); - St=append(["L",I,"\\leftrightarrow L",R[1]+I],St); - } - Out=cons(St,Out); - } - }else if(C==1){ - P=1/N[I0][I0];N[I0][I0]=1; - if(P!=1){ - for(J=I;J<L;J++) - N[I0][J]=muldo(P,N[I0][J],XX); - - if(Tr){ - St=append(["L",I,"\\leftarrow(",P,")","\\times L",I],St); - Out=cons(St,Out); - NN=mperm(N,Is1,Js1); - for(K=S[0];K<Is1;K++){ - for(L=S[1];L<Js1;L++) - NN[K][L]=" "; - } - Out=cons(["\\to",mperm(NN,Is,Js)],Out); - } - } - for(F=0,J=I;J<S[0];J++){ - if((P=N[J][I0])==0) continue; - F++; - N[J][I0]=0; - for(K=I;K<L;K++) - N[J][K]=red(N[J][K]-muldo(P,N[I0][K],XX)); - - } - if(F){ - if(Tr){ - Out=cons(["Li\\ -\\!=\\ \\circ\\times L",I,"\\quad(i>",I,")"],Out); - NN=mperm(N,Is1,Js1); - for(K=S[0];K<Is1;K++){ - for(L=S[1];L<Js1;L++) - NN[K][L]=" "; - } - Out=cons(["\\to",mperm(NN,Is,Js)],Out); - } - } - for(F=0,J=I;J<S[1];J++){ - if((P=N[I0][J])==0) continue; - F++; - N[I0][J]=0; - for(K=I;K<L;K++) - N[K][J]=red(N[K][J]-muldo(N[K][I0],P,XX)); - } - if(F&&Tr) Out=cons(["Cj\\ -\\!=\\ C",I,"\\times\\circ\\quad(j>",I,")"],Out); - else continue; - }else if(C==2){ - C=mat(N[I0],N[R[1]+I0]);C=muldo(R[2],C,XX); - for(J=0;J<L;J++){ - N[I0][J]=C[0][J];N[R[1]+I0][J]=C[1][J]; - } - if(Tr) Out=cons([dupmat(R[2]),"\\begin{pmatrix}L",I,"\\\\L",R[1]+I, - "\\end{pmatrix}"],Out); - }else if(C==3){ - C=newmat(L,2); - for(J=0;J<L;J++){ - C[J][0]=N[J][I0];C[J][1]=N[J][R[1]+I0]; - } - C=muldo(C,R[2],XX); - for(J=0;J<L;J++){ - N[J][I0]=C[J][0];N[J][R[1]+I0]=C[J][1]; - } - if(Tr) Out=cons(["\\begin{pmatrix}C",I,"&C",R[1]+I,"\\end{pmatrix}", - dupmat(R[2])],Out); - }else if(C==4){ - for(J=0;J<L;J++) - N[J][I0]=red(N[J][I0]+N[J][R[1]+I0]); - if(Tr) Out=cons(["C",I,"\\ +\\!=\\ C",R[1]+I],Out); - }else if(C==5){ - for(J=0;J<L;J++) - N[I0+R[1]][J]=red(R[2]*N[I0+R[1]][J]); - if(Tr) Out=cons(["L",I+R[1],"\\leftarrow(", R[2],")\\times L",I+R[1]], - Out); - }else if(C==6){ - for(J=0;J<L;J++) - N[J][I0]=N[J][I0]+muldo(N[J][I0+R[1]],R[2],XX); - if(Tr) Out=cons(["C",I,"\\ +\\!=\\ C",I+R[1],"\\times(", R[2],")"], - Out); - }else if(C==7){ - mycat(["line",I+1,"\\leftrightarrow",R[1]+I]); - for(J=0;J<L;J++){ - C=N[I][J];N[I][J]=N[R[1]+I0][J];N[R[1]+I0][J]=C; - } - if(Tr) Out=cons(["L",I+1,"\\leftrightarrow L",R[1]+I],Out); - } - if(Tr){ - NN=mperm(N,Is,Js); - for(K=S[0];K<Is1;K++){ - for(L=S[1];L<Js1;L++) - NN[K][L]=" "; - } - Out=cons(["\\to",NN],Out); - } - } - } - if(!Tr){ - NN=mperm(N,Is,Js); - Out=[]; - } - if(S[0]+S[1]==Is1){ - N1=mperm(NN,[0,[S[0]]],[S[1],[S[0]]]); - N2=mperm(NN,[S[0],[S[1]]],[0,[S[1]]]); - N3=mperm(NN,[0,[S[0]]],[0,[S[1]]]); - R1=mdivisor(N1,X|trans=1)[1]; - R2=mdivisor(N2,X|trans=1)[1]; - if(Tr){ - Out=cons(["\\text{As a result,}"],Out); - Out=cons([N3,"=",N1,MM,N2],Out); - if(S[0]==S[1] && N3==mgen(S[0],0,1,0)){ - Out=cons(["=",muldo(N2,N1,XX),MM,"."],Out); - }else{ - Out=cons([N1,"^{-1}=",R1,","],Out); - Out=cons([N2,"^{-1}=",R2,"."],Out); - } - }else{ - Out=cons([N3,"=P",MM,"Q,"],Out); - Out=cons(["P=",N1,"=",R1,"^{-1},"],Out); - Out=cons(["Q=",N2,"=",R2,"^{-1}."],Out); - } - } - Out = ltotex(reverse(Out)|opt=["cr","spts0"],str=1,cr=15,var=Var); - if(S[0]+S[1]==Is1) - Out=str_subst(Out,"\\texttt{ }",""); - if(VV>0){ - dviout(Out|eq=6); - return NN; - } - return Out; - }else if(type(V)!=5) V=0; - - if(type(St=getopt(step))!=1) St=0; - for(FF=": start";;){ - if(St && V==0){ - if(Tr){ - mycat0([St,FF,"\n"],0); - mycat([GR,"\n"]);mycat([M,"\n"]);mycat([GC,"\n"]); - } - else mycat0([St,FF,"\n",M,"\n"],0); - } - if(X==0||X==[0,0]){ /* search minimal non-zero element */ - for(K=F=I=0; I<S0; I++){ - for(J=0; J<S1; J++){ - if((P=abs(M[I][J]))!=0 && (K>P || K==0)){ - K=P; R=[I,J]; - } - } - } - R=cons(K-1,[R]); - } - else R=mymindeg(M,XX[1]|opt=1); - if(R[0]<0){ /*zero matrix */ - if(Tr) return [[],mgen(S0,0,1,0),mgen(S1,0,1,0)]; - return []; - } - R0=R[1][0];R1=R[1][1]; - if(R0!=0){ - M=rowx(M,0,R0); - if(Tr) GR=rowx(GR,0,R0); - } - if(R1!=0){ - M=colx(M,0,R1); - if(Tr) GC=colx(GC,0,R1); - } - if(St>0 && (R0!=0 || R1!=0)) - if(type(V)==5) V[St]=cons([0,R0,R1],V[St]); - else if(Tr){ - mycat0([St,": (",R0+1,",",R1+1,") -> (1,1)\n"],0); - mycat([GR,"\n"]);mycat([M,"\n"]);mycat([GC,"\n"]); - }else mycat0([St,": (",R0+1,",",R1+1,") -> (1,1)\n",M,"\n"],0); - if(R[0]==0){ /* (1,1) : invertible */ - if(type(V)==5) V[St]=cons([1],V[St]); - P=M[0][0]; M[0][0]=1; - for(J=0;J<S1;J++){ /* (1,1) -> 1 */ - if(J>0) M[0][J]= red(M[0][J]/P); - if(Tr) GR[0][J]=red(GR[0][J]/P); - } - if(S0>1 && S1>1) N=newmat(S0-1,S1-1); - else N=0; - for(I=1;I<S0;I++){ - P=M[I][0]; M[I][0]=0; - for(J=1;J<S1;J++) - N[I-1][J-1]=M[I][J]=red(M[I][J] - muldo(P,M[0][J],XX)); - if(Tr){ - for(J=0;J<S0;J++) - GR[I][J] = red(GR[I][J] -muldo(P,GR[0][J],XX)); - } - } - if(Tr){ - for(J=1;J<S1; J++){ - for(I=0;I<S1;I++) GC[I][J]=red(GC[I][J]-muldo(GC[I][0],M[0][J],XX)); - M[0][J]=0; - } - } - if(St>0 && V==0){ - if(Tr){ - mycat0([St,": unit\n"],0); - mycat([GR,"\n"]);mycat([M,"\n"]);mycat([GC,"\n"]); - } - else mycat0([St,": unit\n",M,"\n"],0); - } - if(N==0){ - if(!Tr) return [1]; - if(Tr==2){ - GR0=mdivisor(GR,X|trans=1)[1]; - GC0=mdivisor(GC,X|trans=1)[1]; - return [[1],GR,GC,GR0,GC0]; - } - return [[1],GR,GC]; - } - R=mdivisor(N,XX|dviout=V,trans=Tr0,step=(St>0)?St+1:St); - if(!Tr) return cons(1,R); - GR=muldo(newbmat(2,2,[[1],[0,R[1]]]),GR,XX); - GC=muldo(GC,newbmat(2,2,[[1],[0,R[2]]]),XX); - if(S0==S1 && countin(1,1,R[0])==S0-1){ - GR=muldo(GC,GR,XX); GC=mgen(S0,0,1,0); - } - if(Tr==2){ - GR0=mdivisor(GR,X|trans=1)[1]; - GC0=mdivisor(GC,X|trans=1)[1]; - return [cons(1,R[0]),GR,GC,GR0,GC0]; - } - return [cons(1,R[0]),GR,GC]; - } - for(I=1;I<S0;I++){ - if(M[I][0]!=0){ -/* Error! when mygcd(A,B,0) with A<=0 or B<=0 */ - R=mygcd(M[I][0],M[0][0],XX); /* R[0]=R[1]*M[I][0]+R[2]*M[0][0] */ - M[0][0]=R[0]; M[I][0]=0; /* 0=R[3]*M[I][0]+R[4]*M[0][0] */ - for(J=1;J<S1;J++){ - T=red(muldo(R[1],M[I][J],XX)+muldo(R[2],M[0][J],XX)); - M[I][J]=red(muldo(R[3],M[I][J],XX)+muldo(R[4],M[0][J],XX)); - M[0][J]=T; - } - if(Tr){ - for(J=0;J<S0;J++){ - T=red(muldo(R[1],GR[I][J],XX)+muldo(R[2],GR[0][J],XX)); - GR[I][J]=red(muldo(R[3],GR[I][J],XX)+muldo(R[4],GR[0][J],XX)); - GR[0][J]=T; - } - } - if(St && V==0){ - mycat([" [",R[2],R[1],"]*"]); - mycat([" [",R[4],R[3],"]"]); - } - if(type(V)==5) V[St]=cons([2,I,mat([R[2],R[1]],[R[4],R[3]])],V[St]); - FF=": line 1 & "+rtostr(I+1); I=S0; - } - } - if(I>S0) continue; - for(J=1;J<S1;J++){ - if(M[0][J]!=0){ - R=mygcd(M[0][J],M[0][0],XX|rev=1); /* R[0]=M[0][J]*R[1]+M[0][0]*R[2] */ - M[0][0]=R[0]; M[0][J]=0; /* 0=M[0][J]*R[3]+M[0][0]*R[4] */ - for(I=1;I<S0;I++){ - T=red(muldo(M[I][J],R[1],XX)+muldo(M[I][0],R[2],XX)); - M[I][J]=red(muldo(M[I][J],R[3],XX)+muldo(M[I][0],R[4],XX)); - M[I][0]=T; - } - if(Tr){ - for(I=0;I<S1;I++){ - T=red(muldo(GC[I][J],R[1],XX)+muldo(GC[I][0],R[2],XX)); - GC[I][J]=red(muldo(GC[I][J],R[3],XX)+muldo(GC[I][0],R[4],XX)); - GC[I][0]=T; - } - } - if(type(V)==5) V[St]=cons([3,J,mat([R[2],R[4]],[R[1],R[3]])],V[St]); - FF=": column 1 & "+rtostr(J+1);J=S1; - if(St && V==0){ - mycat([" *[",R[2],R[4],"]"]); - mycat([" [",R[1],R[3],"]"]); - } - } - } - if(J>S1) continue; - if(S0==1 || S1==1){ - P=M[0][0]; - if(X==0){ - if(P<0){ - P=-P; - if(Tr) for(J=0;J<S0;J++) GR[0][J]=-GR[0][J]; - if(type(V)==5) V[St]=cons([5,0,-1],V[St]); - } - }else{ - P=nm(P); - if((R=fctr(P)[0][0])!=1){ - P/=R; - if(Tr) for(J=0;J<S0;J++) GR[0][J]/=R; - if(type(V)==5) V[St]=cons([5,0,1/R],V[St]); - } - } - if(!Tr) return [P]; - if(Tr==2){ - GR0=mdivisor(GR,X|trans=1)[1]; - GC0=mdivisor(GC,X|trans=1)[1]; - return [[P],GR,GC,GR0,GC0]; - } - return [[P],GR,GC]; - } - if(XX==0 || (type(XX)==4 && XX[0]==0)){ /* commutative case */ - P=M[0][0]; - for(I=1; I<S0; I++){ - for(J=1; J<S1; J++) - if(divdo(M[I][J],P,XX)[1]!=0) break; - if(J<S1){ - if(type(V)==5) V[St]=cons([4,J],V[St]); - FF=": column 1 += col"+rtostr(J+1); - for(I=1;I<S0;I++) M[I][0]=M[I][J]; - if(Tr) for(I=0;I<S1;I++) GC[I][0]=red(GC[I][0]+GC[I][J]); - break; - } - } - if(J<S1) continue; - N=newmat(S0-1,S1-1); - for(I=1;I<S0;I++) - for(J=1;J<S1;J++) N[I-1][J-1]=red(M[I][J]/P); - if(X==0){ - if(P<0) P=-P; - if(Tr) for(J=0;J<S0;J++) GR[0][J]=-GR[0][J]; - }else{ - P=M[0][0]; - P=nm(P); - P/=fctr(P)[0][0]; - if(Tr) for(J=0;J<S0;J++) GR[0][J]/=fctr(P)[0][0]; - } - R=mdivisor(N,XX|dviout=V,trans=Tr0,step=(St>0)?St+1:St); - RT=(Tr)?R[0]:R; - for(RR=[],L=reverse(RT);L!=[];L=cdr(L)) - RR=cons(red(P*car(L)),RR); - RR=cons(P,RR); - if(!Tr) return RR; - GR=muldo(newbmat(2,2,[[1],[0,R[1]]]),GR,XX); - GC=muldo(GC,newbmat(2,2,[[1],[0,R[2]]]),XX); - if(S0==S1 && countin(1,1,RR)==S0){ - GR=muldo(GC,GR,XX); GC=mgen(S0,0,1,0); - } - if(Tr==2){ - GR0=mdivisor(GR,X|trans=1)[1]; - GC0=mdivisor(GC,X|trans=1)[1]; - return [RR,GR,GC,GR0,GC0]; - } - return [RR,GR,GC]; - } /* End of commutative case */ - for(I=1; I<S0; I++){ - for(J=1; J<S1; J++){ - if(M[I][J] != 0){ - for(T=1;I<S0;T*=XX[0]){ - R=divdo(muldo(M[I][J],T,XX),M[0][0],XX); - if(R[1]!=0){ - if(type(V)==5) V[St]=cons([6,J,T],V[St]); - FF=": column 1 += col"+rtostr((J+1)*T); - if(I>1){ - M=rowx(M,1,I); - if(Tr) GR=rowx(GR,1,I); - if(type(V)==5) V[St]=cons([7,I],V[St]); - FF+=", line 2<->"+rtostr(I+1); - } - for(I=1;I<S0;I++) M[I][0]=muldo(M[I][J],T,XX); - if(Tr) - for(I=1;I<S1;I++) GC[I][0]=red(GC[I][0]+muldo(GC[I][J],T,XX)); - I=S0+1; J=S1; - break; - } - } - } - } - if(I>S0) break; - } - if(I==S0) return []; /* zero matrix : never happen */ - } -} - -def mdsimplify(L) -{ - T=getopt(type); - SS=0; - if(type(L)==6){ - L=[L]; SS=1; - } - if(type(L)==5){ - SS=2; - L = vtol(L); - } - M=car(L); - S=size(M)[0]; -#if 0 - MN=newmat(S,S); - MD=newmat(S,S); - for(I=0;I<S;I++){ - for(J=0;J<S;J++){ - TN=0;TD=1; - for(PL=L;PL!=[];PL=cdr(PL)){ - TM=red(car(PL)[I][J]); - TN=lgcd([TN,nm(TM)]|pol=1); - TD=llcm([TD,dn(TM)]|pol=1); - } - MN[I][J]=TM; - MD[I][J]=TN; - } - } - for(I=0;I<S;I++){ - for(J=0;J<S;J++){ - if(I==J||type(TD[I][J])<2||type(TN[J][I])<2) continue; - for(FC=cdr(fctr(TD[I][J]));FC!=[];){ - TFC=car(FC); - if(type(red(TN[J][I]/TFC[0]))>2) continue; - } - } - } -#endif - DD=newvect(S); - for(I=0; I<S; I++){ - LN=RN=[]; - LD=RD=1; - for(LL=L; LL!=[]; LL=cdr(LL)){ - M = car(LL); - for(J=0; J<S; J++){ - if(J==I) continue; - if((MM=M[I][J]) != 0){ - LN = cons(nm(MM),LN); - if(type(MM)==3 && tdiv(LD,P=dn(MM))==0) - LD=tdiv(LD*P,gcd(LD,P)); - } - if((MM=M[J][I]) != 0){ - RN = cons(nm(MM),RN); - if(type(MM)==3 && tdiv(RD,P=dn(MM))==0) - RD=tdiv(RD*P,gcd(RD,P)); - } - } - } - if(T==1 || T==3) LQ=RD; - else{ - P=lpgcd(LN); - LQ=gcd(P,RD); - if(P!=0) LQ *= nm(fctr(P)[0][0]); - } - if(T==1 || T==2) RQ=LD; - else{ - P=lpgcd(RN); - RQ=gcd(P,LD); - if(P!=0) RQ *= nm(fctr(P)[0][0]); - } - if((P=gcdz(LQ,RQ))!=1){ - LQ = red(LQ/P); RQ=red(RQ/P); - } - DD[I]=red(LQ/RQ); - if(LQ!=1 || RQ!=1){ - for(LA=[],LL=L; LL!=[]; LL=cdr(LL)){ - M = car(LL); - for(J=0; J<S; J++){ - if(I!=J){ - if(LQ!=1){ - M[I][J] = red(M[I][J]/LQ); - M[J][I] = red(M[J][I]*LQ); - } - if(RQ!=1){ - M[J][I] = red(M[J][I]/RQ); - M[I][J] = red(M[I][J]*RQ); - } - } - } - } - } - } - if(SS==2) L=ltov(L); - if(SS==1) L=L[0]; - if(getopt(show)==1) L=[L,DD]; - return L; -} - -def m2mc(M,X) -{ - if(type(M)<2){ - mycat([ -"m2mc(m,t) or m2mc(m,[t,s])\t Calculation of Pfaff system of two variables\n", -" m : list of 5 residue mat. or GRS/spc for rigid 4 singular points\n", -" t : [a0,ay,a1,c], swap, GRS, GRSC, sp, irreducible, pair, pairs, Pfaff, All\n", -" s : TeX, dviout, GRSC\n", -" option : swap, small, simplify, operator, int\n", -" Ex: m2mc(\"21,21,21,21\",\"All\")\n" -]); - return 0; - } - if(type(M)==7) M=s2sp(M); - if(type(X)==7) X=[X]; - Simp=getopt(simplify); - if(Simp!=0 && type(Simp)!=1) Simp=2; - Small=(getopt(small)==1)?1:0; - if(type(M[0])==4){ - if(type(M[0][0])==1){ /* spectral type */ - XX=getopt(dep); - if(type(XX)!=4 || type(XX[0])>1) XX=[1,length(M[0])]; - M=sp2grs(M,[d,a,b,c],[XX[0],XX[1],-2]|mat=1); - if(XX[0]>1 && XX[1]<2) XX=[XX[0],2]; - if(getopt(int)!=0){ - T=M[XX[0]-1][XX[1]-1][1]; - for(V=vars(T);V!=[];V=cdr(V)){ - F=coef(T,1,car(V)); - if(type(F)==1 && dn(F)>1) - M = subst(M,car(V),dn(F)*car(V)); - } - } - V=vars(M); - if(findin(d1,V)>=0 && findin(d2,V)<0 && findin(d3,V)<0) - M=subst(M,d1,d); - } - RC=chkspt(M|mat=1); - if(RC[2] != 2 || RC[3] != 0){ /* rigidity idx and Fuchs cond */ - erno(0);return 0; - } - R=getbygrs(M,1|mat=1); - if(getopt(anal)==1) return R; /* called by mc2grs() */ - Z=newmat(1,1,[[0]]); - N=[Z,Z,Z,Z,Z]; - for(RR=R; RR!=[]; RR=cdr(RR)){ - RT=car(RR)[0]; - if(type(RT)==4){ - if(RT[0]!=0) N=m2mc(N,RT[0]|simplify=Simp); - N=m2mc(N,[RT[1],RT[2],RT[3]]|simplify=Simp); - } - } - if(type(X)==4 && type(X[0])==7) - return m2mc(N,X|keep=Keep,small=Small); - return N; - } - if(type(X)==4 && type(X[0])==7){ - Keep=(getopt(keep)==1)?1:0; - if(X[0]=="All"){ - dviout("Riemann scheme"|keep=1); - m2mc(M,[(findin("GRSC",X)>=0)?"GRSC":"GRS","dviout"]|keep=1); - dviout("Spectral types : "|keep=1); - m2mc(M,["sp","dviout"]|keep=1); - dviout("\\\\\nBy the decompositions"|keep=1); - R=m2mc(M,["pairs","dviout"]|keep=1); - for(R0=R1=[],I=1; R!=[]; I++, R=cdr(R)){ - for(S=0,RR=car(R)[1][0];RR!=[]; RR=cdr(RR)) S+=RR[0]; - if(S==0) R0=cons(I,R0); - else if(S<0) R1=cons(I,R1); - } - S="irreducibility\\ $"+((length(R0)==0)?"\\Leftrightarrow":"\\Leftarrow") - +"\\ \\emptyset=\\mathbb Z\\cap$"; - dviout(S|keep=1); - m2mc(M,["irreducible","dviout"]|keep=1); - if(R0!=[]) - dviout(ltotex(reverse(R0))|eq=0,keep=1, - title="The following conditions may not be necessary for the irreducibility."); - if(R1!=[]) - dviout(ltotex(reverse(R1))|eq=0,keep=1,title="The following conditions can be omitted."); - if(getopt(operator)!=0){ - dviout("The equation in a Pfaff form is"|keep=1); - m2mc(M,["Pfaff","dviout"]|keep=Keep,small=Small); - } - else if(Keep!=1) dviout(" "); - return M; - } - Show=0; - if(length(X)>1){ - if(X[1]=="dviout") Show=2; - if(X[1]=="TeX") Show=1; - } - if(X[0]=="GRS"||X[0]=="GRSC"||X[0]=="sp"){ - Y=radd(-M[0],-M[1]-M[2]); - if(X[0]!="GRSC"){ - L=meigen([M[0],M[1],M[2],M[3],M[4],Y,radd(-M[1],-M[3]-M[4]),radd(Y,-M[3]-M[4])]|mult=1); - if(X[0]=="sp"){ - L=chkspt(L|opt="sp"); - V=[L[1],L[0],L[2],L[5]]; W=[L[1],L[3],L[4],L[6]]; - if(Show==2) dviout(s2sp(V)+" : "+s2sp(W)|keep=Keep); - return [V,W]; - } - S="x=0&x=y&x=1&y=0&y=1&x=\\infty&y=\\infty&x=y=\\infty\\\\\n"; - }else{ - L=meigen([M[0],M[1],M[2],M[3],M[4],Y,radd(-M[1],-M[3]-M[4]),radd(Y,-M[3]-M[4]), - radd(M[0],M[1]+M[3]),radd(M[1],M[2]+M[4])]|mult=1); - S="x=0&x=y&x=1&y=0&y=1&x=\\infty&y=\\infty&x=y=\\infty&x=y=0&x=y=1\\\\\n"; - } - T=ltotex(L|opt="GRS",pre=S,small=Small); - if(Show==2) dviout(T|eq=0,keep=Keep); - if(Show==1) L=T; - return L; - } - if(X[0]=="Pfaff"){ - S=ltotex(M|opt=["Pfaff",u,x,x-y,x-1,y,y-1],small=Small); - if(Show==2) dviout(S|eq=0,keep=Keep); - return S; - } - if(X[0]=="irreducible"){ - L=meigen([M[0],M[1],M[2],radd(-M[0],-M[1]-M[2])]|mult=1); - S=getbygrs(L,10|mat=1); - if(Show==2) dviout(ltotex(S)|eq=0,keep=Keep); - return S; - } - if(X[0]=="pairs"||X[0]=="pair"){ - L=meigen([M[0],M[1],M[2],radd(-M[0],-M[1]-M[2])]|mult=1); - S=chkspt(L|opt=0); - V=(Show==2)?1:0; - S=sproot(L,X[0]|dviout=V,keep=Keep); - return S; - } - if(X[0]=="swap"){ - Swap=getopt(swap); - if(type(Swap)<1 || Swap==1) - return newvect(5,[M[3],M[1],M[4],M[0],M[2]]); - if(Swap==2) - return newvect(5,[radd(M[0],M[1]+M[3]),M[4],M[2],radd(-M[1],-M[3]-M[4]),M[1]]); - if(type(Swap)==4 && length(Swap)==3){ - MX=radd(-M[0],-M[1]-M[2]); MY=radd(-M[3],-M[1]-M[4]); - if(Swap[0]==1){ - MX0=M[2];MY0=M[4]; - } - else if(Swap[0]==2){ - MX0=MX;MY0=MY; - }else{ - MX0=M[0];MY0=M[3]; - } - if(Swap[1]==1){ - MX1=M[2];MY1=M[4]; - } - else if(Swap[1]==2){ - MX1=MX;MY1=MY; - }else{ - MX1=M[0];MY1=M[3]; - } - return newvect(5,MX0,M[1],MX1,MY0,MY1); - } - } - return 0; - } - if(getopt(swap)==1) - return m2mc(m2mc(m2mc(M,"swap"),X),"swap"); - N=newvect(5); - for(I=0;I<5;I++) - N[I]=M[I]; - S=size(N[0])[0]; - if(type(X)==4){ - for(I=0;I<3;I++){ - if(X[I] != 0) - N[I] = radd(N[I],X[I]); - } - if(length(X)==3) return N; - X=X[3]; - } - MZ = newmat(S,S); - ME = mgen(S,0,[X],0); - MM = newvect(5); - MM[0] = newbmat(3,3, [[N[0]+ME,N[1],N[2]], [MZ], [MZ]]); - MM[1] = newbmat(3,3, [[MZ], [N[0],N[1]+ME,N[2]], [MZ]]); - MM[2] = newbmat(3,3, [[MZ], [MZ], [N[0],N[1],N[2]+ME]]); - MM[3] = newbmat(3,3, [[N[3]+N[1],-N[1]], [-N[0],radd(N[0],N[3])], [MZ,MZ,N[3]]]); - MM[4] = newbmat(3,3, [[N[4]], [MZ,N[4]+N[2],-N[2]], [MZ,-N[1],radd(N[4],N[1])]]); - M0 = newbmat(3,3, [[N[0]], [MZ,N[1]], [MZ,MZ,N[2]]]); - M1 = radd(MM[0],MM[1]+MM[2]); - KE = append(mykernel(M0|opt=1),mykernel(M1|opt=1)); - if(length(KE) == 0) return MM; - KK = mtoupper(lv2m(KE),0); - for(I=0;I<5;I++) - MM[I] = mmod(MM[I],KK); - if(Simp!=0) MM = mdsimplify(MM|type=Simp); - return MM; -} - -def easierpol(P,X) -{ - if(type(X) == 4){ - for( Y = [] ; X != []; X = cdr(X) ) - Y = cons([0,car(X)], Y); - }else - Y = [0,X]; - return rede(P,Y); -} - -def l2p(L,V) -{ - if(type(L)==4){ - for(S=I=0;L!=[];L=cdr(L),I++) - S+=car(L)*V^I; - return S; - }else if(type(L)==5){ - for(S=0,I=size(L)-1;I>=0;I--) - S+=L[I]*V^I; - return S; - }else{ - if(type(D=getopt(size))==1) D--; - else D=mydeg(L,V); - for(S=[];D>=0;D--) - S=cons(mycoef(L,D,V),S); - return S; - } -} - -def paracmpl(L,V) -{ - if(type(L)==4) L=ltov(L); - S=length(L); - Lim=getopt(lim);Low=getopt(low); - if((F=type(L[0]))>3){ - SV=length(L[0]); - V0=makenewv(L); - for(LL=[];S>0;S--) - LL=cons(l2p(L[S-1],V0),LL); - G=paracmpl(LL,V|option_list=getopt()); - H=(Lim==1)?G:G[0]; - for(HH=[];H!=[];H=cdr(H)){ - HT=l2p(car(H),V0|size=SV); - if(F==5) HT=ltov(HT); - HH=cons(HT,HH); - } - H=reverse(HH); - return (Lim==1)?H:[H,G[1]]; - } - H=newvect(S);D=newvect(S); - for(Dn=1,I=0;I<S;I++){ - P=dn(L[I]=red(L[I])); - Dn=red(Dn*P/gcd(Dn,P)); - } - if(Dn!=1){ - for(I=0;I<S;I++) L[I]=red(Dn*L[I]); - } - G=diagm(S,[1]); - if(type(V)<4) V=[V]; - VV=lsort(vars(L),V,1); - V=car(V); - for(I=0;I<S;I++){ - P=L[I]; - for(J=0,C=P;J<I;J++){ - if(D[J]!=[]){ - C=mycoef(C,DT,VV); - P-=C*H[J]; - G=cola(G,I,J,-C); - } - } - if(P==0){ - D[I]=[];continue; - } - P0=nm(red(P)); - K=mymindeg(P0,V); - C=mycoef(P0,K,V); - if(K>0){ - P=red(P/V^K); - G=colm(G,I,1/V^K); - } - for(DT=[],VT=VV;VT!=[];VT=cdr(VT)){ - K=(Low==1)?mymindeg(C,car(VT)):mydeg(C,car(VT)); - C=mycoef(C,K,car(VT)); - DT=cons(K,DT); - } - D[I]=DT=reverse(DT); - for(C=P,VT=VV;VT!=[];VT=cdr(VT),DT=cdr(DT)) - C=mycoef(C,car(DT),car(VT)); - H[I]=P=red(P/C); - G=colm(G,I,1/C); - } - if(Dn!=1){ - for(I=0;I<S;I++){ - TH=red(H[I]/Dn); - F=fctr(dn(TH));F=cdr(F); - if(Lim!=1||subst(Dn,V,0)==0){ - for(;F!=[];F=cdr(F)){ - if(lsort(vars(car(F)[0]),VV,2)==[]){ - C=car(F)[0]^car(F)[1]; - TH=red(TH*C); - G=colm(G,I,C); - } - } - } - H[I]=TH; - } - } - H=vtol(H); - if(Lim==1){ - H=subst(H,V,0); - return map(red,H); - } - return [H,map(red,G)]; -} - -def mykernel(M) -{ - if(getopt(opt) == 1) - M = mtranspose(M); - S = size(M); - R = []; - MM = mtoupper(M,-1); - for(I = S[0]-1; I >= 0; I--){ - for(J = S[1]-1; J >= 0; J--){ - if(MM[I][J] != 0) - return R; - } - P = easierpol(MM[I][S[1]],zz); - RR = newvect(S[0]); - for(J = 0; J < S[0]; J++) - RR[J] = mycoef(P,J,zz); - R = cons(RR,R); - } - return R; -} - -def myimage(M) -{ - if(getopt(opt) == 1) - M = mtranspose(M); - S = size(M); - V = []; - M0 = newvect(S[1]); - M = mtoupper(M,0|opt=1); - for(I = S[0]-1; I >= 0; I--) - if(M0 != M[I]) - V = cons(vtozv(M[I])[0], V); - return V; -} - -def mymod(V,L) -{ - Opt = getopt(opt); - S = length(V); - VP = newvect(S); - if(type(L)==6) - L=m2lv(L); - CT = length(L); - for(LT = L; LT != []; LT = cdr(LT)){ - for(VT = car(LT), I = 0; I < S; I++) - if(VT[I] != 0) break; - if(I >= S){ - CT--; - continue; - } - VP[I] = 1; - MI = -red(V[I]/VT[I]); - if(MI != 0) - V = radd(V,rmul(MI,VT)); - } - if(Opt==1){ - for(I = 0; I < S; I++) - if(V[I] != 0) - return 1; - return 0; - } - if(Opt==2){ - W=newvect(S-CT); - for(CC = I = 0; I < S; I++){ - if(VP[I]==0) W[CC++] =V[I]; - } - return W; - } - return V; -} - -def mmod(M,L) -{ - S=size(M)[1]; - MM=mtranspose(M); - VP = newvect(S); - if(type(L)==6) - L=m2lv(L); - for(CT = 0, LT = L; LT != []; LT = cdr(LT)){ - for(VT = car(LT), I = 0; I < S; I++){ - if(VT[I] != 0){ - VP[I] = 1; - break; - } - } - } - if(getopt(opt)==1) - NE=1; - for(D=I=0; I<S; I++){ - if(NE != 1 && VP[I] == 1) continue; - T = mymod(MM[I],L|opt=2); - if(D==0){ - K=length(T); - MN=newmat((NE==1)?S:K,K); - } - for(J=0;J<K;J++) - MN[J][D]=T[J]; - D++; - } - return MN; -} - -def llsize(V) -{ - for(I=J=0;V!=[];V=cdr(V),I++) - if(length(car(V))>J) J=length(car(V)); - return [I,J]; -} - -def llbase(VV,L) -{ - S = length(VV); - V = dupmat(VV); - if(type(V) == 4) - V = ltov(V); - T = length(L); - for(I = 0; I < S; I++) - V[I] = nm(red(V[I])); - LV = 0; - for(J = 0; J < T; J++){ - X = var(L[J]); N = deg(L[J],X); - for(I = LV; I < S; I++){ - if((C2=coef(V[I],N,X)) != 0){ - if(I > LV){ - Temp = V[I]; - V[I] = V[LV]; - V[LV] = Temp; - } - for(I = 0; I < S; I++){ - if(I == LV || (C1 = coef(V[I],N,X)) == 0) - continue; - Gcd = gcd(C1,C2); - V[I] = V[I]*tdiv(C2,Gcd)-V[LV]*tdiv(C1,Gcd); - } - LV++; - } - } - } - return V; -} - -def lsort(L1,L2,T) -{ - C1=getopt(c1);C2=getopt(c2); - if(type(T)==4){ - K=T; - if(length(T)>0){ - T=K[0]; - K=cdr(K); - }else T=0; - }else K=0; - if(type(TT=T)==7) - T = findin(T,["cup","setminus","cap","reduce","sum","subst"]); - if(type(L2)==7&&T<0) - T=findin(TT,["put","get","sub"]); - if(K){ /* [[..],..] */ - if(K!=[]) KN=K[0]; - if(L2==[]||L2=="sort"){ /* sort or deduce duplication */ - if((T!=0&&T!=3)||length(K)!=1) return L1; - if(KN<0){ - KN=-KN-1; - F=-1; - }else F=1; - L1=msort(L1,[F,0,KN]); - if(T==3){ - R=[car(L1)];L1=cdr(L1); - for(;L1!=[];L1=cdr(L1)){ - if(car(L1)[KN]!=car(R)[KN]) R=cons(car(L1),R); - } - L1=reverse(R); - } - return L1; - }else if((L2==0||L2=="col")&&type(C1)==4){ - if(T==0||T==1){ /* extract or delete columns */ - for(R=[];L1!=[];L1=cdr(L1)){ - if(T==1&&C1==[0]){ /* delete top column */ - R=cons(cdr(car(L1)),R); - continue; - } - LT=car(L1);RT=[]; - if(T==0){ - for(CT=C1;CT!=[];CT=cdr(CT)) RT=cons(LT[car(CT)],RT); - }else{ - for(I=0;LT!=[];I++,LT=cdr(LT)) - if(findin(I,C1)<0) RT=cons(car(LT),RT); - RT=reverse(RT); - } - R=cons(RT,R); - } - return reverse(R); - } - }else if(type(L2)==1||type(L2)==7){ - if(L2==1||L2=="num"){ - if(T==4) T=3; - I=(length(K)<2)?(-1):K[1]; - if(T==0||T==1||T==2||T==3){ - S=F=CT=0;R=[]; - if(K==[] || type((S=K[0]))==1 || S==0){ - if(T==0||T==1||T==2){ - for(J;L1!=[];L1=cdr(L1),J++){ - if(T==0) R=cons(cons(J+S,car(L1)),R); - else if(T==1){ - for( ;C1!=[]; C1=cdr(C1)) - R=cons(L1[car(C1)],R); - }else{ - if(findin(J,C1)<0) R=cons(car(L1),R); - } - } - return reverse(R); - }else if(T==3) return length(L1); - }else{ - if(type(S)==2&&vtype(S)>2) F=1; - else if(type(S)==4) F=2; - else if(S=="+") F=3; - else return L1; - } - for(R=[];L1!=[];L1=cdr(L1)){ - L1T=car(L1); - if(F==1) V=call(S,(I<0)?L1T:L1T[I]); - else if(F==2) V=calc((I<0)?L1T:L1T[I],S); - else if(F==3){ - for(C=C1,V=0;C!=[];C=cdr(C)) - if(type(X=L1T[car(C)])==1) V+=X; - } - if(T==0) R=cons(cons(V,L1T),R); - else if(T==1){ - if(V) R=cons(L1T,R); - }else if(T==2){ - if(!V) R=cons(L1T,R); - }else if(T==3){ - if(F==3) CT+=V; - else if(V) CT++; - } - } - return (T==3)?CT:reverse(R); - }else if(TT=="col"){ - J=(length(K)>0)?car(K):0; - I=length(car(L1))+J; - for(V=[];I>J;) - V=cons(--I,V); - return cons(V,L1); - } - }else if(L2=="transpose") return mtranspose(L1); - else if(L2=="subst"||L2=="adjust"){ - Null=(!K)?"":car(K); - if(L2=="adjust") C1=[]; - R=lv2m(L1|null=""); - for(;C1!=[];C1=cdr(C1)) R[car(C1)[0]][car(C1)[1]]=car(C1)[2]; - return m2ll(R); - } - return L1; - }else{ /* [[..],..], [[..],..] */ - if(type(L2[0])<4){ - for(R=[];L2!=[];L2=cdr(L2)) R=cons([car(L2)],R); - L2=reverse(R); - } - if(TT=="sum") T=3; - if(TT=="over") T=4; - if(findin(T,[0,1,2,3,4,5])<0) return L1; - if(T==4||T==5){ - if(type(C1)<2) C1=[C1]; - if(type(C2)<2) C2=[C2]; - } - if(type(car(L2))!=4){ - for(R=[];L2!=[];L2=cdr(L2)) R=cons([car(L2)],R); - R=reverse(R); - if(length(K)==1) K=[K[0],0]; - C2=0; - } - L1=lsort(L1,"num",["put",0]); /* insert number */ - K0=(length(K)>0)?K[0]+1:1; - K1=(length(K)>1)?K1=K[1]:0; - L1=lsort(L1,"sort",[0,K0]); - if(T<4&&type(C2)==4&&length(L2[0])>1){ - L2=lsort(L2,"col",["put"]|c1=cons(K1,C2)); /* add key and extract columns */ - C2=0;K1=0; - } - L2=lsort(L2,"sort",[0,K1]); - for(R0=[],S=S1=length(L1[0]);S>0;S--) R0=cons("",R0); - for(R1=[],S=length(L2[0]);S>0;S--) R1=cons("",R1); - if(!K1&&T!=3) R1=cdr(R1); - for(R=[];L1!=[];L1=cdr(L1)){ - while(L2!=[]&&car(L1)[K0]>car(L2)[K1]){ - if(T==3) R=cons(append(R0,car(L2)),R); - L2=cdr(L2); - } - if(L2==[]||car(L1)[K0]<car(L2)[K1]){ - if(T!=2) R=cons((T==1||T>3||R1==[])?car(L1):append(car(L1),R1),R); - }else if(T==0||T==2||T==3){ - if(R0==[]) R=append(car(L1),R); - else R=cons(append(car(L1),(!K1&&T!=3)?cdr(car(L2)):car(L2)),R); - L2=cdr(L2); - }else if(T==4||T==5){ - V1=ltov(car(L1));V2=ltov(car(L2)); - for(D1=C1,D2=C2;D1!=[];D1=cdr(D1),D2=cdr(D2)) - if((I=V2[car(D2)])!=""||T==4) V1[car(D1)+1]=I; - R=cons(vtol(V1),R); - } - } - if(T==3){ - while(L2!=[]){ - R=cons(append(R0,car(L2)),R); - L2=cdr(L2); - } - } - R=lsort(R,"sort",["put",0]); /* original order */ - D=(((T==0||T==2)&&!K1)||T==3)?[0]:[0,S1+K1]; - R=lsort(R,0,[1]|c1=D); /* delete */ - if(type(C1)!=4||T==1||T==4||T==5) return R; - C=[];S0=size(L1[0]); - for(;C1!=[];C1=cdr(C1)) C=cons(car(C1),C); - for(I=0;I<S0-S1;I++) C=cons(I+S1,C); - C=reverse(C); - return lsort(R,"col",[1]|c1=C); - } - } - if(L2 == []){ /* [...] */ - if(T==8||TT=="count") return [length(L1),length(lsort(L1,[],1))]; - if(T==7||TT=="cut"){ - K=length(L1); - if(C1<0) C1=K+C1; - for(R=[],I=0;I<C1&&L1!=[];I++,L1=cdr(L1)) - R=cons(car(L1),R); - for(S=[];L1!=[];L1=cdr(L1)) - S=cons(car(L1),S); - return [reverse(R),reverse(S)]; - } - if(T==2) return L2; - if(T==3) return [L1,L2]; - L1 = ltov(L1); qsort(L1); - if(T != 1) - return vtol(L1); - L3 = []; - for(I = length(L1)-1; I >= 0; I--){ - if(I > 0 && L1[I] == L1[I-1]) - continue; - L3 = cons(L1[I], L3); - } - return L3; - } - if(T==8||TT=="count"){ - K=length(lsort(L1,L2,3)[0]); - R=[length(L2),length(L1)]; - L1 = lsort(L1,[],1); - L2 = lsort(L2,[],1); - R=append([length(L2),length(L1)],R); - R=cons(length(lsort(L1,L2,2)),R); - return reverse(cons(K,R)); - } - if((T==9||TT=="cons")&&type(car(L1))==4){ - if(type(L2)!=4) L2=[L2]; - for(R=[];L1!=[];L1=cdr(L1)){ - R=cons(cons(car(L2),car(L1)),R); - if(length(L2)>1) L2=cdr(L2); - } - return reverse(R); - } - if(T==10||TT=="cmp"){ - if(length(L1)!=length(L2)){ - mycat("Different length!"); - return 1; - } - R=[]; - if(type(car(L1))==4){ - for(U=[],I=0;L1!=[];I++,L1=cdr(L1),L2=cdr(L2)){ - if(length(S=car(L1))!=length(T=car(L2))){ - mycat(["Different size : line ",I]); - return 0; - } - for(J=0;S!=[];S=cdr(S),T=cdr(T),J++) - if(car(S)!=car(T)) U=cons([[I,J],car(S),car(T)],U); - } - if(U!=[]) R=cons(reverse(U),R); - }else{ - for(I=0;L1!=[];L1=cdr(L1),L2=cdr(L2),I++) - if(car(L1)!=car(L2)) R=cons([I,car(L1),car(L2)],R); - } - return reverse(R); - } - if(T==11||TT=="append"){ - if(type(car(L1))!=4) return append(L1,L2); - for(R=[];L1!=[];L1=cdr(L1),L2=cdr(L2)) - R=cons(append(car(L1),car(L2)),R); - return reverse(R); - } - if(T == 1 || T == 2){ - L1 = lsort(L1,[],1); - L2 = lsort(L2,[],1); - L3 = []; - if(T == 1){ - while(L1 != []){ - if(L2 == [] || car(L1) < car(L2)){ - L3 = cons(car(L1), L3); - L1 = cdr(L1); - continue; - } - if(car(L1) > car(L2)){ - L2 = cdr(L2); - continue; - } - L1 = cdr(L1); L2 = cdr(L2); - } - return reverse(L3); - } - if(T==2){ - while(L1 != [] && L2 != []){ - if(car(L1) != car(L2)){ - if(car(L1) <= car(L2)) - L1 = cdr(L1); - else L2 = cdr(L2); - continue; - } - while(car(L1) == car(L2)) - L1 = cdr(L1); - L3 = cons(car(L2), L3); - } - return reverse(L3); - } - } - if(T==3){ - L1 = qsort(L1); L2 = qsort(L2); - L3 = L4 = []; - while(L1 != [] && L2 != []){ - if(car(L1) == car(L2)){ - L1 = cdr(L1); L2 = cdr(L2); - }else if(car(L1) < car(L2)){ - L3 = cons(car(L1),L3); - L1 = cdr(L1); - }else{ - L4 = cons(car(L2), L4); - L2 = cdr(L2); - } - } - L4 = append(reverse(L4),L2); - L3 = append(reverse(L3),L1); - return [L3,L4]; - } - L1 = append(L1,L2); - return lsort(L1,[],1); -} - -def mqsub(X,Y) -{ - for(L=LQS;L!=[];L=cdr(L)){ - F=(T=car(L))[0];M=(T=cdr(T))[0]; - X0=X;Y0=Y; - for(T=cdr(T);T!=[];T=cdr(T)){ - X0=X0[car(T)];Y0=Y0[car(T)]; - } - if(type(M)==1){ - if(M==3){ - X0=type(X0);Y0=type(Y0); - }else if(M==4&&type(X0)<2&&type(Y0)<2){ - X0=abs(X0);Y0=abs(Y0); - }else if(M==5){ - X0=str_len(rtostr(X0));Y0=str_len(rtostr(Y0)); - }else if(type(X0)==type(Y0)&&type(X0)>3&&type(X0)<7){ - if(M==1){ - X0=length(X0);Y0=length(Y0); - }else if(M==2){ - LX=length(X0);LY=length(Y0); - L0=(LX<LY)?LX:LY; - for(I=0;;I++){ - if(I==L0){ - X0=LX;Y0=LY;break; - } - if(X0[I]==Y0[I]) continue; - X0=X0[I];Y0=Y0[I];break; - } - } - } - }else if(type(M)==2){ - X0=(*M)(X0,Y0);Y0=0; - }else if(type(M)==4&&length(M)==1){ - X0=(*car(M))(X0);Y0=(*car(M))(Y0); - } - if(X0==Y0) continue; - return (X0<Y0)?-F:F; - } - return 0; -} - -def msort(L,S) -{ - if(type(S)!=4) return qsort(L); - if(type(S[0])!=4) S=[S]; - LQS=S; - return qsort(L,os_md.mqsub); -} - -def lmax(L) -{ - if(type(L)==4){ - V=car(L); - while((L=cdr(L))!=[]) - if(V < car(L)) V=car(L); - return V; - }else if(type(L)==5||type(L)==6) - return lmax(m2l(L)); - return []; -} - -def lmin(L) -{ - if(type(L)==4){ - V=car(L); - while((L=cdr(L))!=[]) - if(V > car(L)) V=car(L); - return V; - }else if(type(L)==5||type(L)==6) - return lmin(m2l(L)); - return []; -} - -def lgcd(L) -{ - if(type(L)==4){ - F=getopt(poly); - V=car(L); - while((L=cdr(L))!=[]&&V!=1){ - if(V!=0) - V=(F==1)?gcd(V,car(L)):igcd(V,car(L)); - } - return V; - }else if(type(L)==5||type(L)==6) - return lgcd(m2l(L)|option_list=getopt()); - return []; -} - -def llcm(L) -{ - if(type(L)==4){ - F=getopt(poly); - V=car(L); - while((L=cdr(L))!=[]){ - if(V!=0){ - if((V0=car(L))!=0) - V=(F==1)?red(V*V0/gcd(V,V0)):ilcm(V,V0); - } - else V=car(L); - } - if(F!=1&&V<0) V=-V; - return V; - } - else if(type(L)==5||type(L)==6) - return llcm(m2l(L)|option_list=getopt()); - return []; -} - -def ldev(L,S) -{ - M=abs(lmax(L));N=abs(lmin(L)); - if(M<N) M=N; - for(C=0,LT=L;;C++){ - LT=ladd(LT,S,1); - MT=abs(lmax(LT));NT=abs(lmin(LT)); - if(MT<NT) MT=NT; - if(MT>=M) break; - M=MT; - } - if(!C){ - for(C=0,LT=L;;C--){ - LT=ladd(LT,S,-1); - MT=abs(lmax(LT));NT=abs(lmin(LT)); - if(MT<NT) MT=NT; - if(MT>=M) break; - M=MT; - } - } - return [C,ladd(L,S,C)]; -} - -def lchange(L,P,V) -{ - if(getopt(flat)==1&&type(P)==4){ - for(L=ltov(L);P!=[];P=cdr(P),V=cdr(V)) - L[car(P)]=car(V); - return vtol(L); - } - if(type(P)==4){ - IP=car(P); P=cdr(P); - }else{ - IP=P; P=[]; - } - for(I=0, LL=[], LT=L; LT!=[]; I++,LT=cdr(LT)){ - if(I==IP){ - LL=cons((P==[])?V:lchange(car(LT),P,V),LL); - }else - LL=cons(car(LT),LL); - } - return reverse(LL); -} - -def lsol(VV,L) -{ - if(type(VV)<4 && type(L)==2) - return red(L-VV/mycoef(VV,1,L)); - S = length(VV); - T = length(L); - V = llbase(VV,L); - for(J = K = 0; J < T; J++){ - X = var(L[J]); N = deg(L[J],X); - for(I = K; I < S; I++){ - if((C=mycoef(V[I], N, X)) != 0){ - V[I] = [L[J],red(X^N-V[I]/C)]; - K++; - break; - } - } - } - return V; -} - -def lnsol(VV,L) -{ - LL=lsort(vars(VV),L,1); - VV=ptol(VV,LL|opt=0); - return lsol(VV,L); -} - - -def ladd(X,Y,M) -{ - if(type(X)==4) X=ltov(X); - if(type(Y)==4) Y=ltov(Y); - return vtol(X+M*Y); -} - -def mrot(X) -{ - if(getopt(deg)==1) X=@pi*X/180; - X=deval(X); - return mat([dcos(X),dsin(X)],[-dsin(X),dcos(X)]); -} - -def m2v(M) -{ - S = size(M); - V = newvect(S[0]*S[1]); - for(I = C = 0; I < S[0]; I++){ - MI = M[I]; - for(J = 0; J < S[1]; J++) - V[C++] = MI[J]; - } - return V; -} - -def lv2m(L) -{ - if(type(L)==5) L=vtol(L); - II=length(L); - for(J=1,T=L; T!=[]; T=cdr(T)) - if(length(car(T))>JJ) JJ=length(car(T)); - M = newmat(II,JJ); - N = getopt(null); - if(type(N)<0) N=0; - for(I=0; I<II; I++){ - V=car(L); L=cdr(L); - for(J=length(V);--J>=0;) - M[I][J] = V[J]; - if(N!=0){ - for(J=length(V); J<JJ; J++) - M[I][J]=N; - } - } - return M; -} - -def m2lv(M) -{ - I=size(M)[0]; - for(N=[],I=size(M)[0];I-->0;) - N=cons(M[I],N); - return N; -} - -def s2m(S) -{ - if(type(S)==6) return S; - if(type(S)==7){ - if(str_chr(S,0,"[")!=0) S=s2sp(S); - else if(str_chr(S,0,",")>=0) return eval_str(S); - else{ - for(L=LL=[],I=0; ; ){ - II=str_chr(S,I+2,"]"); - if(II<0) return 0; - J=str_chr(S,I+2," "); - while(str_chr(S,J+1," ")==J+1) J++; - if(J>II-2 || J<0) J=II; - V=eval_str(sub_str(S,I+1,J-1)); - L=cons(V,L); - I=J; - if(J==II){ - LL=cons(ltov(reverse(L)),LL); - L=[]; - if((I=str_chr(S,II+1,"["))<0) - return lv2m(reverse(LL)); - } - } - } - } - if(type(S)==5) S=vtol(S); - if(type(S[0])==5) return lv2m(S); - I=length(S); - for(J=1,T=S; T!=[]; T=cdr(T)) - if(length(car(T))>J) J=length(car(T)); - return newmat(I,J,S); -} - -def c2m(L,V) -{ - if(type(Pow=getopt(pow))!=1){ - if(isvar(V)==1){ - for(Pow=0,LT=L;LT!=[];LT=cdr(LT)){ - if(mydeg(car(LT),V)>JJ) Pow=mydeg(car(LT),V); - } - JJ=Pow+1; - }else{ - Pow=-1; - JJ=length(V); - } - }else JJ=Pow+1; - M=newmat(length(L),JJ); - for(I=0;L!=[];L=cdr(L),I++){ - for(J=0;J<JJ;J++){ - LT=car(L); - M[I][J]=(Pow>=0)?mycoef(LT,J,V):mycoef(LT,1,V[J]); - } - } - return M; -} - -#if 0 -def m2diag(M,N) -{ - S = size(M); - MM = mtoupper(M,N); - for(I = S[0]-1; I >= 0; I--){ - for(J = 0; I < S[1]-N; I++){ - if(MM[I][J] != 0){ - P = MM[I][J]; - for(K = 0; K < I; K++){ - Q = -rmul(MM[K][J],1/P); - MM[K][J] = 0; - if(Q != 0){ - for(L = J+1; L < S[1]; L++){ - if(MM[I][L] != 0) - MM[K][L] = radd(MM[K][L], rmul(MM[I][L],Q)); - } - } - } - } - } - } - return MM; -} -#endif - -def myinv(M) -{ - S = size(M); - if((T=S[0]) != S[1]) - return 0; - MM = mtoupper(M,-T|opt=2); - if(MM[T-1][T-1] != 1) return 0; - return mperm(MM,0,[T,[T]]); -} - -def madj(G,M) -{ - H=myinv(G); - if(type(M)==6) - return rmul(rmul(G,M),H); - if(type(M)==4||type(M)==5){ - L=length(M); - N=newvect(L); - for(I=0;I<L;I++){ - N[I]=rmul(rmul(G,M[I]),H); - } - if(type(N)==4) N=vtol(N); - return N; - } - return -1; -} - -def mpower(M,N) -{ - if(type(M)<=3) return (red(M))^N; - S = size(M); - if(S[0] != S[1]) - return 0; - if(N == 0) return mgen(S[0],0,[1],0); - if(N < 0) - return(mpower(myinv(M), -N)); - R = dupmat(M); - V=1; - for(V=1;;){ - if(iand(N,1)){ - V=map(red,R*V); - N--; - } - if((N/=2)==0) break; - R=map(red,R*R); - } - return V; -} - -def texlen(S) -{ - if(type(S)!=7) return 0; - LF=I=J=0; - LM=str_len(S); - while((I=str_str(S,"\\frac{"|top=J))>=0){ - if(I>J) LF+=texlen(str_cut(S,J,I-1)); - I+=6; - for(F=L=0,J=I;F<2 && J<LM-1;F++){ - for(C=1;C>0 && J<LM;){ - if((K0=str_char(S,J,"}"))<0) K0=LM; - if((K1=str_char(S,J,"{"))<0) K1=LM; - if(K0<0 && K1<0){ - J = str_len(S)-1; - break; - } - if(K0<K1){ - J=K0+1; C--; - }else{ - J=K1+1; C++; - } - } - T=str_cut(S,I,J-1); - if(F==0){ - I=J=K1+1;C=1; - }else J=K0+1; - if(type(T)==7 && (LL=texlen(T))>L) L=LL; - } - LF+=L; - } - if(J>0) S=str_cut(S,J,str_len(S)-1); - if(S==0) return LF; - S=ltov(strtoascii(S)); - L=LL=length(S); - for(I=F=0; I<L; I++){ - if(S[I]==92) F=1; - else if(F==1){ - if((S[I]>96 && S[I]<123)||(S[I]>64 && S[I]<91)) LL--; - else F=0; - } - if(S[I]<=32||S[I]==123||S[I]==125||S[I]==94||S[I]==38) LL--; /* {}^& */ - else if(S[I]==95){ - LL--; - if(I+2<L && S[I+2]==94) LL--; /* x_2^3 */ - else if(I+6<L && S[I+1]==123 && S[I+4]==125){ /* x_{11}^2 */ - if(S[I+5]==94 || (S[I+5]==125 && S[I+6]==94)) LL-- ; /* x_{11}}^2 */ - } - } - } - return LL+LF; -} - -def isdif(P) -{ - if(type(P)<1 || type(P)>3) return 0; - for(Var=[],R=vars(P);R!=[];R=cdr(R)){ - V0=rtostr(car(R)); - if(V0>"d" && V0<"e"){ - V=sub_str(V0,1,str_len(V0)-1); - if(V>="a" && V<"{") Var=cons([strtov(V),strtov(V0)],Var); - } - } - if(Var==[]) return 0; - for(V=Var; V!=[]; V=cdr(V)) - if(ptype(P,car(V)[1])==3) return 0; - return Var; -} - -def texsp(P) -{ - Q=strtoascii(P); - if((J=str_char(Q,0,92))<0 || (C=Q[L=str_len(P)-1])==32||C==41||C==125) - return P; - for(;;){ - if((I=str_char(Q,J+1,92))<0) break; - J=I; - }; - for(I=J+1;I<L&&isalpha(Q[I]);I++); - return(I==L)?P+" ":P; -} - -def fctrtos(P) -{ - /* extern TeXLim; */ - - if(!chkfun("write_to_tb", "names.rr")) - return 0; - - TeX = getopt(TeX); - if(TeX != 1 && TeX != 2 && TeX != 3) - TeX = 0; - if((Dvi=getopt(dviout)==1) && TeX<2) TeX=3; - if(TeX>0){ - Lim=getopt(lim); - if(Lim!=0 && TeX>1 && (type(Lim)!=1||Lim<30)) Lim=TeXLim; - else if(type(Lim)!=1) Lim=0; - CR=(TeX==2)?"\\\\\n":"\\\\\n&"; - if(TeX==1 || Lim==0) CR=""; - else if((Pages=getopt(pages))==1) CR="\\allowdisplaybreaks"+CR; - if(!chkfun("print_tex_form", "names.rr")) - return 0; - Small=getopt(small); - } - Dif=getopt(dif); - Var=getopt(var); - if(Lim>0 && type(Var)<2 && TeX!=1) Var=[strtov("0"),""]; - Dif=0; - if(Var=="dif"){ - Dif=DV=1; - }else if (Var=="dif0") Dif=1; - else if(Var=="dif1") Dif=2; - else if(Var=="dif2") Dif=3; - if(Dif>0){ - for(Var=[],R=vars(P);R!=[];R=cdr(R)){ - V=rtostr(car(R)); - if(V>"d" && V<"e"){ - V=sub_str(V,1,str_len(V)-1); - if(V>="a" && V<"{"){ - if(TeX>0){ - V=my_tex_form(strtov(V)); - if(Dif>=1){ - if(Dif==1){ - if(str_len(V)==1) V="\\partial_"+V; - else V="\\partial_{"+V+"}"; - } - Var=cons([car(R),V],Var); - } - else Var=cons([car(R)],Var); - }else Var=cons([car(R)],Var); - } - } - } - if(TeX>0){ - if(length(Var)==1){ - if(DV==1 && str_len(Var[0][1])==10) Var=[[Var[0][0],"\\partial"]]; - }else if(DV==1){ - for(V=Var;V!=[];V=cdr(V)){ - VV=rtostr(car(V)[0]); - if(VV<"dx0" || VV>= "dx:" || str_len(VV)>4) break; - } - if(V==[]){ - for(VT=[],V=Var;V!=[];V=cdr(V)){ - VV=str_cut(rtostr(car(V)[0]),2,3); - if(str_len(VV)==1) VT=cons([car(V)[0],"\\partial_"+VV],VT); - else VT=cons([car(V)[0],"\\partial_{"+VV+"}"],VT); - } - Var=reverse(VT); - } - }else - if(Dif==2 && length(Var)>1) Dif=3; - } - if(Dif>0) Dif--; - } - if(type(Var)>1 && Var!=[]){ /* as a polynomial of Var */ - Add=getopt(add); - if(type(Add)>0){ - if(type(Add)!=7){ - Add=my_tex_form(Add); - if(str_char(Add,0,"-")>=0 || str_char(Add,0,"+")>=0) Add="("+Add+")"; - } - if(str_char(Add,0,"(")!=0) Add = " "+Add; - }else Add=0; - if(type(Var)!=4) Var=[Var]; - if(length(Var)==2 && type(Var[1]) == 7) - Var = [Var]; - for(VV=VD=[]; Var!=[];Var=cdr(Var)){ - VT=(type(car(Var))==4)?car(Var):[car(Var)]; - VT0=var(car(VT)); - VV=cons(VT0,VV); - if(length(VT)==1){ - VD=cons((TeX>=1)?my_tex_form(VT0):rtostr(VT0),VD); - }else VD=cons(VT[1],VD); - } - VV=reverse(VV);VD=reverse(VD); - Rev=(getopt(rev)==1)?1:0; - Dic=(getopt(dic)==1)?1:0; - TT=terms(P,VV|rev=Rev,dic=Dic); - if(TeX==0){ - Pre="("; Post=")"; - }else{ - Pre="{"; Post="}"; - } - Out = string_to_tb(""); - for(L=C=0,Tm=TT;Tm!=[];C++,Tm=cdr(Tm)){ - for(I=0,PC=P,T=cdr(car(Tm)),PW="";T!=[];T=cdr(T),I++){ - PC=mycoef(PC,D=car(T),VV[I]); - if(PC==0) continue; - PT=""; - if(D!=0 && VD[I]!=""){ - if(TeX==0 && PW!="") PW+="*"; - if(D>1){ - if(D>9) PT="^"+Pre+rtostr(D)+Post; - else PT="^"+rtostr(D); - } - if(Dif>0) PW+=(Dif==1)?"d":"\\partial "; - PW+=VD[I]+PT; - } - } - D=car(Tm)[0]; - if(Dif>0 && D>0){ - Op=(Dif==1)?"\\frac{d":"\\frac{\\partial"; - if(D>1) Op+="^"+((D>9)?(Pre+rtostr(D)+Post):rtostr(D)); - PW=Op+Add+"}{"+PW+"}"; - }else if(Add!=0) PW=PW+Add; - if(TeX>=1){ - if(type(PC)==1 && ntype(PC)==0 && PC<0) - OC="-"+my_tex_form(-PC); - else OC=fctrtos(PC|TeX=1,br=1); - }else OC=fctrtos(PC|br=1); - if(PW!=""){ - if(OC == "1") OC = ""; - else if(OC == "-1") OC = "-"; - } - if(TeX==0 && D!=0 && OC!="" && OC!="-") PW= "*"+PW; - if((TOC=type(OC)) == 4){ /* rational coef. */ - if(Lim>0 && (texlen(OC[0])>Lim || texlen(OC[0])>Lim)){ - OC = (Small==1)?"("+OC[0]+")/("+OC[1]+")" - :"\\Bigl("+OC[0]+"\\Bigr)\\Bigm/\\Bigl("+OC[1]+"\\Bigr)"; - TOC = 7; - }else{ - if(str_char(OC[0],0,"-")==0){ - OC = fctrtos(-PC|TeX=1,br=1); - OC = "-\\frac{"+OC[0]+"}{"+OC[1]+"}"; - } - else - OC = "\\frac{"+OC[0]+"}{"+OC[1]+"}"; - } - } - if(Lim>0){ - LL=texlen(OC)+texlen(PW); - if(LL+L>=Lim){ - if(L>0) str_tb(CR,Out); - if(LL>Lim){ - if(TOC==7) OC=texlim(OC,Lim|cut=CR); - PW+=CR; L=0; - }else L=LL; - }else L+=LL; - }else if(length(Tm)!=1) PW += CR; /* not final term */ - if(TeX) OC=texsp(OC); - if(str_chr(OC,0,"-") == 0 || C==0) str_tb([OC,PW], Out); - else{ - str_tb(["+",OC,PW],Out); - if(LL<=Lim) L++; - } - } - S=str_tb(0,Out); - if(S=="") S="0"; - }else{ /* Var is not specified */ - if((TP=type(P)) == 3){ /* rational function */ - P = red(P); Nm=nm(P); Dn=dn(P); - Q=dn(ptozp(Nm|factor=1)[1]); - if(Q>1){ - Nm*=Q;Dn*=Q; - } - if(TeX>0){ - return (TeX==2)? - "\\frac\{"+fctrtos(Nm|TeX=1)+"\}\{"+fctrtos(Dn|TeX=1)+"\}" - :[fctrtos(Nm|TeX=1),fctrtos(Dn|TeX=1)]; - } - else{ - S=fctrtos(Nm); - if(nmono(Nm)>1) S="("+S+")"; - return S+"/("+fctrtos(Dn)+")"; - } - } - if(imag(P)==0) P = fctr(P); /* usual polynomial */ - else P=[[P,1]]; - S = str_tb(0,0); - for(J = N = 0; J < length(P); J++){ - if(type(P[J][0]) <= 1){ - if(P[J][0] == -1){ - write_to_tb("-",S); - if(length(P) == 1) - str_tb("1", S); - }else if(P[J][0] != 1){ - str_tb((TeX>=1)?my_tex_form(P[J][0]):rtostr(P[J][0]), S); - N++; - }else if(length(P) == 1) - str_tb("1", S); - else if(getopt(br)!=1 && length(P) == 2 && P[1][1] == 1){ - str_tb((TeX>=1)?my_tex_form(P[1][0]):rtostr(P[1][0]), S); - J++; - } - continue; - } - if(N > 0 && TeX != 1 && TeX != 2 && TeX != 3) - write_to_tb("*", S); - SS=(TeX>=1)?my_tex_form(P[J][0]):rtostr(P[J][0]); - N++; - if(P[J][1] != 1){ /* (log(x))^2 */ - if(nmono(P[J][0])>1|| - (!isvar(P[J][0])||vtype(P[J][0]))&&str_len(SS)>1) SS="("+SS+")"; - write_to_tb(SS,S); - str_tb(["^", (TeX>1)?rtotex(P[J][1]):monotos(P[J][1])],S); - }else{ - if(nmono(P[J][0])>1) SS="("+SS+")"; - write_to_tb(SS,S); - } - } - S = str_tb(0,S); - if((Lim>0 || TP!=2) && CR!="") S=texlim(S,Lim|cut=CR); - } - if(TeX>0){ - if(Small==1) S=str_subst(S,"\\frac{","\\tfrac{"); - if(Dvi==1){ - dviout(strip(S,"(",")")|eq=(Pages==1)?6:0); S=1; - } - } - return S; -} - -def strip(S,S0,S1) -{ - SS=strtoascii(S); - if(length(SS)>1){ - if(SS[0]==40&&SS[length(SS)-1]==41&&str_pair(SS,1,S0,S1)==length(SS)-1) - S=str_cut(SS,1,length(SS)-2); - } - return S; -} - -def texlim(S,Lim) -{ - /* extern TeXLim; */ - if(S==1 && Lim>10){ - TeXLim=Lim; - mycat(["Set TeXLim =",Lim]); - return 1; - } - if(type(Out=getopt(cut))!=7) Out="\\\\\n&"; - if(type(Del=getopt(del))!=7) Del=Out; - if(Lim<30) Lim=TeXLim; - S=ltov(strtoascii(S)); - for(L=[0],I=F=0;F==0; ){ - II=str_str(S,Del|top=I)+2; - if(II<2){ - F++;II=/* str_len(S) */ length(S)-1; - } - for(J=JJ=I+1;;JJ=K+1){ - K=str_char(S,JJ,43); /* + */ - if((K1=str_char(S,JJ,45))>2 && K1<K){ /* - */ - if(S[K1-1]!=123 && S[K1-1]!=40) K=K1; /* {, ( */ - } - if((K1=str_char(S,JJ,40))>0 && K1-JJ>6 && K1<K && S[K1-1]!=43 && S[K1-1]!=45){ /* ( */ - T=str_char(S,K1-6,"\\"); /* \Big*(, \big*( */ - if((T==K1-6 || T==K1-5) - && (str_str(S,"big"|top=T+1,end=T+1)>0 || str_str(S,"Big"|top=T+1,end=T+1)>0)) - K=T; - else if(K1>0 && K1<K) K=K1; - } - if(K<0 || K>II) break; - if(K-J>Lim && texlen(str_cut(S,J,K-1))>=Lim){ - J=K+1; L=cons(JJ-1,L); SL=0; - } - } - I=II; - } - SS=str_tb(0,0); - L=cons(length(S),L); - L=reverse(L); - for(I=0; L!=[]; I=J,L=cdr(L)){ - str_tb((I==0)?"":Out,SS); - J=car(L); - str_tb(str_cut(S,I,J-1),SS); - } - return str_tb(0,SS); -} - -def fmult(FN,M,L,N) -{ - Opt=getopt(); - for(I = 0; I < length(M); I++) - M = call(FN, cons(M,cons(L[I],N))|option_list=Opt); - return M; -} - -def radd(P,Q) -{ - if(type(P) <= 3 || type(Q) <= 3){ - if(type(P) >= 5) - return radd(Q,P); - if(type(Q) >= 5){ - R = dupmat(Q); - if(P == 0) - return R; - if(type(Q) == 6){ - S = size(Q); - if(S[0] != S[1]) - return 0; - for(I = 0; I < S[0]; I++) - R[I][I] = radd(R[I][I], P); - }else{ - for(I = length(R)-1; I >= 0; I--) - R[I] = radd(R[I],P); - } - return R; - } - /* P=red(P);Q=red(Q); */ - if((P1=dn(P)) == (Q1=dn(Q))){ - if(P1==1) return P+Q; - return red((nm(P)+nm(Q))/P1); - } - R=gcd(P1,Q1);S=tdiv(P1,R); - return red((nm(P)*tdiv(Q1,R)+nm(Q)*S)/(S*Q1)); - } - if(type(P) == 5){ - S = length(P); - R = newvect(S); - for(I = 0; I < S; I++) - R[I] = radd(P[I],Q[I]); - return R; - } - if(type(P) == 6){ - S = size(P); - R = newmat(S[0],S[1]); - for(I = 0; I < S[0]; I++){ - for(J = 0; J < S[1]; J++) - R[I][J] = radd(P[I][J],Q[I][J]); - } - return R; - } - erno(0); -} - -def getel(M,I) -{ - if(type(M) >= 4 && type(M) <= 6 && type(I) <= 1) - return M[I]; - if(type(M) == 6 && type(I) == 5) - return M[I][J]; - return M; -} - -def ptol(P,X) -{ - F=(getopt(opt)==0)?0:1; - if(type(P) <= 3) - P = [P]; - if(type(X) == 4){ - for( ; X != []; X = cdr(X)) - P=ptol(P,car(X)|opt=F); - return P; - } - P = reverse(P); - for(R=[]; P != []; P = cdr(P)){ - Q = car(P); - for(I = mydeg(Q,X); I >= 0; I--){ - S=mycoef(Q,I,X); - if(F==1 || S!=0) R = cons(S,R); - } - } - return R; -} - -def rmul(P,Q) -{ - if(type(P) <= 3 && type(Q) <= 3){ - P=red(P);Q=red(Q); - P1=dn(P);P2=nm(P);Q1=dn(Q);Q2=nm(Q); - if(P1==1 && Q1==1) - return P*Q; - if((R=gcd(P1,Q2)) != 1){ - P1=tdiv(P1,R);Q2=tdiv(Q2,R); - } - if((R=gcd(Q1,P2)) != 1){ - Q1=tdiv(Q1,R);P2=tdiv(P2,R); - } - return P2*Q2/(P1*Q1); - } -#ifdef USEMODULE - return mmulbys(os_md.rmul,P,Q,[]); -#else - return mmulbys(rmul,P,Q,[]); -#endif -} - -def mtransbys(FN,F,LL) -{ - Opt=getopt(); - if(type(F) == 4){ - F = ltov(F); - S = length(F); - R = newvect(S); - for(I = 0; I < S; I++) - R[I] = mtransbys(FN,F[I],LL|option_list=Opt); - return vtol(R); - } - if(type(F) == 5){ - S = length(F); - R = newvect(S); - for(I = 0; I < S; I++) - R[I] = mtransbys(FN,F[I],LL|option_list=Opt); - return R; - } - if(type(F) == 6){ - S = size(F); - R = newmat(S[0],S[1]); - for(I = 0; I < S[0]; I++){ - for(J = 0; J < S[1]; J++) - R[I][J] = mtransbys(FN,F[I][J],LL|option_list=Opt); - } - return R; - } - if(type(F) == 7) return F; - return call(FN, cons(F,LL)|option_list=Opt); -} - -def drawopt(S,T) -{ - if(type(S)!=7) return -1; - if(T==0||T==1){ - for(I=0,R=LCOPT;I<7;I++,R=cdr(R)) - if(str_str(S,car(R))>=0) return(T==0)?COLOPT[I]:car(R); - return -1; - } - if(T==2){ - V0=V1=0; - for(I=0,R=LPOPT;R!=[];I++,R=cdr(R)){ - if(str_str(S,car(R))>=0){ - if(I==0) V1++; - else if(I==1) V1--; - else if(I==2) V0--; - else V0++; - } - } - if(V0==0&&V1==0) return -1; - return [V0,V1]; - } - if(T==3){ - V=0; - for(I=1,R=LFOPT;R!=[];R=cdr(R),I*=2){ - if(str_str(S,car(R))>=0) V+=I; - } - return (V==0)?-1:V; - } - return -1; -} - -def execdraw(L,P) -{ - if((Proc=getopt(proc))!=1) Proc=0; - if(type(P)<2) P=[P]; - if(L!=[]&&type(L[0])!=4) L=[L]; - /* special command */ - if(P[0]<0){ - if(length(P)==1&&(P[0]==-1||P[0]==-2||P[0]==-3)){ /* Bounding Box */ - W=WS=N=LS=0; - for(LL=L;LL!=[];LL=cdr(LL)){ - T=car(LL); - if(P[0]!=-3 && T[0]==0){ - if(length(T)>3) S=" by "+rtostr(T[3])+" cm"; - else S=""; - if(P[0]==-1){ - mycat(["Windows : ",T[1][0],"< x <",T[1][1],", ", - T[2][0],"< y <",T[2][1],S]); - if(length(T)>4 && type(T[4])==4) mycat(["ext :",T[4]]); - if(length(T)>5) mycat(["shift :",T[5]]); - } - return cdr(T); - } - if(type(T[0])==1){ - if(T[0]==1){ - for(TT=cdr(cdr(T));TT!=[];TT=cdr(TT)){ - D=car(TT); - if(type(D[0][0])==4){ - for(DT=D;DT!=[];DT=cdr(DT)){ - if(N++==0) W=ptbbox(car(DT)); - else W=ptbbox(car(DT)|box=W); - } - }else{ - if(N++==0) W=ptbbox(D); - else W=ptbbox(D|box=W); - } - } - }else if(T[0]==2){ - V=T[2]; - if(type(V[0])>1||type(V[1])>1) continue; /* not supported */ - if((Sc=delopt(T[1],"scale"|inv=1))!=[]){ - Sc=car(Sc)[1]; - if(type(Sc)==1) V=[Sc*V[0],Sc*V[1]]; - else V=[Sc[0]*V[0],Sc[1]*V[1]]; - } - if(LS==0) WS=ptbbox([V]); - else WS=ptbbox([V]|box=WS); - if(length(T)>4) S=T[4]; - else if(type(S=T[3])==4){ - S=S[0]; - if(type(S)==4) S=S[length(S)-1]; - S=rtostr(S); - } - if(str_len(S)>LS) LS=str_len(S); - }else if(T[0]==3||T[0]==4){ - if(N++==0) W=ptbbox(cdr(cdr(T))); - else W=ptbbox(cdr(cdr(T))|box=W); - } - } - } - if(W!=0&&WS!=0) W=ptbbox([W,WS]|box=1); - return (P[0]==-3)?[W,LS,WS]:W; - }else if(length(P)>1&&P[0]==-1){ /* set Bounding Box */ - P=cons(0,cdr(P)); - Ex=Sft=[0,0]; - if(type(X=getopt(ext))==4) Ex=X; - if(type(X=getopt(shift))==4) Sft=X; - if(Ex!=Sft||Ex!=[0,0]){ - if(Sft==[0,0]) Sft=[Ex]; - else Sft=[Ex,Sft]; - if(length(P)==3) Sft=cons(1,Sft); - if(length(P)==3||length(P)==4) P=append(P,Sft); - } - return cons(P,delopt(L,0)); - } - if(P[0]==-4){ - for(N=0,LT=L;LT!=[];LT=cdr(LT)){ /* count coord. */ - T=car(LT); - if(T[0]==1){ - for(T=cdr(cdr(T));T!=[];T=cdr(T)){ - if(type((S=car(T))[0][0])==4) N+=length(S); - else for(;S!=[];S=cdr(S)) if(type(car(S))==4) N++; - } - }else if(T[0]==2) N++; - else if(T[0]==3||T[0]==4) N+=2; - } - return N; - } - if(P[0]==-5){ /* functions */ - for(N=0,R=[],LT=L;LT!=[];LT=cdr(LT)){ - T=car(LT); - if(T[0]==0) N=ior(N,1); - else if(type(T[0])==1){ - if(T[0]>0) N=ior(N,2^T[0]); - } - else if(Type(T[0])==2){ - if(findin(T[0],R)<0) R=cons(T[0],R); - } - } - for(I=5;I>=0;I--) if(iand(N,2^I)) R=cons(I,R); - return R; - } - return 0; - } - - if(length(P)>1){ - if(type(P[1])==6||(type(P[1])<2&&P[1]>0)) M=P[1]; - else if(type(P[1])==4&&length(P[1])==2) M=diagm(2,P[1]); - } - if(length(P)>2&&type(P[2])==4){ - Org=[["shift",P[2]]]; - if(M==0) M=1; - }else Org=[]; - if(P[0]==0||(type(P[0])==4&&P[0][0]==0)){ /* Risa/Asir */ - PP=car(P);PPP=0; - if(type(PP)!=4) PP=[PP]; - if(length(PP)<3){ - if(length(PP)==1 || type(PP[1])==4){ - if(ID_PLOT<0) ID_PLOT=ox_launch_nox(0,"ox_plot"); - Id=ID_PLOT; - if(length(PP)==1&&type(Canvas)==4&&length(Canvas)==2) - PP=cons(PP[0],[Canvas]); - if(length(PP)>1){ - PPP=PP[1][0]; - PPQ=(length(PP[1])==2)?PP[1][1]:PPP; - open_canvas(Id,[PPP,PPQ]); - }else open_canvas(Id); - Ind=ox_pop_cmo(Id); - }else{ - Ind=PP[1]; - if(getopt(cl)==1) clear_canvas(Id,Ind); - } - }else{ - Id=PP[1];Ind=PP[2]; - if(length(PP)>3 && type(PP[3])==1) PPP=PP[3]; - if(length(PP)>4 && type(PP[4])==1) PPQ=PP[4]; - if(getopt(cl)==1) clear_canvas(Id,Ind); - } - if(L==[]) return (PPP>0)? [0,Id,Ind,PPP,PPQ]:[0,Id,Ind]; - Ex0=Ex0;Sft=[0,0]; - if(length(P)>1&&P[1]==0&&length(P)<4){ - R=execdraw(L,-3); - Ex0=Ex1=Ex2=10; - if((U=R[1])>0){ /* string */ - if(U>20) U=16; /* adj 16,8,2,7,15 */ - if(R[0][0][0]>R[2][0][0]-(R[0][0][1]-R[0][0][0])/256) Ex0+=8*U; /* adj 256 */ - else Ex0+=2*U; - if(R[0][0][1]<R[2][0][1]+(R[0][0][1]-R[0][0][0])/256) Ex1+=7*U; - else Ex1+=2*U; - if(R[0][1][1]<R[2][1][1]+(R[0][1][1]-R[0][1][0])/256) Ex2+=15; - } - R=[R[0][0],R[0][1],0,[Ex0,Ex1],[0,-Ex2]]; - if(length(P)>2 && P[2]==1) - mycat0(["Box:",[R[0],R[1]], ", ext=",R[3],", shift=",R[4]],1); - }else R=execdraw((length(P)>3)?P[3]:L,-2); /* Windows */ - XW=R[0];YW=R[1]; - if(length(R)>3){ - if(R[3]!=0 && R[3]!=[0,0]) Ex=R[3]; - if(length(R)>4) Sft=R[4]; - } - if(type(X=getopt(ext))==4) - Ex=(Ex0)?[X[0]+Ex[0],X[1]+Ex[1]]:X; - if(type(M)<2){ - if(length(P)>1&&type(P[1])==1) M=P[1]; - else if((length(P)==1||P[1]==0||P[1]==1)&& PPP>0) M=PPP; - if(M<2) M=400; - if(Ex!=0 && type(Ex)==4){ - M-=Ex[0]+Ex[1]; - } - M=(M/(XW[1]-XW[0]))*diagm(2,[1,-1]); - } - if(type(X=getopt(shift))==4) Sft=(Ex0)?[Sft[0]+X[0],Sft[1]+X[1]]:X; - if(type(Sft)==4) Sft=[Sft[0],-Sft[1]]; - if(Ex!=0) Sft=[Sft[0]+Ex[0],Sft[1]]; - Org=[["shift",ptaffine(M,[-XW[0],-YW[1]]|shift=Sft)]]; - for(CT=0;CT<2;CT++){ - for(LT=L;LT!=[];LT=cdr(LT)){ - T=car(LT); - if(!CT && T[0]!=2) continue; - if(CT && T[0]==2) continue; - if(T[0]==1){ - for(TT=cdr(cdr(T));TT!=[];TT=cdr(TT)){ - D=car(TT); - if(type(D[0][0])==4){ - for(DT=D;DT!=[];DT=cdr(DT)){ - V=car(DT); - if(M) V=ptaffine(M,V|option_list=Org); - draw_bezier(Id,Ind,V|option_list=T[1]); - } - }else{ - if(M) D=ptaffine(M,D|option_list=Org); - draw_bezier(Id,Ind,D|option_list=T[1]); - } - } - }else if(T[0]==2){ /* put */ - if(length(T)<4) continue; - V=T[2]; - if(type(VLB)==4&&V[0]=="_") V=VLB; - else if(type(V[0])>1||type(V[1])>1) continue; /* not supported */ - if(length(T)>3&&type(T[3])==4&&length(T[3])>1&&T[3][1]==1) VLB=V; - F++;MM=M; - if((Sc=delopt(T[1],"scale"|inv=1))!=[]){ - if(!MM) MM=1; - Sc=car(Sc)[1]; - if(type(Sc)==1) MM=MM*Sc; - else if(type(Sc)==6) MM=MM*diagm(2,Sc); - } - if(MM) V=ptaffine(MM,V|option_list=Org); - if(type(S=S0=T[3])==4) S=S0[0]; - if(length(T)>4) S=T[4]; /* subst. string */ - if(type(S0)==4&&type(S0[0])==4){ - if((Col=drawopt(S0[0][0],0))<0) Col=0; /* attrib. */ - if(type(S)!=7) S=rtostr(S0[0][1]); - S=str_subst(S,[["$\\bullet$","*"],["$\\times$","x"],["$",""]],0); - if(type(Pos=drawopt(S0[0][0],2))==4) - V=[V[0]+4*str_len(S)*Pos[0],V[1]-10*Pos[1]]; /* adjustable */ - }else S=str_subst(rtostr(S),[["$\\bullet$","*"],["$\\times$","x"],["$",""]],0); - V=[V[0]-str_len(S)*4,V[1]-8]; /* adjustable */ - draw_string(Id,Ind,V,S,Col); - }else if(T[0]==3){ /* arrow */ - F++; - T1=T[2];T2=T[3]; - if(M){ - T1=ptaffine(M,T1|option_list=Org); - T2=ptaffine(M,T2|option_list=Org); - } - draw_bezier(Id,Ind,[T1,T2]|option_list=T[1]); - }else if(T[0]==4){ /* line */ - F++; - T1=T[2];T2=T[3]; - if(M){ - T1=ptaffine(M,T1|option_list=Org); - T2=ptaffine(M,T2|option_list=Org); - } - V=delopt(T1=T[1],"opt"|inv=1); - if(V!=[]&&str_str(V[1],".")>=0) - T1=cons(["opt",cons("dotted,",V[1])],delopt(T1,"opt")); - draw_bezier(Id,Ind,[T1,T2]|option_list=T1); - }else if(T[0]==5){ /* TeX */ - mycat(rtostr(T[2])); - if(F){ - S=str_tb(0,Out); - Out=str_tb(0,0); - F=0; - if(S!=""){ - if(P[0]==2) dviout(xyproc(S)|keep=1); - else LOut=cons(xyproc(S),LOut); - } - if(P[0]==2) dviout(T[2]|option_list=T[1]); - else{ - LOut=cons(T[2],Out); - } - } - }else if(Proc==1&&type(T[0])==2){ - if(length(T)<3) call(T[0],T[1]); - else call(T[0],T[1]|option_list=T[2]); - } - } - } - S=(PPP>0)? [0,Id,Ind,PPP,PPQ]:[0,Id,Ind]; - if(Ex==0&&Sft!=[0,0]) Ex=[0,0]; - return (Ex!=0&&length(P)>2&&P[2]==-1)? - [S,0,0,[0,R[0],R[1],0,Ex,[Sft[0]-Ex[0],-Sft[1]]]]:S; - } - if(P[0]==1||P[0]==2){ /* TeX */ - Out=str_tb(0,0);LOut=[];F=0; - if(getopt(cl)==1) dviout0(0); - for(;L!=[];L=cdr(L)){ - T=car(L);Opt=T[1]; - if(type(T[0])>=2) continue; - if(T[0]==0){ - XW=T[1];YW=T[2]; - if(length(P)>1&&type(P[1])==1&&P[1]<0) - M=-P[1]/(XW[0]-XW[1]); - }else if(T[0]==1){ - F++; - for(TT=cdr(cdr(T));TT!=[];TT=cdr(TT)){ - D=car(TT); - if(type(D[0][0])==4){ - for(DT=D;DT!=[];DT=cdr(DT)){ - V=car(DT); - if(M) V=ptaffine(M,V|option_list=Org); - str_tb(xybezier(V|option_list=Opt),Out); - } - }else{ - if(M) D=ptaffine(M,D|option_list=Org); - str_tb(xybezier(D|option_list=Opt),Out); - } - } - }else if(T[0]==2){ - F++;V=T[2]; - Opt=delopt(Opt,"scale"|inv=1); - MM=M; - if(Opt!=[]){ - Opt=car(Opt)[1]; - if(type(Opt)==1) Opt=[Opt,Opt]; - if(Opt!=[1,1]){ - if(!MM) MM=1; - MM=MM*diagm(2,[Opt[0],Opt[1]]); - } - } - if(MM) V=ptaffine(MM,V|option_list=Org); - if(length(T)>3) V=append(V,T[3]); - str_tb(xyput(V),Out); - }else if(T[0]==3){ - F++; - T1=T[2];T2=T[3]; - if(M){ - T1=ptaffine(M,T1|option_list=Org); - T2=ptaffine(M,T2|option_list=Org); - } - str_tb(xyarrow(T1,T2|option_list=Opt),Out); - }else if(T[0]==4){ - F++; - T1=T[2];T2=T[3]; - if(M){ - T1=ptaffine(M,T1|option_list=Org); - T2=ptaffine(M,T2|option_list=Org); - } - str_tb(xyline(T1,T2|option_list=Opt),Out); - }else if(T[0]==5){ - if(F){ - S=str_tb(0,Out); - Out=str_tb(0,0); - F=0; - if(S!=""){ - if(P[0]==2) dviout(xyproc(S)|keep=1); - else LOut=cons(xyproc(S),LOut); - } - if(P[0]==2) dviout(T[2]|option_list=T[1]); - else LOut=cons(T[2],Out); - } - }else if(T[0]==-2) - str_tb(["%",T[1],"\n"],Out); - else if(Proc==1&&type(T[0])==2){ - if(length(T)<3) call(T[0],T[1]); - else call(T[0],T[1]|option_list=T[2]); - } - } - S=str_tb(0,Out); - if(P[0]==1){ - if(F) LOut=cons(xyproc(S),LOut); - Out=str_tb(0,0); - for(L=reverse(LOut);L!=[];L=cdr(L)) - str_tb(car(L),Out); - return str_tb(0,Out); - } - if(F) dviout(xyproc(S)); - else dviout(" "); - } -} - -def execproc(L) -{ - if(type(N=getopt(var))!=1&&N!=0) N=2; - for(R=[];L!=[];L=cdr(L)){ - P=car(L); - if(type(P[0])==2&&vtype(P[0])==3){ - if((VS=vars(cdr(P)))!=[]){ - for(I=0;I<N;I++){ - V=makev(["v",I+1]); - if(findin(V,VS)>=0) P=mysubst(P,[V,R[I]]); - } - } - if(length(P)<3) R=cons(call(P[0],P[1]),R); - else R=cons(call(P[0],P[1]|option_list=P[2]),R); - } - } - return (getopt(all)==1)?R:car(R); -} - -def myswap(P,L) -{ - X=makenewv(P); - for(L=reverse(L);length(L)>1;L=cdr(L)) - P=subst(P,L[0],X,L[1],L[0],X,L[1]); - return P; -} - -def mysubst(P,L) -{ - if(P==0) return 0; - Inv=getopt(inv); - if(type(L[0]) == 4){ - while((L0 = car(L))!=[]){ - P = mysubst(P,(Inv==1)?[L0[1],L0[0]]:L0); - L = cdr(L); - } - return P; - } - if(Inv==1) L=[L[1],L[0]]; - if(type(P) > 3){ - if(type(P)==7) return P; - if(type(P)>7) - return subst(P,L[0],L[1]); -#ifdef USEMODULE - return mtransbys(os_md.mysubst,P,[L]); -#else - return mtransbys(mysubst,P,[L]); -#endif - } - P = red(P); - if(type(P) == 3){ - A=mysubst(nm(P),L);B=mysubst(dn(P),L); - return red(nm(A)/nm(B))*red(dn(B)/dn(A)); - } - L1=(type(L[1])==3)?red(L[1]):L[1];X=L[0]; - if(ptype(L1,X)==3){ - LN=nm(L1);LD=dn(L1); - Deg=mydeg(P,X); - if(Deg <= 0) return P; - V = newvect(Deg+1); - for(V[I=Deg]=1;I >= 1;I--) - V[I-1]=V[I]*LD; - for(R = 0, I = Deg; I >= 0; I--) - R = R*LN + mycoef(P,I,X)*V[I]; - return red(R/V[0]); - } - return subst(P,X,L1); -} - -def mmulbys(FN,P,F,L) -{ - Opt=getopt(); - if(type(F) <= 3){ - if(type(P) <= 3) - return call(FN, cons(P,cons(F,L))|option_list=Opt); - if(type(P) == 5){ - S = length(P); - R = newvect(S); - for(I = 0; I < S; I++) - R[I] = call(FN, cons(P[I],cons(F,L))|option_list=Opt); - return R; - }else if(type(P) == 6){ - S = size(P); - R = newmat(S[0],S[1]); - for(I = 0; I < S[0]; I++){ - for(J = 0; J < S[1]; J++) - R[I][J] = call(FN, cons(P[I][J],cons(F,L))|option_list=Opt); - } - return R; - } - } - if(type(F) == 5){ - S = length(F); - if(type(P) <= 3){ - R = newvect(S); - for(I = 0; I < S; I++) - R[I] = call(FN, cons(P,cons(F[I],L))|option_list=Opt); - return R; - } - if(type(P) == 5){ - for(J=R=0; J<S; J++) - R = radd(R, call(FN, cons(P[J],cons(F[J],L)))|option_list=Opt); - return R; - } - T = size(P); - R = newvect(T[0]); - for(I = 0; I < T[0]; I++){ - for(J = 0; J < S; J++) - R[I] = radd(R[I], call(FN, cons(P[I][J],cons(F[J],L))|option_list=Opt)); - } - return R; - } - if(type(F) == 6){ - S = size(F); - if(type(P) <= 3){ - R = newmat(S[0],S[1]); - for(I = 0; I < S[0]; I++){ - for(J = 0; J < S[1]; J++) - R[I][J] = call(FN, cons(P,cons(F[I][J],L))|option_list=Opt); - } - return R; - } - if(type(P) == 5){ - R = newvect(S[1]); - for(J = 0; J < S[1]; J++){ - for(K = U = 0; K < S[0]; K++) - U = radd(U, call(FN, cons(P[K],cons(F[K][J],L))|option_list=Opt)); - R[J] = U; - } - return R; - } - T = size(P); - R = newmat(T[0],S[1]); - for(I = 0; I < T[0]; I++){ - for(J = 0; J < S[1]; J++){ - for(K = U = 0; K < S[0]; K++) - U = radd(U, call(FN, cons(P[I][K],cons(F[K][J],L)|option_list=Opt))); - R[I][J] = U; - } - } - return R; - } - erno(0); - return 0; -} - -def appldo(P,F,L) -{ - if(type(F) <= 3){ - if(type(L) == 4 && type(L[0]) == 4) - return applpdo(P,F,L); - L = vweyl(L); - X = L[0]; DX = L[1]; - J = mydeg(P,DX); - for(I = R = 0; I <= J; I++){ - if(I > 0) - F = mydiff(F,X); - R = radd(R,mycoef(P,I,DX)*F); - } - return R; - } -#ifdef USEMODULE - return mmulbys(os_md.appldo,P,F,[L]); -#else - return mmulbys(appldo,P,F,[L]); -#endif -} - -def appledo(P,F,L) -{ - if(type(F) <= 3){ - L = vweyl(L); - X = L[0]; DX = L[1]; - J = mydeg(P,DX); - for(I = R = 0; I <= J; I++){ - if(I > 0) - F = myediff(F,X); - R = radd(R,mycoef(P,I,DX)*F); - } - return R; - } -#ifdef USEMODULE - mmulbys(os_md.appledo,P,F,[L]); -#else - mmulbys(appledo,P,F,[L]); -#endif -} - -def muldo(P,Q,L) -{ - if(type(Lim=getopt(lim))!=1) Lim=100; - if(type(Q) <= 3){ - if(type(L) == 4 && type(L[0]) == 4) - return mulpdo(P,Q,L|lim=Lim); /* several variables */ - R = rmul(P,Q); - L = vweyl(L); - X = L[0]; DX = L[1]; - if(X != 0){ - for(I = F = 1; ; I++){ - P = mydiff(P,DX); - if(I>Lim){ - mycat(["Over", Lim,"derivations!"]); - break; - } - if(P == 0) - break; - Q = mydiff(Q,X); - if(Q == 0) - break; - F *= I; - R = radd(R,P*Q/F); - } - } - return R; - } -#ifdef USEMODULE - return mmulbys(os_md.muldo,P,Q,[L]); -#else - return mmulbys(muldo,P,Q,[L]); -#endif -} - -def jacobian(F,X) -{ - F=ltov(F);X=ltov(X); - N=length(F); - M=newmat(N,N); - for(I=0;I<N;I++) - for(J=0;J<N;J++) M[I][J]=red(diff(F[I],X[J])); - if(getopt(mat)==1) return M; - return mydet(M); -} - -def hessian(F,X) -{ - X=ltov(X); - N=length(X); - M=newmat(N,N); - for(I=0;I<N;I++){ - G=red(diff(F,X[I])); - for(J=0;J<N;J++) M[I][J]=red(diff(G,X[J])); - } - if(getopt(mat)==1) return M; - return mydet(M); -} - -def wronskian(F,X) -{ - N=length(F); - M=newmat(N,N); - for(I=0;F!=[];F=cdr(F),I++){ - M[I][0]=car(F); - for(J=1;J<N;J++) M[I][J]=red(diff(M[I][J-1],X)); - } - if(getopt(mat)==1) return M; - return mydet(M); -} - -def adj(P,L) -{ - if(type(P) == 4) -#ifdef USEMODULE - return map(os_md.adj,mtranspose(P),L); -#else - return map(adj,mtranspose(P),L); -#endif - if(type(L) == 4 && type(L[0]) == 4) -#ifdef USEMODULE - return fmult(os_md.adj,P,L,[]); -#else - return fmult(adj,P,L,[]); -#endif - L = vweyl(L); - X = L[0]; DX = L[1]; - P = R = subst(P, DX, -DX); - for(I = 1; (R = mydiff(mydiff(R, X), DX)/I) != 0 && I < 100; I++) - P = radd(P,R); - return P; -} - -def laplace1(P,L) -{ - if(type(L) == 4 && type(L[0]) == 4) -#ifdef USEMODULE - return fmult(os_md.laplace,P,L,[]); -#else - return fmult(laplace,P,L,[]); -#endif - L = vweyl(L); - X = L[0]; DX = L[1]; - P = adj(P, L); - return subst(P,X,o_1,DX,X,o_1,DX); -} - -def laplace(P,L) -{ - if(type(L) == 4 && type(L[0]) == 4) -#ifdef USEMODULE - return fmult(os_md.laplace1,P,L,[]); -#else - return fmult(laplace1,P,L,[]); -#endif - L = vweyl(L); - X = L[0]; DX = L[1]; - P = adj(P, L); - return subst(P,X,o_1,DX,-X,o_1,-DX); -} - -def mce(P,L,V,R) -{ - L = vweyl(L); - X = L[0]; DX = L[1]; - P = sftexp(laplace1(P,L),L,V,R); - return laplace(P,L); -} - -def mc(P,L,R) -{ - return mce(P,L,0,R); -} - -def rede(P,L) -{ - Q = ltov(fctr(nm(red(P)))); - P = 1; - if(type(L) < 4) - L = [L]; - if(type(L[0]) < 4) - L = [L]; - for( ; L != []; L = cdr(L)){ - DX = vweyl(car(L))[1]; - for(I = 1; I < length(Q); I++){ - if(mydeg(Q[I][0],DX) > 0){ - P *= (Q[I][0])^(Q[I][1]); - Q[I]=[1,0]; - } - } - } - return P; -} - -def ad(P,L,R) -{ - L = vweyl(L); - DX = L[1]; - K = mydeg(P,DX); - S = mycoef(P,0,DX); - Q = 1; - for(I=1; I <= K;I++){ - Q = muldo(Q,DX-R,L); - S = radd(S,mycoef(P,I,DX)*Q); - } - return S; -} - -def add(P,L,R) -{ - return rede(ad(P,L,R),L); -} - - -def vadd(P,L,R) -{ - L = vweyl(L); - if(type(R) != 4) - return 0; - N = length(R); - DN = 1; Ad = PW = 0; - for( ; R != []; R = cdr(R), PW++){ - DN *= (T=1-car(R)[0]*L[0]); - Ad = Ad*T-car(R)[1]*x^PW; - } - Ad /= DN; - return add(P,L,Ad); -} - -def addl(P,L,R) -{ - return laplace1(add(laplace(P,L),L,R),L); -} - -def cotr(P,L,R) -{ - L = vweyl(L); - X = L[0]; DX = L[1]; - T = 1/mydiff(P,DX); - K = mydeg(P,DX); - S = mysubst(mycoef(P,0,DX), [X, R]); - Q = 1; - for(I = 1; I <= K; I++){ - Q = muldo(Q, K*DX, L); - S = radd(S,mysubst(mycoef(P,I,DX), [X, R])*Q); - } -} - -def rcotr(P,L,R) -{ - return rede(cotr(P,L,R), L); -} - -def muledo(P,Q,L) -{ - if(type(Q)>3) -#ifdef USEMODULE - return mmulbys(os_md.muledo,P,Q,[L]); -#else - return mmulbys(muledo,P,Q,[L]); -#endif - R = P*Q; - L = vweyl(L); - X = L[0]; DX = L[1]; - for(I = F = 1; I < 100; I++){ - P = mydiff(P,DX); - if(P == 0) - break; - Q = myediff(Q,X); - if(Q == 0) - break; - F = rmul(F,I); - R = radd(R,P*Q/F); - } - return R; -} - - -#if 1 -def mulpdo(P,Q,L) -{ - if(type(Q)>3) -#ifdef USEMODULE - return mmulbys(os_md.mulpdo,P,Q,[L]); -#else - return mmulbys(mulpdo,P,Q,[L]); -#endif - if(type(Lim=getopt(lim))!=1) Lim=100; - M = vweyl(car(L)); X= M[0]; DX = M[1]; - L = cdr(L); - R = 0; - for(I = 0; Q != 0 && I <= Lim; I++){ - if(I>Lim){ - mycat(["Over", Lim,"derivations!"]); - break; - } - if(I > 0) - P /= I; - if(length(L)==0) - R = radd(R,P*Q); - else - R = radd(R,mulpdo(P,Q,L)); - if(X==0) break; - P = mydiff(P,DX); - if(P == 0) - break; - Q = mydiff(Q,X); - } - if(I>Lim) mycat(["Over", Lim,"derivations!"]); - return R; -} - -#else -def mulpdo(P,Q,L); -{ - if(type(Q)>3) -#ifdef USEMODULE - return mmulbys(os_md.mulpdo,P,Q,[L]); -#else - return mmulbys(mulpdo,P,Q,[L]); -#endif - if(type(Lim=getopt(lim))!=1) Lim=100; - N = length(L); - VO = newvect(2*N); - VN = newvect(2*N); - for(I = J = 0; I < N; J += 2, I++){ - M = vweyl(L[I]); - P = subst(P, VO[J]=M[0], VN[J]=strtov("o_"+rtostr(V[J])), - VO[J+1]=M[1], VN[J+1] = strtov("o_"+rtostr(V[J+1]))); - } - for(PQ = P*Q, I = 0; I < 2*N; I += 2){ - for(R = PQ, J = 1; J < Lim; J++){ - R = mydiff(R, VN[I+1])/J; - if(R == 0) - break; - R = mydiff(R, VO[I]); - if(R == 0) - break; - PQ = radd(PQ,R); - } - if(I==Lim) mycat(["Over", Lim,"derivations!"]); - PQ = red(subst(PQ,VN[I],VO[I],VN[I+1],VO[I+1])); - } -} -#endif - -def transpdosub(P,LL,K) -{ - Len = length(K)-1; - if(Len < 0 || P == 0) - return P; - KK=K[Len]; - if(type(KK)==4){ - KK0=KK[0]; KK1=KK[1]; - }else{ - L = vweyl(LL[Len]); - KK0=L[1]; KK1=K[Len]; - } - Deg = mydeg(P,KK0); - K1 = reverse(cdr(reverse(K))); - R = transpdosub(mycoef(P,0,KK0),LL,K1); - for(I = M = 1; I <= Deg ; I++){ - M = mulpdo(M,KK1,LL); - S = mycoef(P,I,KK0); - if(Len > 0) - S = transpdosub(S,LL,K1); - R = radd(R,mulpdo(S,M,LL)); - } - return R; -} - -def transpdo(P,LL,K) -{ - if(type(K[0]) < 4) - K = [K]; - Len = length(K)-1; - K1=K2=[]; - if(type(LL)!=4) LL=[LL]; - if(type(LL[0])!=4) LL=[LL]; - if(getopt(ex)==1){ - for(LT=LL, KT=K; KT!=[]; LT=cdr(LT), KT=cdr(KT)){ - L = vweyl(LL[J]); - K1=cons([L[0],car(KT)[0]],K1); - K2=cons([L[1],car(KT)[1]],K2); - } - K2=append(K1,K2); - }else{ - for(J = length(K)-1; J >= 0; J--){ - L = vweyl(LL[J]); - if(L[0] != K[J][0]) - K1 = cons([L[0],K[J][0]],K1); - K2 = cons(K[J][1],K2); - } - P = mulsubst(P, K1); - } - return transpdosub(P,LL,K2); -} - -def translpdo(P,LL,M) -{ - S=length(LL); - L0=newvect(S);L1=newvect(S); - K=newvect(S); - for(J=0;J<S;J++){ - L = vweyl(LL[J]); - L0[J]=L[0]; - L1[J]=L[1]; - } - K=rmul(M,L0); - for(T=[],J=0;J<S;J++) - T=cons([L0[J],K[J]],T); - P=mulsubst(P,T); - K=rmul(myinv(M),L1); - for(T=[],J=0;J<S;J++) - T=cons([L1[J],K[J]],T); - return mulsubst(P,T); -} - -/* - return [R, M, S] : R = M*P - S*Q - deg(R,X) < deg(Q,X) -*/ -def rpdiv(P,Q,X) -{ - if(P == 0) - return [0,1,0]; - DQ = mydeg(Q,X); - CO = mycoef(Q,DQ,X); - S = 0; - while((DP = mydeg(P,X)) >= DQ){ - R = mycoef(P,DP,X)/CO; - S = radd(S,R*X^(DP-DQ)); - P = radd(P, -R*Q*X^(DP-DQ)); - } - Lcm = lcm(dn(S),dn(P)); - Gcd = gcd(nm(S),nm(P)); - return [red(P*Lcm/Gcd), red(Lcm/Gcd),red(S*Lcm/Gcd)]; -} - -def texbegin(T,S) -{ - if(type(Opt=getopt(opt))==7) Opt="["+Opt+"]\n"; - else Opt="\n"; - return "\\begin{"+T+"}"+Opt+S+"%\n\\end{"+T+"}\n"; -} - -def mygcd(P,Q,L) -{ - if((Dvi=getopt(dviout))==3 || Dvi==-3){ /* dviout=3 */ - if((Rev=getopt(rev))!=1) Rev=0; - R=mygcd(P,Q,L|rev=Rev); - if(type(L)<2) Var=0; - else if(type(L)==2){ - Val=L;L=[0,L]; - }else if(type(L)==4){ - L=vweyl(L); - Var=[[L[1],"\\partial"]]; - } - S=mat([P],[Q]);T=mat([R[0]],[0]); - M=mat([R[1],R[2]],[R[3],R[4]]); - if(type(Val)==4) - N=mdivisor(M,L|trans=1)[1]; - else N=myinv(M); - Tb=str_tb(mtotex(S|var=Var),0); - str_tb("&="+mtotex(N|var=Var)+mtotex(T|var=Var)+",\\\\\n",Tb); - str_tb(mtotex(T|var=Var),Tb); - str_tb("&="+mtotex(M|var=Var)+mtotex(S|var=Var)+".",Tb); - Out=str_tb(0,Tb); - if(Dvi<0) return Out; - dviout(Out|eq="align*"); - return 1; - } - if((type(Dvi)==1||Dvi==0) && getopt(rev)!=1) V=[[P,Q]]; - else V=0; - if(L==0){ /* integer case */ - if(type(P) > 1 || type(Q) > 1 || Q==0 /* P <= 0 || Q <= 0 */ - || dn(P) > 1 || dn(Q) > 1) - return 0; - CPP = CQQ = 1; CQP = CPQ = 0; - P1 = P; Q1 = Q; - /* P1 = CPP*P + CPQ*Q - Q1 = CQP*P + CQQ*Q */ - while(Q1 != 0){ - Div1 = idiv(P1,Q1); Div2 = irem(P1,Q1); - if(type(V)==4) V=cons([Div1,Div2],V); - P1 = Q1 ; Q1 = Div2; - TP = CQP; TQ = CQQ; - CQP = CPP-Div1*CQP; - CQQ = CPQ-Div1*CQQ; - CPP = TP; CPQ = TQ; - } - if(V!=0){ - V=reverse(V); - if((DVI=abs(Dvi))==0) return V; - PT=P;QT=Q; - if(DVI==1 || DVI==2){ - Tb=str_tb(0,0); - for(C=0,V=cdr(V);V!=[];V=cdr(V)){ - T=car(V); - if(C++) str_tb(texcr(11),Tb); - if(DVI==1){ - Qs=rtostr(QT); - if(QT<0) Qs="("+Qs+")"; - if(T[1]>0) Qs=Qs+"+"; - if(T[1]!=0) Qs=Qs+rtostr(T[1]); - str_tb(rtostr(PT)+"&=" - +rtostr(T[0])+"\\times"+Qs,Tb); - }else{ - N=mat([T[0],1],[1,0]); - if(C==1){ - str_tb(S0=mtotex(mat([PT],[QT])),Tb); - M=N; - } - str_tb("&=",Tb); - if(C>1) str_tb(mtotex(M),Tb); - str_tb(mtotex(N),Tb); - str_tb(S=mtotex(mat([QT],[T[1]])),Tb); - if(C>1){ - str_tb("=",Tb); - str_tb(mtotex(M=M*N),Tb); - str_tb(S,Tb); - } - } - PT=QT;QT=T[1]; - } - if(DVI==2){ - str_tb(texcr(43)+S+"&=",Tb); - str_tb(mtotex(myinv(M)),Tb); - str_tb(S0,Tb); - } - Out=str_tb(0,Tb); - if(Dvi>0){ - dviout(Out|eq="align*"); - return 1; - } - return Out; - } - } - if(P1<0) return [-P1,-CPP,-CPQ,CQP,CQQ]; - return [P1, CPP, CPQ, CQP, CQQ]; - } - if(type(L) == 2) /* polynomical case */ - L = [0,L]; - if(getopt(rev)==1 && L[0]!=0){ - R=mygcd(adj(P,L),adj(Q,L),L); - return [adj(R[0],L),adj(R[1],L),adj(R[2],L),adj(R[3],L),adj(R[4],L)]; - } - if(type(P) == 3) - P = red(P); - if(type(Q) == 3) - Q = red(Q); - CP=newvect(2,[1/dn(P),0]); CQ=newvect(2,[0,1/dn(Q)]); - P=PT=nm(P); Q =QT=nm(Q); - L = vweyl(L); - while(Q != 0){ - R = divdo(P,Q,L); - if(type(V)==4) V=cons(R,V); -/* R[1] = R[2]*P - R[0]*Q - = R[2]*(CP[0]*P0+CP[1]*Q0) - R[0]*(CQ[0]*P0+CQ[1]*Q0) */ -/* - P(n) |0 1 | P(n-1) - = | | - R[1] |R[2] -R[0]| P(n) - P(n+1) = R[1], P(n) = P, P(n-1) = Q -*/ - P = Q; - Q = R[1]; - { - CT = dupmat(CQ); - CQ = [R[2]*CP[0]-muldo(R[0],CQ[0],L), - R[2]*CP[1]-muldo(R[0],CQ[1],L)]; - CP = CT; - } - } - if(V!=0){ - V=reverse(V); - if((DVI=abs(Dvi))==0) return V; - if(type(L[0])<1) Var=L[1]; - else Var=[L[1],"\\partial"]; - if(DVI==1 || DVI==2){ - Tb=str_tb(0,0); - PT=car(V)[0];QT=car(V)[1]; - for(C=0,V=cdr(V);V!=[];V=cdr(V)){ - T=car(V); - if(C++) str_tb(texcr(11),Tb); - if(DVI==1){ - if(T[2]!=1){ - str_tb(monototex(T[2]),Tb); - str_tb("(",Tb); - str_tb(fctrtos(PT|var=Var,TeX=2),Tb); - str_tb(")&=",Tb); - }else{ - str_tb(fctrtos(PT|var=Var,TeX=2),Tb); - str_tb("&=",Tb); - } - str_tb("(",Tb); - str_tb(fctrtos(T[0]|var=Var,TeX=2),Tb); - str_tb(")(",Tb); - str_tb(fctrtos(QT|var=Var,TeX=2),Tb); - if(T[1]!=0){ - str_tb(")+(",Tb); - str_tb(fctrtos(T[1]|var=Var,TeX=2),Tb); - } - str_tb(")",Tb); - }else{ - N=mat([red(T[0]/T[2]),1],[1,0]); - if(C==1){ - str_tb(S0=mtotex(mat([PT],[QT])|var=Var),Tb); - M=N; - } - str_tb("&=",Tb); - if(C>1) str_tb(mtotex(M),Tb); - str_tb(mtotex(N|var=Var),Tb); - str_tb(S=mtotex(mat([QT],[T[1]])|var=Var),Tb); - if(C>1){ - str_tb("=",Tb); - str_tb(mtotex(M=muldo(M,N,L)|var=Var),Tb); - str_tb(S,Tb); - } - } - PT=QT;QT=T[1]; - } - if(DVI==2){ - FT=fctr(PT); - for(R=1;FT!=[];FT=cdr(FT)){ - if(mydeg(car(FT)[0],L[1])<1) - for(J=car(FT)[1];J>0;J--) R*=car(FT)[0]; - } - if(R!=1){ - str_tb(texcr(79),Tb); - M=muldo(M,mat([R,0],[0,1]),L); - str_tb(mtotex(M|var=Var),Tb); - str_tb(S=mtotex(mat([PT/R],[QT])|var=Var),Tb); - } - str_tb(texcr(43)+S+"&=",Tb); - if(type(Var)==4){ - N=mdivisor(M,L|trans=1); - N=N[1]; - }else - N=myinv(M); - str_tb(mtotex(N|var=Var),Tb); - str_tb(S0,Tb); - } - Out=str_tb(0,Tb); - if(Dvi>0){ - dviout(Out|eq="align*"); - return 1; - } - return Out; - } - } - Q = rede(P,L); - R = red(P/Q); - return [Q,red(CP[0]/R),red(CP[1]/R),red(CQ[0]/R),red(CQ[1]/R)]; -} - -def mylcm(P,Q,L) -{ - Rev=(getopt(rev)==1)?1:0; - if(Rev==1){ - P=adj(P); Q=adj(Q); - } - R = mygcd(P,Q,L); - S=(type(L)<=2)?R[3]*P:muldo(R[3],P,L); - S = nm(S); - if(type(S) <= 1 && type(L) <= 1){ - if(S<0) S = -S; - return S; - } - if(type(L) == 2) - return easierpol(S,L); - S=rede(easierpol(S,L[1]),L); - return (Rev==1)?adj(S):S; -} - -def sftpexp(P,LL,F,Q) -{ - if(type(LL[0]) < 4) - LL = [LL]; - for(L0=L1=[],LT=LL;LT!=[];LT=cdr(LT)){ - W=vweyl(car(LT)); - L0=cons(W,L0); - D=mydiff(F,W[0]); - if(D!=0) L1=cons(W[1]+Q*D/F,L1); - else L1=cons(W[1],L1); - } - return rede(transpdosub(P,L0,L1),L0); -} - -def applpdo(P,F,LL) -{ - if(type(F)>3) -#ifdef USEMODULE - return mmulbys(os_md.applpdo,P,F,[LL]); -#else - return mmulbys(applpdo,P,F,[LL]); -#endif - L = vweyl(LL[0]); - LL = cdr(LL); - Deg = deg(P,L[1]); - S = F; - for(I = R = 0; I <= Deg ; I++){ - if(I > 0) - S = mydiff(S,L[0]); - if(LL == []) - R = radd(R,mycoef(P,I,L[1])*S); - else - R = radd(R,applpdo(mycoef(P,I,L[1]), S, LL)); - } - return R; -} - -def tranlpdo(P,L,M) -{ - N = length(L); - R = size(M); - if(R[0] != N || R[1] != N){ - print("Strange size"); - return; - } - InvM = M; - if(InvM[1] == 0){ - print("Not invertible"); - return; - } - XL = newvector(N); - DL = newvector(N); - for(I = 0; I < 0; I++){ - R = vweyl(L[I]); - XL[I] = R[0]; - DL[I] = R[1]; - } - for(I = 0; I < N; I++){ - for(J = XX = D0 = 0; J < N; J++){ - XX = radd(XX,M[I][J]*XL[J]); - DD = radd(DD, red(InvM[0][I][J]/InvM[1])*DL[J]); - P = mysubst(P,[[XL[I],XX],[DL[I],DD]]); - } - } - return P; -} - -def divdo(P,Q,L) -{ - if(L==0){ - R=P-idiv(P,Q)*Q; - if(R<0){ - if(Q>0) R+=Q; - else R-=Q; - } - return [(P-R)/Q,R,1]; - } - L = vweyl(L); - if(getopt(rev)==1){ - R=divdo(adj(P,L),adj(Q,L),L); - return [adj(R[0],L),adj(R[1],L),R[2]]; - } - X = L[0]; DX = L[1]; - S = 0; - M = 1; - I = mydeg(Q,DX); - CQ = mycoef(Q,I,DX); - while((J=mydeg(P,DX)) >= I){ - C = mycoef(P,J,DX); - SR = red(C/CQ); - if(dn(SR) != 1){ - M *= dn(SR); - P *= dn(SR); - S *= dn(SR); - SR = nm(SR); - } - P -= muldo(SR*(DX)^(J-I),Q,L); - S += SR*(DX)^(J-I); - } - return [S,P,M]; -} - -def qdo(P,Q,L) -{ - L = vweyl(L); DX = L[1]; OD = deg(P,DX); - V = newvect(OD+1); - for(I = 0; I <= OD; I++){ - if(I) - Q = muldo(DX,Q,L); - S = divdo(Q,P,L); - V[I] = S[1]*DX-S[2]*zz^I; - } - for(K = [], I = OD; I >= 0; I--) - K = cons(DX^(I+1), K); - R = lsol(V,K); - S = length(R); - for(I = P1 = 0; I < S; I++){ - if(type(R[I]) < 4 && mydeg(R[I],DX) == 0 && R[I] != 0 - && (mydeg(R[I],zz) <= mydeg(P,DX))) - P1 = R[I]; - else if(type(R[I]) == 4 && R[I][0] == DX) - P2 = R[I][1]; - } - T=fctr(P1); - for(I=0, S=length(T), P1=1; I<S; I++){ - if(mydeg(T[I][0],zz) > 0) - P1 *= T[I][0]^(T[I][1]); - } - return subst([P1,P2],zz,DX); -} - -def sqrtdo(P,L) -{ - L = vweyl(L); - P = toeul(P,L,0); - V = -1; - for(R = 0, Ord = mydeg(P,L[1]); Ord >= 0; Ord--){ - Q = coef(P,Ord,L[1]); - M = mydeg(Q,L[0]); - N = mymindeg(Q,L[0]); - if(V < 0) - V = M+N; - else if(V != M+N){ - print("Cannot be transformed!"); - return; - } - Q = tohomog(red(Q/L[0]^N), [L[0]], z_z); - if(irem(Ord,2)) - B = x-z_z; - else - B = x+z_z; - Q = substblock(Q,x,B,z_zz); - if(mydeg(Q,x) > 0){ - print("Cannot be transformed!"); - return; - } - R += mysubst(Q,[z_zz,x])*L[1]^Ord; - } - return fromeul(R,L,0); -} - -def ghg(A,B) -{ - R = dx; - while(length(B)>0){ - R = muldo(x*dx+car(B),R,[x,dx]); - B = cdr(B); - } - T = 1; - while(length(A)>0){ - T = muldo(x*dx+car(A),T,[x,dx]); - A = cdr(A); - } - return R-T; -} - -def ev4s(A,B,C,S,T) -{ - R4 = x^2*(x-1)^2; - R3 = x*(x-1)*((2*A-2*B-8)*x-2*A+5); - R2 = (-3/2*(A^2+B^2)+3*A*B+9*A-9*B-29/2+1/4*(S^2+T^2))*x^2 - +(5*A^2/2-13*A-3*A*B+B^2/2+7*B-C^2+C+35/2 - 1/4*(S^2+T^2))*x - - (2*A+2*C-5)*(2*A-2*C-3)/4; - R1 = 1/4*(A-B-2)*(2*A^2-4*A*B-8*A+2*B^2+8*B+10-S^2-T^2)*x - +15/4+3*B^2/4-C^2/2+11*A^2/4 - 11*A/2+3*B+B*C-7*A*B/2+C/2-A*B^2/2 -#if 1 - + A^2*B -#endif - - B*C^2 - A^3/2+(2*A-3)*(S^2+T^2)/8; -/* OK? for the above term added */ - R0 = -(A-B-1-S)*(A-B-1+S)*(A-B-1-T)*(A-B-1+T)/16; - return (R4*dx^4-R3*dx^3-R2*dx^2-R1*dx-R0); -} - -def b2e(A,B,C,S,T) -{ - R4 = x^2*(x-1)^2; - R3 = x*(x-1)*(2*x-1)*(2*c-5); - R2 = (-6*C^2+24*C-25+1/2*S^2+1/2*T^2)*x^2 - +(6*C^2-24*C+25-1/2*S^2-1/2*T^2-A^2+B^2+A-B)*x - +A^2-C^2-A+4*C-15/4; - R1 = (2*C-3)*(2*C^2-6*C+5-1/2*S^2-1/2*T^2)*x - +(2*C-3)*(-C^2+3*C+1/2*A^2-1/2*B^2+1/2*B-1/2*A-5/2+1/4*S^2+1/4*T^2); - R0 = -(2-2*C+S+T)*(2-2*C-S-T)*(2-2*C+S-T)*(2-2*C-S+T)/16; - return (R4*dx^4-R3*dx^3-R2*dx^2-R1*dx-R0); -} - - -/* - T^m = T(T-1)....(T-m+1) - f(t) -> g(t) - - f(t) = a_mt^m + ... + a_1t+a_0 - g(x*dx) = a_m*x^m*dx^m + ... + a_1*x*dx+a_0 - - ret: x(x-1)...(x-i+1) - */ -def sftpow(X,I) -{ - R = 1; - for(J=0;J<I;J++) - R *= X-J; - return(R); -} - -/* - ret: x(x+K)(x+2*k)...(x+(i-1)*k) -*/ -def sftpowext(X,I,K) -{ - R = 1; - for(J=0;J<I;J++) - R *= X+K*J; - return(R); -} - -def polinsft(F,A) -{ - R = 0; - while(F != 0){ - D = mydeg(F,A); - C = mycoef(F,D,A); - R += C*A^D; - F -= C*sftpow(A,D); - } - return R; -} - -def pol2sft(F,A) -{ - S=getopt(sft); - if(type(S)<0 || type(S)>2) S=1; - R = 0; - for(I = mydeg(F,A); I >= 0; I--) - R = R*(A-I*S) + mycoef(F,I,A); - return R; -} - -def binom(P,N) -{ - if(type(N)!=1 || N<0) return 1; - for(S=1;N>0;N--,P-=1) S*=P/N; - return red(S); -} - -def expower(P,R,N) -{ - if(type(N)!=1 || N<0) return 0; - for(S=S0=K=1;K<=N;K++,R-=1){ - S0*=P*R/K;S+=S0; - } - return red(S); -} - -def seriesHG(A,B,X,N) -{ - if(type(N)!=1 || N<0) return 0; - if(type(X)<4){ - for(K=0,S=S0=1;K<N;K++){ - for(T=A; T!=[]; T=cdr(T)) S0*=car(T)+K; - for(T=B; T!=[]; T=cdr(T)) S0/=car(T)+K; - S0=red(S0*X/(K+1)); - DN=dn(S0); - S=red((red(S*DN)+nm(S0))/DN); - } - return S; - } - S=0; - for(K=0;K<=N;K++){ - for(I=0;I<=N-K;I++){ - C=1/sftpowext(1,I,1)/sftpowext(1,J,1); - for(T=A[0];T!=[];T=cdr(T)) C*=sftpowext(car(T),I+K,1); - for(T=A[1];T!=[];T=cdr(T)) C*=sftpowext(car(T),I,1); - for(T=A[2];T!=[];T=cdr(T)) C*=sftpowext(car(T),K,1); - for(T=B[0];T!=[];T=cdr(T)) C/=sftpowext(car(T),I+K,1); - for(T=B[1];T!=[];T=cdr(T)) C/=sftpowext(car(T),I,1); - for(T=B[2];T!=[];T=cdr(T)) C/=sftpowext(car(T),K,1); - S+=red(C*X[0]^I*X[1]^K); - } - } - return S; -} - -def evalred(F) -{ - Opt=getopt(opt); - if(type(Opt)!=4){ - Opt=[]; - }else if(length(Opt)==2 && type(Opt[0])!=4) Opt=[Opt]; - for(;;){ - G=mysubst(F,[[tan(0),0],[asin(0),0],[atan(0),0],[sinh(0),0],[tanh(0),0], - [log(1),0],[cosh(0),1],[exp(0),1]]); - for(Rep=Opt; Rep!=[]; Rep=cdr(Rep)) - G=subst(G,car(Rep)[0],car(Rep)[1]); - Var=vars(G); - for(V=Var; V!=[]; V=cdr(V)){ - if(!(VV=args(CV=car(V)))) continue; - if((functor(CV)==sin||functor(CV)==cos)){ - P=2*red(VV[0]/@pi); - if(functor(CV)==sin) P=1-P; - if(isint(P)){ - if(iand(P,1)) G=subst(G,CV,0); - else if(!iand(P,3)) G=subst(G,CV,1); - else G=subst(G,CV,-1); - continue; - } - if(isint(P*=3/2)){ - if(iand(P,3)==1) G=subst(G,CV,1/2); - else G=subst(G,CV,-1/2); - } - } - for(;VV!=[];VV=cdr(VV)) - if(car(VV)!=(TV=evalred(car(VV)))) G=subst(G,car(VV),TV); - if(functor(CV)!=pow || (args(CV)[0])!=1) continue; - G=subst(G,CV,1); - } - if(G==F) return F; - F=G; - } -} - -def seriesMc(F,N,V) -{ - if(type(V)<4) V=[V]; - V=reverse(V); - L=length(V); - if(type(Opt=getopt(evalopt))!=4) Opt=[]; - P=newvect(L); - G=newvect(L+1); - G[0]=F; - for(I=0;I<L;I++) - G[I+1]=eval(evalred(subst(G[I],V[I],0)|opt=Opt)); - R=G[L]; - for(;;){ - for(M=0,I=0;I<L;I++){ - M+=P[I]; - if(M==N) break; - } - if(M<N){ - P[L-1]++; - G[L-1]=mydiff(G[L-1],V[L-1]); - G[L]=eval(evalred(mysubst(G[L-1],[V[L-1],0])|opt=Opt)); - }else{ - if(I--==0) break; - P[I]++; - G[I]=mydiff(G[I],V[I]); - while(I++<L){ - G[I]=eval(evalred(mysubst(G[I-1],[V[I-1],0])|opt=Opt)); - if(I<L) P[I]=0; - } - } - K=1; - for(I=0;I<L;I++) K*=V[I]^P[I]/fac(P[I]); - R+=G[L]*K; - } - return R; -} - -def seriesTaylor(F,N,V) -{ - G=F; - if(isvar(V)) V=[V]; - if(length(V)==2 && type(car(V))!=4 && !isvar(V[1])) V=[V]; - for(V0=V1=[];V!=[];V=cdr(V)){ - if(type(T=car(V))!=4) T=[T]; - V0=cons(X=car(T),V0); - if(length(T)==1 || T[1]==0){ - V1=cons(X,V1);continue; - } - S=my_tex_form(-T[1]); - if(str_char(S,0,"-")!=0) S="+"+S; - S="("+my_tex_form(X)+S+")"; - V1=cons([X,S],V1); - F=red(subst(F,T[0],T[0]+T[1])); - } - V0=reverse(V0);V1=reverse(V1); - F=seriesMc(F,N,V0|option_list=getopt()); - if(getopt(frac)==0) F=frac2n(F); - T=getopt(dviout); - if(type(T)!=1) T=0; - F=fctrtos(F|var=V1,rev=1,TeX=(T==0||T==2)?2:3); - if(getopt(small)==1) F=str_subst(F,"\\frac{","\\tfrac{"); - if(T<0 || T==1) F="\\begin{align}\\begin{split}\n"+ - my_tex_form(G)+"&="+F+"+\\cdots\n\\end{split}\\end{align}\n"; - if(T==1) dviout(F); - else if(T==1) dviout(F|eq=4); - return F; -} - -def toeul(F,L,V) -{ - L = vweyl(L); - X = L[0]; DX = L[1]; - I = mydeg(F,DX); - if(V == "infty"){ - for(II=I; II>=0; II--){ - J = mydeg(P=mycoef(F,I,DX),X); - if(II==I) S=II-J; - else if(P!=0 && II-J>S) S=II-J; - } - F *= X^S; - R = 0; - for( ; I >= 0; I--) - R += red((mysubst(mycoef(F,I,DX),[X,1/X])*(x*DX)^I)); - return(subst(pol2sft(R,DX),DX,-DX)); - } - F = subst(F,X,X+V); - for(II=I; II>=0; II--){ - J = mymindeg(P=mycoef(F,II,DX),X); - if(II==I) S=II-J; - else if(P!=0 && II-J>S) S=II-J; - } - F *= X^S; - R = 0; - for( ; I >= 0; I--) - R += (red(mycoef(F,I,DX)/X^I))*DX^I; - return pol2sft(R,DX); -} - -/* -def topoldif(P,F,L) -{ - L = vweyl(L); - P = nm(red(P)); - while(deg(P,L[1]) > 0){ - R = coef(P,0,L[0]); - Q = red((P-R)/(F*L[0]); - P = nm(Q)*zz+F*R*dn(Q); - } -} -*/ - -def fromeul(P,L,V) -{ - if(P == 0) - return 0; - L = vweyl(L); - X = L[0]; DX = L[1]; - I = mydeg(P,DX); - if(V == "infty"){ - P = subst(P,DX,-DX); - J = mydeg(P,X); - P = red(mysubst(P,[X,1/X])*X^J); - } - R = mycoef(P,0,DX); - S = 1; - for(S = J = 1; J <= I; J++){ - S = DX*(S*X + mydiff(S,DX)); - R += mycoef(P,J,DX)*S; - } - while(mycoef(R,0,X) == 0) - R = tdiv(R,X); - if(V != "infty" && V != 0) - R = mysubst(R,[X,X-V]); - return R; -} - -def sftexp(P,L,V,N) -{ - L = vweyl(L); DX = L[1]; - P = mysubst(toeul(P,L,V),[DX,DX+N]); - return fromeul(P,L,V); -} - - -def fractrans(P,L,N0,N1,N2) -{ - L = vweyl(L); - if(N2 != "infty"){ - if(N0 == "infty") - N0 = 0; - else - N0 = red(1/(N0-N2)); - if(N1 == "infty") - N1 = 0; - else - N1 = red(1/(N1-N2)); - P = mysubst(P,[L[0],L[0]+N2]); - P = fromeul(toeul(P,L,"infty"),L,0); - } - if(N0 != 0){ - P = mysubst(P,[L[0],L[0]+N0]); - N1 -= N0; - } - if(N1 != 1) - P = mysubst(P,[[L[0],L[0]/N1],[L[1],L[1]*N1]]); - return P; -} - -def soldif(P,L,V,Q,N) -{ - L = vweyl(L); X = L[0]; DX = L[1]; - P = mysubst(toeul(P,L,V),[DX,DX+Q]); - DEG = mydeg(P,X); - P0 = newvect(DEG+1); - for(I = 0; I <= DEG; I++) - P0[I] = coef(P,I,X); - if(P0[0] == 0) - return 0; - if(subst(P0[0],DX,0) != 0){ - mycat([Q,"is not the exponent at", V])$ - return 0; - } - R = newvect(N+1); - R[0] = 1; - for(I = 1; I <= N; I++){ - for(S = 0, K = 1; K <= DEG && K <= I; K++) - S += mysubst(P0[K],[DX,I-K])*R[I-K]; - S = red(S); - M = mysubst(P0[0],[DX,I]); - if(M != 0){ - R[I] = -red(S/M); - if(R1 != 0){ - for(S = 0, K = 1; K <= DEG && K <= I; K++) - S += mysubst(P0[K],[DX,I-K])*R1[I-K] + - mysubst(P1[K],[DX,I-K])*R[I-K]; - R1[I] = -red(S/M); - } - }else{ - if(S == 0){ - if(R1 != 0){ - for(S = 0, K = 1; K <= DEG && K <= I; K++) - S += mysubst(P0[K],[DX,I-K])*R1[I-K] + - mysubst(P1[K],[DX,I-K])*R[I-K]; - } - if(S == 0) - continue; - } - R1 = newvect(N+1); - for(K = 0; K < I; K++){ - R1[K] = R[K]; - R[K] = 0; - } - R1[I] = 0; - P1 = newvect(DEG); - for(K = 0; K <= DEG; K++) - P1[K] = mydiff(P0[K], DX); - M = mysubst(P1[0],[DX,I]); - if(M == 0){ - cat(["multiple log at ", I])$ - return 0; - } - R[I] = -red(S/M); - } - } - if(R1 != 0) - return [R1, R]; - else - return R; -} - -def chkexp(P,L,V,Q,N) -{ - L = vweyl(L); X = L[0]; DX = L[1]; - P = mysubst(toeul(P,L,V),[DX,DX+Q]); - P = fromeul(P,L,0); - D = mydeg(P,DX); - Z = mindeg(mycoef(P,D,DX), X) - (D-N); - R = []; - for(I = 0; I < Z; I++){ - S = mycoef(P,I,X); - if(S != 0){ - for(J = mydeg(S,DX); J >= 0; J--){ - T = mycoef(S,J,DX); - if(T != 0) - R = cons(T,R); - } - } - } - return R; -} - - -def sqrtrat(P) -{ - if(P==0) return 0; - if(type(P)==3||type(P)==2){ - P=red(P); - if(imag(dn(P))!=0||imag(nm(P))!=0){ - if(imag(dn(P))==0&&real(P)!=0){ - F=red(imag(P)/real(P)); - if(F==3^(1/2)||F==-3^(1/2)){ - if(eval(real(P))<0) - return -real(P)+imag(P)*@i; - else{ - if(eval(imag(P))>0) return imag(P)+real(P)*@i; - else return -imag(P)-real(P)*@i; - } - } - } - return []; - } - F=fctr(dn(P)); - R=sqrtrat(car(F)[0]); - for(F=cdr(F);F!=[];F=cdr(F)){ - if(!iand(car(F)[1],1)) R*=car(F)[0]^(car(F)[1]/2); - else return []; - } - F=fctr(nm(P)); - R=sqrtrat(car(F)[0])/R; - for(F=cdr(F);F!=[];F=cdr(F)){ - if(!iand(car(F)[1],1)) R*=car(F)[0]^(car(F)[1]/2); - else return []; - } - return R; - } - if(ntype(P)==4){ - P0=real(P);P1=imag(P)/2; - X=makenewv(P); - for(R=fctr(X^4-P0*X^2-P1^2);R!=[];R=cdr(R)){ - RT=car(R)[0]; - if(deg(RT,X)==1){ - X=-mycoef(RT,0,X)/mycoef(RT,1,X); - return X+P1/X*@i; - } - if(deg(RT,X)==2){ - if((D=mycoef(RT,1,X)^2-4*mycoef(RT,2,X)*mycoef(RT,0,X))<0) continue; - X=(-mycoef(RT,1,X)+sqrtrat(D))/(2*mycoef(RT,2,X)); - return X+P1*sqrt2rat(1/X)*@i; - } - } - D=P0^2+4*P1^2; - if(P1>0) return ((sqrtrat(D)+P0)/2)^(1/2)+((sqrtrat(D)-P0)/2)^(1/2)*@i; - return ((sqrtrat(D)+P0)/2)^(1/2)-((sqrtrat(D)-P0)/2)^(1/2)*@i; - }else if(ntype(P)!=0) return []; - if(P==1) return P; - Dn=dn(P);Nm=nm(P);C=R=1; - N=pari(factor,Dn); - if(N){ - for(II=car(size(N))-1;II>=0;II--){ - if(iand(K=N[II][1],1)){ - R*=N[II][0]; - K++; - } - C/=N[II][0]^(K/2); - } - } - N=pari(factor,Nm); - if(N){ - for(II=car(size(N))-1;II>=0;II--){ - if(N[II][0]==-1){ - C*=@i; - continue; - } - K=N[II][1]; - if(iand(K,1)){ - R*=N[II][0]; - K--; - } - if(K!=0) C*=N[II][0]^(K/2); - } - } - if(R!=1) C*=R^(1/2); - return C; -} - -def fctri(F) -{ - R=(iscoef(F,os_md.israt))?fctr(F):[[1,1],[F,1]]; - if(!iscoef(F,os_md.iscrat)||chkfun("af_noalg",0)==0) return R; - X=makenewv(vars(F)); - for(S=[];R!=[];R=cdr(R)){ - if(length(Var=vars(R0=car(R)[0])) == 1 && (D=mydeg(R0,Var=car(Var))) > 0){ - if(imag(T=mycoef(R0,D,Var))!=0) R0/=T; - T=af_noalg(real(R0)+imag(R0)*X,[[X,X^2+1]]); - if(length(T)>1||T[0][1]>1){ - T=subst(T,X,@i); - for(; T!=[];T=cdr(T)){ - if(vars(T[0])!=[]) - S=cons([car(T)[0],car(T)[1]*car(R)[1]],S); - } - continue; - } - } - S=cons(R[0],S); - } - return reverse(S); -} - -def getroot(F,X) -{ - S=[]; - if(type(Cpx=getopt(cpx))!=1) Cpx=0; - M=getopt(mult); - if(type(F) == 3) - F = nm(red(F)); - for(R=fctri(F); length(R)>0; R = cdr(R)){ - T=car(R); - P=car(T); - I=car(cdr(T)); - if(mydeg(P,X)>0){ - if(mydeg(P,X)==1){ - C = mycoef(P,1,X); - P = X - red(P/C); - }else if(mydeg(P,X)==2 && Cpx>0){ - C2=mycoef(P,2,X);C1=mycoef(P,1,X);C0=mycoef(P,0,X); - C=sqrt2rat(C1^2-4*C0*C2); - C0=[]; - if(type(C)==0&&ntype(C)==0&&pari(issquare,-C)) C0=sqrt(C); - else if(Cpx>1) C0=sqrtrat(C); - if(C0==[]&&Cpx>2) C0=C^(1/2); - if(C0!=[]){ - if(M==1) - S=cons([I,sqrt2rat((-C1+C0)/(2*C2))],S); - else{ - for(II=I; II>0; II--) - S=cons(sqrt2rat((-C1+C0)/(2*C2)),S); - } - P=sqrt2rat((-C1-C0)/(2*C2)); - } - }else if(mydeg(P,X)==3 && Cpx>1){ - Omg=(-1+3^(1/2)*@i)/2; - PP=P/mycoef(P,3,X); - C2=mycoef(PP,2,X)/3; - PP=subst(PP,X,X-C2); - if((C1=mycoef(PP,1,X))==0){ - C0=mycoef(PP,0,X); - if(real(C0)==0||imag(C0)==0){ - if(real(C0)==0){ - PP=getroot(X^3+imag(C0),X); - if(length(PP)==3){ - for(;PP!=[];PP=cdr(PP)){ - if(imag(PP[0])==0){ - C0=PP[0]*@i; - break; - } - } - if(PP==[]) C0=0; - } - }else{ - if(C0>0) C0=C0^(1/3); - else C0=-(-C0)^(1/3); - } - if(C0!=0){ - if(M==1){ - S=cons([I,C0-C2],S); - S=cons([I,C0*Omg-C2],S); - S=cons([I,C0*(-1-Omg)-C2],S); - }else{ - for(II=I; II>0; II--){ - S=cons(C0-C2,S); - S=cons(C0*Omg-C2,S); - S=cons(C0*(-1-Omg)-C2,S); - } - } - continue; - } - } - } - if(Cpx>2){ - Q=X^2+(mycoef(PP,1,X)/3)*X+mycoef(PP,0,X)^3; - SQ=getroot(Q,X|cpx=2); - SQ=SQ[0]^(1/3);SQ2=mycoef(PP,0,X)/SQ; - if(M==1){ - S=cons([I,SQ+SQ2-C2],S); - S=cons([I,SQ*Omg+SQ2*(-1-Omg)-C2],S); - S=cons([I,SQ*(-1-Omg)+SQ2*Omg-C2],S); - }else{ - for(II=I; II>0; II--){ - S=cons(SQ+SQ2-C2,S); - S=cons(SQ*Omg+SQ2*(-1-Omg)-C2,S); - S=cons(SQ*(-1-Omg)+SQ2*Omg-C2,S); - } - } - continue; - } - }else if(mydeg(P,X)==4 && Cpx>0){ - C2=mycoef(P,3,X)/(4*mycoef(P,4,X)); - PP=subst(P,X,X-C2); - if(mycoef(PP,1,X)==0){ - PP=mycoef(PP,4,X)*X^2+mycoef(PP,2,X)*X+(SQ2=mycoef(PP,0,X)); - SQ=getroot(PP,X|cpx=2); - if(length(SQ)==2){ - if((C0=sqrtrat(SQ[0]))==[]){ - if(mycoef(PP,1,X)==0){ - if(SQ2<0) C0=(-SQ2)^(1/4); - else C0=SQ2^(1/4)*(1+@i)/2; - } - else if(Cpx>2) C0=SQ[0]^(1/2); - else C0=0; - } - if((C1=sqrtrat(SQ[1]))==[]){ - if(mycoef(PP,1,X)==0) C1=-C0; - else C1=SQ[1]^(1/2); - } - if(C0!=0){ - if(M==1) - S=append([[I,C0-C2],[I,-C0-C2],[I,C1-C2],[I,-C1-C2]],S); - else{ - for(II=I; II>0; II--) - S=append([C0-C2,-C0-C2,C1-C2,-C1-C2],S); - } - continue; - } - } - }else{ - PP/=mycoef(PP,4,X); - CC=mycoef(PP,2,X);C1=mycoef(PP,1,X);C0=mycoef(PP,0,X); - SQ=getroot(X*(CC+X)^2-4*C0*X-C1^2,X|cpx=Cpx); - if(length(SQ)>1){ - SQ=sqrt2rat(SQ[0]); - SQ2=getroot(X^2-SQ,X|cpx=Cpx); - if(length(SQ2)>1){ - C1=SQ2[0]*X-C1/SQ2[0]/2; - C0=getroot(X^2+CC/2+SQ/2+C1,X|cpx=Cpx); - C1=getroot(X^2+CC/2+SQ/2-C1,X|cpx=Cpx); - if(length(C0)>1&&length(C1)>1){ - C0=[sqrt2rat(C0[0]-C2),sqrt2rat(C0[1]-C2), - sqrt2rat(C1[0]-C2),sqrt2rat(C1[1]-C2)]; - if(M==1) for(II=0;II<4;II++) S=cons([I,C0[II]],S); - else for(II=I; II>0; II--) S=append(C0,S); - continue; - } - } - } - } - } - if(M==1) - S=cons([I,P],S); - else for( ; I>0; I--) S=cons(P,S); - } - } - S=qsort(S); - if(M==1) S=reverse(S); - return S; -} - -def expat(F,L,V) -{ - L = vweyl(L); - if(V == "?"){ - Ans = []; - - F = nm(red(F)); - S = fromeul(toeul(F,L,"infty"),L,0); - S = mycoef(S,mydeg(S,L[1]),L[1]); - if(mydeg(S,L[0]) > 0) - Ans = cons(["infty", expat(F,L,"infty")],Ans); - - S = mycoef(F,mydeg(F,L[1]), L[1]); - R = getroot(S,L[0]); - for(I = 0; I < length(R); I++){ - if(I > 0 && R[I-1] == R[I]) - continue; - if(mydeg(R[I], L[0]) <= 0) - Ans = cons([R[I], expat(F,L,R[I])], Ans); - else - Ans = cons([R[I]], Ans); - } - return Ans; - } - return getroot(subst(toeul(F,L,V),L[0],0),L[1]); -} - -def polbyroot(P,X) -{ - R = 1; - while(length(P)){ - R *= X-car(P); - if(type(R)>2) R = red(R); - P = cdr(P); - } - return R; -} - -def polbyvalue(P,X) -{ - R = 1; S = 0; - while(length(P)){ - T = car(P); - V0 = T[1] - mysubst(S,[X,T[0]]); - if(V0 != 0){ - if(type(R) > 2) R = red(R); - V1 = mysubst(R,[X,T[0]]); - if(V1 == 0){ - erno(0); - return 0; - } - S += (V0/V1)*R; - if(type(S) > 2) S = red(S); - } - R *= X - T[0]; - P = cdr(P); - } - return S; -} - - -def pcoef(P,L,Q) -{ - if(L==0) - return 1; - Coef=TP=0; - if(type(Q)>=4){ - TP=1; - V=Q[0]; - if(type(V)==4) - V=ltov(V); - else V=dupmat(V); - N=length(V); - if(type(Q[1])==5) MR=dupmat(Q[1]); - else{ - MR=newvect(N); - for(K=Q[1], I=0; I< N; I++){ - MR[I] = car(K); - K = cdr(K); - } - } - }else{ - V=ltov(vars(P)); - N=length(V); - MR=newvect(N); - for(I=0;I<N;I++){ - MR[I]=mydeg(Q,V[I]); - Q=mycoef(Q,MR[I],V[I]); - } - if(type(Q)>1) return 0; - } - if(L==1){ - for(I=0;I<N;I++) - P=mycoef(P,MR[I],V[I]); - return P; - } - for(I=1;I<N;I++){ /* sorted by required degrees */ - for(K1=MR[I],K2=V[I],J=I-1; J>=0 && MR[J]<K1; J--); - for(II=I-1;II>J;II--){ - MR[II+1]=MR[II];V[II+1]=V[II]; - } - MR[II+1]=K1;V[II+1]=K2; - } - for(NN=N; N>0 && MR[N-1]==0; N--); - Mon=[];Coe=[];Q=P; - while(Q!=0){ - M=newvect(N); - for(R=Q,F=I=0,MT=1;I<NN;I++){ - K=mydeg(R,V[I]); - R=mycoef(R,K,V[I]); - if(I<N) M[I]=K; - if(K>0) MT*=V[I]^K; - if(K>MR[I]) F=1; - } - Q -= R*MT; - if(F==0){ - Mon=cons(M,Mon); - Coe=cons(R,Coe); - } - } - Mon=ltov(reverse(Mon)); - Coe=ltov(reverse(Coe)); - Len=length(Mon); - S=newvect(Len); - for(JL=0; JL<Len;JL++){ - if(L*Mon[JL][0]<MR[0]) break; - } - S[0]=L; - - K0=Mon[0][0]; - K=L*K0-MR[0]; - for(I=II=0;II<Len && K>=0;II++){ - if((K1=K0-Mon[0][II])>0){ - while(K>K1 && S[I]>0){ - S[I]--;S[II]++; - K-=K1; - I=II; - K0=Mon[0][II]; - } - }else break; - } - - I=0; - while(1){ - for(T=T0=J=JP=0; J<Len; J++){ - if(S[J]!=0){ - if(T0==0 && J>=JL) return Coef; - JP=J;T0=1; - T+=S[J]*Mon[J][I]; - } - } - if(T==MR[I]){ - if(++I<N) continue; - for(TT=1,J=1; J<=L; J++) /* find a solution */ - TT*=J; - for(J=0;J<Len;J++){ - if(S[J]!=0){ - TT*=Coe[J]^S[J]; - for(II=S[J]; II>1; II--) - TT/=II; - } - } - Coef+=TT; - if(TP==1 && type(Coef)==3) Coef=red(Coef); - if(JP<Len-2 && S[JP]>1){ - S[JP]-=2;S[JP+1]++;S[JP+2]++; - }else{ - for(JT=JP-1;JT>=0&&S[JT]==0;JT--); - if(JT<0) break; - if(JT==JP-1){ - S[JT]--; - if(JP<Len-1) - S[JP+1]++; - else - S[JP]++; - }else{ - S[JT]--; - S[JT+1]+=S[JP]+1; - S[JP]=0; - } - } - I=0; - continue; - } - if(JP<Len-1){ - for(JP1=JP+1;JP1<Len-1;JP1++){ - if(Mon[JP1][I]!=Mon[JP][I]) break; - } - - if(I>0 && Mon[JP1][0] < Mon[JP][0]){ - S[JP]--;S[Len-1]++;JP=JP-1; - }else{ - - S[JP]--; - if(JP1<Len){ - S[JP1]++; - }else{ - S[JP1-1]++; - } - } - } - if(JP==Len-1){ - for(JT=JP-1;JT>=0 && S[JT]==0;JT--); - if(JT<0) break; - S[JT]--; - if(JT==JP-1){ - S[JP]++; - }else{ - S[JT+1]+=S[JP]+1; - S[JP]=0; - } - } - I=0; - } - return Coef; -} - -def prehombf(P,Q) -{ - if((Mem=getopt(mem))!=1 && Mem!=-1) - return prehombfold(P,Q); - if(Q==0) Q=P; - V=ltov(vars(P)); - N=length(V); - for(I=1;I<N;I++){ /* sorted by required degrees */ - for(K=mydeg(P,V[I]),K1=V[I],J=I-1; J>=0 && mydeg(P,V[J])<K; J--); - for(II=I-1;II>J;II--) V[II+1]=V[II]; - V[II+1]=K1; - } - S=newvect(N);T=newvect(N);U=newvect(N); - for(R=P,M=1,Deg=I=0;I<N;I++){ /* extreme vector */ - Deg+=(S[I]=mydeg(R,V[I])); - R=mycoef(R,S[I],V[I]); - } - DR=[[-1,0]]; - if((R1=N/Deg)!=1){ - DR=cons([-R1,0],DR); - Sft=1; - }else Sft=0; - if(Deg%2==0) Sg=1; - else Sg=-1; - for(I=0,R=R2=1,QQ=Q; 2*I+Sft < Deg; I++){ - if(Mem==-1){ - print(I+1,0);print("/",0);print(idiv(Deg-Sft+1,2),0);print(" ",2); - } - Coef=0; - Q=QQ; - while(Q!=0){ - for(R=Q,J=0,RR=1;J<N;J++){ - T[J]=mydeg(R,V[J]); - R=mycoef(R,T[J],V[J]); - if(T[J]>0) RR*=V[J]^T[J]; - } - Q-=R*RR; - for(J=0,CC=R;J<N;J++){ - U[J]=I*S[J]+T[J]; - for(II=0; II<T[J]; II++) - CC*=(U[J]-II); - } - CC*=pcoef(P,I+1,[V,U]); - if(Mem==-1) print("*",2); - Coef+=CC; - } - DR=cons([I,Coef],DR); - DR=cons([-R1-1-I,Sg*Coef],DR); - if(Mem==-1) print(""); - } - P = polbyvalue(DR,s); - return fctr(P); -} - -def prehombfold(P,Q) -{ - V = vars(P); - if(Q==0) Q=P; - for(Deg=0, R=P, V1=V, DD=[]; V1!=[]; V1=cdr(V1)){ - VT = car(V1); - D = mydeg(R,VT); - R = mycoef(R,D,VT); - Deg += D; - X = makev(["d",VT]); - Q = subst(Q,VT,X); - DD=cons([VT,X],DD); - } - DR=[[-1,0]]; - NV=length(V); - if((R1=NV/Deg)!=1){ - DR=cons([-R1,0],DR); - Sft=1; - }else - Sft=0; - if(Deg%2==0) - Sg=1; - else Sg=-1; - for(I = 0, R=R2=1; 2*I+Sft < Deg; I++){ - R = R2; - R2 = R*P; - S = appldo(Q,R2,DD); - QQ = sdiv(S,R); - DR=cons([I,QQ],DR); - DR=cons([-R1-1-I,Sg*QQ],DR); - } - P = polbyvalue(DR,s); - return fctr(P); -} - -def sub3e(P0,P1,P2,N0,N1,N) -{ - R = x^N0*(x-1)^N1*dx^N; - for(V = I = 1, J = 1; I <= N; I++){ - S = 0; - M = N-I; - if(I <= N0){ - T = mycoef(P0,N0-I,x); - S += T; - R += T*x^(N0-I)*(x-1)^N1*dx^M; - K1 = N0-I+1; - }else - K1 = 0; - if(I <= N1){ - T = mycoef(P1,N1-I,x); - S += T; - R += T*x^N0*(x-1)^(N1-I)*dx^M; - K2 = N0-1; - }else - K2 = N-I; - for(K = K1; K <= K2; K++){ - if(K == K2){ - R += (mycoef(P2,N-I,x)-S)*x^K*(x-1)^(M-K)*dx^M; - continue; - } - R += strtov("r"+rtostr(V))*x^K*(x-1)^(M-K)*dx^M; - S += strtov("r"+rtostr(V++)); - } - } - if(V > 1) - mycat([V-1, "accessory parameters: r1,r2,..."]); - return R; -} - -def fuchs3e(P,Q,R) -{ - return getbygrs([R,P,Q],3); -} - -def okubo3e(P,Q,R) -{ - if(getopt(opt)==1){ - N=length(R); - M1=N-length(P);M2=N-length(Q); - V=(M1-1)*(M2-1); - if(V>0) mycat([V, "accessory parameters"]); - return getbygrs([R,cons([M1,0],P),cons([M2,0],Q)],3); - } - S = 0; - V = -1; - L = newvect(3,[[],[],[]]); - N = newvect(3,[0,0,0]); - if(type(R) < 4){ - I = -1; - V = 3; - }else{ - I = 2; - V = -1; - } - for( ; I >= 0; I--){ - if(I == 2) - U = R; - else if(I == 1) - U = Q; - else - U = P; - for( ; length(U); U = cdr(U)){ - T = car(U); - if( T == "?"){ - if(V < 0) - V = I; - else - return 0; - }else{ - if(I == 2) - L[I] = cons(-T, L[I]); - else - L[I] = cons(T, L[I]); - S += T; - } - N[I]++; - } - } - if(V == 3){ - N[2] = N[0] + N[1]; - P2 = x^N; - for(I = 1; I <= N; I++) - P2 += makev([R,I])*x^(N-I); - }else{ - if(N[0]+N[1] != N[2]){ - print("Number of exponents are wrong",0); - return -1; - } - S -= N[0]*N[1]; - if(V < 0){ - if(S != 0){ - mycat(["Viorate Fuchs relation ->",S]); - return -2; - } - }else{ - if(V != 2) - S = -S; - L[V] = cons(S, L[V]); - } - P2 = polinsft(polbyroot(L[2],x),x); - } - P0 = polinsft(mysubst(polbyroot(L[0],x),[x,x+N[1]]),x); - P1 = polinsft(mysubst(polbyroot(L[1],x),[x,x+N[0]]),x); - return sub3e(P0,P1,P2,N[0],N[1],N[2]); -} - -/* N = 2*M (N-M = M) or 2*M+1 (N-M = M+1) - 0 : 0 1 ..... M-1 B B+1 ... B+N-M-2 A - 1 : C C+1 ... C+M-1 0 1 .... N-M-2 N-M-1 - */ -def eosub(A,B,C,N) -{ - M = N%2; - P = []; - Q = []; - P = cons(A,P); - for(I = 0; I < N-M-1; I++) - P = cons(B+I,P); - for(I = 0; I < M; I++) - Q = cons(C+I,Q); - P = okubo3e(P,Q,s); - - C = newvect(2); - L = newvect(2); - C[1] = chkexp(P,[x,dx],0,b,N-M-1); - C[0] = chkexp(P,[x,dx],1,c,M); - for(LL = K = 0; K < 2; K++){ - L[K] = length(C[K]); - C[K] = ltov(C[K]); - if(L[K] > LL) - LL = L[K]; - } - JJ = 0; - - for(I = 1; Do; I++){ - Do = 0; - S = makev(["r",I]); - for(J = JJ; J < LL; J++){ - JJ = LL; - for(K = 0; K < 2; K++){ - if(J >= L[K] || C[K][J] == 0) - continue; - if(J < JJ) - JJ = J; - if(Do == 1){ - CC = C[K]; - CC[J] = mysubst(CC[J], [S, Var]); - continue; - } - if(mydeg(C[K][J]) >= 1){ - if(mydeg(C[K][J]) > 1){ - print("Internal error"); - return; - } - Var = getroot(C[K][J],S); - Var = Var[0]; - CC = C[K]; - CC[J] = 0; - P = mysubst(P, [S, Var]); - Do = 1; - J = JJ - 1; - K++; - } - } - } - } - if(JJ != L){ - print("Internal error (non Rigid)"); - return; - } - return P; -} - -def even4e(X,Y){ - if(length(X) != 4 || length(Y) != 2){ - print("Usage: even4e([a,b,c,d],[e,f])"); - print("0: 0 1 e f"); - print("1; 0 1 * *+1"); - print("infty: a b c d"); - return; - } - S = -3; - for(I = 0; I < 4; I++){ - S += X[I]; - if(I < 2) - S += Y[I]; - } - S = -S/2; - P = okubo3e(Y,[S,"?"],X); - T = chkexp(P,x,1,S,2); - T = getroot(T[0],r1); - return mysubst(P,[r1,T[0]]); -} - -def odd5e(X,Y) -{ - if(length(X) != 5 || length(Y) != 2){ - print("Usage: spec6e([a,b,c,d,e],[f,g])"); - print("0: 0 1 f g g+1"); - print("1: 0 1 2 * *+1"); - print("infty: a b c d e"); - return; - } - S = -4; - for(I = 0; I < 5; I++){ - S += X[I]; - if(I < 2) - S += Y[I]; - } - S = -(S + Y[1])/2; - P = okubo3e([Y[0],Y[1],Y[1]+1],[S,"?"],X); - T = chkexp(P,x,1,S,2); - T = getroot(T[0],r1); - P = mysubst(P,[r1,T[0]]); - T = chkexp(P,x,0,Y[1],2); - T = getroot(T[0],r2); - return mysubst(P,[r2,T[0]]); -} - -def extra6e(X,Y) -{ - if(length(X) != 6 || length(Y) != 2){ - print("Usage: extra6e([a,b,c,d,e,f],[g,h])"); - print("0: 0 1 g g+1 h h+1"); - print("1: 0 1 2 3 * *+1"); - print("infty: a b c d e f"); - return; - } - S = -5; - for(I = 0; I < 6; I++){ - S += X[I]; - if(I < 2) - S += 2*Y[I]; - } - S = -S/2; - P = okubo3e([Y[0],Y[0]+1,Y[1],Y[1]+1],[S,"?"],X); - T = chkexp(P,x,1,S,2); - T = getroot(T[0],r1); - P = mysubst(P,[r1,T[0]]); - T = chkexp(P,x,0,Y[0],2); - T = getroot(T[0],r3); - P = mysubst(P,[r3,T[0]]); - T = chkexp(P,x,0,Y[1],2); - T = getroot(T[0],r2); - return mysubst(P,[r2,T[0]]); -} - -def rigid211(X,Y,Z) -{ - if(length(X) != 2 || length(Y) != 2 || length(Z) != 2){ - print("Usage: rigid211([a,b],[c,d],[e,f])"); - print("0: 0 1 a b"); - print("1: 0 1 c d"); - print("infty: e e+1 f *"); - return; - } - P = okubo3e(X,Y,[Z[0],Z[0]+1,Z[1],"?"]); - T = chkexp(P,x,"infty",Z[0],2); - T = getroot(T[0],r1); - return mysubst(P,[r1,T[0]]); -} - -def solpokuboe(P,L,N) -{ - if(type(N) > 1 || ntype(N) != 0 || dn(N) != 1){ - mycat(["Irrigal argument :", N]); - return 0; - } - L = vweyl(L); - DD=N+1; - for(U = S = L[0]^N; U != 0; ){ - D = mydeg(U,L[0]); - if(D>=DD){ - mycat(["Internal Error",D,DD]); - return -1; - } - DD=D; - UU = L[0]^D; - R = appldo(P,UU,L); - if(mydeg(R,L[0]) > D){ - printf("Bad operator\n"); - return 0; - } - CC = mycoef(R,D,L[0]); - if(D == N){ - P -= (E = CC); - U = R-E*U; - continue; - } - if(CC == 0){ - printf("No polynomial\n"); - return 0; - } - CC= mycoef(U,D,L[0])/CC; - S = red(S - UU*CC); - U = red(U - R*CC); - } - return [nm(S),E]; -} - -def stoe(M,L,N) -{ - L = vweyl(L); - Size = size(M); - S = Size[0]; - NN = 0; - if(type(N) == 4){ - NN=N[0]; N=N[1]; - }else if(N < 0){ - NN=-N; N=0; - } - if(S != Size[1] || N >= S || NN >= S) - return; - D = newmat(S+1,S+1); - MN = dupmat(M); - MD = newmat(S,S); - DD = D[0]; - DD[N] = 1; DD[S] = 1; - for(Lcm = I = 1; ; ){ - DD = D[I]; - MM = MN[N]; - for(J = 0; J < S; J++){ - DD[J] = MM[J]; - Lcm = lcm(dn(DD[J]),Lcm); - } - DD[S] = L[1]^I; - for(J = 0; J <= S; J++) - DD[J] = red(DD[J]*Lcm); - if(I++ >= S) - break; - if(I==S && NN>0){ - DD = D[I]; - DD[0]=-z_zz; DD[NN]=1; - break; - } - Mm = dupmat(MN*M); - for(J = 0; J < S; J++){ - for(K = 0; K < S; K++) - MN[J][K] = red(diff(MN[J][K],L[0])+Mm[J][K]); - } - } -#if 0 - P = fctr(mydet2(D)); -#else - P = fctr(det(D)); -#endif - for(I = R = 1; I < length(P); I++){ - if(mydeg(P[I][0],L[1]) > 0) - R *= P[I][0]^P[I][1]; - } - if(NN > 0) - R = -red(coef(R,0,z_zz)/coef(R,1,z_zz)); - return R; -} - -def dform(L,X) -{ - if(type(X)==2) X=[X]; - if(type(L[0])!=4) L=[L]; - if(type(X)==4) X=ltov(X); - M=length(X); - if(length(car(L))==2){ - R=newvect(M); - for(LL=L; LL!=[]; LL=cdr(LL)){ - for(I=0; I<M; I++){ - RT=rmul(car(LL)[0],mydiff(car(LL)[1],X[I])); - R[I] = (R[I]==0)?RT:radd(R[I],RT); - } - } - Dif=getopt(dif); - for(RR=[], I=M-1; I>=0; I--){ - if(Dif==1) RR=cons([1,R[I],X[I]],RR); - else RR=cons([R[I],X[I]],RR); - } - if(Dif==1) RR=dform(RR,X); - return RR; - }else if(length(car(L))!=3) return L; - N=M*(M-1)/2; - R=newvect(N); - S=newvect(N); - for(LL=L; LL!=[]; LL=cdr(LL)){ - for(I=K=0; I<M; I++){ - for(J=I+1; J<M; J++, K++){ - if(LL==L) S[K]=[X[I],X[J]]; - LT=car(LL); - R1=mydiff(LT[2],X[J]); - R2=mydiff(-LT[2],X[I]); - if(R2==0){ - if(R1==0) continue; - R1=rmul(mydiff(LT[1],X[I]),R1); - }else if(R1==0){ - R1=rmul(mydiff(LT[1],X[J]),R2); - }else - R1=rmul(mydiff(LT[1],X[I]),R1)+rmul(mydiff(LT[1],X[J]),R2); - R1=rmul(LT[0],R1); - R[K] = (R[K]==0)?R1:radd(R[K],R1); - } - } - } - for(RR=[],I=N-1; I>=0; I--) - RR=cons([R[I],S[I][0],S[I][1]],RR); - return RR; -} - -def polinvsym(P,Q,Sym) -{ - N = length(Q); - T = polbyroot(Q,zz); - for(I = 1; I <= N; I++){ - P = mysubst(P,[makev([Sym,I]), (-1)^I*coef(T,N-I,zz)]); - } - return P; -} - -def polinsym(P,Q,Sym) -{ - if(type(P) == 3){ - P = red(P); - if(type(P) == 3){ - D = polinsym(dn(P),Q,Sym); - if(D == 0) - return 0; - return polinsym(nm(P),Q,Sym)/D; - } - } - N = length(Q); - V = newvect(N+1); - S = newvect(N+1); - E = newvect(N+1); - E0 = newvect(N+1); - T = polbyroot(Q,zzz); - for(J = 1; J <= N; J++){ - K = coef(T,N-J,zzz); - if(J % 2) - K = -K; - S[J] = K; - V[J] = makev([Sym,J]); - } - K = deg(P,Q[0]); - for(J = 0; J <= N; J++) - E0[J] = K+1; - E[0] = K+1; - while(deg(P,Q[0]) > 0){ - for(P0 = P, J = 1; J <= N; J++){ - E[J] = deg(P0,Q[J-1]); - P0 = coef(P0,E[J],Q[J-1]); - } - /* P0*Q[0]^E[1]*Q[1]^E[2]*... E[1] >= E[2} >= ... */ - for(J = 1; J <= N; J++){ - if(E[J] < E0[J]) - break; - if(E[J-1] < E[J]) - J = N; - } - if(J > N){ - print("Not symmetric"); - return 0; - } - for(J = 1; J <= N; J++) - E0[J] = E[J]; - for(J = N; J > 1; J--){ - if(E[J] != 0) - for(K = 1; K < J; K++) - E[K] -= E[J]; - } - for(R0 = P0, K = 1; K <= N; K++){ - if(E[K] > 0) - P0 *= S[K]^E[K]; - R0 *= V[K]^E[K]; - } - P += R0 - P0; - } - return P; -} - -def tohomog(P,L,V) -{ - while(length(L)>0){ - P = mysubst(P,[car(L),car(L)/V]); - L = cdr(L); - } - P = red(P); - N = mindeg(dn(P),V); - if(N > 0) - P = red(P*V^N); - N = mindeg(dn(P),V); - if(N > 0) - P = red(P/(V^N)); - return P; -} - -def substblock(P,X,Q,Y) -{ - P = red(P); - if(deg(dn(P),X) > 0) - return substblock(nm(P),X,Q,Y)/substblock(dn(P),X,Q,Y); - N = mydeg(Q,X); - if(N < 1) - return P; - R = mycoef(Q,N,X); - while(M = mydeg(P,X), M >= N) - P = red(P - mycoef(P,M,X)*(Q-Y)*X^(M-N)/R); - return P; -} - -def okuboetos(P,L) -{ - L = vweyl(L); X = L[0]; DX = L[1]; - N = mydeg(P,DX); - C = mycoef(P,N,DX); - K = mydeg(C,X); - if(K > N){ - print("Irregular singularity at infinity")$ - return 0; - } - if(N > K) - P *= x^(N-K); - - L = getroot(mycoef(P,N,DX),x); - L = ltov(reverse(L)); - if(length(L) != N || N == 0){ - print("Cannot get exponents")$ - return 0; - } - if( type(LL = getopt(diag)) == 4 ){ - LL = ltov(LL); - if(length(LL) != N){ - mycat(["Length of the option should be", N]); - return 0; - } - Tmp = newvect(N); - for(I = N-1; I >= 0; I--){ - for(LLT = LL[I], J = N-1; J >=0 ; J--){ - if(LLT == L[J] && Tmp[J] == 0){ - Tmp[J] = 1; - break; - } - } - if(J < 0){ - print("option is wrong"); - return 0; - } - } - L = LL; - } - P /= mycoef(C,N,X); - A = newmat(N,N); - AT = newmat(N+1,N+1); - Phi= newvect(N+1); - Phi[0] = 1; - for(J = 0; J < N; J++) - Phi[J+1] = Phi[J]*(X-L[J]); - for(ATT = AT[N], J = 0; J < N; J++) - ATT[J] = mycoef(P,J,DX); - - for(K = 1; K <= N; K++){ - for(J = N; J >= K; J--){ - Aj = A[J-1]; - SIG = AT[J][J-K]; - for(I = 0; I <= K-2; I++) - SIG += Aj[J-I-1]*AT[J-I-1][J-K]; - if(K == 1) - DAT = mydiff(Phi[J-1],X); - else - DAT = mydiff(AT[J-1][J-K],X); - Aj[J-K] = -SIG+(X-L[J-1])*DAT; - Aj[J-K] /= Phi[J-K]; - Aj[J-K] = mysubst(Aj[J-K],[X,L[J-1]]); - if(J < K+1) continue; - ATj = AT[J-1]; - ATj[J-K-1] = SIG+Aj[J-K]*Phi[J-K]; - ATj[J-K-1] /= (X - L[J-1]); - ATj[J-K-1] = red(ATj[J-K-1]-DAT); - } - } - - ATT = newmat(N,N); - for(J = 0; J < N; J++){ - for(K = 0; K < N; K++){ - ATj = ATT[J]; - ATj[K] = AT[J][K]; - } - ATj[J] = Phi[J]; - if(J < N-1){ - ATj = A[J]; - ATj[J+1] = 1; - } - } - return [L,A,ATT]; -} - -def heun(X,P,R) -{ - if(type(X) != 4 || length(X) != 5){ - print("Usage: huen([a,b,c,d,e],p,r)"); - print("0: 0 c"); - print("1: 0 d"); - print("p: 0 e"); - print("infty: a b"); - print("Fuchs relation: a+b+1 = c+d+e"); - return; - } - S = 1; - V = -1; - X = ltov(X); - for(I = 0; I < 5; I++){ - if(X[I] == "?"){ - if(V >= 0) - return; - V = I; - }else if(I < 2){ - S += X[I]; - }else - S -= X[I]; - } - if(V >= 0){ - if(V < 2) - X[V] = -S; - else - X[V] = S; - }else if(S != 0){ - mycat(["Fuch relation:", S,"should be zero!"]); - return; - } - return - x*(x-1)*(x-P)*dx^2 - + (X[2]*(x-1)*(x-P)+X[3]*x*(x-P)+X[4]*x*(x-1))*dx - + X[0]*X[1]*(x-R); -} - -def fspt(M,T) -{ - if(type(M)==7) M=s2sp(M); - if(T == 3) /* 3: cut 0 */ - return cutgrs(M); - if(T == 4 || T== 5){ /* 4: short 5: long */ - for(MN = [] ; M != []; M = cdr(M)){ - MT = car(M); - for(MNT = []; MT != []; MT = cdr(MT)){ - if(type(car(MT)) <= 3){ - if(T == 4) MNT = cons(car(MT),MNT); - else MNT = cons([1,car(MT)],MNT); - }else{ - if(T == 5 || car(MT)[0] > 1) MNT = cons(car(MT),MNT); - else if(car(MT)[0] == 1) MNT = cons(car(MT)[1],MNT); - } - } - MN = cons(reverse(MNT), MN); - } - return reverse(MN); - } - if(type(M[0][0]) == 4){ - for(MN = [] ; M != []; M = cdr(M)){ - MT = car(M); - for(MNT = []; MT != []; MT = cdr(MT)) - MNT = cons(car(MT)[0], MNT); - MN = cons(reverse(MNT), MN); - } - return fspt(reverse(MN),T); - } - if(T == 0) /* 0: sp */ - return M; - for(MN = [] ; M != []; M = cdr(M)){ - MT = qsort(ltov(car(M))); - L = length(MT); - for(MNT = [], I = 0; I < L; I++) - MNT = cons(MT[I], MNT); - MN = cons(MNT, MN); - } - MN = reverse(MN); - if(T==6) return MN; /* 7: sort */ - L = length(MN); - for(M = MN; M != []; M = cdr(M)){ - for(I = 0, MT = car(M); MT != []; MT = cdr(MT)) - I += car(MT); - if(OD == 0) - OD = I; - else if(OD != I || OD == 0) - return 0; - } - ALL = [MN]; - RD=[]; - while(OD > 0){ - for(S = 0, MT = MN; MT != []; MT = cdr(MT)) - S += car(MT)[0]; - S -= (L-2)*OD; - if(S <= 0){ - if(T==7) return [ALL[0],ALL[length(ALL)-1],RD]; - return (T==1)?MN:ALL; - } - RD=cons([S,0,0],RD); - for(NP=0, M = [], MT = MN; MT != []; NP++, MT = cdr(MT)){ - MTT = car(MT); - I = MTT[0] - S; - if(I < 0){ - if(I+OD!=0) return 0; - if(T==7) return [ALL[0],ALL[length(ALL)-1],cdr(RD)]; - return (T==1)?MN:ALL; - } - MTT = cdr(MTT); - NC=1; DO=0; - for(MNT = []; MTT != []; MTT = cdr(MTT)){ - if(MTT[0] > I){ - if(DO==0) RD=cons([MTT[0]-I,NP,NC++],RD); - MNT = cons(MTT[0], MNT); - } - else if(MTT[0] <= I && I != 0){ - DO=1; - MNT = cons(I, MNT); - I = 0; - if(MTT[0] > 0) - MNT = cons(MTT[0], MNT); - } - } - if(I > 0) - MNT = cons(I,MNT); - M = cons(reverse(MNT), M); - } - MN = reverse(M); - ALL = cons(MN,ALL); - OD -= S; - } -} - -def abs(X) -{ - if(vars(X)!=[]) return todf(os_md.abs,[X]); - if(type(X)==4){ - P=X[1];X=X[0]; - }else P=0; - if(type(X)==1){ - if((T=ntype(X))<2 || T==3){ - if(X<0) X=-X; - }else if(T==4) X=P?pari(abs,X,P):pari(abs,X); - } - return X; -} - -def calc(X,L) -{ - if(type(X)<4||type(X)==7){ - if(type(L)==4||type(L)==7){ - V=L[1]; - if(type(X)!=7){ - if((L0=L[0])=="+") X+=V; - else if(L0=="-") X-=V; - else if(L0=="*") X*=V; - else if(L0=="/") X/=V; - else if(L0=="^") X^=V; - } - if((L0=L[0])==">") X=(X>V); - else if(L0=="<") X=(X<V); - else if(L0=="=") X=(X==V); - else if(L0==">=") X=(X>=V); - else if(L0=="<=") X=(X<=V); - else if(L0=="!=") X=(X!=V); - }else if(type(L)==7&&type(X)<4){ - if(L=="neg") X=-X; - else if(L=="abs") X=abs(X); - else if(L=="neg") X=-X; - else if(L=="sqr") X*=X; - else if(L=="inv") X=1/X; - else if(L=="sgn"){ - if(X>0)X=1; - else if(X<0) X=-1; - } - } - } - return X; -} - -def isint(X) -{ - if(X==0||(type(X)==1 && ntype(X)==0 && dn(X)==1)) return 1; - return 0; -} - -def israt(X) -{ - if(X==0||(type(X)==1 && ntype(X)==0)) return 1; - return 0; -} - -def iscrat(X) -{ - if(X==0 || (type(X)==1 && israt(real(X)) && israt(imag(X)))) return 1; - return 0; -} - -def isalpha(X) -{ - return ((X>64&&X<91)||(X>96&&X<123))?1:0; -} - -def isnum(X) -{ - return (X>47&&X<58)?1:0; -} - -def isalphanum(X) -{ - return (isalpha(X)||isnum(X))?1:0; -} - -def isdecimal(X) -{ - if(type(X)!=7) return 0; - F=S=0; - L=strtoascii(X); - while(L!=[]&&car(L)==32) L=cdr(L); - if(L!=[]&&car(L)==45) L=cdr(L); /* - */ - while(L!=[]&&isnum(car(L))){ - F=1; L=cdr(L); - } - while(L!=[]&&car(L)<33){ - S=1;L=cdr(L); - } - if(L==[]) return F; - else if(S||car(L)!=46) return 0; /* . */ - L=cdr(L);F=0; - while(L!=[]&&isnum(car(L))){ - F=1; L=cdr(L); - } - while(L!=[]&&car(L)<33) L=cdr(L); - return (L==[])?F:0; -} - -def isvar(X) -{ - return ([X]==vars(X)&&vtype(X)<3)?1:0; -} - -def isyes(F) -{ - if((CC=getopt(set))==1){ - IsYes=(type(F[0])==4)?F:[F]; - return 1; - }else if(CC==0) return(IsYes); - if(type(CC)!=7) - CC=IsYes; - for(;CC!=[]; CC=cdr(CC)){ - C=car(CC); - V=call(C[0],cons(F,C[1])); - if(type(C[2])!=4){ - if(V!=C[2]) break; - }else{ - if(C[2][0]!="" && V<C[2][0]) break; - if(C[2][1]!="" && V>C[2][1]) break; - } - } - return (CC==[])?1:0; -} - -def isall(FN,M) -{ - if(type(M)<4 || type(M)>6) return ((*FN)(M)==0)?0:1; - if(type(M)==4){ - for(;M!=[];M=cdr(M)) - if((*FN)(car(M))==0) return 0; - }else if(type(M)==5){ - K=length(M); - for(I=0;I<K;I++) - if((*FN)(M[I])==0) return 0; - }else if(type(M)==6){ - K=size(M)[0]; - for(I=0;I<K;I++) - if (isall(FN,M[I])==0) return 0; - } - return 1; -} - -def sproot(MP,T) -{ - if((I=str_chr(T,0,","))>0){ - if(type(MP)==7) M=s2sp(MP); - else M=chkspt(MP|opt=0); - if(I==length(M[0])){ - N=s2sp(T);S=SM=SN=K=0; - for(MM=M,NN=N;MM!=[];MM=cdr(MM),NN=cdr(NN),K++){ - for(MT=car(MM),NT=car(NN);MT!=[];MT=cdr(MT),NT=cdr(NT)){ - S+=car(MT)*car(NT); - if(K==0){ - SM+=car(MT);SN+=car(NT); - } - } - } - return S-(length(M)-2)*SM*SN; - } - } - MM=chkspt(MP|opt=7); - if(T=="base") return MM; - Keep=(getopt(keep)==1)?1:0; - Null=getopt(null); - Only=getopt(only); - if(type(Only)!=1) Only=7; - M0=MM[0]; - M1=MM[1]; - M=MM[2]; - if(T=="length") return length(M); - if(T=="height"){ - for(J=2,S=M1[0][0],M2=M1; M2!=[]; M2=cdr(M2)){ - for(MT=cdr(car(M2)); MT!=[]; J++, MT=cdr(MT)){ - S+= J*car(MT); - } - J=1; - } - return S; - } - for(OD=0, MT=M1[0]; MT!=[]; MT=cdr(MT)) OD+=car(MT); - if(T=="type"){ - R=newvect(OD+1); - for(MT=M; MT!=[]; MT=cdr(MT)) R[MT[0][0]]++; - for(RR=[],I=OD; I>0; I--) - if(R[I]>0) RR=cons([R[I],I],RR); - return RR; - } - if(T=="part"||T=="pair"||T=="pairs"){ - NP=length(M1); - LM=newvect(NP); - R=newvect(length(M)); - for(K=0; K<NP; K++) LM[K]=length(M1[K]); - for(I=0,TM=M; TM!=[]; I++, TM=cdr(TM)){ - V=newvect(NP); - for(K=0; K<NP; K++) V[K]=newvect(LM[K]); - TP=car(TM); - if(TP[2]==0){ - for(K=0;K<NP;K++) V[K][0]=1; - for(J=0; J<I; J++){ - VJ=R[J][1]; - for(S=K=0;K<NP;K++) S+=VJ[K][0]; - for(OD=0,K=0;K<LM[0];K++) OD+=VJ[0][K]; - S-=(NP-2)*OD; - for(K=0;K<NP;K++) VJ[K][0]-=S; - } - }else{ - K=TP[1]; P=TP[2]; - V[K][P-1]=-1; V[K][P]=1; - for(J=0; J<I; J++){ - VJ=R[J][1]; - S=VJ[K][P]; VJ[K][P]=VJ[K][P-1]; VJ[K][P-1]=S; - } - } - R[I]=[TP[0],V]; - } - if(T=="pair"||T=="pairs"){ - MV=ltov(M1); - for(K=0; K<NP; K++) MV[K] = ltov(MV[K]); - for(RR=UU=SS=[],I=0; I<length(M); I++){ - V=newvect(NP); W=newvect(NP); U=newvect(NP); - for(K=0; K<NP; K++){ - U[K]=newvect(LM[K]); V[K]=newvect(LM[K]); W[K]=newvect(LM[K]); - } - S=R[I][0]; - for(K=0; K<NP; K++){ - for(Q=J=0; J<LM[K]; J++){ - V[K][J] = S*(U[K][J] = R[I][1][K][J]); - Q+=(W[K][J] = MV[K][J] - V[K][J]); - } - } - if(Q>0 && iand(Only,1)==0) continue; - if(Q==0 && iand(Only,2)==0) continue; - if(Q<0 && iand(Only,4)==0) continue; - for(K=0; K<NP; K++){ - V[K] = vtol(V[K]); W[K] = vtol(W[K]); U[K]=vtol(U[K]); - } - V=vtol(V); W=vtol(W);U=vtol(U); - if(Q<0) S=-S; - RR = cons([V,W], RR); UU = cons(U,UU); SS=cons(S,SS); - } - RR = reverse(RR); UU=reverse(UU); SS=reverse(SS); - if(getopt(dviout)==1 && (Null!=1 || RR!=[])){ - Out=string_to_tb("\\begin{align}\\begin{split}"+s2sp(M1)+"&="); - for(I=0,R=RR, U=UU; R!=[]; I++, R=cdr(R), U=cdr(U)){ - if(I>0) str_tb("\\\\\n &=",Out); - if(T=="pairs"){ - if((S=SS[I])<0) S=-S; - if(S>1) str_tb([my_tex_form(S),"("],Out); - str_tb(s2sp(car(U)),Out); - if(S>1) str_tb(")",Out); - str_tb(" \\oplus ",Out); - if(SS[I]<0){ -#ifdef USEMODULE - str_tb(["-(",s2sp(mtransbys(os_md.abs,car(R)[1],[])),")"],Out); -#else - str_tb(["-(",s2sp(mtransbys(abs,car(R)[1],[])),")"],Out); -#endif - }else - str_tb(s2sp(car(R)[1]),Out); - }else - str_tb([s2sp(car(R)[0])," \\oplus ",s2sp(car(R)[1])],Out); - } - str_tb("\n\\end{split}\\end{align}",Out); - dviout(str_tb(0,Out)|keep=Keep); - } - return RR; - } - for(I=0; I<length(M); I++){ - for(K=0; K<NP; K++) R[I][1][K] = vtol(R[I][1][K]); - R[I] = [R[I][0],vtol(R[I][1])]; - } - R = vtol(R); - return [M0,M1,R]; - } -} - -def spgen(MO) -{ - Eq=(getopt(eq)==1)?1:0; - Sp=getopt(sp); - if(type(Sp)==7) Sp=s2sp(Sp); - St=getopt(str); - LP=getopt(pt); - F=getopt(std); - if(F!=1&&F!=-1) F=0; - if(type(LP)==4){ - L0=LP[0]; L1=LP[1]; - }else{ - L0=0; L1=MO+1; - } - if(MO<=0){ - MO=-MO; - if(iand(MO,1)==1) return []; - if(MO>1){ - if(isMs()==0) return []; - Cmd="okubo "+rtostr(-MO); - MO/=2; - if(L1>0) Cmd=Cmd+"+"+rtostr(L0)+"-"+rtostr(L1); - else L1=MO+4; - Cmd=Cmd+" B"; - Id=getbyshell(Cmd); - if(Id<0) return []; - B=[]; - while((S=get_line(Id)) !=0){ - P0=str_chr(S,1,":")+1; - if(P0>1){ - P1=str_chr(S,P,"\n"); - if(P1<0) P1=str_len(S); - B=cons(sub_str(S,P0,P1-1),B); - } - } - close_file(Id); - }else{ - MO/=2; - if(L1<=1) L1=MO+4; -BB=[ -["11,11,11,11","111,111,111","1^4,1^4,22","1^6,222,33"], -["11,11,11,11,11","1^4,1^4,211","211,22,22,22","1^6,2211,33", -"2211,222,222","22211,2^4,44","2^511,444,66","1^4,22,22,31", -"2^5,3331,55","1^5,1^5,32","1^8,332,44","111,111,21,21","1^5,221,221"], -["11,11,11,11,11,11","1^4,1^4,1^4","1^4,22,22,22","111,111,111,21", -"1^6,21^4,33","21^4,222,222","221^4,2^4,44","2^41^4,444,66", -"1^5,1^5,311","1^8,3311,44","1^6,222,321","321,33,33,33", -"3321,333,333","33321,3^4,66","3^721,666,99","2^5,3322,55", -"1^6,1^6,42","222,33,33,42","1^a,442,55","1^6,33,33,51", -"222,222,33,51","1^9,333,54","2^7,554,77","1^5,2111,221", -"2^41,333,441","1^7,2221,43","211,211,22,22","2211,2211,222", -"22211,22211,44","1^4,211,22,31","2^411,3331,55","1^4,1^4,31,31", -"22,22,22,31,31","1^7,331,331","2221,2221,331","111,21,21,21,21"], -["11,11,11,11,11,11,11","111,111,111,111","1^6,1^6,33", -"1^6,222,222","222,33,33,33","1^5,1^5,221", -"1^4,211,22,22","1^4,1^4,22,31","22,22,22,22,31", -"111,111,21,21,21","21^6,2^4,44","2221^6,444,66", -"1^6,222,3111","3111,33,33,33","33111,333,333", -"333111,3^4,66","3^5111,666,99","2^5,33211,55", -"1^8,3221,44","3222,333,333","33222,3^4,66", -"3^4222,666,99","1^6,1^6,411","222,33,33,411", -"1^a,4411,55","2^4,2^4,431","431,44,44,44", -"2^6,4431,66","4431,444,444","44431,4^4,88", -"4^531,888,cc","1^a,433,55","1^7,1^7,52", -"1^c,552,66","3^4,444,552","1^8,2^4,53", -"1^8,44,44,71","3^5,555,771","21^4,2211,222", -"221^4,22211,44","2221^4,3331,55","1^6,2211,321", -"2^411,3322,55","1^7,322,331","2211,33,33,42", -"3^42,4442,77","2211,222,33,51","3^51,5551,88", -"2^611,554,77","2221,2221,322","2^41,2^41,54", -"1^5,2111,2111","222111,333,441","1^7,22111,43", -"1^5,1^5,41,41","1^9,441,441","22111,2221,331", -"1^5,221,32,41","221,221,221,41","211,211,211,22", -"2211,2211,2211","1^4,211,211,31","211,22,22,31,31", -"1^4,22,31,31,31","1^5,32,32,32","221,221,32,32","21,21,21,21,21,21"], -["11,11,11,11,11,11,11,11","1^4,1^4,22,22","1^8,2^4,44", -"1^6,2211,222","2211,33,33,33","111,111,111,21,21", -"1^5,1^5,2111","1^4,211,211,22","1^4,1^4,211,31", -"211,22,22,22,31","1^4,22,22,31,31","111,21,21,21,21,21", -"221^8,444,66","2^5,331^4,55","1^8,32111,44", -"32211,333,333","332211,3^4,66","3^42211,666,99", -"2^5,32221,55","1^7,1^7,511","1^c,5511,66", -"3^4,444,5511","541,55,55,55","5541,555,555", -"55541,5^4,aa","5^541,aaa,ff","1^8,1^8,62", -"1^a1^4,662,77","1^a,55,55,91","2^71,555,87", -"21^6,22211,44","221^6,3331,55","1^6,2211,3111", -"2^411,33211,55","1^7,3211,331","2211,33,33,411", -"3^42,44411,77","22211,2^4,431","2^511,4431,66", -"1^8,332,431","3^42,4433,77","1^8,22211,53", -"2221,2221,3211","221^5,333,441","1^7,21^5,43", -"1^b,443,65","21^5,2221,331","2^51,3332,65", -"21^4,21^4,222","221^4,221^4,44","1^6,21^4,321", -"2221^4,3322,55","21^4,33,33,42","21^4,222,33,51", -"2^51^4,554,77","2^4,3311,3311","3^411,4442,77", -"321,321,33,33","3321,3321,333","33321,33321,66", -"222,321,33,42","1^6,321,33,51","222,222,321,51", -"1^9,3321,54","1^7,322,322","3^422,5551,88", -"1^6,33,42,42","1^6,222,42,51","33,33,33,42,51", -"1^6,1^6,51,51","222,33,33,51,51","1^b,551,551", -"1^5,221,311,41","2^41,3321,441","22111,2221,322", -"2^51,443,551","222111,2^41,54","21^4,2211,2211", -"1^5,311,32,32","3331,3331,442","2211,2211,33,51", -"221,221,311,32","22111,22111,331","1^5,2111,32,41", -"2111,221,221,41","2111,221,32,32","211,211,211,211", -"211,211,22,31,31","1^4,211,31,31,31","22,22,31,31,31,31"], -["11,11,11,11,11,11,11,11,11","1^5,1^5,1^5","2^5,2^5,55", -"111,111,111,111,21","2^41,333,333","1^4,1^4,211,22", -"211,22,22,22,22","1^8,22211,44","1^4,1^4,1^4,31", -"1^4,22,22,22,31","1^7,1^7,43","1^7,2221,331", -"2221,2221,2221","1^6,21^4,222","21^4,33,33,33", -"1^6,1^6,321","222,321,33,33","1^6,33,33,42", -"222,222,33,42","1^6,222,33,51","222,222,222,51", -"33,33,33,33,51","1^6,2211,2211","111,111,21,21,21,21", -"1^5,1^5,32,41","1^5,221,221,41","1^5,221,32,32", -"221,221,221,32","1^4,211,211,211","211,211,22,22,31", -"1^4,211,22,31,31","1^4,1^4,31,31,31","22,22,22,31,31,31", -"21,21,21,21,21,21,21","21^a,444,66","1^8,31^5,44", -"321^4,333,333","3321^4,3^4,66","3^421^4,666,99", -"2^5,322111,55","32^41,3^4,66","3332^41,666,99", -"1^8,1^8,611","2^4,44,44,611","1^d,6611,77", -"4^5,66611,aa","2^6,444,651","3^4,3^4,651", -"651,66,66,66","3^6,6651,99","6651,666,666", -"66651,6^4,cc","6^551,ccc,ii","2^8,655,88", -"1^9,1^9,72","1^g,772,88","1^c,444,75", -"2^6,3^4,75","1^c,66,66,b1","3^4,444,66,b1", -"3^7,777,ba","1^7,2221,4111","2^41,333,4311", -"1^9,2^41,63","21^8,3331,55","2^411,331^4,55", -"1^7,31^4,331","2^411,32221,55","22211,2^4,422", -"2^511,4422,66","1^8,332,422","2^5,3331,541", -"22211,44,44,62","2^411,2^5,64","2^711,664,88", -"1^a,3331,64","2221,2221,31^4","21^7,333,441", -"333,333,441,81","2^6111,555,87","21^6,221^4,44", -"221^6,3322,55","2^41^6,554,77","1^6,21^4,3111", -"3111,321,33,33","33111,3321,333","333111,33321,66", -"222,3111,33,42","1^6,3111,33,51","222,222,3111,51", -"1^9,33111,54","2221^4,33211,55","1^7,3211,322", -"3^4211,5551,88","2^4,3221,3311","333221,4442,77", -"3222,3321,333","33222,33321,66","1^9,3222,54", -"21^4,33,33,411","3^411,44411,77","222,321,33,411", -"1^6,33,411,42","1^6,222,411,51","33,33,33,411,51", -"221^4,2^4,431","2^41^4,4431,66","1^8,3311,431", -"3^411,4433,77","33321,444,552","1^8,221^4,53", -"3311,44,44,53","4^42,5553,99","2^4,3311,44,71", -"3^421,555,771","4^52,7771,bb","3^611,776,aa", -"2^41,33111,441","22111,2221,3211","2^41,3222,441", -"2^61,4441,76","3331,3331,4411","22211,22211,431", -"3331,3331,433","3^41,3^41,76","1^7,1^7,61,61", -"1^d,661,661","21^5,2221,322","221^5,2^41,54", -"2^51,33311,65","21^5,22111,331","3^41,4441,661", -"1^7,331,43,61","2221,2221,43,61","2221,331,331,61", -"21^4,21^4,2211","21^4,2211,33,51","22211,3311,3311", -"1^5,311,311,32","2211,321,33,42","2211,222,321,51", -"3322,3331,442","2211,222,42,42","2^411,442,442", -"1^6,2211,42,51","2211,33,33,51,51","221,221,311,311", -"1^5,2111,311,41","222111,3321,441","22111,22111,322", -"222111,222111,54","2111,221,311,32","2111,2111,221,41", -"1^5,221,41,41,41","2221,43,43,43","1^5,32,32,41,41", -"331,331,43,43","221,221,32,41,41","221,32,32,32,41", -"211,211,211,31,31","211,22,31,31,31,31","1^4,31,31,31,31,31"]]; - B=BB[MO]; - } - if(St!=1){ - for(R=[]; B!=[]; B=cdr(B)){ - RT=F?s2sp(car(B)|std=F):s2sp(car(B)); - if(length(RT)<L0 || length(RT)>L1) continue; - R=cons(RT,R); - } - return reverse(R); - }else{ - if(L0<=3 && L1>=MO+4) return B; - for(R=[]; B!=[]; B=cdr(B)){ - RT=s2sp(T=car(B)); - if(length(RT)<L0 || length(RT)>L1) continue; - if(F) T=s2sp(s2sp(T|std=K)); - R=cons(T,R); - } - return reverse(R); - } - } - MP=(L1<MO+1)?L1:MO+1; - LL=newvect(MO+1); - R=newvect(MP+2); - R0=newvect(MP+2); - for(I=1; I<=MO; I++) LL[I]=[]; - if(type(Sp)==4){ - if(getopt(basic)==1) Sp=chkspt(Sp[6]); - R=chkspt(Sp); - if(R[1]>MO) return 0; - LL[R[1]]=R; - K=R[1]; - } - if(K==1||type(Sp)!=4){ - LL[1]=[[[1]]]; - for(I=2; I<=MO && I<MP;I++){ - for(T=[], J=0; J<I+1; J++) - T=cons([I-1,1],T); - LL[I]=cons(T,LL[I]); - } - K=2; - } - for(OD=K; OD<MO; OD++){ - for(LT=LL[OD]; LT!=[]; LT=cdr(LT)){ - for(II=0,L=car(LT); L!=[]; II++, L=cdr(L)){ - R0[II]=R[II]=car(L); - } - for(; ;){ - for(S=-2*OD, I=0; I<II; I++){ - S += OD; - if(R[I]!=[]) S-=car(R[I]); - } - --I; - for(;S+OD<=MO && I<=MP;S+=OD,I++){ - if(S<=0) continue; - for(J=0;J<=I;J++){ - if(J>=II){ - if(S<OD) break; - }else - if(S+((R[J]==[])?0:car(R[J]))<car(R0[J])) break; - } - if(--J>=I){ - V=newvect(I); - RRR=[]; - for(;J>=0;J--){ - if(J>=II) RR=[OD,S]; - else{ - K=length(R[J]); - RR=[S+((K==0)?0:car(R[J]))]; - K=length(R0[J])-K; - for(RT=R0[J]; RT!=[]; K--,RT=cdr(RT)){ - if(K!=0) RR=cons(car(RT),RR); - } - } - RRR=cons(reverse(RR),RRR); - } - RRR=qsort(reverse(RRR)); - if(findin(RRR,LL[S+OD])<0) - LL[S+OD]=cons(RRR,LL[S+OD]); - } - } - for(K=0; K<II; K++){ - if(R[K]!=[]){ - S=car(R[K]); - while((R[K]=cdr(R[K]))!=[] && car(R[K])==S); - break; - }else R[K]=R0[K]; - } - if(K>=II) break; - } - } - } - if(L0>0 || L1<MO+1 || St==1 || F){ - for(J=1; J<=MO; J++){ - for(RT=[],R=LL[J];R!=[];R=cdr(R)){ - L=length(T=car(R)); - if(L<L0 || L>L1) continue; - if(F) T=s2sp(T|std=F); - RT=cons((St==1)?s2sp(T):T,RT); - } - LL[J] = reverse(RT); - } - } - if(Eq==1) return LL[MO]; - return LL; -} - -def spType2(L) -{ - C=0;R=[]; - for(LT=L;LT!=[];LT=cdr(LT)){ - D=-1;LP=car(LT); - for(LPT=LP;LPT!=[];LPT=cdr(LPT)){ - if(D==-1) D=car(LPT); - else D=igcd(D,car(LPT)); - if(D==1){ - C++;break; - } - } - if(C==2) return 0; - R=cons(D,R); - } - if(C==0) return L; - if(C==1){ - for(K=length(R)-1;R[K]!=1;K--); - D=-1; - for(I=length(R)-1;I>=0;I--){ - if(I==K) continue; - if(D==-1) D=R[I]; - else D=igcd(D,R[I]); - if(D==1) return 0; - } - } - return L; -} - - -/* ret [#points, order, idx, Fuchs, reduction order, reduction exponents, fund] */ -def chkspt(M) -{ - Opt= getopt(opt); - Mat= getopt(mat); - if(type(M)==7) M=s2sp(M); - if(type(Opt) >= 0){ - if(type(Opt) == 7) - Opt = findin(Opt, ["sp","basic","construct","strip","short","long","sort","root"]); - if(Opt < 0){ - erno(2); - return 0; - } - return fspt(M,Opt); - } - MR = fspt(M,1); - P = length(M); - OD = -1; - XM = newvect(P); - Fu = 0; - for( I = SM = SSM = 0; I < P; I++ ){ - LJ = length(M[I]); - JM = JMV = 0; - for(J = SM = 0; J < LJ; J++){ - MV = M[I][J]; - if(type(MV) == 4){ - Fu += MV[0]*MV[1]; - MV = MV[0]; - } - if(MV > JMV){ - JM = J; JMV = MV; - } - SM += MV; - SSM += MV^2; - } - if(OD < 0) - OD = SM; - else if(OD != SM){ - print("irregal partitions"); - return 0; - } - XM[I] = JM; - } - SSM -= (P-2)*OD^2; - for(I = SM = JM = 0; I < P; I++){ - MV = M[I][XM[I]]; - if(type(MV) == 4){ - MV = MV[0]; JM = 1; - } - if(I == 0) - SMM = MV; - else if(SMM > MV) - SMM = MV; - SM += MV; - } - SM -= (P-2)*OD; - if(SM > SMM && SM != 2*OD){ - print("not realizable"); - return -1; - } - if(JM==1 && Mat!=1) - Fu -= OD - SSM/2; - return [P, OD, SSM, Fu, SM, XM, MR]; -} - -def cterm(P) -{ - V = getopt(var); - if(type(V) != 4) - V=vars(P); - for(; V !=[]; V = cdr(V)) - P = mycoef(P,0,car(V)); - return P; -} - -def terms(P,L) -{ - Lv=getopt(level); - if(type(Lv)!=1) Lv=0; - V=car(L);L=cdr(L); - for(R=[],D=mydeg(P,V);D>=0; D--){ - if((Q=mycoef(P,D,V))==0) continue; - if(L!=[]){ - R0=terms(Q,L|level=Lv+1); - for(;R0!=[];R0=cdr(R0)) R=cons(cons(D,car(R0)),R); - }else R=cons([D],R); - } - if(Lv>0) return R; - R=qsort(R); - Rev = getopt(rev); Dic=getopt(dic); - if(Dic==1 && Rev==1) R=reverse(R); - for(R0=[];R!=[];R=cdr(R)){ - for(RT=car(R),S=0;RT!=[];RT=cdr(RT)) S+=car(RT); - R0=cons(cons(S,car(R)),R0); - } - if(Dic==1) return R0; - if(Rev==1){ - for(R=[];R0!=[];R0=cdr(R0)){ - T=car(R0); - R=cons(cons(-car(T),cdr(T)),R); - } - R0=R; - } - R0=qsort(R0); - if(Rev==1){ - for(R=[];R0!=[];R0=cdr(R0)){ - T=car(R0); - R=cons(cons(-car(T),cdr(T)),R); - } - R0=R; - } - return (Rev==1)?R0:reverse(R0); -} - -def polcut(P,N,L) -{ - if(type(L)==2) L=[L]; - M=getopt(top); - if(type(M)!=1) M=0; - T=terms(P,L); - for(S=0;T!=[];T=cdr(T)){ - LT=car(T); - if(LT[0]<M || LT[0]>N) continue; - for(PW=1,LT=cdr(LT),V=L,Q=P;LT!=[];LT=cdr(LT),V=cdr(V)){ - Q=mycoef(Q,car(LT),car(V));PW*=car(V)^car(LT); - } - S+=Q*PW; - } - return S; -} - -def redgrs(M) -{ - Mat = getopt(mat); - if(Mat!=1) Mat=0; - R = chkspt(M|mat=Mat); - if(type(R) < 4) - return -1; - if(R[4] <= 0) - return 1-R[4]; - if(R[4] == 2*R[1]) - return 0; - V = newvect(R[0]); - Type = type(M[0][0]); - if(Type > 3){ - Mu = Mat-1; - for(I = 0; I < R[0]; I++) - Mu += M[I][R[5][I]][1]; - } - for(I = 0; I < R[0]; I++){ - IR = R[5][I]; L = []; MI = M[I]; MIE=MI[IR]; - for(J = length(MI)-1; J >= 0; J--){ - if(Type <= 3){ - VM = MI[J]; - if(J == IR){ - VM -= R[4]; - if(VM < 0) return -1; - } - L = cons(VM, L); - }else{ - VM = MI[J][0]; - if(J == IR){ - VM -= R[4]; - if(VM < 0) - return -1; - if(I == 0) - EV = 1-Mat-Mu; - else - EV = 0; - }else{ - if(I == 0) - EV = MI[J][1] - M[0][R[5][0]][1] + 1-Mat; /* + MX - Mu; */ - else - EV = MI[J][1] - MIE[1] + Mu; - } - L = cons([VM,EV], L); -/* - if(R[2] >= 2){ */ /* digid */ -/* P = dx^(R[1]); - } */ - } - } - V[I] = L; - } - return [R[5], vtol(V)]; -} - -def cutgrs(A) -{ - for(AL=[] ; A!=[]; A=cdr(A)){ /* AT: level 2 */ - for(ALT=[], AT=car(A); AT!=[]; AT=cdr(AT)){ - M = (type(car(AT)) < 4)?car(AT):car(AT)[0]; - if(M > 0) - ALT = cons(car(AT), ALT); /* ALT: level 2 */ - } - AL = cons(reverse(ALT), AL); /* AL: level 3 */ - } - return reverse(AL); -} - -def mcgrs(G, R) -{ - NP = length(G); - Mat = (getopt(mat)==1)?0:1; - for(R = reverse(R) ; R != []; R = cdr(R)){ - GN = []; - L = length(G)-1; - RT = car(R); - if(type(RT) == 4){ - RT = reverse(RT); S = 0; - for(G = reverse(G); G != []; G = cdr(G), L--){ - AD = car(RT); RT = cdr(RT); - if(L > 0) - S += AD; - else - AD = -S; - for(GTN = [], GT = reverse(car(G)); GT != []; GT = cdr(GT)) - GTN = cons([car(GT)[0],car(GT)[1]+AD], GTN); - GN = cons(GTN, GN); - } - G = GN; - continue; - } - VP = newvect(L+1); GV = ltov(G); - for(I = S = OD = 0; I <= L; I++){ - RTT = (I==0)?(Mat-RT):0; - VP[I] = -1; - for(J = M = 0, GT = GV[I]; GT != []; GT = cdr(GT), J++){ - if(I == 0) - OD += car(GT)[0]; - if(car(GT)[1] == RTT && car(GT)[0] > M){ - S += car(GT)[0]-M; - VP[I] = J; - } - } - S -= (L-1)*OD; - for(GN = [] ; L >= 0; L--){ - GT = GV[L]; - RTT = (L==0)?(-RT):RT; - FTN = (VP[L] >= 0 || S == 0)?[]:[-S,(L==0)?(Mat-RT):0]; - for(J = 0; GT != []; GT = cdr(GT), J++){ - if(J != VP[L]){ - GTN = cons([car(GT)[0],car(GT)[1]+RTT], GTN); - continue; - } - K = car(GT)[0] - S; - if(K < 0){ - print("Not realizable"); - return; - } - GTN = cons([K,(L==0)?(Mat-RT):0], GTN); - } - GN = cons(reverse(GTN), GN); - } - } - G = cutgrs(GN); - } - return G; -} - -/* - F=0 : unify - F=["add",S] : - F=["sub",S] : - F=["+",A,B] : - F=["*",A,B] : - F=["mul",K]; - F=["get",F,V] : - F=["put",F,V] : - F=["get1",F,V] : - F=["put1",F,V] : - F=["put1"] : - F=["val",F]; - F=["swap"]; - */ -def anal2sp(R,F) -{ - if(type(F)==4&&type(F[0])==4){ /* multiple commands */ - for(;F!=[];F=cdr(F)) R=anal2sp(R,car(F)); - return R; - } - if(type(F)==7) F=[F]; - if(F==0){ /* unify */ - R=ltov(R); - L=length(R); - for(J=1;J<L;J++){ - for(I=0;I<J;I++){ - if(cdr(R[I])==cdr(R[J])){ - R[I]=cons(R[I][0]+R[J][0],cdr(R[I])); - R[J]=cons(0,cdr(R[J])); - break; - } - } - } - for(G=[],I=L-1;I>=0;I--) - if(R[I][0]!=0) G=cons(R[I],G); - if(length(G[0])==2){ /* sort by multiplicity */ - R=ltov(G); - L=length(R); - for(I=1;I<L;I++){ - for(J=I;J>0;J--){ - if(R[J-1][0]>R[J][0]) break; - if(R[J-1][0]==R[J][0]){ - S1=rtostr(R[J-1][1]);S2=rtostr(R[J][1]); - if((K=str_len(S1)-str_len(S2))<0) break; - if(!K&&S1<S2) break; - } - S=R[J-1];R[J-1]=R[J];R[J]=S; - } - } - G=vtol(R); - } - return G; - } - if(F[0]=="add") return append(R,F[1]); - R=reverse(R); - if(F[0]=="sub"){ - for(S=F[1];S!=[];S=cdr(S)) - R=cons(cons(-car(S)[0],cdr(car(S))),R); - return reverse(R); - } - if(F[0]=="swap"){ - for(G=[];R!=[];R=cdr(R)) - G=cons([car(R)[0],car(R)[2],car(R)[1]],G); - return G; - } - if(F[0]=="+"){ - for(G=[];R!=[];R=cdr(R)) - G=cons([car(R)[0],car(R)[1]+F[1],car(R)[2]+F[2]],G); - return G; - } - if(F[0]=="*"){ - for(G=[];R!=[];R=cdr(R)) - G=cons([car(R)[0],car(R)[1]*F[1]+car(R)[2]*F[2]],G); - return G; - } - if(F[0]=="mult"){ - K=F[1]; - for(G=[];R!=[];R=cdr(R)) G=cons(cons(K*car(R)[0],cdr(car(R))),G); - return G; - } - if(F[0]=="get"){ - for(G=[];R!=[];R=cdr(R)) - if(car(R)[F[1]]==F[2]) G=cons(car(R),G); - return G; - } - if(F[0]=="put"){ - if(F[1]==1){ - for(G=[];R!=[];R=cdr(R)) G=cons([car(R)[0],F[2],car(R)[2]],G); - }else{ - for(G=[];R!=[];R=cdr(R)) G=cons([car(R)[0],car(R)[1],F[2]],G); - } - return G; - } - if(F[0]=="get1"){ - if(length(F)==2){ - for(G=[];R!=[];R=cdr(R)) G=cons([R[0][0],car(R)[F[1]]],G); - return G; - } - for(G=[];R!=[];R=cdr(R)) - if(car(R)[F[1]]==F[2]) G=cons([R[0][0],car(R)[3-F[1]]],G); - return G; - } - if(F[0]=="put1"){ - if(length(F)==1) - for(G=[];R!=[];R=cdr(R)) G=cons([car(R)[0],car(R)[1],car(R)[1]],G); - else if(F[1]==1) - for(G=[];R!=[];R=cdr(R)) G=cons([car(R)[0],F[2],car(R)[1]],G); - else{ - for(G=[];R!=[];R=cdr(R)) G=cons([car(R)[0],car(R)[1],F[2]],G); - } - return G; - } - if(F[0]=="val"){ - V=(length(F)==1)?1:F[1]; - for(I=J=0;R!=[];R=cdr(R)){ - I+=car(R)[0]; - J+=car(R)[0]*car(R)[V]; - } - return [I,J]; - } - return 0; -} - -/* - G=0 get trivial common spct - G="..,..," spectre type of 4 singular points - P=["get"] all spct - P=["get",L] - L=n for variable x_n - L=[m,n] for residue [m,n] - L=[[m,n],[m',n']] for common spct - P=["get0",[m,n],[m',n']] for the sum of residues - P=["swap",[m,n]] for symmetry - P=["perm",[...]] for symmetry - P=["deg"] - P=["homog"] - P=["sort"] - P=[[[m,n],c],...] for addition - P=[c] or [[c],...] for middle convolution wrt 0 - P=[m,c] or [[m,c],...] for general middle convolution - P=[[a,b,c]] for special additions - P=[[d,a,b,c]] for middle convotution and additions - P=["multi",...] multiple commands - P=0,1,3 : return sim. spectre of 4 singular points -*/ -def mc2grs(G,P) -{ - if(G==0){ - G=[]; - for(I=4;I>=0;I--){ - V=lsort([0,1,2,3,4],[I],1); - for(J=1;J<4;J++){ - for(T=[],K=3;K>0;K--) - if(K!=J) T=cons(V[K],T); - G=cons([[[V[0],V[J]],T],[1,0,0]],G); - } - } - G=mc2grs(G,"sort"); - }else if(type(G)==7||(type(G)==4&&length(G)==4)){ - if(type(G)==7) G=s2sp(G); - F=(getopt(top)==0)?1:0; - K=[]; - if(type(P)==1&&iand(P,1)&&type(G[0][0])<4){ - G=s2sp(G|std=1); - if(F) G=[G[1],G[2],G[3],G[0]]; - G=sp2grs(G,[d,c,b,a],[1,length(G[0]),-1]|mat=1); - G=reverse(G); - if(iand(P,3)==3){ - V=vars(G); - for(H=L=[a,b,c,d];H!=[];H=cdr(H)) - if(findin(car(H),V)>=0) G=subst(G,car(H),makev([car(H),1])); - G=shortv(G,[a,b,c,d]); - V=vars(G); - for(H=G[3];H!=[];H=cdr(H)){ - T=car(H)[1]; - if(type(T)>1&&!isvar(T)){ - K=[car(H)[0],T]; - break; - } - } - } - F=1; - } - if(F) G=[G[3],G[0],G[1],G[2]]; - S=cons(["anal",1],getopt()); - if(!(R=m2mc(G,0|option_list=S))) return R; - for(G=0,R=cdr(R);R!=[];R=cdr(R)){ - TR=car(R)[0]; - if(TR[0]) G=mc2grs(G,[[TR[0]]]); - G=mc2grs(G,[cdr(TR)]); - } - if(type(P)==1&&K!=[]){ - for(T=10;T<36;T++){ - if(findin(X=makev([T]),V)>=0) continue; - F=K[0]*(X-K[1]); - return [F,simplify(G,[F],4)]; - } - } - } - if(type(P)<2) return G; - F=0; - if(type(P)==7||(type(P)==4&&type(P[0])<4)) P=[P]; - if((Dvi=getopt(dviout))!=1&&Dvi!=2&&Dvi!=-1) Dvi=0; - Keep=(Dvi==2)?1:0; - if(type(P)==4&&type(F=car(P))==7){ - if(F=="mult"){ - for(P=cdr(P);P!=[];P=cdr(P)) G=mc2grs(G,car(P)|option_list=getopt()); - return G; - } - if(F=="show"){ - for(R=str_tb(0,0);G!=[];){ - L=car(G); - I=L[0][0];J=L[0][1]; - str_tb("[A_{"+rtostr(I[0])+rtostr(I[1])+"}:A_{"+rtostr(J[0])+rtostr(J[1]) - +"}]&=\\left\\{",R); - for(L=cdr(L);;){ - S=car(L); - str_tb("["+my_tex_form(S[1])+":"+my_tex_form(S[2])+"]",R); - if(S[0]!=1) str_tb("_{"+rtostr(S[0])+"}",R); - if((L=cdr(L))==[]) break; - str_tb(",\\,",R); - } - str_tb("\\right\\}",R); - if((G=cdr(G))==[]) break; - str_tb(",\\\\\n",R); - } - R=texbegin("align*",str_tb(0,R)); - if(Dvi!=-1) dviout(R|keep=Keep); - return R; - } - if(F=="show0"){ - for(S="",L=[];G!=[];G=cdr(G)){ - for(TL=[],TG=cdr(car(G));TG!=[];TG=cdr(TG)) TL=cons(car(TG)[0],TL); - TL=msort(TL,[-1,0]); - if(Dvi){ - if(S!="") S=S+","; - for(I=J=0,T=append(TL,[[0]]);T!=[];T=cdr(T)){ - if(car(T)==I) J++; - else{ - if(I>0&&J>0){ - if(I>9) S=S+"("+rtostr(I)+")"; - else S=S+rtostr(I); - if(J>1){ - if(J>9) S=S+"^{"+rtostr(J)+"}"; - else S=S+"^"+rtostr(J); - } - } - I=car(T);J=1; - } - } - } - L=cons(TL,L); - } - if(Dvi){ - if(Dvi!=-1) dviout(S|eq=0); - return S; - } - return reverse(L); - } - if(F=="sort"){ - G=ltov(G);L=length(G); - for(I=0;I<L;I++){ - S=G[I][0]; - if(S[0][0]>S[0][1]) S=[[S[0][1],S[0][0]],S[1]]; - if(S[1][0]>S[1][1]) S=[S[0],[S[1][1],S[1][0]]]; - if(S[0]>S[1]){ - F=0;S=[S[1],S[0]]; - } - if(S!=G[I][0]){ - if(F==0) G[I]=cons(S,anal2sp(cdr(G[I]),"swap")); - else G[I]=cons(S,cdr(G[I])); - } - for(J=I;J>0;J--){ - if(G[J-1][0]<G[J][0]) break; - S=G[J-1];G[J-1]=G[J];G[J]=S; - } - } - return vtol(G); - } - if(F=="get"||F=="get0"){ - if(Dvi!=0) F="get"; - if(length(P)==1||type(P[1])<2){ - L=[]; - if(length(P)==1){ - for(I=3;I>=0;I--){ - for(J=4;J>I;J--) L=cons(mc2grs(G,[F,[I,J]]),L); - } - }else{ - for(I=P[1],J=4;J>=0;J--){ - if(I==J) continue; - L=cons(mc2grs(G,[F,(I<J)?[I,J]:[J,I]]),L); - } - } - if(Dvi){ - if(length(L)==10){ - R=ltov(L); - if(R[6][0]==[1,4]){ - S=R[6];R[6]=R[7];R[7]=S; - L=vtol(R); - } - } - for(R=S=[],L=reverse(L);L!=[];L=cdr(L)){ - T=car(L); - R=cons(cdr(T),R); - if(S==[]) S="A_{"+rtostr(T[0][0])+rtostr(T[0][1])+"}\\\\\n"; - else S="A_{"+rtostr(T[0][0])+rtostr(T[0][1])+"}&"+S; - } - L=ltotex(R|opt="GRS",pre=S); - if(Dvi>0) dviout(L|eq=0,keep=Keep); - } - return L; /* get all spct */ - } - if(type(T=P[1])==4){ - if(F=="get0"&&length(P)==3&&type(I=P[1])==4&&type(J=P[2])==4){ - if(I[0]>I[1]) I=[I[1],I[0]]; - if(J[0]>J[1]) J=[J[1],J[0]]; - if(I[0]>I[0]){S=I;I=J;J=S;}; - K=lsort(I,J,0); - if(length(K)==4){ - S=sp2grs(G,["get0",[I,J]]); - return anal2sp(S,[["*",1,1],0]); - } - I=lsort(K,lsort(I,J,2),1); - S=lsort([0,1,2,3,4],K,1); - D=sp2grs(G,"deg"); - if(findin(4,S)<0) D=-D; - J=sp2grs(G,["get0",[I,S]]); - if(I[0]>S[0]) J=sp2grs(J,"swap"); - return anal2sp(J,[["+",0,D],["*",-1,1]]); - } - if(type(car(T))==4){ - if(T[0][0]>T[0][1]) T=[[T[0][1],T[0][0]],T[1]]; - if(T[1][0]>T[1][1]) T=[T[0],[T[1][1],T[1][0]]]; - if(T[0][0]>T[1][0]) T=[T[1],T[0]]; - for(PG=G;PG!=[];PG=cdr(PG)) - if(car(PG)[0]==T) return (F=="get")?car(PG):cdr(car(PG)); - return []; /* get common spct */ - } - if(T[0]>T[1]) T=[T[1],T[0]]; - for(FT=0,PG=G;PG!=[];PG=cdr(PG)){ - if(car(PG)[0][0]==T){ - FT=1;break; - } - if(car(PG)[0][1]==T){ - FT=2;break; - } - } - if(!FT) return []; - L=anal2sp(cdr(car(PG)),[["get1",FT],0]); - return (F=="get")?cons(T,L):L; - } - } - if(F=="deg"){ - for(S=I=0;I<3;I++){ - for(J=I+1;J<4;J++){ - L=mc2grs(G,["get0",[I,J]]); - L=anal2sp(L,"val"); - S+=L[1]; - } - } - return S/L[0]; - } - if(F=="spct"){ - G=mc2grs(G,"get"); - M=newmat(5,5); - for(;G!=[];G=cdr(G)){ - GT=car(G);I=GT[0][0];J=GT[0][1]; - for(S=0,L=[],GT=cdr(GT);GT!=[];GT=cdr(GT)){ - L=cons(car(GT)[0],L); - } - L=reverse(qsort(L)); - M[I][J]=M[J][I]=L; - } - for(D=0,GT=M[0][1];GT!=[];GT=cdr(GT)) D+=car(GT); - for(I=0;I<5;I++){ - S=-2*D^2; - for(J=0;J<5;J++){ - if(I==J) continue; - for(L=M[I][J];L!=[];L=cdr(L)) S+=car(L)^2; - } - M[I][I]=S; - } - if(Dvi){ - S=[]; - for(I=4;I>=0;I--){ - L=[M[I][I]]; - for(J=4;J>=0;J--){ - if(I==J) L=cons("",L); - else L=cons(s2sp([M[I][J]]),L); - } - S=cons(L,S); - } - S=cons([x0,x1,x2,x3,x4,"idx"],S); - M=ltotex(S|opt="tab",hline=[0,1,z],vline=[0,1,z-1,z],left=["","$x_0$","$x_1$","$x_2$","$x_3$","$x_4$"]); - if(Dvi>0) dviout(M|keep=Keep); - } - return M; - } - if(F=="swap"||F=="perm"){ - if(F=="perm") TR=P[1]; - else{ - TR=newvect(5,[0,1,2,3,4]); - K=P[1][0];L=P[1][1]; - TR[K]=L;TR[L]=K; - if(TR[4]!=4) G=mc2grs(G,"deg"); - } - V=newvect(2); - for(L=[],T=G;T!=[];T=cdr(T)){ - TP=car(T)[0]; - for(TQ=[],I=1;I>=0;I--){ - V=[TR[TP[I][0]],TR[TP[I][1]]]; - if(V[0]>V[1]) V=[V[1],V[0]]; - TQ=cons(V,TQ); - } - if(TQ[0][0]<TQ[1][0]){ - L=cons(cons(TQ,cdr(car(T))),L); - continue; - } - TQ=[[TQ[1],TQ[0]]]; - for(TP=cdr(car(T));TP!=[];TP=cdr(TP)) - TQ=cons([car(TP)[0],car(TP)[2],car(TP)[1]],TQ); - L=cons(reverse(TQ),L); - } - return mc2grs(L,"sort"); - } - if(F=="homog"){ - V=mc2grs(G,"deg"); - return mc2grs(G,[[[2,3],-V]]); - }else if(F=="deg"){ - R=mc2grs(G,4); - for(V=0;R!=[];R++){ - for(TR=cdr(R);TR!=[];TR=cdr(TR)) - V+=car(TR)[0]*car(TR)[1]; - } - return -V; - } - } - if(type(F)!=4) return 0; - if(type(P[0])!=4) P=[P]; - for(;P!=[];P=cdr(P)){ - if(type((S=P[0])[0])==4){ /* addition */ - T=P[0][0]; - if(T[0]>T[1]) T=[T[1],T[0]]; - T1=[T[0],4];T2=[T[1],4]; - for(L=[],PG=reverse(G);PG!=[];PG=cdr(PG)){ - R=car(PG);R0=R[0];F=0;K=P[0][1]; - if(R0[0]==T) F=1; - else if(R0[1]==T) F=2; - else if(getopt(unique)!=1){ - K=-K; - if(R0[0]==T1||R0[0]==T2) F=1; - else if(R0[1]==T1||R0[1]==T2) F=2; - } - if(F==0) L=cons(R,L); - else{ - R1=anal2sp(cdr(R),(F==1)?["+",K,0]:["+",0,K]); - L=cons(cons(R0,R1),L); - } - } - G=L; - }else if(type(S[0])<4){ - if(length(S)==1){ /* mc wrt0 4:cases */ - U=mc2grs(G,"deg"); - C=P[0][0]; - L=[]; - /* [[0,1],[2,3]] : [K=[0,k],J=[i,j]], S=[k,4] : 3 cases */ - for(K=1;K<4;K++){ - J=lsort([1,2,3],[K],1); - K4=[K,4];K0=[0,K]; - G0=mc2grs(G,["get0",[K0,J]]); - LT=anal2sp(G0,["+",C,0]); - G0=mc2grs(G,["get0",J]); - L0=anal2sp(G0,["put1",1,0]); - LT=anal2sp(LT,["add",L0]); - G0=mc2grs(G,["get0",K4]); - L0=anal2sp(G0,[["put1",1,0],["+",0,U]]); - LT=anal2sp(LT,["add",L0]); - G0=mc2grs(G,["get0",[[0,J[0]],K4]]); - L0=anal2sp(G0,[["get",1,0],["+",0,U]]); - LT=anal2sp(LT,["sub",L0]); - G0=mc2grs(G,["get0",[[0,J[1]],K4]]); - L0=anal2sp(G0,[["get",1,0],["+",0,U]]); - LT=anal2sp(LT,["sub",L0]); - G0=mc2grs(G,["get0",[K0,J]]); - L0=anal2sp(G0,[["get",1,0],["+",C,0]]); - LT=anal2sp(LT,["sub",L0]); - G0=mc2grs(G,["get0",[[0,4],J]]); - L0=anal2sp(G0,[["+",-C,0],["get",1,0]]); - LT=anal2sp(LT,[["sub",L0],0]); - L=cons(cons([K0,J],LT),L); - } - /* [[0,1],[2,4]] : [K,I]=[[0,k],[i,4]] S=[j,k] : 6 cases */ - for(K=1;K<4;K++){ - for(I=1;I<4;I++){ - if(I==K) continue; - for(J=1;J<4;J++) if(J!=I&&J!=K) break; - I4=[I,4];S=(J<K)?[J,K]:[K,J];K0=[0,K]; - G0=cdr(mc2grs(G,["get",[K0,I4]])); - LT=anal2sp(G0,["+",C,0]); - G0=cdr(mc2grs(G,["get",I4])); - L0=anal2sp(G0,["put1",1,0]); - LT=anal2sp(LT,["add",L0]); - G0=cdr(mc2grs(G,["get",S])); - L0=anal2sp(G0,[["put1",1,0],["+",0,-C-U]]); - LT=anal2sp(LT,["add",L0]); - - G0=cdr(mc2grs(G,["get",[[0,I],S]])); - L0=anal2sp(G0,[["get",1,0],["+",0,-C-U]]); - LT=anal2sp(LT,["sub",L0]); - G0=cdr(mc2grs(G,["get",[[0,J],I4]])); - L0=anal2sp(G0,["get",1,0]); - LT=anal2sp(LT,["sub",L0]); - G0=cdr(mc2grs(G,["get",[K0,I4]])); - L0=anal2sp(G0,[["get",1,0],["+",C,0]]); - LT=anal2sp(LT,["sub",L0]); - G0=cdr(mc2grs(G,["get",[[0,4],S]])); - L0=anal2sp(G0,[["get",1,C],["+",-C,-C-U]]); - LT=anal2sp(LT,[["sub",L0],0]); - L=cons(cons([K0,I4],LT),L); - } - } - /* [[0,4],[2,3]] : [[0,4],J]=[[0,4],[i,j]] 3 cases */ - for(K=3;K>0;K--){ - J=lsort([1,2,3],[K],1); - G0=mc2grs(G,["get0",[[0,4],J]]); - LT=anal2sp(G0,["+",-C,0]); - G0=mc2grs(G,["get0",J]); - L0=anal2sp(G0,["put1",1,-C]); - LT=anal2sp(LT,["add",L0]); - G0=mc2grs(G,["get0",[K,4]]); - L0=anal2sp(G0,[["put1",1,-C],["+",0,U]]); - LT=anal2sp(LT,["add",L0]); - - G0=mc2grs(G,["get0",[[0,J[0]],[K,4]]]); - L0=anal2sp(G0,[["get",1,0],["+",-C,U]]); - LT=anal2sp(LT,["sub",L0]); - G0=mc2grs(G,["get0",[[0,J[1]],[K,4]]]); - L0=anal2sp(G0,[["get",1,0],["+",-C,U]]); - LT=anal2sp(LT,["sub",L0]); - G0=mc2grs(G,["get0",[[0,K],J]]); - L0=anal2sp(G0,[["get",1,0],["+",-C,0]]); - LT=anal2sp(LT,["sub",L0]); - G0=mc2grs(G,["get0",[[0,4],J]]); - L0=anal2sp(G0,[["get",1,C],["put",1,0]]); - LT=anal2sp(LT,[["sub",L0],0]); - L=cons(cons([[0,4],J],LT),L); - } - /* [[1,2],[3,4]] : [J,K]=[[i,j],[k,4]] 3 cases */ - for(K=3;K>0;K--){ - J=lsort([1,2,3],[K],1); - if(K>1) - LT=mc2grs(G,["get0",[J,[K,4]]]); - else{ - LT=mc2grs(G,["get0",[[K,4],J]]); - LT=anal2sp(LT,"swap"); - } - G0=mc2grs(G,["get0",J]); - L0=anal2sp(G0,[["put1"],["+",0,-C-U]]); - LT=anal2sp(LT,["add",L0]); - G0=mc2grs(G,["get0",[K,4]]); - L0=anal2sp(G0,[["put1"],["+",U,0]]); - LT=anal2sp(LT,["add",L0]); - - G0=mc2grs(G,["get0",[[0,J[0]],[K,4]]]); - L0=anal2sp(G0,[["get1",1,0],["put1"],["+",U,0]]); - LT=anal2sp(LT,["sub",L0]); - G0=mc2grs(G,["get0",[[0,J[1]],[K,4]]]); - L0=anal2sp(G0,[["get1",1,0],["put1"],["+",U,0]]); - LT=anal2sp(LT,["sub",L0]); - G0=mc2grs(G,["get0",[[0,K],J]]); - L0=anal2sp(G0,[["get1",1,0],["put1"],["+",0,-C-U]]); - LT=anal2sp(LT,["sub",L0]); - G0=mc2grs(G,["get0",[[0,4],J]]); - L0=anal2sp(G0,[["get1",1,C],["put1"],["+",0,-C-U]]); - LT=anal2sp(LT,[["sub",L0],0]); - if(K==1){ - LT=anal2sp(LT,"swap"); - L=cons(cons([[K,4],J],LT),L); - }else L=cons(cons([J,[K,4]],LT),L); - } - G=L; - }else if(length(S)==2){ /* general mc */ - if(S[1]!=0){ - I=S[0]; - if(I!=0) G=mc2grs(G,["swap",[0,I]]); - G=mc2grs(G,[S[1]]); - if(I!=0) G=mc2grs(G,["swap",[0,I]]); - } - }else if(length(S)==3||length(S)==4){ /* addition */ - for(I=1;I<4;I++,S=cdr(S)) - if(S[0]) G=mc2grs(G,[[[0,I],S[0]]]); - if(length(S)==1 && S[0]) /* mc */ - G=mc2grs(G,[S[0]]); - } - } - } - return mc2grs(G,"sort"); -} - -def mcmgrs(G,P) -{ - if(type(G)<2){ - if(G>1){ - N=G+2;G=[]; - for(I=1;I<=N;I++){ - for(J=1;J<N;J++){ - if(I==J) continue; - for(K=J+1;K<=N;K++){ - if(I==K) continue; - G=cons([[[0,I],[J,K]],[1,0,0]],G); - } - } - } - for(I=1;I<=N;I++){ - for(J=1;J<I;J++) G=cons([[[0,I],[0,J,I]],[1,0,0]],G); - for(J=I+1;J<=N;J++) G=cons([[[0,I],[0,I,J]],[1,0,0]],G); - } - return reverse(G); - } - return 0; - } - if(type(G)==7) G=os_md.s2sp(G); - if(type(G)!=4||type(G[0])!=4) return 0; - if(type(G[0][0])!=4){ /* spectre type -> GRS */ - G=s2sp(G|std=1); - L=length(G); - for(V=[],I=L-2;I>=0;I--) V=cons(makev([I+10]),V); - V=cons(makev([L+9]),V); - G=sp2grs(G,V,[1,length(G[0]),-1]|mat=1); - if(getopt(short)!=0){ - V=append(cdr(V),[V[0]]); - G=shortv(G,V); - } - R=chkspt(G|mat=1); - if(R[2] != 2 || R[3] != 0 || !(R=getbygrs(G,1|mat=1))) return 0; - if(getopt(anal)==1) return R; /* called by mcmgrs() */ - if(!(G=mcmgrs(L-2,0))) return 0; - for(R=cdr(R);R!=[];R=cdr(R)){ - TR=car(R)[0]; - if(TR[0]) G=mcmgrs(G,[[TR[0]]]); - G=mcmgrs(G,[cdr(TR)]); - } - } - L=length(G); - for(N=4;N<25;N++){ - K=N^2*(N-1)/2; - if(K>L) return 0; - if(K==L) break; - } - if(type(P)<2) return G; - F=0; - if(type(P)==7||(type(P)==4&&type(P[0])<4)) P=[P]; - if((Dvi=getopt(dviout))!=1&&Dvi!=2&&Dvi!=-1) Dvi=0; - Keep=(Dvi==2)?1:0; - if(type(P)==4 && type(F=car(P))==7){ - if(F=="mult"){ - for(P=cdr(P);P!=[];P=cdr(P)) G=os_md.mc2grs(G,car(P)|option_list=getopt()); - return G; - } - if(F=="get"||F=="get0"){ - if(Dvi!=0) F="get"; - if(length(P)==2){ - if(type(P[1])==4){ - if(type(P[1][1])==4){ /* [[,],[,]] */ - for(PG=reverse(G);PG!=[];PG=cdr(PG)){ - TP=car(PG); - if(TP[0]==P[1]) return (F=="get")?TP:cdr(TP); - } - return []; - } - if(P[1][0]==0){ - if(length(P[1])==2){ /* [0,] */ - for(J=1;J<=N;J++) if(J!=P[1][1]) break; - for(K=J+1;K<=N;K++) if(K!=P[1][1]) break; - L=mcmgrs(G,["get0",[P[1],[J,K]]]); - L=anal2sp(L,["get1",1]); - }else{ /* [0,*,*] */ - L=mcmgrs(G,["get0",[[P[1][0],P[1][1]],P[1]]]); - L=anal2sp(L,["get1",2]); - } - }else{ /* [,] */ - for(J=1;J<=N;J++) if(J!=P[1][0]&&J!=P[1][1]) break; - L=mcmgrs(G,["get0",[[0,J],P[1]]]); - L=anal2sp(L,["get1",2]); - } - L=anal2sp(L,0); - if(F=="get") L=cons(P[1],L); - return L; - }else{ /* I */ - for(L=[],I=P[1],J=0;J<=N;J++){ - if(I==J) continue; - II=(I<J)?[I,J]:[J,I]; - L=cons(mcmgrs(G,[F,II]),L); - } - } - }else{ - for(L=[],I=0;I<N;I++){ - for(J=I+1;J<=N;J++) L=cons(mcmgrs(G,[F,[I,J]]),L); - } - } - if(Dvi){ - for(R=S=[];L!=[];L=cdr(L)){ - T=car(L); - R=cons(cdr(T),R); - if(S==[]) S="A_{"+rtostr(T[0][0])+rtostr(T[0][1])+"}\\\\\n"; - else S="A_{"+rtostr(T[0][0])+rtostr(T[0][1])+"}&"+S; - } - L=ltotex(R|opt="GRS",pre=S); - if(type(V=getopt(div))!=4) V=[]; - if(V==[]&&(K=length(R))>10) - for(I=9;I<K;I+=9) V=cons(I,V); - V=reverse(V); - if(V!=[]) L=divmattex(L,V); - if(Dvi>0){ - if(V!=[]) dviout(L|keep=Keep); - else dviout(L|eq=0,keep=Keep); - } - }else L=reverse(L); - return L; - } - if(F=="show"){ - for(R=str_tb(0,0);G!=[];){ - L=car(G); - I=L[0][0];J=L[0][1]; - str_tb("[A_{"+rtostr(I[0])+rtostr(I[1])+"}:A_{"+rtostr(J[0])+rtostr(J[1]),R); - if(length(J)==3) str_tb(rtostr(J[2]),R); - str_tb("}]&=\\left\\{",R); - for(L=cdr(L);;){ - S=car(L); - str_tb("["+my_tex_form(S[1])+":"+my_tex_form(S[2])+"]",R); - if(S[0]!=1) str_tb("_{"+rtostr(S[0])+"}",R); - if((L=cdr(L))==[]) break; - str_tb(",\\,",R); - } - str_tb("\\right\\}",R); - if((G=cdr(G))==[]) break; - str_tb(texcr(43),R); - } - R=texbegin("align*",str_tb(0,R)); - if(Dvi!=-1) dviout(R|keep=Keep); - return R; - } - if(F=="show0"){ - for(C=N*(N-1)*(N-2)/2,S="",L=[];G!=[];G=cdr(G)){ - for(TL=[],TG=cdr(car(G));TG!=[];TG=cdr(TG)) TL=cons(car(TG)[0],TL); - TL=msort(TL,[-1,0]); - if(Dvi){ - if(S!=""){ - if(--C==0) S=S+";"; - else S=S+","; - } - for(I=J=0,T=append(TL,[[0]]);T!=[];T=cdr(T)){ - if(car(T)==I) J++; - else{ - if(I>0&&J>0){ - if(I>9) S=S+"("+rtostr(I)+")"; - else S=S+rtostr(I); - if(J>1){ - if(J>9) S=S+"^{"+rtostr(J)+"}"; - else S=S+"^"+rtostr(J); - } - } - I=car(T);J=1; - } - } - } - L=cons(TL,L); - } - if(Dvi){ - if(Dvi!=-1) dviout(S|eq=0); - return S; - } - return reverse(L); - } - if(F=="spct"){ - G=mcmgrs(G,"get"); - M=newmat(N+1,N+1); - for(;G!=[];G=cdr(G)){ - GT=car(G);I=GT[0][0];J=GT[0][1]; - for(S=0,L=[],GT=cdr(GT);GT!=[];GT=cdr(GT)){ - L=cons(car(GT)[0],L); - } - L=reverse(qsort(L)); - M[I][J]=M[J][I]=L; - } - for(D=0,GT=M[0][1];GT!=[];GT=cdr(GT)) D+=car(GT); - for(I=0;I<=N;I++){ - S=-(N-2)*D^2; - for(J=0;J<=N;J++){ - if(I==J) continue; - for(L=M[I][J];L!=[];L=cdr(L)) S+=car(L)^2; - } - M[I][I]=S; - } - if(Dvi){ - S=[]; - for(LS=[],I=N;I>=0;I--){ - L=[M[I][I]]; - for(J=N;J>=0;J--){ - if(I==J) L=cons("",L); - else L=cons(s2sp([M[I][J]]),L); - } - S=cons(L,S); - LS=cons("$x_"+rtostr(I)+"$",LS); - } - S=cons(append(LS,["idx"]),S); - M=ltotex(S|opt="tab",hline=[0,1,z],vline=[0,1,z-1,z],left=cons("",LS)); - if(Dvi>0) dviout(M|keep=Keep); - } - return M; - } - if(F=="deg"){ - for(S=I=0;I<N-1;I++){ - for(J=I+1;J<N;J++){ - L=mcmgrs(G,["get0",[I,J]]); - L=anal2sp(L,"val"); - S+=L[1]; - } - } - return S/L[0]; - } - } - L=[]; - if(type(F)!=4) return 0; - if(type(P[0])!=4||length(P[0])==2) P=[P]; - for(;P!=[];P=cdr(P)){ - if(type(T=(S=car(P))[0])==4){ /* addition */ - if((K=P[0][1])!=0){ - if(T[0]>T[1]) T=[T[1],T[0]]; - T1=[T[0],N];T2=[T[1],N]; - T01=cons(0,T1);T02=cons(0,T2); - for(PG=G;PG!=[];PG=cdr(PG)){ - R=car(PG);R0=R[0];K1=K2=0; - TP=R0[0]; - if(TP==T) K1=K; - else if(TP==T1||TP==T2) K1=-K; - if(length(TP=R0[1])==2){ - if(TP==T) K2=K; - else if(TP==T1||TP==T2) K2=-K; - }else{ - S=0; - if(findin(T[0],TP)>=0) S++; - if(findin(T[1],TP)>=0) S++; - if(S>0&&TP[2]==N) K2=-K; - else if(S==2) K2=K; - } - R1=anal2sp(cdr(R),["+",K1,K2]); - L=cons(cons(R0,R1),L); - } - G=reverse(L); - } - }else if(length(S)==1){ /* middle convolution */ - C=S[0];L=[]; - for(I=1;I<=N;I++){ - for(J=1;J<=N;J++){ - if(I==J) continue; - for(K=J+1;K<=N;K++){ /* [[0,I],[J,K]] */ - if(I==K)continue; - T=[[0,I],JK=[J,K]]; - if(I==N){ - LT=mcmgrs(G,["get0",T]); - G0=mcmgrs(G,["get0",JK]); - L0=anal2sp(G0,[["put1",1,0],["mult",N-3]]); - G0=mcmgrs(G,["get0",[0,J,K]]); - LT=anal2sp(LT,["add",L0]); - L0=anal2sp(G0,["put1",1,0]); - LT=anal2sp(LT,["add",L0]); - for(V=1;V<=N;V++){ - if(V==I){ - G0=mcmgrs(G,["get0",T]); - L0=anal2sp(G0,["get",1,C]); - }else if(V==J||V==K){ - G0=mcmgrs(G,["get0",[[0,V],[0,J,K]]]); - L0=anal2sp(G0,["get",1,0]); - }else{ - G0=mcmgrs(G,["get0",[[0,V],JK]]); - L0=anal2sp(G0,["get",1,0]); - } - LT=anal2sp(LT,["sub",L0]); - } - LT=anal2sp(LT,["+",-C,0]); - }else if(K==N){ - LT=mcmgrs(G,["get0",T]); - LT=anal2sp(LT,["+",C,0]); - G0=mcmgrs(G,["get0",JK]); - L0=anal2sp(G0,[["put1",1,0],["mult",N-3]]); - LT=anal2sp(LT,["add",L0]); - G0=mcmgrs(G,["get0",[0,J,K]]); - L0=anal2sp(G0,[["put1",1,0],["+",0,-C]]); - LT=anal2sp(LT,["add",L0]); - for(V=1;V<=N;V++){ - if(V==I){ - G0=mcmgrs(G,["get0",T]); - L0=anal2sp(G0,[["get",1,0],["+",C,0]]); - }else if(V==J){ - G0=mcmgrs(G,["get0",[[0,V],[0,J,K]]]); - L0=anal2sp(G0,[["get",1,0],["+",0,-C]]); - }else if(V==N){ - G0=mcmgrs(G,["get0",[[0,V],[0,J,K]]]); - L0=anal2sp(G0,[["get",1,C],["+",-C,-C]]); - }else{ - G0=mcmgrs(G,["get0",[[0,V],JK]]); - L0=anal2sp(G0,["get",1,0]); - } - LT=anal2sp(LT,["sub",L0]); - } - }else{ - G0=mcmgrs(G,["get0",T]); - LT=anal2sp(G0,["+",C,0]); - G0=mcmgrs(G,["get0",JK]); - L0=anal2sp(G0,[["put1",1,0],["mult",N-3]]); - LT=anal2sp(LT,["add",L0]); - G0=mcmgrs(G,["get0",[0,J,K]]); - L0=anal2sp(G0,["put1",1,0]); - LT=anal2sp(LT,["add",L0]); - for(V=1;V<=N;V++){ - if(V==I){ - G0=mcmgrs(G,["get0",T]); - L0=anal2sp(G0,[["get",1,0],["+",C,0]]); - }else if(V==J||V==K){ - G0=mcmgrs(G,["get0",[[0,V],[0,J,K]]]); - L0=anal2sp(G0,["get",1,0]); - }else if(V==N){ - G0=mcmgrs(G,["get0",[[0,V],JK]]); - L0=anal2sp(G0,[["get",1,C],["+",-C,0]]); - }else{ - G0=mcmgrs(G,["get0",[[0,V],JK]]); - L0=anal2sp(G0,["get",1,0]); - } - LT=anal2sp(LT,["sub",L0]); - } - } - LT=anal2sp(LT,0); - L=cons(cons(T,LT),L); - } - T=[[0,I],(I<J)?[0,I,J]:[0,J,I]]; /* [0,I], [0,I,J] */ - JK=(I<J)?[I,J]:[J,I]; - if(I==N){ - G0=mcmgrs(G,["get0",T]); - LT=anal2sp(G0,["+",-C,0]); - G0=mcmgrs(G,["get0",JK]); - L0=anal2sp(G0,[["put1",1,-C],["mult",N-3]]); - LT=anal2sp(LT,["add",L0]); - G0=mcmgrs(G,["get0",T[1]]); - L0=anal2sp(G0,["put1",1,-C]); - LT=anal2sp(LT,["add",L0]); - for(V=1;V<=N;V++){ - if(V==J){ - G0=mcmgrs(G,["get0",T]); - L0=anal2sp(G0,[["get",1,0],["+",-C,0]]); - }else if(V==N){ - G0=mcmgrs(G,["get0",[[0,V],T[1]]]); - L0=anal2sp(G0,[["get",1,C],["+",-C,0]]); - }else{ - G0=mcmgrs(G,["get0",[[0,V],JK]]); - L0=anal2sp(G0,[["get",1,0],["+",-C,0]]); - } - LT=anal2sp(LT,["sub",L0]); - } - LT=anal2sp(LT,["+",0,C]); - }else if(J==N){ - G0=mcmgrs(G,["get0",T]); - LT=anal2sp(G0,["+",C,0]); - G0=mcmgrs(G,["get0",T[0]]); - L0=anal2sp(G0,[["put1",1,0],["mult",N-3]]); - LT=anal2sp(LT,["add",L0]); - G0=mcmgrs(G,["get0",T[1]]); - L0=anal2sp(G0,["put1",1,0]); - LT=anal2sp(LT,["add",L0]); - for(V=1;V<=N;V++){ - if(V==I){ - G0=mcmgrs(G,["get0",T]); - L0=anal2sp(G0,[["get",1,0],["+",C,0]]); - }else if(V==N){ - G0=mcmgrs(G,["get0",[[0,V],T[1]]]); - L0=anal2sp(G0,[["get",1,C],["+",-C,0]]); - }else{ - G0=mcmgrs(G,["get0",[[0,V],JK]]); - L0=anal2sp(G0,["get",1,0]); - } - LT=anal2sp(LT,["sub",L0]); - } - LT=anal2sp(LT,["+",0,-C]); - }else{ - G0=mcmgrs(G,["get0",T]); - LT=anal2sp(G0,["+",C,C]); - G0=mcmgrs(G,["get0",JK]); - L0=anal2sp(G0,[["put1",1,0],["mult",N-3]]); - LT=anal2sp(LT,["add",L0]); - G0=mcmgrs(G,["get0",T[1]]); - L0=anal2sp(G0,[["put1",1,0],["+",0,C]]); - LT=anal2sp(LT,["add",L0]); - for(V=1;V<=N;V++){ - if(V==I){ - G0=mcmgrs(G,["get0",T]); - L0=anal2sp(G0,[["get",1,0],["+",C,C]]); - }else if(V==J){ - G0=mcmgrs(G,["get0",[[0,V],T[1]]]); - L0=anal2sp(G0,[["get",1,0],["+",0,C]]); - }else if(V==N){ - G0=mcmgrs(G,["get0",[[0,V],JK]]); L0=anal2sp(G0,[["get",1,C],["+",-C,0]]); - }else{ - G0=mcmgrs(G,["get0",[[0,V],JK]]); - L0=anal2sp(G0,["get",1,0]); - } - LT=anal2sp(LT,["sub",L0]); - } - } - LT=anal2sp(LT,0); - L=cons(cons(T,LT),L); - } - } - for(G0=G=[];L!=[];L=cdr(L)){ - if(length(car(L)[0][1])==2) G0=cons(car(L),G0); - else G=cons(car(L),G); - } - G=append(G0,G); - }else{ - if(length(S)==N-1||length(S)==N){ /* [a_1,...,a_{N-1},c] */ - for(I=1;I<N;S=cdr(S),I++) G=mcmgrs(G,[[0,I],car(S)]); - if(length(S)==1) G=mcmgrs(G,[S[0]]); - }else return 0; - } - } - return G; -} - - -def delopt(L,S) -{ - if((Inv=getopt(inv))!=1) Inv=0; - for(R=[];L!=[];L=cdr(L)){ - if(type(car(L))!=4) F=0; - else if(type(S)==4) F=(findin(car(L)[0],S)<0)?0:1; - else F=(car(L)[0]==S)?1:0; - if(F==Inv) R=cons(car(L),R); - } - return reverse(R); -} - -def str_char(S,N,L) -{ - if(type(S)==7){ - if(type(L)==1) L=asciitostr([L]); - return str_chr(S,N,L); - } - if(type(L)==7) L=strtoascii(L)[0]; - if(type(S)==4){ - M=N; - while(M-->0) S=cdr(S); - M=findin(L,S); - return (M>=0)?findin(L,S)+N:-1; - }else if(type(S)==5){ - K=length(S); - for(I=N;I<K;I++) - if(S[I]==L) return I; - } - return -1; -} - -def str_pair(S,N,I,J) -{ - if(type(I)==7) I=(II=strtoascii(I))[0]; - if(type(J)==7) J=(JJ=strtoascii(J))[0]; - if(type(S)==7) S=strtoascii(S); - if(getopt(inv)==1){ - if(II!=0){ - I=asciitostr(reverse(II)); - IL=length(II); - }else IL=1; - if(JJ!=0) J=asciitostr(reverse(JJ)); - R=str_pair(reverse(S),length(S)-N-1,J,I); - if(R>=0) R=length(S)-IL-R; - return R; - } - if((SJIS=getopt(sjis))!=1) SJIS=0; - if((II!=0&&length(II)>1)||(JJ!=0&&length(JJ)>1)){ - for(;;){ - MJ=str_str(S,N|top=JJ,sjis=SJIS); - if(MJ>=0){ - MI=str_str(S,II|top=N,sjis=SJIS); - if(MI<0 || MI>MJ){ - if(C==0) return MJ; - C--; N=MJ+length(II); - }else if(MI>=0){ - C++; N=MI+length(JJ); - } - } - return -1; - } - } - if(type(S)==4){ - M=N; - while(M-->0) S=cdr(S); - while(S!=[]){ - if(car(S)==I) C++; - else if(car(S)==J){ - if(C==0) return N; - C--; - } - S=cdr(S);N++; - } - }else if(type(S)==5){ - K=length(S); - for(T=N;T<K && C>=0;T++){ - if(S[T]==I) C++; - else if(S[T]==J){ - if(C==0) return T; - C--; - } - } - } - return -1; -} - - -def str_cut(S,I,J) -{ - if(type(S)==7) return sub_str(S,I,J); - if((JJ=length(S))<=J) J=JJ-1; - if(type(S)==5){ - for(L=[],K=J; K>=I; K--) L=cons(S[K],L); - }else if(type(S)==4){ - J-=I; - while(I-->0) S=cdr(S); - for(L=[];J-->=0;S=cdr(S)) L=cons(car(S),L); - L=reverse(L); - } - return asciitostr(L); -} - -def str_str(S,T) -{ - if(S==0) return -1; - if(type(S) == 7) - S = strtoascii(S); - if(type(J=getopt(top))!=1 || J<0) J=0; - LS=length(S); - if(LS-J<1) return -1; - if(type(S)==4){ - LS-=(J0=J); - for( ; J>0 && S!=[]; S=cdr(S),J--); - } - if(type(JJ=getopt(end))!=1 && JJ!=0) JJ=LS; - else JJ-=J0; - if((SJIS=getopt(sjis))!=1) SJIS=0; - if(JJ-J<0) return -1; - /* search from J-th to JJ-th */ - if(type(T)==1) T=[T]; - else if(type(T)==7) T = strtoascii(T); - else if(type(T)==4 && type(T[0])>3){ - for(K=(KF=-1)-J0; T!=[]; F++,T=cdr(T)){ - JK=str_str(S,car(T)|top=J,end=JJ,sjis=SJIS); - if(JK>=0){ - JJ=(K=JK)-1; KF=F; - if(J>JJ) break; - } - } - return [KF,J0+K]; - } - if(type(T)==4) T=ltov(T); - LT = length(T); - if(LT>0){ - LE = LS-LT; - LP = T[0]; - if(JJ==0 ||(type(JJ)==1 && JJ<LE)) LE=JJ; - if(type(S)==5){ - for(; J <= LE; J++){ - if(S[J] != LP){ - if(SJIS && (V=S[J])>128){ - if(V<160 || (V>223 && V<240)) J++; - } - continue; - } - for(I = 1; I < LT && S[I+J] == T[I]; I++); - if(I >= LT) return J; - } - }else if(type(S)==4){ - for(; J<=LE; S=cdr(S),J++){ - if(car(S) != LP){ - if(SJIS && (V=S[J])>128){ - if(V<160 || (V>223 && V<240)) J++; - } - continue; - } - for(ST=cdr(S), I = 1; I < LT && car(ST) == T[I]; I++, ST=cdr(ST)); - if(I >= LT) return J0+J; - } - } - } - return -1; -} - -def str_times(S,N) -{ - if(!isint(N)) return ""; - if(type(S)==7){ - for(Tb=str_tb(0,0);N-->0;) - str_tb(S,Tb); - return str_tb(0,Tb); - } - if(type(S)==4){ - for(LT=[],I=0;I<N;I++){ - if(type(car(S))==7){ - LT=cons(car(S),LT); - S=cdr(S); - if(S==[]) S=[[""]]; - }else if(type(car(S))==4){ - ST=car(S); - for(J=0;I<N;I++){ - if(J==length(ST)) J=0; - LT=cons(ST[J++],LT); - } - } - } - return reverse(LT); - } - return S; -} - -def ssubgrs(M,L) -{ - if(type(L)==7) L=s2sp(L); - for(S=0, L=L, M=M; L!=[]; L=cdr(L), M=cdr(M)){ - for(LT=car(L), MT=car(M); LT!=[]; LT=cdr(LT), MT=cdr(MT)){ - S += car(LT)*car(MT)[1]; - } - } - return S; -} - -def s2os(S) -{ - return str_subst(S,[["\\","\\\\"],["\"","\\\""]],0); -} - -def l2os(S) -{ - if(type(S)==6) - S=m2ll(S); - else if(type(S)==5) - S=vtol(S); - else if(type(S)==7) return "\""+s2os(S)+"\""; - else if(type(S)<4) return rtostr(S); - if(type(S)==4){ - for(F=0,Tb=str_tb("[",0);S!=[];S=cdr(S)){ - if(F++) str_tb(", ",Tb); - str_tb(l2os(car(S)),Tb); - } - str_tb("]",Tb); - return str_tb(0,Tb); - } - return 0; -} - -def r2os(S) -{ - if(type(S)==6){ - for(T="",S=m2ll(S);S!=[];S=cdr(S)){ - if(T!="") T=T+","+r2os(car(S)); - else T=r2os(car(S)); - } - return "mat("+T+")\n"; - }else if(type(S)==5){ - for(T="",S=v2l(S);S!=[];S=cdr(S)){ - if(T!="") T=T+","+r2os(car(S)); - else T=r2os(car(S)); - } - return "vect("+T+")\n"; - }else if(type(S)<4) return rtostr(S); - else if(type(S)==4){ - for(T="";S!=[];S=cdr(S)){ - if(T!="") T=T+","+r2os(car(S)); - else T=r2os(car(S)); - } - return "["+T+"]"; - }else if(type(S)==7) return "\""+s2os(S)+"\""; - return ""; -} - -def s2euc(S) -{ - for(R=[],CR=0,L=strtoascii(S);L!=[];L=cdr(L)){ - if((C=car(L)) == 0x1b && length(L)>1) { - if((C=car(L=cdr(L)))==0x24 && length(L)>1){ /* $ */ - if((C = car(L=cdr(L))) == 0x40 || C == 0x42) { /* @, B */ - Mode = 1; - } else return 0; - }else if(C == 0x28 && length(L)>1) { /* ( */ - if((C = car(L=cdr(L)))== 0x42 || C == 0x4a) { /* B, J */ - Mode = 0; - }else if(C == 0x49) { /* I */ - Mode = 2; - }else{ - R=cons(0x1b,R);R=cons(0x28,R);R=cons(C,R); - } - }else if (C == 0x26 && length(L)>1 && car(cdr(L))==0x1b) { /* & ESC */ - L=cdr(L); - }else{ - R=cons(0x1b,R);R=cons(C,R); - } - }else if(C == 0x0e) { - Mode = 2; - }else if(C == 0x0f) { - Mode = 0; - }else if(Mode == 1 && C>0x20 && C<0x7f && length(L)>1) { /* JIS KANJI */ - D=car(L=cdr(L)); - if(D>0x20 && D<0x7f) { - R=cons(ior(C,0x80),R);R=cons(ior(D,0x80),R); - } else return 0; - }else if(Mode == 2 && C > 0x1f && C < 0x60) { /* JIS KANA */ - R=cons(0x8e,R); R=cons(ior(C,0x80),R); - }else if(((C>0x80 && C<0xa0) || (C>0xdf && C<0xf0)) && length(L)>1) { /* ShiftJIS */ - D=car(L=cdr(L)); - if(D>0x3f && D<0xfd && D!=0x7f) { - T=sjis2jis([C,D]); - R=cons(ior(T[0],0x80),R); R=cons(ior(T[1],0x80),R); - }else return 0; - }else if(C>0x9f && C<0xe0) { /* HanKana */ - R=cons(0x8e,R); R=cons(C,R); - }else if(C == 0x0a){ - CR++; - }else if(C == 0x0d){ - R=cons(0x0d,R); - CR=0; - }else{ - while(CR-->0) R=cons(0x0d,R); - R=cons(C,R); - } - } - while(CR-->0) R=cons(0x0d,R); - return asciitostr(reverse(R)); -} - -def s2sjis(S) -{ - for(R=[],CR=0,L=strtoascii(S);L!=[];L=cdr(L)){ - if((C=car(L)) == 0x1b && length(L)>1) { - if((C=car(L=cdr(L)))==0x24 && length(L)>1){ /* $ */ - if((C = car(L=cdr(L))) == 0x40 || C == 0x42) { /* @, B */ - Mode = 1; - } else return 0; - }else if(C == 0x28 && length(L)>1) { /* ( */ - if((C = car(L=cdr(L)))== 0x42 || C == 0x4a) { /* B, J */ - Mode = 0; - }else if(C == 0x49) { /* I */ - Mode = 2; - }else{ - R=cons(0x1b,R);R=cons(0x28,R);R=cons(C,R); - } - }else if (C == 0x26 && length(L)>1 && car(cdr(L))==0x1b) { /* & ESC */ - L=cdr(L); - }else{ - R=cons(0x1b,R);R=cons(C,R); - } - }else if(C == 0x0e) { - Mode = 2; - }else if(C == 0x0f) { - Mode = 0; - }else if(Mode == 1 && C>0x20 && C<0x7f && length(L)>1) { /* JIS KANJI */ - D=car(L=cdr(L)); - if(D>0x20 && D<0x7f) { - T=jis2sjis([C,D]); - R=cons(T[0],R);R=cons(T[1],R); - } else return 0; - }else if(Mode == 2 && C > 0x1f && C < 0x60) { /* JIS KANA */ - R=cons(ior(C,0x80),R); - }else if(C>0xa0 && C<0xff && length(L)>1) { /* EUC */ - D=car(L=cdr(L)); - if(D>0xa0 && D<0xff) { - T=jis2sjis([iand(C,0x7f),iand(D,0x7f)]); - R=cons(T[0],R);R=cons(T[1],R); - }else return 0; - }else if(C == 0x0a){ - CR++; - }else if(C == 0x0d){ - R=cons(0x0a,R);R=cons(0x0d,R); - CR=0; - }else{ - while(CR-->0){ - R=cons(0x0a,R);R=cons(0x0d,R); - } - R=cons(C,R); - } - } - while(CR-->0){ - R=cons(0x0a,R);R=cons(0x0d,R); - } - return asciitostr(reverse(R)); -} - -def r2ma(S) -{ - return evalma(S|inv=1); -} - -def evalma(S) -{ - L0=["\n","\d","{","}","[","]","Log","Exp","Sinh","Cosh","Tanh","Sin","Cos","Tan", - "ArcSin","ArcCos","ArcTan"]; - L1=["", "" ,"[","]","(",")","log","exp","sinh","cosh","tanh","sin","cos","tan", - "asin", "acos", "atan"]; - if(getopt(inv)==1){ - if(type(S)==6) S=m2ll(S); - else if(type(S)==5) S=vtol(S); - if(type(S)==4){ - for(L=[];S!=[];S=cdr(S)){ - if(type(car(S))==6) L=cons(m2ll(car(S)),L); - else if(type(car(S))==5) L=cons(vtol(car(S)),L); - else L=cons(car(S),L); - } - S=reverse(L); - }else return 0; - return str_subst(rtostr(S),cdr(cdr(L1)),cdr(cdr(L0))); - } - if(S==0){ - print("Mathematica text (terminated by ;) ?"); - purge_stdin(); - Tb=str_tb(0,0); - for(;;){ - S=get_line(); - str_tb(S,Tb); - if(str_char(S,0,";")>=0) break; - } - S=str_tb(0,Tb); - } -/* - while((P=str_chr(S,0,";"))>=0){ - V0=evalma(str_cut(S,0,P+1)); - S=str_cut(S,P+1,length(S)); - } - if((P=str_char(S,0,"="))>=0){ - X=strtoascii(str_cut(S,0,P)); - L=length(X); - for(P0=P1=-1,I=0;I<L;I++){ - if(L(I)<=32) continue; - if(isalphanum(L[I])){ - if(P0<0){ - if(isnum(L[I])) break; - P0=I; - } - else if(P1!=I+1) break; - P1=I; - } - } - if(I==L && P0>=0){ - for(I==P0;I-->0;) X=cdr(X); - if((X0=car(X))>96) X0-=32; - Y=[X0];X=cdr(X); - for(I=P1-P0;I-->0;X=cdr(X)) - Y=cons(car(X),Y); - Y=cons(61,Y); - Var=asciitostr(reverse(Y)); - S=str_cut(S,P,length(S)); - } - } -*/ - S=eval_str(str_subst(S,L0,L1)); - if(type(S)==4){ - for(L=-1,T=S;T!=[];T=cdr(T)){ - if(type(T0=car(T))>4) break; - if(type(T0)<4){ - if(L>=0) break; - L=-2;continue; - } - if(L<-2) break; - if(L==-1) L=length(T0); - else if(L!=length(T0)) break; - } - if(T==[]){ - if(L>0) S=s2m(S); - else S=ltov(S); - } - } -/* - if(S==0 && V0!=0) return V0; - if(type(Var)==7){ - T=rtostr(S); - if(type(S)==7) T="\""+T+"\""; - S=eval_str(Var+T); - mycat(["Define",Var]); - } -*/ - return S; -} - -def i2hex(N) -{ - Opt=getopt(); - if(type(N)==4 && isint(car(N))){ -#ifdef USEMODULE - L=mtransbys(os_md.i2hex,N,[]|option_list=Opt); -#else - L=mtransbys(i2hex,N,[]|option_list=Opt); -#endif - return rtostr(L); - } - if(!isint(N) || N<0) return 0; - if(!N) L=[]; - else{ - Cap=(getopt(cap)==1)?32:0; - for(L=[];N!=0;N=ishift(N,4)){ - J=iand(N,15); - L=cons(((J>9)?(87-Cap):48)+J,L); - } - } - if(!isint(Min=getopt(min))) Min=2; - for(Min-=length(L);Min-->0;) - L=cons(48,L); - if(getopt(num)==1){ - L=cons(120,L);L=cons(48,L); - } - return asciitostr(L); -} - -def sjis2jis(L) -{ - L1=L[1]; - if((L0=L[0])<=0x9f){ - if(L1<0x9f) L0=L0*2-0xe1; - else L0=(L0*2)-0xe0; - }else{ - if(L1<0x9f) L0=L0*2-0x161; - else L0=L0*2-0x160; - } - if(L1<0x7f) return [L0,L1-0x1f]; - else if(L1<0x9f) return [L0,L1-0x20]; - return [L0,L1-0x7e]; -} - -def jis2sjis(L) -{ - L1=L[1]; - if(iand(L0=L[0],1)){ - if(L1<0x60) L=[L1+0x1f]; - else L=[L1+0x20]; - }else L=[L1+0x7e]; - if(L0<0x5f) return cons(ishift(L0+0xe1,1),L); - return cons(ishift(L0+0x161,1),L); -} - -def verb_tex_form(P) -{ - L = reverse(strtoascii(rtostr(P))); - for(SS = []; L != []; L = cdr(L)){ - Ch = car(L); /* ^~\{} */ - if(Ch == 92 || Ch == 94 || Ch == 123 || Ch == 125 || Ch == 126){ - SS = append([92,Ch,123,125],SS); /* \Ch{} */ - if(Ch != 94 && Ch != 126) /* \char` */ - SS = append([92,99,104,97,114,96],SS); - continue; - } - SS = cons(Ch, SS); - if((Ch >= 35 && Ch <= 38) || Ch == 95) /* #$%&_ */ - SS = cons(92, SS); /* \Ch */ - } - return asciitostr(SS); -} - -def tex_cuteq(S,P) -{ - if(P==0) return 0; - if(S[P]==125){ /* } */ - if((Q=str_pair(S,P-1,"{","}"|inv=1))<0) return -1; - if(Q<2||S[Q-1]!=95) return Q; - return tex_cuteq(S,Q-2); - } - if(!isalphanum(S[Q=P--])) return -1; - while(P>0&&isalphanum(S[P])) P--; - if(S[P]==92){ /* \ */ - if(P==0) return P; - else P--; - } - if(S[P]!=95||P==0) return Q; /* _ */ - return tex_cuteq(S,P-1); -} - - -def texket(S) -{ - if(!isint(F=getopt(all))) F=0; - if(type(S)==7){ - L=str_len(S); - SS=strtoascii(S); - }else{ - L=length(S); - SS=S; - } - for(T="",I=I0=0;I<L-1;){ - J=str_char(SS,I,"("); - if(J<0) break; - if(J<L-1 && J>4 && str_str(SS,"\\left"|top=J-5,end=J-1)>=0){ - I=J+1;continue; - } - if((K=str_pair(SS,J+1,"(",")"))>=0){ - KK=str_char(SS,J+2,"("); - if(KK>K||KK<0){ - if(F!=1){ - if(!F){ - for(N=J+1;N<K;N++) /* + - _ { } */ - if(!isalphanum(P=SS[N])&&findin(P,[32,43,45,95,123,125])<0) break; - }else N=K; - if(N==K){ - I=K+1;continue; - } - } - T=T+str_cut(SS,I0,J-1)+"\\left"+str_cut(SS,J,K-1)+"\\right)"; - I0=I=K+1; - }else{ - T=T+str_cut(SS,I0,J-1)+"\\left("+texket(str_cut(SS,J+1,K-1)|all=F) +"\\right)"; - I0=I=K+1; - } - }else break; - } - return T+str_cut(SS,I0,L); -} - - -def my_tex_form(S) -{ - if(getopt(skip) != 1){ - if(type(S)==1 && S<0) return "-"+print_tex_form(-S); - if(type(S)==6) return mtotex(S); - S = print_tex_form(S); - for(F=Top=0;(L=str_str(S,"\\verb`"|top=Top))>=0;Top=LV+1){ - F++; - if(Top==0) Tb = string_to_tb(""); - LV = str_chr(S, L+6, "`"); - if(LV<0) LV=str_len(S); - str_tb([my_tex_form(sub_str(S, Top, L-1)|skip=1), "\\texttt{"], Tb); - str_tb([verb_tex_form(sub_str(S,L+6, LV-1)),"}"], Tb); - Top=LV+1; - } - if(F>0){ - str_tb(my_tex_form(sub_str(S, Top,str_len(S)-1)|skip=1), Tb); - return tb_to_string(Tb); - } - } - if(S==0) return ""; - S = ltov(strtoascii(S)); - L = length(S)-1; - while(L >= 1 && S[L] == 10) - L--; - if((Fr=getopt(frac))!=0 && Fr!=1) Fr=2; - for(I = L+1, T = K = 0, SS = []; --I >= 0; ){ - if(S[I] == 32 && I!=L){ - if(I==L) continue; - if(findin(S[I+1], [32,40,41,43,45,123,125]) >= 0 /* " ()+-{}" */ - || (S[I+1] >= 49 && S[I+1] <= 57)) /* 1 - 9 */ - if(I == 0 || S[I-1] >= 32) continue; - } - if(Fr && S[I]>=48 && S[I]<=57){ /* 2/3 -> \tfrac{2}{3} */ - for(K=0,II=I; II>=0; II--){ - if(S[II]>=48 && S[II]<=57) continue; - if(S[II]==47){ /* / */ - if(K>0) break; - K=II; - }else break; - } - if(K>II+1){ - SS=cons(125,SS); - for(J=I; J>K; J--) SS=cons(S[J],SS); - if(AMSTeX){ - SS=cons(123,SS);SS=cons(125,SS); - }else{ - for(J=[114,101,118,111,92];J!=[];J=cdr(J)) /* \over */ - SS=cons(car(J),SS); - } - for(J=K-1;J>II;J--) SS=cons(S[J],SS); - SS=cons(123,SS); - if(AMSTeX){ - J=(Fr==2)?[99,97,114,102,116,92]:[99,97,114,102,92]; - for(;J!=[];J=cdr(J)) /* \tfrac */ - SS=cons(car(J),SS); - } - I=II+1; - }else{ - for(;I>II;I--) SS = cons(S[I], SS); - I++; - } - continue; - } - SS = cons(S[I], SS); - } - SS=str_subst(SS,"\\\\\n\\end{pmatrix}","\n\\end{pmatrix}"|raw=1); - Subst=getopt(subst); - Sub0=["{asin}","{acos}","{atan}"]; - Sub1=["\\arcsin ","\\arccos","\\arctan "]; - if(type(Subst) == 4){ - Sub0=append(Sub0,Subst[0]);Sub1=append(Sub1,Subst[1]); - } - SS = str_subst(SS,Sub0,Sub1|raw=1); - S = ltov(SS); - L = length(S); - SS = []; - while(--L >= 0){ - if(S[I=L] == 125){ - while(--I >= 0 && S[I] == 125); - J = 2*I - L; - if(J >= 0 && S[I] != 123){ - for(K = J; K < I && S[K] == 123; K++); - if(K == I){ - if(J-- <= 0 || S[J] < 65 || S[J] > 122 || (S[J] > 90 && S[J] < 97)){ - SS = cons(S[I],SS); - L = J+1; - continue; - } - } - } - } - SS = cons(S[L],SS); - } - RT=getopt(root); - for(Top=0;;Top++){ /* ((x+1))^{y} , 1/y=2,3,...,9 */ -#if 1 - P=str_str(SS,["))^","^{\\tfrac{1}"]|top=Top); - if(P[0]<0) break; - Sq=0; - if(P[0]==0){ - P=P[1]; - if((Q=str_pair(SS,P,"(",")"|inv=1))<0||SS[Q+1]!=40) continue; - if((RT==2||(RT!=0 && P-Q<33)) && str_str(SS,"{\\tfrac{1}"|top=P+3,end=P+3)==P+3 - && SS[P+14]==125){ - if((Sq=SS[P+13]-48)<2||Sq>9) Sq=0; - } - F=2; - }else{ - P=P[1]; - if(SS[P+12]!=125||(Sq=(SS[P+11]-48))<2||Sq>9) break; - if(SS[P-1]==125){ - if((Q=str_pair(SS,P-2,"{","}"|inv=1))<0) break; - if(Q>1&&SS[Q-1]==95){ - if((Q=tex_cuteq(SS,Q-2))<0) break; - F=0; - }else F=1; - }else{ - if(!isalphanum(SS[Q=P-1]) || (Q=tex_cuteq(SS,Q))<0) break; - F=0; - } - if(RT!=2&&P-Q>32) break; - } -#else - if((P=str_str(SS,"))^"|top=Top))<0 || (Q=str_pair(SS,P,"(",")"|inv=1))<0) break; - else F=2; - Sq=0; - if((RT==2||(RT!=0 && P-Q<33)) && str_str(SS,"{\\tfrac{1}"|top=P+3,end=P+3)==P+3 - && SS[P+14]==125){ - if((Sq=SS[P+13]-48)<2||Sq>9) Sq=0; - } -#endif - for(I=0,S=[];SS!=[];SS=cdr(SS),I++){ - if(I==Q){ - if(Sq){ - S=append([116,114,113,115,92],S); - if(Sq>2) S=append([93,Sq+48,91],S); - S=cons(123,S); - if(F==2) SS=cdr(SS); - else if(F==0) S=cons(car(SS),S); - }else if(F==2&&P-Q==3){ /* (2)^x -> 2^x*/ - SS=cdr(SS);SS=cdr(SS); - S=cons(123,S);S=cons(car(SS),S);S=cons(125,S); - SS=cdr(SS);SS=cdr(SS); - I+=3; - } - continue; - }else if(I==P){ - if(Sq){ - if(F>0) S=cdr(S); - S=cons(125,S); - if(F==2) SS=cdr(SS); - for(J=0;J<12;J++) SS=cdr(SS); - } - continue; - } - S=cons(car(SS),S); - } - SS=reverse(S); - Top=P; - } - S=asciitostr(SS); - if((K=getopt(ket))==1) S=texket(S); - else if(K==2) S=texket(S|all=1); - return S; -} - -def smallmattex(S) -{ - return str_subst(S,[["\\begin{pmatrix}","\\left(\\begin{smallmatrix}"], - ["\\end{pmatrix}","\\end{smallmatrix}\\right)"], - ["\\begin{Bmatrix}","\\left\\{\\begin{smallmatrix}"], - ["\\end{Bmatrix}","\\end{smallmatrix}\\right\\}"], - ["\\begin{bmatrix}","\\left[{\\begin{smallmatrix}"], - ["\\end{bmatrix}","\\end{smallmatrix}\\right]"], - ["\\begin{vmatrix}","\\left|\\begin{smallmatrix}"], - ["\\end{vmatrix}","\\end{smallmatrix}\\right|"], - ["\\begin{Vmatrix}","\\left\\|\\begin{smallmatrix}"], - ["\\end{Vmatrix}","\\end{smallmatrix}\\right\\|"], - ["\\begin{matrix}","\\begin{smallmatrix}"], - ["\\end{matrix}","\\end{smallmatrix}"]],0); -} - - -def divmattex(S,T) -{ - TF=["matrix","pmatrix","Bmatrix","bmatrix","vmatrix","Vmatrix"]; - TG=[0,"(","\\{","[","|","\\|"]; - TH=[0,")","\\}","]","|","\\|"]; - if(type(S)!=7) S=mtotex(S); - S=strtoascii(S0=S); - if((P0=str_str(S,"\\begin{"))<0 || (P1=str_str(S,"}"|top=P0+7))<0) - return S0; - F=str_cut(S,P0+7,P1-1); - if((K=findin(F,TF))<0) return S0; - Q=str_str(S,"\\end{"+F+"}"); - if(Q<0) return S0; - for(J=P1+1;S[J]<33;J++); - for(L0=L=[],I=J;J<Q;J++){ - if(S[J]==38){ /* & */ - if(I>=J) L0=cons(0,L0); - else L0=cons(str_cut(S,I,J-1),L0); - I=J+1; - } - if(S[J]==92&&S[J+1]==92){ /* \\ */ - if(I>=J) L0=cons(0,L0); - else L0=cons(str_cut(S,I,J-1),L0); - L=cons(reverse(L0),L); - L0=[]; - J++; - for(I=J+1;S[I]<33;I++); - } - } - J--; - if(S[J]<33) J--; - if(I<=J) L0=cons(str_cut(S,I,J),L0); - if(length(L0)>0) L=cons(reverse(L0),L); - L=lv2m(reverse(L)); /* get matrix */ - if(T==0) return L; - Size=size(L);S0=Size[0]; - if(type(T[0])!=4){ - S1=Size[1]; - T=append(T,[S1]); - for(TT=[],I=0;T!=[];T=cdr(T)){ - J=car(T); - if(J>S1) J=S1; - for(T0=[];J>I;J--) T0=cons(J-1,T0); - if(T0!=[]) TT=cons(T0,TT); - I=car(T); - } - T=reverse(TT); - } - SS=length(T); - St=str_tb(0,0); - if(SS==1) St=str_tb("\\begin{"+F+"}\n",St); - else{ - if(K>0) St=str_tb("&\\left"+TG[K],St); - St=str_tb("\\begin{matrix}\n",St); - } - for(;T!=[];T=cdr(T)){ - for(I=0;I<S0;I++){ - for(J=0,TT=car(T);TT!=[];TT=cdr(TT),J++){ - if(J>0) St=str_tb("&",St); - if(L[I][car(TT)]!=0) St=str_tb(L[I][car(TT)],St); - } - if(I<S0-1) St=str_tb("\\\\",St); - St=str_tb("\n",St); - } - if(length(T)>1) - St=str_tb("\\end{matrix}\\right.\\\\\n&\\quad\\left.\\begin{matrix}\n",St); - else{ - if(SS==1) St=str_tb("\\end{"+F+"}\n",St); - else St=str_tb("\\end{matrix}\\right"+TH[K]+"\n",St); - } - } - S=str_tb(0,St); - if(SS==1) return S; - return texbegin("align*",S); -} - -def str_subst(S, L0, L1) -{ - if(type(S) == 7) - S = strtoascii(S); - if(type(S) == 4) - S = ltov(S); - SE = length(S); - if(L1 == 0){ - for(L1 = L = [], L0 = reverse(L0); L0 != []; L0 = cdr(L0)){ - L = cons(car(L0)[0], L); - L1 = cons(car(L0)[1], L1); - } - L0 = L; - } - if(type(L0)==7) L0 = [strtoascii(L0)]; - else{ - for(LT = []; L0 != []; L0 = cdr(L0)) - LT = cons(strtoascii(car(L0)), LT); - L0 = ltov(LT); - } - E0 = length(L0); - if(type(L1)==7) L1 = [strtoascii(L1)]; - else{ - for(LT = []; L1 != []; L1 = cdr(L1)) - LT = cons(strtoascii(car(L1)), LT); - L1 = ltov(LT); - } - if(getopt(inv)==1){ - L2=L0;L0=L1;L0=L2; - } - if((SJIS=getopt(sjis))!=1) SJIS=0; - for(J = JJ = 0, ST = []; J < SE; J++){ - SP = S[J]; - for(I = E0-1; I >= 0; I--){ - if(SP != L0[I][0] || J + (K = length(L0[I])) > SE) - continue; - while(--K >= 1) - if(L0[I][K] != S[J+K]) break; - if(K > 0) continue; - for(KE = length(L1[I]), K = 0 ;K < KE; K++) - ST = cons(L1[I][K],ST); - J += length(L0[I])-1; - break; - } - if(I < 0){ - ST = cons(S[J],ST); - if(SJIS && (V=S[J])>128){ - if(V<160 || (V>223 && V<240)) ST = cons(S[J++],ST); - } - } - } - if(getopt(raw)==1) return reverse(ST); - return asciitostr(reverse(ST)); -} - -def dviout0(L) -{ - Cmd=["TikZ","TeXLim","TeXEq","DVIOUT","XYPrec","XYcm","XYLim","Canvas"]; - if(type(Opt=getopt(opt))==7){ - if((F=findin(Opt,Cmd)) < 0) return -1; - if(L==-1){ - if(F<=3){ - if(F==0) V=TikZ; - else if(F==1) V=TeXLim; - else if(F==2) V=TeXEq; - else V=iand(DVIOUTF,1); - }else{ - if(F==4) V=XYPrec; - else if(F==5) V=XYcm; - else if(F==6) V=XYLim; - else V=Canvas; - } - return V; - } - if(F==0) TikZ=L; - else if(F==2) TeXEq=L; - else if(F==3){ - if(iand(DVIOUTF,1)==L) - mycat0(["DVIOUTA=\"", DVIOUTA,"\""],1); - else dviout0(4); - return 1; - }else if(F==7&&type(L)==4) - Canvas=L; - else if(L>0){ - if(F==1) TeXLim=L; - else if(F==4) XYPrec=L; - else if(F==5) XYcm=L; - else if(F==6) XYLim=L; - } - mycat0([Cmd[F],"=",L],1); - return 1; - } - if(type(L) == 4){ - for( ; L != []; L = cdr(L)) dviout0(car(L)); - return 1; - } - if(type(L) == 7){ - if(L=="") dviout(" \n"|keep=1); - else if(L=="cls") dviout0(0); - else if(L=="show") dviout(" "); - else if(L=="?") dviout0(3); - else dviout("\\"+L+"\n"|keep=1); - return 1; - } - if(L == 0) - dviout(" "|keep=1,clear=1); - else if(L == 1) - dviout(" "); - else if(L == 2) - dviout(" "|clear=1); - else if(L>10) - dviout("\\setcounter{MaxMatrixCols}{"+rtostr(L)+"}%"|keep=1); - else if(L < 0) - dviout(" "|delete=-L,keep=1); - else if(L == 3){ - mycat0(["DIROUT =\"", DIROUT,"\""],1); - mycat0(["DVIOUTH=\"", DVIOUTH,"\""],1); - mycat0(["DVIOUTA=\"", DVIOUTA,"\""],1); - mycat0(["DVIOUTB=\"", DVIOUTB,"\""],1); - mycat0(["DVIOUTL=\"", DVIOUTL,"\""],1); - mycat(["Canvas =", Canvas]); - mycat(["TeXLim =", TeXLim]); - mycat(["TeXEq =", TeXEq]); - mycat(["AMSTeX =", AMSTeX]); - mycat(["TikZ =", TikZ]); - mycat(["XYPrec =", XYPrec]); - mycat(["XYcm =", XYcm]); - mycat(["XYLim =", XYLim]); - }else if(L==4){ - Tmp=DVIOUTA; DVIOUTA=DVIOUTB; DVIOUTB=Tmp; - mycat0(["DVIOUTA=\"", DVIOUTA,"\""],1); - DVIOUTF++; - }else if(L==5){ - if(!iand(DVIOUTF,1)) dviout0(4); - }else if(L==6){ - TikZ=1;mycat("TikZ=1"); - }else if(L==7){ - TikZ=0;mycat("TikZ=0"); - } - return 1; -} - -def myhelp(T) -{ - /* extern DVIOUT; */ - /* extern HDVI; */ - /* extern DVIOUTH; */ - - if(type(T)==2){ - if(T==getbygrs){ - getbygrs(0,0); - return 0; - } - else if(T==m2mc){ - m2mc(0,0); - return 0; - } - else if(T==mgen){ - mgen(0,0,0,0); - return 0; - } - else T=rtostr(T); - } - if(type(T)==4 && typeT[0]==7){ - if(length(T)==2 && type(T[1])==1){ - DVIOUTH="start "+T[0]+" -"+rtostr(T[1])+"-hyper:0x90 \"%ASIRROOT%\\help\\os_muldif.dvi\" #r:%LABEL%"; - }else if(str_len(T[0])>2) DVIOUTH=T[0]; - mycat(["DVIOUTH="+DVIOUTH,"\nmyhelp(fn) is set!"]); - return 0; - } - if(T==0){ - mycat([ - "myhelp(t) : show help\n", -#ifdef USEMODULE - " t : -1 (dvi), 1 (pdf) or os_md.getbygrs, os_md.m2mc, os_md.mgen\n", -#else - " t : -1 (dvi), 1 (pdf) or getbygrs, m2mc, mgen\n", -#endif - " \"fn\" : Help of the function fn\n", - " [path,n] : path of dviout, n = # dviout\n", - " [DVIOUTH] : Way to jump to the help of a function\n", - " default: start dviout -2 \"%ASIRTOOT%\\help\\os_muldif.dvi\" #r:%LABEL%" - ]); - return 0; - } - if(type(T)==7){ - if(str_str(T,"os_md.")==0) T=str_cut(T,6,str_len(T)-1); - Dr=str_subst(DVIOUTH,["%ASIRROOT%","%LABEL%"],[get_rootdir(),"r:"+str_subst(T,"_","")]); - shell(Dr); - return 0; - } - Dr=get_rootdir(); - if(T==-1) Dr+="\\help\\os_muldif.dvi"; - else Dr+="\\help\\os_muldif.pdf"; - if(!isMs()) Dr=str_subst(Dr,"\\","/"); - shell(Dr); - return 0; -} - -def isMs() -{ - if(type(Tmp=getenv("TEMP"))!=7) { - if (type(Tmp=getenv("TMP")) != 7) Tmp=getenv("HOME"); - } - if(type(Tmp)==7 && str_chr(Tmp,0,"\\")==2) return 1; - else return 0; -} - -def tocsv(L) -{ - if(type(L)==6) L=m2ll(L); - else if(type(L)==5) L=vtol(L); - Null=getopt(null); - Tb=str_tb(0,0); - for(LL=L; LL!=[]; LL=cdr(LL)){ - LT=car(LL); - if(type(LT)==5) LT=vtol(LT); - if(type(LT)<4) LT=[LT]; - for(N=0; LT!=[]; LT=cdr(LT),N++){ - if(N) str_tb(", ",Tb); - if((T=car(LT))==Null) continue; - if(type(T)==7){ - K=str_len(T); - T=str_subst(T,["\""],["\"\""]); - if(str_len(T)>K||str_char(T,0,",")>=0) T="\""+T+"\""; - str_tb(T,Tb); - }else str_tb(rtostr(T),Tb); - } - str_tb("\n",Tb); - } - S=str_tb(0,Tb); - if(type(EXE=getopt(exe))!=1&&EXE!=0&&type(EXE)!=7) return S; - if(type(F)!=7){ - F="risaout"; - if(EXE>=2&&EXE<=9) F+=rtostr(EXE); - F=DIROUTD+F+".csv"; - }else F=S; - if(EXE!=0 && access(F)) remove_file(F); - fcat(F,S|exe=1); - return 1; -} - -def readcsv(F) -{ - if((ID=open_file(F))<0) return -1; - SJIS=isMs(); - L=[]; - if(type(V=getopt(eval))!=4){ - if(V=="all") V=1; - else if(type(V)==1) V=[V]; - else V=[]; - } - Eq=getopt(eq); - Sp=getopt(sp); - if(type(T=getopt(col))!=1) T=0; - Null=getopt(null); - if(type(Null)<0) Null=(Eq==1)?0:""; - while((S=get_line(ID))!=0){ - S=strtoascii(S); - N=length(S); - for(I=J=F=0,LL=LT=[];I<N;I++){ - C=S[I]; - if(F==0){ - if(C<=32) continue; - if(C==34){F=2;continue;} - F=1; - } - if(F==2 && C==34){ - if(I<N-1&& S[I+1]==34){ - LT=cons(34,LT);I++;continue; - } - F=-2; - } - if(F==1){ - if((C==44&&Sp!=1)||(C<=32&&Sp==1)) F=-1; - else if(C<32 && C!=9) continue; - } - if(SJIS && I<N-1 && ((C>128 && C<160)||(C>223 && C<240))){ - LT=cons(C,LT);LT=cons(S[++I],LT);continue; - } - if(F>0){ - LT=cons(C,LT);continue; - } - LS=asciitostr(reverse(LT)); - if(V==1||findin(++J,V)>=0){ - if(Eq==1) LS=(LS=="")?Null:eval_str(LS); - else LS=(isdecimal(LS))?eval_str(LS):((LS=="")?Null:LS); - } - if(!T || T==J) LL=cons(LS,LL); - if(F==-2) while(++I<N && Sp!=1 && S[I]!=44); - F=0;LT=[]; - } - if(I<=N && (Sp!=1 || length(LT)>0)){ /* lastline */ - LS=asciitostr(reverse(LT)); - if(V==1||findin(++J,V)>=0){ - if(Eq==1) LS=(LS=="")?Null:eval_str(LS); - else LS=(isdecimal(LS))?eval_str(LS):((LS=="")?Null:LS); - } - if(!T || T==J) LL=cons(LS,LL); - } - L=cons(reverse(LL),L); - } - close_file(ID); - if(T) L=m2l(L|flat=1); - L=reverse(L); - return L; -} - -def showbyshell(S) -{ - Id = getbyshell(S); - if(Id<0) return Id; - while((S=get_line(Id))!=0) print(S,2); - return close_file(Id); -} - - -def getbyshell(S) -{ - /* extern DIROUT; */ - - Home=getenv("HOME"); - if(type(Home)!=7) Home=""; - if(type(Tmp=getenv("TEMP"))!=7 && type(Tmp=getenv("TMP")) != 7) - Tmp=str_subst(DIROUT,["%HOME%","%ASIRROOT%"],[Home,get_rootdir()]); - Sep=isMs()?"\\":"/"; - F=Tmp+Sep+"muldif.tmp"; - if(type(S)<=1 && S>=0) close_file(S); - remove_file(F); - if(type(S)<=1) return -1; - shell(S+" > \""+F+"\""); - return open_file(F); -} - -def show(P) -{ - T=type(P); - S=P; - Var=getopt(opt); - if(Var=="verb"){ - dviout("{\\tt"+verb_tex_form(T)+"}\n\n"); - return; - } - if(type(Var)<0) Var=getopt(var); - if(T==6){ - if((Sp=getopt(sp))==1 || Sp==2) - S=mtotex(P|lim=1,small=2,sp=Sp,null=1,mat="B"); - else if(type(Var)==4 || type(Var)==7) - S=mtotex(P|lim=1,small=2,var=Var); - else - S=mtotex(P|lim=1,small=2); - Size=size(P); - Size=(Size[0]>Size[1])?Size[0]:Size[1]; - if(Size>10) dviout0(Size); - }else if(T<=3){ - X=0; - if(Var=="pfrac") X=var(P); - else X=getopt(pfrac); - if(isvar(X)){ - pfrac(P,X|dviout=1); - return; - } - Opt=cons(["dviout",1],getopt()); - if(type(Var)==2||type(Var)==4||type(Var)==7) fctrtos(P|option_list=Opt); - else{ - if(isdif(P)!=0) Opt=cons(["var","dif"],Opt); - else Opt=cons(["br",1],Opt); - fctrtos(P|option_list=Opt); - } - return; - }else if(T==4){ - if(type(Var)==4 || type(Var)==7){ - S=ltotex(P|option_list=getopt()); - if(Var=="text"){ - dviout(S); - return; - } - }else{ - for(F=0,L=P;L!=[] && F!=-1;L=cdr(L)){ - LL=car(L); - if(type(LL)==4){ - if(F==0){ - T=type(LL[0]); - if(T==4) F=2; /* [[[? */ - else if(T==1 || T==0) F=1; /* [[num,.. */ - } - if(F==1){ - if(length(LL)!=2 || !isint(LL[0]) || LL[0]<0 || type(LL[1])>3) - F=-1; /* [[num,rat],[num,rat],...] */ - }else if(F==2){ - for(LLT=LL; LLT!=[] && F!=-1; LLT=cdr(LLT)){ - LLL=car(LLT); /* [[[num,rat],[num,rat],...],[[..],..]],....] */ - if(length(LLL)!=2 || !isint(LLL[0]) || LLL[0]<0 || type(LLL[1])>3) - F=-1; - } - } - }else if((F==0 || F==7) && type(LL)==7){ - F=7; - }else F=-1; - } - if(F==1) S=ltotex(P|opt="spt"); - else if(F==2){ - M=mtranspose(lv2m(S)); - show(M|sp=1); /* GRS */ - return; - }else if(F==7) S=ltotex(P|opt="spts"); - else{ - for(F=0,L=P;L!=[] && F!=-1;L=cdr(L)){ - LL=car(L); - if(type(LL)!=4){ - F=-1; break; - } - for(LLT=LL; LLT!=[] && F!=-1; LLT=cdr(LLT)){ - T=type(LLL=car(LLT)); - if(T<7 && T!=4) F0++; - else if(T==7){ - if(str_char(LLL,0,"\\")<0) F1++; - else F2++; - }else F=-1; - } - } - } - if(F==0 && F0>0 && (F1+F2)>0){ /* list of list of eq and str */ - if(F2>0) S=ltotex(P|opt=["cr","spts0"],str=1); - else S=ltotex(P|opt=["cr","spts"]); - }else{ - for(S="[";;){ - S+=my_tex_form(car(P)); - if((P=cdr(P))==[]){ - S+="]";break; - } - S+=","; - } - } - } - }else if(T==7){ - if(Var=="raw" || - (Var !="eq" && str_chr(P,0,"\\")<0 && str_char(P,0,"^")<0 && str_char(P,0,"_")<0 - && str_char(P,0,"&")<0)){ - dviout(P+"\n\n"); - return; - } - } - dviout(S|eq=5); -} - - -/* options : eq = 1 - 8, clear=1, keep=1, delete=1, title=s, - fctr=1, begin=s */ -def dviout(L) -{ - /* extern AMSTeX, TeXEq, DIROUT, DVIOUTA, DVIOUTB, DVIOUTL; */ - - MyEq = [ - ["\\[\n ","\\]"], - ["\\begin{align}\n","\\end{align}"], - ["\\begin{gather}\n ","\\end{gather}"], - ["\\begin{multline}\n ","\\\\[-15pt]\\end{multline}"], - ["\\begin{align}\\begin{split}\n &","\\end{split}\\end{align}"], - ["\\begin{align*}\n &","\\end{align*}"], - ["\\begin{gather*}\n ","\\end{gather*}"], - ["\\begin{equation}\n ","\\end{equation}"] - ]; - if(!chkfun("print_tex_form", "names.rr")) - return 0; - Home=getenv("HOME"); - if(type(Home)!=7) Home=""; - Dir=str_subst(DIROUT,["%HOME%","%ASIRROOT%","\\"],[Home,get_rootdir(),"/"]); - Dirout=Dir+(AMSTeX?"/out.tex":"/out0.tex"); - Risaout=(AMSTeX)?"risaout":"risaout0"; - Dirisa=Dir+"/"+Risaout+".tex"; - Viewer="dviout"; - SV=["c:/w32tex/dviout","c:/dviout"]; - Risatex=str_subst(AMSTeX?DVIOUTA:DVIOUTL, - ["%HOME%","%ASIRROOT%","%TikZ%"],[Home,get_rootdir(),rtostr(TikZ)]); - if(isMs() && !access(Risatex)){ - for(TV=SV; TV!=[]; TV=cdr(TV)){ - VV=car(TV)+"/dviout.exe"; - if(access(VV)){ - Viewer=str_subst(VV,"/","\\"); - break; - } - } - output(Risatex); - print("cd \""+str_subst(Dir,"/","\\")+"\""); - print("latex -src=cr,display,hbox,math,par "+Risaout); - print("start "+Viewer+" -1 \""+Dr+"\\tex\\"+Risaout+"\" 1000"); - output(); - } - if(access(Dirisa) == 0){ - D0="\""+(isMs()?str_subst(Dir,"/","\\")+"\"":Dir); - shell("mkdir "+D0); - output(Dirisa); - if(AMSTeX){ - print("\\documentclass[a4paper]{amsart}"); - print("\\usepackage{amsmath,amssymb,amsfonts}"); - }else - print("\\documentclass[a4paper]{article}"); - print("\\pagestyle{empty}\n\\begin{document}\n\\thispagestyle{empty}"); - print(AMSTeX?"\\input{out}\n\\end{document}":"\\input{out0}\n\\end{document}"); - output(); - } - if((K = getopt(delete)) >= 1){ /* delete */ - LC = 0; - if(type(K) == 1 && K > 10) K = 10; - if(type(K) == 4){ - K = qsort(K); - LC = 1; /* specific lines */ - } - Done = 1; - Id = open_file(Dirout); - if(Id >= 0){ - Buf = Buf0 = Buf1 = Key = ""; - PE = 0; - if(type(K) == 1) - BufE = newvect(K--); - Dout = Dirout+"0"; - remove_file(Dout); - output(Dout); - while((S = get_line(Id)) != 0){ - if(LC){ - while(K != [] && car(K) < LC) - K = cdr(K); - if(K == [] || car(K) > LC) - output(S); - } - if(Key == ""){ - if((P0 = str_str(S,"\\begin{")) == 0){ - Key = sub_str(S,7,str_str(S,"}")-1); - if(findin(Key,["align", "gather","multline", "equation","align*"]) < 0) - Key = ""; - else{ - Key = "\\end{"+Key+"}"; - if(!LC){ - if(Buf != ""){ - if(PE < K) - BufE[PE++] = Buf1+Buf; - else{ - if(K > 0){ - print(BufE[0]); - for(I = 1; I < K; I++) - BufE[I-1]=BufE[I]; - BufE[K-1] = Buf1+Buf; - }else - print(Buf1+Buf); - Done = 0; - } - Buf1 = Buf0; - Buf = Buf0 =""; - } - } - } - } - if(Key == "" && !LC) Buf0 += S; - } - if(Key != ""){ - if(!LC) Buf += S; - if(str_str(S,Key) >= 0){ - Key = ""; - if(LC) LC++; - } - } - } - output(); - close_file(Id); - } - if(Done==0){ - Id = open_file(Dout); - if(Id >= 0){ - remove_file(Dirout); - output(Dirout); - while((S = get_line(Id)) != 0) - print(S,0); - output(); - close_file(Id); - } - remove_file(Dout); - }else L=" "; - } - if(getopt(clear) == 1 || Done == 1){ /* clear */ - remove_file(Dirout); - if(L == "" || L == " "){ - output(Dirout); - print("\\centerline{Risa/Asir}"); - output(); - } - } - if(L != " "){ - Eq=1; - Eqo = getopt(eq); - Fc = getopt(fctr); - if(Fc == 1 && (type(L) == 2 || type(L) == 3)){ - L = fctrtos(L|TeX=1); - if(type(L) == 4) - L = "\\fact{"+L[0]+"}{"+L[1]+"}"; - if(type(Eqo) != 0 && type(Eqo) !=7){ - Eqo=0; - } - } - if(type(L) != 4 || getopt(mult) != 1) - L = [L]; - if(type(Eqo)!=7 && (Eqo<1 || Eqo>8)) - Eqo = (AMSTeX==1)?TeXEq:1; - Title = getopt(title); - if(type(Title) == 7){ - output(Dirout); - print(Title); - output(); - } - Sb = getopt(subst); - for( ; L != []; L = cdr(L)){ - Eq = 1; - if(type(LT=car(L)) != 7 && type(LT) != 21) - LT = my_tex_form(LT); - else if(type(getopt(eq)) < 0) - Eq = 0; - if(type(Sb) == 4) - LT = str_subst(LT,Sb[0],Sb[1]); - output(Dirout); - if(Eq == 1){ - if(type(Eqo)==7) - print(texbegin(Eqo,LT)); - else if(Eqo >= 1 && Eqo <= 8){ - mycat0([MyEq[Eqo-1][0],LT,"%"],1); - print(MyEq[Eqo-1][1]); - }else print(LT); - }else print(LT); - output(); - } - } - if(str_char(Risatex,0," ")>=0 && str_char(DVIOUTA,0," ")<0 && str_char(DVIOUTB,0," ")<0 - && str_char(DVIOUTL,0," ")<0) - Risatex="\""+Risatex+"\""; - if(getopt(keep) != 1) shell(Risatex); - return 1; -} - -def rtotex(P) -{ - S = my_tex_form(P); - return (str_len(S) == 1)?S:"{"+S+"}"; -} - -def mtotex(M) -{ - /* extern TexLim; */ - - MB=mat(["(",")","p"],["\\{","\\}","B"],["[","]","b"],["|","|","v"], - ["\\|","\\|","V"], [".",".",""]); - if(type(MT=getopt(mat))==7){ - MT=findin(MT,["p","B","b","v","V",""]); - if(MT<0) MT=0; - } - else MT=0; - MT=MB[MT]; - if((F=getopt(small))!=1 && F!=2) F=0; - Lim=getopt(lim); - if(type(Lim)==1){ - if(Lim<30 && Lim!=0) Lim = TexLim; - }else Lim=0; - FL=getopt(len); - Rw=getopt(raw); - Sp=getopt(sp); - Idx=getopt(idx); - if(type(Idx)==4) Idx=ltov(Idx); - if(type(Idx)==6 && length(Idx)==0) Idx=-1; - Var=getopt(var); - if(Lim>0) FL=1; - Null=getopt(null); - if(Null!=1 && Null!=2) Null=0; - if(type(M)==5) M=lv2m([V]); - else if(type(M)!=6) return monototex(M); - S=size(M); - if(FL==1){ - L=newmat(S[0],S[1]); LL=newvect(S[1]); - } - SS=newmat(S[0],S[1]); - for(I=0; I<S[0]; I++){ - for(J=0; J<S[1]; J++){ - if(type(P=M[I][J])<=3){ - if(P!=0 || Null == 0 || (Null==2 && I==J)){ - SS[I][J]=(type(Var)>1)?fctrtos(P|TeX=2,lim=0,var=Var):fctrtos(P|TeX=2,lim=0); - if(type(P)==1 && str_str(SS[I][J],"\\frac{-"|end=0)==0) - SS[I][J]="-\\frac{"+str_cut(SS[I][J],7,100000); - } - }else if(type(P)==6){ - ST= mtotex(P|small=1,len=1); - SS[I][J]=ST[0]; - L[I][J]=ST[1]; - }else if(type(P)==7){ - if(Rw==1) SS[I][J]=P; - else SS[I][J]="\\text{"+P+"\}"; - }else if(type(P)==4 && length(P)==2 && P[0]>0 && (Sp==1 || Sp==2)){ - if(P[0]==1){ - SS[I][J]=fctrtos(P[1]|TeX=2,lim=0); - }else{ - ST=my_tex_form(P[0]); - if(Sp==2) ST="("+ST+")"; - SS[I][J]="["+fctrtos(P[1]|TeX=2,lim=0)+"]_"; - if(str_len(ST)<2) SS[I][J]+=ST; - else SS[I][J]+="{"+ST+"}"; - } - }else - SS[I][J]=my_tex_form(P); - if(FL==1) L[I][J]=texlen(SS[I][J]); - } - } - if(Lim>0 || FL==1){ - for(LLL=J=0; J<S[1];J++){ - for(I=K=0; I<S[0];I++){ - if(K<L[I][J]) K=L[I][J]; - } - LLL+=(LL[J]=K); - } - } - if(Lim>0){ - if(F==2 && LLL>Lim-2*S[1]-2) F=1; - if(F==1) - Lim=idiv(Lim*6,5); - if(LLL<=Lim-(2-F)*S[I]-2) Lim=0; - } - Mat=(F==1)?"smallmatrix}":"matrix}"; - if(F==1) Out=str_tb("\\left"+MT[0]+"\\begin{",0); - else Out=str_tb((Lim==0)?"\\begin{"+MT[2]:"\\left"+MT[0]+"\\begin{",0); - Out = str_tb(Mat,Out); - for(I=II=LT=0; II<=S[0]; II++){ - if(Lim==0) II=S[0]; - if(II<S[0]){ - K=LL[II]+(2-F); - if(I==II){ - LT+=K; - continue; - } - if(LT+K<Lim-2) continue; - LT=K; - } - for(I0=I; I<II; I++){ - if(I==I0){ - str_tb((I==0)? - "\n ": - "\\right.\\\\\n \\allowdisplaybreaks\\\\\n &\\ \\left.\\begin{"+Mat+"\n ", Out); - if(Idx==1||Idx==0||type(Idx)==5){ - for(J=I; J<II; J++){ - if(type(Idx)!=4) - str_tb("("+rtostr(J+Idx)+")",Out); - else{ - JJ=length(Idx)-1; - if(J<JJ) JJ=J; - str_tb(my_tex_form(Idx[JJ]),Out); - } - if(J<II) str_tb(" & ",Out); - } - str_tb("\\\\\n ",Out); - } - } - else str_tb("\\\\\n ",Out); - for(J=0; J<S[1]; J++){ - if(J!=0) str_tb(" & ",Out); - if(type(SS[I][J])==7) str_tb(SS[I][J],Out); - } - } - Out=str_tb("\n\\end{", Out); - if(II==S[0]) Out=str_tb((Lim==0&&F!=1)?MT[2]+Mat:Mat+"\\right"+MT[1],Out); - else Out=str_tb(Mat+"\\right.",Out); - } - SS = str_tb(0,Out); - if(FL!=1) return SS; - if(F==1) LLL=idiv((LLL+S[1])*5+13,6); - else LLL+=2*(1+S[1]); - return [SS,LLL]; -} - -def sint(N,P) -{ - if( type(N)==1 || N==0 ) { - NT=ntype(N); - if((type(Opt=getopt(str))==1 || Opt==0) && Opt>=0 && P>=0){ - if(Opt==2 || Opt==4 || Opt==0){ - if(N==0) return (Opt>0)?"0":0; - Pw=0; - if(NT==4){ - NN=abs(real(N));N1=abs(imag(N)); - if(NN<N1) NN=N1; - }else NN=abs(N); - while(NN<1 && NN>-1){ - Pw--; - N*=10;NN*=10; - } - while(N>=10 || N<=-10){ - Pw++; - N/=10;NN/=10; - } - if(Opt==0) return sint(N*10^Pw,P-Pw-1); - S=(getopt(sqrt)==1)?sint(N,P|str=(Opt==4)?3:1,sqrt=1):sint(N,P|str=(Opt==4)?3:1); - if(Pw==0) return S; - if(NT==4) - S="("+S+")"; - if(Pw==1){ - if(Opt==2) - return S+"*10"; - else - return S+"\\times10"; - } - if(Opt==2) - return S+"*10^("+rtostr(Pw)+")"; - else - return S+"\\times10^{"+rtostr(Pw)+"}"; - } - if(NT==4){ - NN=real(N); - if(NN!=0){ - S=sint(NN,P|str=1); - if(imag(N)>0) S=S+"+"; - } - else S=""; - S=S+sint(imag(N),P|str=1)+((Opt==3)?((getopt(sqrt)==1)?"\\sqrt{-1}":"i"):"@i"); - return S; - } - if(N<0){ - N=-N; - Neg="-"; - }else Neg=""; - N=rint(N*10^P)/10^P; - NN=floor(N); - NV=(N-NN+1)*10^P; - NS=rtostr(NN); - if(P<=0) return Neg+NS; - if(NN==0 && getopt(zero)==0) NS=""; - return Neg+NS+"."+str_cut(rtostr(NV),1,P); - } - if(NT==4) - return sint(real(N),P)+sint(imag(N),P)*@i; - X = rint( N*10^P ); - return deval(X/10^P); - } - if( (type(N)==2) || (type(N)==3) ){ - NN = eval(N); - if( type(NN)==1 ) - return sint(NN,P|option_list=getopt()); - else return N; - } - if( type(N)>3 && type(N) < 7) -#ifdef USEMODULE - return mtransbys(os_md.sint,N,[P]|option_list=getopt()); -#else - return mtransbys(sint,N,[P]|option_list=getopt())); -#endif - return N; -} - -def frac2n(N) -{ - if((T=type(N))<0) return N; - E=(getopt(big)==1)?eval(@e):0.1; - if(T==1){ - if(ntype(N)==0) return (E*N)/E; - else if(ntype(N)!=4) return N; - else return (E*(1+@i)*N)/(E*(1+@i)); - } - if(T==3||T==2){ - N=red(N); - Nm=nm(N);Var=vars(Nm);V=car(Var);K=length(Var); - for(S=0,I=mydeg(Nm,V);I>=0;I--) S+=frac2n(mycoef(Nm,I,V))*V^I; - return S/dn(N); - } - if(T<4) return (E*N)/E; -#ifdef USEMODULE - return mtransbys(os_md.frac2n,N,[]|option_list=getopt()); -#else - return mtransbys(frac2n,N,[]|option_list=getopt()); -#endif -} - -def xyproc(F) -{ - if(type(Opt=getopt(opt))!=7) Opt=""; - if(type(Env=getopt(env))!=7) - Env=(!TikZ)?"xy":"tikzpicture"; - if(F==1) - return(Opt=="")?"\\begin{"+Env+"}\n":"\\begin{"+Env+"}["+Opt+"]\n"; - if(F==0) return "\\end{"+Env+"}\n"; - if(type(F)==7){ - F=xyproc(1|opt=Opt,env=Env)+F+xyproc(0|env=Env); - if(getopt(dviout)==1) dviout(F); - else return F; - } -} - -def xypos(P) -{ - if(type(P[0])==7){ - if(P[0]=="") S=""; - else S=(!TikZ)?"\""+P[0]+"\"":"("+P[0]+")"; - } - else{ - if(TikZ==0 && XYcm==1){ - X=sint(P[0]*10,XYPrec); Y=sint(P[1]*10,XYPrec); - }else{ - X=sint(P[0],XYPrec); Y=sint(P[1],XYPrec); - } - S="("+rtostr(X)+","+rtostr(Y)+")"; - } - if(!TikZ){ - if(length(P)>2 && (PP=P[2])!=""){ - S=S+" *"; - if(type(PP)==4 && length(PP)==2 && type(PP[0])==7){ - S=S+PP[0]; - PP=PP[1]; - } - if(type(PP)==7){ - L=str_len(PP); - if(str_chr(PP,0,"$")==0 && str_chr(PP,L-1,"$")==L-1){ - PP=str_cut(PP,1,L-2); - }else S+="\\txt"; - } - else PP=my_tex_form(PP); - S=S+"{"+PP+"}"; - } - if(length(P)>3){ - if(type(P[3])==7 && P[3]!="") S=S+"=\""+P[3]+"\""; - if(length(P)>4 && type(P[4])==7) S=S+P[4]; - } - }else{ - T=""; - if(length(P)>2 && (PP=P[2])!=""){ - F=1; - if(type(PP)==4){ - if(length(PP)==2 && type(PP[0])==7){ - T="["+PP[0]+"]"; - PP=PP[1]; - } - } - if(type(PP)!=7) PP="$"+my_tex_form(PP)+"$"; - S=S+"{"+PP+"}"; - }else F=0; - if(length(P)>3){ - if(type(P[3])==7 && P[3]!="") T=T+"("+P[3]+")"; - else if(P[3]==1) T=T+"(_)"; - if(length(P)>4 && type(P[4])==7) S=S+P[4]; - } - if(length(P)>2){ - if(F) S="node"+T+" at"+S; - else S="coordinate"+T+" at"+S; - } - } - return S; -} - -def xyput(P) -{ - if((type(Sc=getopt(scale))==1 && Sc!=1) || type(Sc)==4){ - if(type(Sc)==1) Sc=[Sc,Sc]; - Sx=Sc[0];Sy=Sc[1]; - if(length(P)>2) - P1=cons(Sy*P[1],cdr(cdr(P))); - else P1=[Sy*P[1]]; - P=cons((type(P[0])==7)?P[0]:(Sx*P[0]),P1); - } - if(!TikZ) return "{"+xypos(P)+"};\n"; - return "\\"+xypos(P)+";\n"; -} - -def xyline(P,Q) -{ - if(!TikZ) return "{"+xypos(P)+" \\ar@{-} "+xypos(Q)+"};\n"; - if(type(T=getopt(opt))!=7) T=""; - else T="["+T+"]"; - if(length(P)<3 && length(Q)<3) - return "\\draw"+T+xypos(P)+"--"+xypos(Q)+";\n"; - if(length(P)==2) P=[P[0],P[1],"","_0"]; - else if(length(P)==3 || (length(P)==4 && P[3]=="")) - P=[P[0],P[1],P[2],"_0"]; - else if(length(P)>4 && P[3]=="") - P=[P[0],P[1],P[2],"_0",P[4]]; - if(length(Q)==2) Q=[Q[0],Q[1],"","_1"]; - else if(length(Q)==3 || (length(Q)==4 && Q[3]=="")) - Q=[Q[0],Q[1],Q[2],"_1"]; - else if(length(Q)>4 && Q[3]=="") - Q=[Q[0],Q[1],Q[2],"_1",Q[4]]; - return "\\draw "+T+xypos(P)+" "+xypos(Q)+"("+P[3]+")--("+Q[3]+");\n"; -} - -def xylines(P) -{ -/* mycat([P,getopt()]); */ - Lf=getopt(curve); - if(type(Lf)!=1) Lf=0; - SS=getopt(opt); - SF=(SS==0)?1:0; - if((Proc=getopt(proc))==1||Proc==2||Proc==3){ - OL=cons(["opt",0],delopt(getopt(),["opt","proc"])); - R=xylines(P|option_list=OL); - OP=(type(SS)<0)?[]:((type(SS)==4)?[["opt",SS[0]],["cmd",SS[1]]]:[["opt",SS]]); - return [1,OP,R]; - } - if(type(SS)!=7 && type(SS)!=4){ - if(Lf==0 && !TikZ) SS="@{-}"; - else SS=""; - } - if(type(Sc=getopt(scale))==1 || type(Sc)==4){ - if(type(Sc)==1) Sc=[Sc,Sc]; - Sx=Sc[0];Sy=Sc[1]; - if(Sx!=1 || Sy!=1){ - for(PP=[], P0=P; P0!=[]; P0=cdr(P0)){ - PT=car(P0); - if((type(PT)!=4 && type(PT)!=5) || (type(PT[0])!=1 && PT[0]!=0)) - PP=cons(PT,PP); - else{ - if(length(PT)>2 && type(PT)==4) - P1=cons(Sy*PT[1],cdr(cdr(PT))); - else P1=[Sy*PT[1]]; - PP=cons(cons(Sx*PT[0],P1),PP); - } - } - P=reverse(PP); - } - } - if(type(Cl=CL0=getopt(close))!=1) Cl=0; - if((Vb=getopt(verb))!=1&&type(Vb)!=4) Vb=0; - if(type(Lf)!=1 || Lf==0){ /* lines */ - if(TikZ||SF){ - for(L=[],F=0,PT=P;PT!=[];PT=cdr(PT)){ - if(type(car(PT))<4){ - L=cons(car(PT),L); - F=0; - }else{ - if(F++>1) L=cons(1,L); - L=cons(car(PT),L); - } - } - if(Cl==1){ - L=cons(1,L);L=cons(-1,L); - } - if(L) L=reverse(L); - if(SF) return L; - if(type(SS)!=4) S=xybezier(L|opt=SS); - else S=xybezier(L|opt=SS[0],cmd=SS[1]); - - }else{ - Out = str_tb(0,0); - for(PT=P; PT!=[]; ){ - PS1=car(PT); - PT=cdr(PT); - if(PT==[]){ - if(Cl==1) PS2=car(P); - else PS2=0; - }else PS2=car(PT); - str_tb(xyarrow(PS1,PS2|opt=SS),Out); - } - S=str_tb(0,Out); - } - }else if(Lf==2){ /* B-spline */ - if(SF) return P; - if(!TikZ){ - Out = str_tb("{\\curve{",0); - for(PT=P;PT!=[];PT=cdr(PT)){ - if(car(PT)==0){ - str_tb("}};\n{\\curve{",Out); - continue; - } - if(PT!=P) str_tb("&",Out); - str_tb(xypos([car(PT)[0],car(PT)[1]]),Out); - } - str_tb("}};\n",Out); - S=str_tb(0,Out); - }else Out=str_tb(xybezier(P|opt=SS),0); - for(I=0;I<2;I++){ - Q=car(P); - if(length(Q)>2) - str_tb(xyput(Q),Out); - P=reverse(P); - } - S=str_tb(0,Out); - }else{ /* extended Bezier */ - RTo=getopt(ratio); - if(type(Acc=getopt(Acc))!=1) Acc=0; - if(type(RTo)!=1 || RTo>1.5 || RTo<0.001) RTo=0; - if(Cl==1){ - PR=reverse(P); - PT=car(PR); - PR=cons(P[0],PR); - PR=cons(P[1],PR); - P=cons(PT,reverse(PR)); - }else if(Cl==-1) Cl=1; - for(L=P2=P3=0,PT=P;;){ - P1=P2;P2=P3;P3=P4; - P4=(PT==[])?0:car(PT); - if(PT==[] && (Cl==1 || P3==0)) break; - PT=cdr(PT); - if(P3==0) str_tb("%\n", Out); - if(P2==0 || P3==0 || (Cl==1 && P1==0)) continue; - if(L!=0){ - if(car(L)==P2) - L=cons(1,L); - else{ - L=cons(0,L); L=cons(P2,L); - } - }else L=[P2]; - X=P3[0]-P2[0];Y=P3[1]-P2[1]; - DL1=DL2=0;DL=Acc?sqrt(X^2+Y^2):dsqrt(X^2+Y^2); - if(P4!=0){ - XD1=P4[0]-P2[0];YD1=P4[1]-P2[1];DL1=Acc?sqrt(XD1^2+YD1^2):dsqrt(XD1^2+YD1^2); - } - if(P1!=0){ - XD2=P3[0]-P1[0];YD2=P3[1]-P1[1];DL2=Acc?sqrt(XD2^2+YD2^2):dsqrt(XD2^2+YD2^2); - } - if(RTo!=0) - R=RTo; - else if(DL1>0 && DL2>0){ - Cos=(XD1*XD2+YD1*YD2)/(DL1*DL2); - RT=4/(3*(Acc?sqrt((1+Cos)/2):dsqrt((1+Cos)/2))+3); - R=DL*RT/(DL1+DL2); - }else if(DL1!=0) - R=DL/(2*DL1); - else if(DL2!=0) - R=DL/(2*DL2); - if(DL2!=0) L=cons([P2[0]+R*XD2,P2[1]+R*YD2],L); - if(DL1!=0) L=cons([P3[0]-R*XD1,P3[1]-R*YD1],L); - L=cons([P3[0],P3[1]],L); - } - if(CL0==1) L=cons(-1,cdr(L)); - if(L!=0) L=reverse(L); - if(SF) return L; - if(type(SS)==4) - S=xybezier(L|opt=SS[0],cmd=SS[1],verb=Vb); - else - S=xybezier(L|opt=SS,verb=Vb); - } - if(getopt(dviout)!=1) return S; - xyproc(S|dviout=1); -} - -def saveproc(S,Out) -{ - if(type(Out)==4){ - Out=cons(S,Out); - return Out; - }else{ - str_tb(S,Out); - return Out; - } -} - -def xy2graph(F0,N,Lx,Ly,Lz,A,B) -{ - /* (x,y,z) -> ( -x sin A + y cos A, z cos B - x cos A sin B - y sin A sin B) */ - if((Proc=getopt(proc))==1||Proc==2){ - OPT0=[["proc",3]]; - }else{ - Proc=0;OPT0=[]; - } - if(type(DV=getopt(dviout))==4){ - S=["ext","shift","cl","dviout"]; - OL=delopt(getopt(),S); - OL=cons(["proc",1],OL); - R=xy2graph(F0,N,Lx,Ly,Lz,A,B|option_list=OL); - OL=delopt(getopt(),S|inv=1); - return execdraw(R,DV|optilon_list=OL); - } - if(N==0 || N>100 || N<-100) N=-16; - if(N<0){ - N=-N;N1=-1;N2=NN+1; - }else{ - N1=0;N2=NN=N; - } - - Ratio=Ratio2=1; - if(type(Sc=Sc0=getopt(scale))!=1 && type(Sc)!=4) Sc=1; - if(type(Sc)==4){ - Ratio=Sc[1]/Sc[0]; - if(length(Sc)>2) Ratio2=Sc[2]/Sc[0]; - Sc=Sc[0]; - } - if(type(Vw=getopt(view))!=1) Vw=0; - if(type(Raw=getopt(raw))!=1) Raw=0; - if(type(M1=getopt(dev))==1) M2=M1; - else if(type(M1)==4){ - M2=M1[1];M1=M1[0]; - }else M1=0; - if(type(M3=getopt(acc))!=1 || (M3<0.5 && M3>100)) M3=1; - if(M1<=0) M1=16; - if(M2<=0) M2=16; - OL=[["para",1],["scale",Sc]]; - if(Raw==1) OL=cons(["raw",1],OL); - if(type(Prec=getopt(prec))>=0) OL=cons(["prec",Prec],OL); - L=newvect(4,[[Lx[1],Ly[0]],[Lx[1],Ly[1]],[Lx[0],Ly[1]],[Lx[0],Ly[0]]]); - Lx=[deval(Lx[0]),deval(Lx[1])]; - Ly=[deval(Ly[0]),deval(Ly[1])]; - Lz=[deval(Lz[0]),deval(Lz[1])]; - A=(A0=A)%360; - F00=F0; - if(type(F0)<4){ - FC=f2df(F0); - if(findin(z,Vars=vars(FC))>=0 && findin(x,Vars)<0 && findin(y,Vars)<0) - F0=[w,[z,0,x+y*@i],[w,os_md.abs,FC]]; - } - if(type(Org=getopt(org))==4){ /* shift origin */ - Lx=[Lx[0]-Org[0],Lx[1]-Org[0]]; - Ly=[Ly[0]-Org[1],Ly[1]-Org[1]]; - Lz=[Lz[0]-Org[2],Lz[1]-Org[2]]; - F0=mysubst(F0,[[x,x+Org[0]],[y,y+Org[1]]]); - if(type(F0)==4){ - F0=cons(F0[0]-Org[2],cdr(F0)); - } - else F0-=Org[2]; - }else Org=[0,0,0]; - Cpx=getopt(cpx); - if(type(Cpx)<0){ - if(str_str(rtostr(F0),"@i")>=0) Cpx=1; - else Cpx=0; - } - if(A<0) A+=360; - if(A<90){ - Sh=1;F1=F0;Cx=x-Org[0];Cy=y-Org[1]; - }else if(A<180){ /* x -> y, y -> -x */ - Sh=2;A-=90; F1=mulsubst(F0,[[x,-y],[y,x]]); - LL=Ly;Ly=[-Lx[1],-Lx[0]];Lx=LL;Cx=y-Org[1];Cy=-x+Org[0]; - }else if(A<270){ - Sh=3;A-=180; F1=subst(F0,[[x,-x],[y,-y]]); - Lx=[-Lx[1],-Lx[0]];Ly=[-Ly[1],-Ly[0]];Cx=-x+Org[0];Cy=-y+Org[1]; - }else{ - Sh=4;A-=270;F1=mulsubst(F0,[[x,y],[y,-x]]); - LL=Lx;Lx=[-Ly[1],-Ly[0]];Ly=LL;Cx=-y+Org[1];Cy=x-Org[0]; - } - A=@pi*A/180; B=@pi*B/180; - if(A==0) A=@pi/3; - if(B==0) B=@pi/12; - NN=N*M2; - Ac=dcos(deval(A)); As=dsin(deval(A)); - if(Ac<=0.087 || As<=0.087){ - mycat(["Unsuitable angle",A0,"(6-th argument)!"]); - return -1; - } - Bc=Ratio*dcos(deval(B)); Bs=dsin(deval(B)); - if(Bc<0){ - mycat("Unsuitable angle (7-th argument)!"); - return -1; - } - /* - z = f(x,y) => X=-As*x+Ac*y, Y= Bc*f(x,y)-Bsc*x-Bss*y - Out X-coord is in [X0,X1], dvided by Dev segments - J-th segment of Y-coord : ZF[J]==1 => [Z0[0],Z1[J]] - */ - Bsc=Bs*Ac;Bss=Bs*As; - if(Ratio2!=1){ - if(Sh%2==1){ - Ac*=Ratio2;Bss*=Ratio2; - }else{ - As*=Ratio2;Bsc*=Ratio2; - } - } - CX=-As*Cx+Ac*Cy;CY=Bc*(z-Org[2])-Bsc*Cx-Bss*Cy; - if(type(Dvi=getopt(dviout))!=1 && getopt(trans)==1) return [CX*Sc,CY*Sc]; - if(type(N1=getopt(inf))==1){ - if(Proc) Dvi=N1; - else if(Dvi<=0) Dvi=-N1; - } - X0=-As*Lx[1]+Ac*Ly[0];X1=-As*Lx[0]+Ac*Ly[1]; - F1=mysubst(F1,[@pi,deval(@pi)]); - Tf=type(F1=f2df(F1|opt=0)); - if(Tf!=4) F=Bc*F1-Bsc*x-Bss*y; - else F=append([Bc*F1[0]-Bsc*x-Bss*y],cdr(F1)); - Dx=(Lx[1]-Lx[0])/NN; Dy=(Ly[1]-Ly[0])/NN; - if(type(Err=getopt(err))==1) - F=mysubst(F,[[x,x+Err*Dx/1011.23],[y,y+Err*Dy/1101.34]]); - Out=(Proc)?[]:str_tb(0,0); - Dev=N*M1; - XD=(X1-X0)/Dev; - OLV=newvect(2,[OL,OL]); - if(type(Ura=getopt(opt))==4 || type(Ura)==7){ - if(type(Ura)==7) Ura=[Ura,Ura]; - else{ - OLV[0]=cons(["opt",Ura[0]],OL); - OLV[1]=cons(["opt",Ura[1]],OL); - } - } - for(KC=0; KC<=1; KC++){ /* draw curves */ - Z0=newvect(Dev+1); Z1=newvect(Dev+1); ZF=newvect(Dev+1); - for(I=0; I<=NN; I++){ - FV=I%M2; - if(KC==0){ - X=x; Y=Ly[1]-I*Dy; LX=Lx; DD=Dx; G=mysubst(F,[y,Y]); - if(!FV){ - if(!Proc) str_tb(["%y=",rtostr(Y),"\n"],Out); - else Out=cons([-2,"y="+rtostr(Y)],Out); - } - }else{ - X=Lx[1]-I*Dx; Y=x; LX=Ly; DD=Dy; G=mysubst(F,[[x,X],[y,Y]]); - if(!FV){ - if(!Proc) str_tb(["%x=",rtostr(X),"\n"],Out); - else Out=cons([-2,"x="+rtostr(X)],Out); - } - } - XX=-As*X+Ac*Y; A1=coef(XX,1,x); A0=coef(XX,0,x); /* XX = A1*x + A0, x = (XX-A0)/A1 */ - if(!FV && Vw==1){ - if(Proc) Out=cons(xygraph([XX,G],N,LX,[X0,X1],Lz|scale=Sc,para=1,proc=3),Out); - else str_tb(xygraph([XX,G],N,LX,[X0,X1],Lz|scale=Sc,para=1),Out); - continue; - } - V=VT=LX[1]; - J0=(subst(XX,x,LX[0])-X0)/XD; J1=(subst(XX,x,LX[1])-X0)/XD; - if(J0<J1){ - J0=ceil(J0); J1=floor(J1); JD=1; /* fixed x: y: dec => (x,z):(dec,inc) */ - }else{ - J0=floor(J0); J1=ceil(J1); JD=-1; /* fixed y: x: dec => (x,z):(inc,inc) */ - } - for(FF=1,J=J1;;J-=JD){ - V1=VT; - VT=(X0+J*XD-A0)/A1;GG=mysubst(G,[x,VT]); - if(Cpx>=1) VV=myeval(GG); - else VV=(Tf==4)? mydeval(GG):deval(GG); /* J -> V */ - if(ZF[J]==0 || VV<=Z0[J] || VV>=Z1[J]){ /* visible */ - if(FF==0){ - V0=(VT+V1)/2; - if(!FV && Vw==-1 && Raw!=1){ /* draw doted line */ - K=ceil(M3*(V-V0)/(M2*DD)); - if(N1<0) K=-K; - OPT=append(OPT0,[["opt",(TikZ)?"dotted":"~*=<3pt>{.}"],["scale",Sc],["para",1]]); - Out=saveproc(xygraph([XX,G],K,[V0,V],[X0-1,X1+1],Lz| - option_list=OPT),Out); - } - V=V0; - } - if(ZF[J]==0){ - ZF[J]=1; Z0[J]=Z1[J]=VV; - }else if(VV<=Z0[J]) Z0[J]=VV; - else Z1[J]=VV; - - if(VV>=Z1[J]) FF=1; - else if(VV<=Z0[J]) FF=-1; - }else{ - if(FF!=0){ - V0=(VT+V1)/2; - K=ceil(M3*(V-V0)/(M2*DD)); - if(N1<0) K=-K; - if(!FV){ - OPT=append(OPT0,OLV[(1-FF)/2]); - Out=saveproc(xygraph([XX,G],K,[V0,V],[X0-1,X1+1],Lz|option_list=OPT),Out); - } - V=V0; - } - FF=0; - } - if(J==J0) break; - } - if(FV) continue; - V0=LX[0];K=ceil(M3*(V-V0)/(M2*DD)); - if(N1<0) K=-K; - if(FF!=0){ - if(Raw!=1){ - OPT=append(OPT0,OLV[(1-FF)/2]); - Out=saveproc(xygraph([XX,G],K,[V0,V],[X0-1,X1+1],Lz|option_list=OPT),Out); - }else if(Vw==-1 && Raw!=1){ - OPT=append(OPT0,[["opt",(TikZ)?"dotted":"~*=<3pt>{.}"]]); - Out=saveproc(xygraph([XX,G],K,[V0,V],[X0-1,X1+1],Lz|option_list=OPT),Out); - } - } - } - } - OptSc=(Sc==1)?[]:[["scale",Sc]]; - if(type(LZ=getopt(ax))==4){ /* draw box */ - FC=0; - if(length(LZ)==3) FC=LZ[2]; - P0=newvect(2,[-As*Lx[1]+Ac*Ly[1],Bc*(LZ[0]-Org[0])-Bsc*Lx[1]-Bss*Ly[1]]); - Vx=newvect(2,[As*(Lx[1]-Lx[0]),Bsc*(Lx[1]-Lx[0])]); - Vy=newvect(2,[Ac*(Ly[0]-Ly[1]),Bss*(Ly[1]-Ly[0])]); - Vz=newvect(2,[0,Bc*(LZ[1]-LZ[0])]); - OL=OL0=append(OPT0,OL); - if(TikZ && type(Ura)==4 && length(Ura)>2) OL0=cons(["opt",Ura[2]],OL); - LL=[[P0+Vz,P0+Vx+Vz],[P0,P0+Vx]]; - if(Bs>0){ - LL=cons([P0+Vy+Vz,Pz=P0+Vx+Vy+Vz],LL); - LL=cons([P0+Vx+Vz,Pz],LL); - PP=Pz-Vz; - } - else{ - LL=cons([P0+Vy,Pz=P0+Vx+Vy+Vz],LL); - LL=cons([P0+Vx,Pz],LL); - PP=Pz+Vz; - } - J=ceil((PP[0]-X0)/XD+0.5); - LL=append([[P0+Vy,P0+Vy+Vz],[P0+Vy,P0+Vy+Vz],[P0+Vx,P0+Vx+Vz],[P0,P0+Vz], - [P0+Vz,P0+Vy+Vz],[P0,P0+Vy]],LL); - for(LL=reverse(LL);LL!=[];LL=cdr(LL)) Out=saveproc(xylines(car(LL)|option_list=OL0),Out); - if(Dev>4) Dev2=ceil(Dev/2); - if(FC<0 && Raw!=1){ - if(TikZ){ - if(type(Ura)==4 && length(Ura)>2) - OL1=cons(["opt",Ura[2]+",dotted"],OL); - else OL1=cons(["opt","dotted"],OL); - }else OL1=cons(["opt","@{.}"],OL); - if(FC==-8) FC=0; - } - for(I=0;I<3;I++){ /* box with hidden part */ - if(I==1) Pz=PP-Vx; - else if(I==2) Pz=PP-Vy; - LP=Pz-PP; - for(FV=-1,K=0;K<=Dev2; K++){ - PPx=PP[0]+(K/Dev2)*LP[0]; PPy=PP[1]+(K/Dev2)*LP[1]; - J=ceil((PPx-X0)/XD); - if(K!=Dev2 && (J<0||J>Dev)) continue; - if(K!=Dev2 && (ZF[J]==0 || PPy<Z0[J] || PPy>Z1[J])){ /* visible */ - if(FV!=1){ - FV=1; - PPP=[PPx,PPy]; - } - }else{ - if(FV!=0){ - if(FV==1) Out=saveproc(xylines([PPP,[PPx,PPy]]|option_list=OL1),Out); - FV=0; - } - } - } - } - if(FC!=0 && Raw!=1){ /* show coordinate*/ - if(iand(FC,4)){ - Sub=1; - if(TikZ){ - S0="\\scriptsize";S1=""; - }else{ - S0="{}_{"; S1="}"; - } - }else Sub=0; - if(iand(FC,2)) - LLL=[[1,0,P0+Vx,(TikZ)?"right":"+!L"],[3,0,P0+Vy,(TikZ)?"left":"+!R"]]; - else LL=[]; - if(Bs>0){ - LLL=cons([0,0,P0,(TikZ)?"below":"+!U"],LLL); - LLL=cons([2,1,P0+Vx+Vy+Vz,(TikZ)?"above":"+!D"],LLL); - }else{ - LLL=cons([2,0,P0+Vx+Vy,(TikZ)?"below":"+!U"],LLL); - LLL=cons([0,1,P0+Vz,(TikZ)?"above":"+!D"],LLL); - } - for(TLL=LLL;TLL!=[];TLL=cdr(TLL)){ - TL=car(TLL);LL=L[(Sh+TL[0])%4]; - if(Cpx==0 || Cpx==3){ - S=ltotex([LL[0],LL[1],LZ[TL[1]]]|opt="coord"); - SS="("+rtostr(LL[0]) +","+rtostr(LL[1])+","+rtostr(LZ[TL[1]])+")"; - }else{ - S=ltotex([LL[0]+LL[1]*@i,LZ[TL[1]]]|opt="coord",cpx=Cpx); - SS="("+rtostr(LL[0])+"+"+rtostr(LL[1])+"i,"+ rtostr(LZ[TL[1]])+")"; - } - if(TikZ) S="$"+S+"$"; - if(Sub) S=S0+S+S1; - if(!TikZ) S="$"+S+"$"; - if(Proc) Out=cons([2,OptSc,[TL[2][0],TL[2][1]],[[TL[3],S]],SS],Out); - else str_tb(xyput([TL[2][0],TL[2][1],[TL[3],S]]|option_list=OptSc),Out); - } - } - } - if(type(Pt=getopt(pt))==4){ /* option pt=[] */ - if(type(Pt[0])<4) Pt=[[Pt]]; - if(length(Pt)>1&&type(Pt[1])!=4) Pt=[Pt]; - for(PT=Pt;PT!=[];PT=cdr(PT)){ - PP=car(PT); - if(type(PP)==4 && length(PP)==3 && type(PP[0])<2 && type(PP[2])<2) PP=[PP]; - P=car(PP); - if(type(P)==7) Q=[P,0]; - else if(P==1) Q=["_",0]; - else Q=mysubst([CX,CY],[[x,deval(P[0])],[y,deval(P[1])],[z,deval(P[2])]]); - if(length(PP)>1 && type(PP[1])==4 && length(PP[1])==3){ /* draw line */ - PP=cdr(PP);P=car(PP); - if(type(P)==7) Q1=P; - else if(P==1) Q="_"; - else Q1=mysubst([CX,CY],[[x,deval(P[0])],[y,deval(P[1])],[z,deval(P[2])]]); - if(length(PP)<2 || PP[1]==0 || iand(PP[1],1)) OL2=""; - else OL2=(TikZ)?"dotted":"@{.}"; - if(length(PP)>2 && type(PP[2])==7){ - if(OL2=="") OL2=PP[2]; - else{ - if(TikZ) OL2=OL2+","; - OL2=OL2+PP[2]; - } - } - OL1=OL; - if(OL2!="") OL1=cons(["opt",OL2],OL1); - if(length(PP)<2 || PP[1]>=0) - Out=saveproc(xylines([Q,Q1]|option_list=OL1),Out); - else{ - LP0=Q1[0]-Q[0];LP1=Q1[1]-Q[1]; - for(FV=-1,K=0;K<=Dev2; K++){ - PPx=Q[0]+(K/Dev2)*LP0; PPy=Q[1]+(K/Dev2)*LP1; - J=ceil((PPx-X0)/XD); - if(K!=Dev2 && (J<0 || J>Dev || ZF[J]==0 || PPy<Z0[J] || PPy>Z1[J])){ - /* visible */ - if(FV!=1){ - FV=1; - PPP=[PPx,PPy]; - } - }else{ - if(FV!=0){ - if(FV==1) Out=saveproc(xylines([PPP,[PPx,PPy]]|option_list=OL1),Out); - FV=0; - } - } - } - } - continue; - } - if(length(PP)==1) S="$\\bullet$"; - else if(type(PP[1])==7) S=PP[1]; - else if(type(PP[1])==4){ - if(length(PP[1])>1 && type(PP[1][1])!=7) - S=cons(car(PP),cons("$\\bullet$",cdr(cdr(PP)))); - else S=PP[1]; - }else S="$\\bullet$"; - if(length(PP)<=2){ - if(Proc) Out=cons([2,OptSc,[Q[0],Q[1]],[S]],Out); - else str_tb(xyput([Q[0],Q[1],S]|option_list=OptSc),Out); - }else if(!TikZ){ - if(Proc) Out=cons([2,OptSc,[Q[0],Q[1]],[S,"",PP[2]]],Out); - else str_tb(xyput([Q[0],Q[1],S,"",PP[2]]|option_list=OptSc),Out); - }else{ - if(Proc) Out=cons([2,OptSc,[Q[0],Q[1]],cons(S,cdr(cdr(PP)))],Out); - else str_tb(xyput(append([Q[0],Q[1],S],cdr(cdr(PP)))|option_list=OptSc),Out); - } - } - } - if(Proc){ - S=reverse(Out); - if(Proc==1||Proc==3){ - for(W=[],I=0;I<2;I++) for(J=0;J<2;J++) for(K=0;K<2;K++) - W=cons(mysubst([CX*Sc,CY*Sc],[[x,Lx[I]],[y,Ly[J]],[z,Lz[K]]]),W); - W=ptbbox(W); - S=cons([0,W[0],W[1],(TikZ)?1:1/10],S); - } - }else S=str_tb(0,Out); - if(type(Dvi)!=1||(Proc&&abs(Dvi)<2)) return S; - Lout=[]; - if(abs(Dvi)>=2){ - /* show title */ - L0=[]; - Title=getopt(title); - if(type(Title)!=7) - Title=(type(F00)==4)?("\\texttt{"+verb_tex_form(F00)+"}"):my_tex_form(F00); - if(type(Title)==7){ - T=my_tex_form(L[3][0])+"\\le x\\le "+my_tex_form(L[1][0])+",\\,"+ - my_tex_form(L[3][1])+"\\le y\\le "+my_tex_form(L[1][1])+")"; - if(Proc){ - if(Cpx>=1) L0=[[5,[["eq",1]],"|"+Title+"|\\quad(z=x+yi,\\ "+T]]; - else L0=[[5,[["eq",1]],"z="+Title+"\\ \\ ("+T]]; - }else{ - if(Cpx>=1) dviout("|"+Title+"|\\quad(z=x+yi,\\ "+T|eq=1,keep=1); - else dviout("z="+Title+"\\ \\ ("+T|eq=1,keep=1); - } - } - A=rint(deval(180*A/@pi))+90*(Sh-1); - if(A>=180) A-=180; - B=rint(deval(180*B/@pi)); - if(abs(Dvi)>=3){ - T="\\text{angle } ("+my_tex_form(A)+"^\\circ,"+my_tex_form(B)+"^\\circ)"; - if(Ratio!=1 || Ratio2!=1) T=T+"\\quad\\text{ratio }1:" - +my_tex_form(sint(Ratio2,2))+":"+my_tex_form(sint(Ratio,2)); - if(Proc) L0=cons([5,[["eq",1]],T],L0); - else dviout(T|eq=1,keep=1); - } - SS="% range "+rtostr([L[3][0],L[1][0]])+"x"+rtostr([L[3][1],L[1][1]])+ - " angle ("+ rtostr(A) +","+ rtostr(B)+") dev="; - if(M1==M2) SS=SS+rtostr(M1); - else SS=SS+rtostr([M1,M2]); - if(M3!=1) SS=SS+" acc="+rtostr(M3); - if(type(Sc0)>=0) SS=SS+" scale="+rtostr(Sc0); - if(Proc){ - S=cons([5,[],SS],S); - for(;L0!=[];L0=cdr(L0)) S=cons(car(L0),S); - return S; - } - if(Dvi>0){ - dviout(SS|keep=1); - dviout(xyproc(S)|eq=8); - }else Lout=[SS,S]; - }else{ - if(Dvi>0) dviout(xyproc(S)); - else Lout=[S]; - } - if(getopt(trans)==1) return cons([CX*Sc,CY*Sc],Lout); - if(Dvi<0) return Lout; -} - -def fouriers(A,B,X) -{ - if(A!=[]&&type(car(A))>1){ - for(C=[],I=A[1];I>=0;I--) C=cons(myfeval(car(A),I),C); - A=C; - } - if(B!=[]&&type(car(B))>1){ - for(C=[],I=B[1];I>0;I--) C=cons(myfeval(car(B),I),C); - B=C; - } - R=0; - if(getopt(cpx)==1){ - if(type(X=eval(X))>1) return todf([os_md.fouriers,[["cpx",1]]],[[A],[B],[X]]); - V=dexp(@i*X); - for(C=A,P=1,I=0;C!=[];C=cdr(C),I++){ - R+=car(C)*P; - P*=V; - } - V=dexp(-@i*X); - for(C=B,P=1,I=0;C!=[];C=cdr(C),I++){ - P*=V; - R+=car(C)*P; - } - return R; - } - if(type(X=eval(X))>1) return todf(os_md.fouriers,[[A],[B],[X]]); - for(C=A,I=0;C!=[];C=cdr(C),I++) - R+=car(C)*mycos(I*X); - for(C=B,I=1;C!=[];C=cdr(C),I++) - R+=car(C)*mysin(I*X); - return R; -} - - -def myexp(Z) -{ - if(type(Z=eval(Z))>1) return todf(os_md.myexp,[Z]); - if((Im=imag(Z))==0) return dexp(Z); - return dexp(real(Z))*(dcos(Im)+@i*dsin(Im)); -} - -def mycos(Z) -{ - if(type(Z=eval(Z))>1) return todf(os_md.mycos,[Z]); - if((Im=imag(Z))==0) return dcos(Z); - V=myexp(Z*@i); - return (V+1/V)/2; -} - -def mysin(Z) -{ - if(type(Z=eval(Z))>1) return todf(os_md.mysin,[Z]); - if((Im=imag(Z))==0) return dsin(Z); - V=myexp(Z*@i); - return (1/V-V)*@i/2; -} - -def mytan(Z) -{ - if(type(Z=eval(Z))>1) return todf(os_md.mytan,[Z]); - if((Im=imag(Z))==0) return dtan(Z); - V=myexp(2*Z*@i); - return @i*(1-V)/(1+V); -} - -def mylog(Z) -{ - if(type(Z=eval(Z))>1) return todf(os_md.mylog,[Z]); - if((Im=imag(Z))==0) return dlog(Z); - return dlog(dabs(Z))+@i*myarg(Z); -} - -def mypow(Z,R) -{ - if(type(Z=eval(Z))>1||type(R=eval(R))>1) return todf(os_md.mypow,[Z,R]); - if(Z==0) return 0; - if(isint(2*R)){ - if(R==0) return 1; - if(isint(R)) return Z^R; - V=dsqrt(Z); - if(R==1/2) return V; - return Z^(R-1/2)*V; - } - return myexp(R*mylog(Z)); -} - -def myarg(Z) -{ - if(type(Z=map(eval,Z))==4){ - if(length(Z)!=2) return todf(os_md.myarg,[Z]); - Re=Z[0];Im=Z[1]; - }else if(type(Z)>1){ - return todf(os_md.myarg,[Z]); - }else { - Im=imag(Z);Re=real(Z); - } - if(Re==0) return (Im<0)?-deval(@pi)/2:deval(@pi)/2; - V=datan(Im/Re); - if(Re>0) return V; - return (V>0)?(V-deval(@pi)):(V+deval(@pi)); -} - -def myatan(Z) -{ - if(type(Z=eval(Z))>1) return todf(os_md.myatan,[Z]); - if((Im=imag(Z))==0) return datan(Z); - mylog((1-Z*@i)/(1+Z*@i))*@i/2; -} - -def myasin(Z) -{ - if(type(Z=eval(Z))>1) return todf(os_md.myasin,[Z]); - return deval(@pi/2)-myacos(Z); -} - -def frac(X) -{ - if(type(X=eval(X))>1) return todf(os_md.frac,[X]); - return (ntype(X)==3)? pari(frac,X):(X-floor(X)); -} - -def myacos(Z) -{ - if(type(Z=eval(Z))>1) return todf(os_md.myacos,[Z]); - if(imag(Z)==0 && Z<=1 && Z>=-1) return dacos(Z); - return mylog(Z-dsqrt(Z^2-1))*@i; -} - -def arg(Z) -{ - if(vars(Z=map(eval,Z))!=[]) return todf(os_md.arg,[Z]); - return (type(Z)==4)?pari(arg,Z[0],Z[1]):arg(sqrt,Z); -} - -def sqrt(Z){ - if(vars(Z=map(eval,Z))!=[]) return todf(os_md.sqrt,[Z]); - R=(type(Z)==4)?Z[1]:Z; - if(ntype(R)==0){ - if(R==0) return 0; - if(R>0){ - if(pari(issquare,R)) return pari(isqrt,nm(R))/pari(isqrt,dn(R)); - }else{ - R=-R; - if(pari(issquare,R)) return pari(isqrt,nm(R))/pari(isqrt,dn(R))*@i; - } - } - return (type(Z)==4)?pari(sqrt,Z[0],Z[1]):pari(sqrt,Z); -} - -def gamma(Z) -{ - if(vars(Z=map(eval,Z))!=[]) return todf(os_md.gamma,[Z]); - return (type(Z)==4)?pari(gamma,Z[0],Z[1]):pari(gamma,Z); -} - -def lngamma(Z) -{ - if(vars(Z=map(eval,Z))!=[]) return todf(os_md.lngamma,[Z]); - return (type(Z)==4)?pari(lngamma,Z[0],Z[1]):pari(lngamma,Z); -} - -def digamma(Z) -{ - if(vars(Z=map(eval,Z))!=[]) return todf(os_md.digamma,[Z]); - return (type(Z)==4)?pari(digamma,Z[0],Z[1]):pari(digamma,Z); -} - -def dilog(Z) -{ - if(vars(Z=map(eval,Z))!=[]) return todf(os_md.dilog,[Z]); - return (type(Z)==4)?pari(dilog,Z[0],Z[1]):pari(dilog,Z); -} - -def erfc(Z) -{ - if(vars(Z=map(eval,Z))!=[]) return todf(os_md.erfc,[Z]); - return (type(Z)==4)?pari(erfc,Z[0],Z[1]):pari(erfc,Z); -} - -def zeta(Z) -{ - if(vars(Z=map(eval,Z))!=[]) return todf(os_md.zeta,[Z]); - return (type(Z)==4)?pari(zeta,Z[0],Z[1]):pari(zeta,Z); -} - -def eta(Z) -{ - if(vars(Z=map(eval,Z))!=[]) return todf(os_md.eta,[Z]); - return (type(Z)==4)?pari(eta,Z[0],Z[1]):pari(eta,Z); -} - -def jell(Z) -{ - if(vars(Z=map(eval,V))>1) return todf(os_md.jell,[Z]); - return (type(Z)==4)?pari(jell,Z[0],Z[1]):jell(jell,Z); -} - -def evals(F) -{ - if(type(F)==7){ - if(type(Del=getopt(del))!= 7) return eval_str(F); - S=strtoascii(Del);K=length(S); - if(K==0) return [eval_str(F)]; - Raw=getopt(raw); - F=strtoascii(F);L=[];T1=0; - do{ - T2=str_str(F,S|top=T1); - if(T2<0) T2=10000; - FT=str_cut(F,T1,T2-1); - L=cons((Raw==1)?FT:evals(FT),L); - T1=T2+K; - }while(T2!=10000); - return reverse(L); - } - if(type(F)==4){ - if(type(S=car(F))==7){ - S+="("; - for(I=0,FT=cdr(F); FT!=[]; I++,FT=cdr(FT)){ - if(type(ST=car(FT))!=7) ST=rtostr(ST); - if(I>0) S=S+","+ST; - else S=S+ST; - } - S=S+")"; - return eval_str(S); - }else return call(S,cdr(F)); - } - return F; -} - -def myval(F) -{ - if(type(F)!=4){ - F=f2df(sqrt2rat(F)); - if(type(F)!=4) return F; - }; - if(length(F)==1) V=car(F); - else for(V=car(F),F=cdr(F); F!=[];){ - FT=car(F); - if(type(G=FT[1])==2){ - if(length(FT)>2){ - FT2=myval(FT[2]); - if(length(FT)>3) FT3=myval(FT[3]); - }; - X=red(FT2/@pi);Vi=-red(FT2*@i/@pi);W=red(FT2/@e); - if(G==os_md.mypow && FT3==1/2){ - G=os_md.sqrt; - FT=[FT[0],G,FT[2]]; - } - if((T=findin(G, - [sin,os_md.mysin,cos,os_md.mycos,tan,os_md.mytan]))>=0 - &&(isint(6*X)||isint(4*X))){ - if(T==2||T==3){ - T=0;X=1/2-X; - } - X=X-floor(X/2)*2; - if(T==0||T==1){ - if(X>1){ - S=-1;X-=1; - }else S=1; - if(X>1/2) X=1-X; - if(X==0) R=0; - else if(X==1/6) R=1/2; - else if(X==1/4) R=2^(1/2)/2; - else if(X==1/3) R=3^(1/2)/2; - else R=1; - R*=S; - }else{ - if(X>1) X-=1; - if(X>1/2){ - S=-1;V=1-X; - }else S=1; - if(X==0) R=0; - else if(X==1/6) R=3^(1/2)/3; - else if(X==1/4) R=1; - else if(X==1/3) R=3^(1/2); - else R=2^512; - R*=S; - } - }else if((G==exp||G==os_md.myexp)&&(isint(FT2)||isint(6*Vi)||isint(4*Vi))){ - if(isint(FT2)) R=@e^FT2; - else R=myval([z+w*@i,[z,cos,Vi*@pi],[w,sin,Vi*@pi]]); - }else if((G==pow||G==os_md.mypow) && (isint(FT3)||FT2==1||FT2==0)){ - if(FT2==0) R=0; - else if(FT2==1) R=1; - else R=FT2^FT3; - }else if(G==os_md.abs&&ntype(P=eval(FT2))<4){ - R=FT2; - if(P<0) R=-R; - }else if((G==os_md.sqrt||G==dsqrt)&&type(FT2)<2&&ntype(FT2)==0) - R=sqrtrat(FT2); - else if((G==os_md.mylog||G==dlog)&&(FT2==@e||FT2==1)) - R=(FT2==1)?0:1; - else if(length(FT)==3) R=eval((*G)(myeval(FT2))); -#ifdef USEMODULE - else R=call(G,map(os_md.myeval,cdr(cdr(FT)))); -#else - else R=call(G,map(myeval,cdr(cdr(FT)))); -#endif - } - else if(G==0) R=FT[2]; -#ifdef USEMODULE - else R=eval(call(G[0],map(os_md.myeval,cdr(cdr(FT)))|option_list=G[1])); -#else - else R=eval(call(G[0],map(myeval,cdr(cdr(FT)))|option_list=G[1])); -#endif - V=mysubst(V,[FT[0],R]); - F=mysubst(cdr(F),[FT[0],R]); - } - if(type(V)<4 && !iscoef(V,os_md.iscrat)) V=eval(V); -#if 0 - return (type(V)<4)?myeval(V):mtransbys(os_md.myeval,V,[]); -#else - return V; -#endif -} - -/* -1:空 0:整数 1:有理数 2:Gauss整数 3:Gauss有理数 4:それ以外の複素数 */ -/* def vntype(F) -{ - if((T=type(F))<2){ - if(T<0) return -1; - if((Tn=ntype(F))==0){ - return (isint(F))?0:1; - } - if(Tn==4){ - if(ntype(real(F))==0&&ntype(real(F))==0) - return (isint(F)&&isint(F))?2:3; - return 4; - } - } - if(T==2){ - V=vars(F); - if((VV=lsort(V,[@e,@pi],1))==[]){ - FT=mycoef( - }else{ - if(length(VV)==1){ - }else - } - }else if(T==3){ - - } -} -*/ - - -def myeval(F) -{ - if(type(F)!=4) V=F; - else if(length(F)==1) V=car(F); - else for(V=car(F),F=cdr(F); F!=[];){ - FT=car(F); - if(type(G=FT[1])==2){ - if(length(FT)==3) R=(*G)(myeval(FT[2])); -#ifdef USEMODULE - else R=call(G,map(os_md.myeval,cdr(cdr(FT)))); -#else - else R=call(G,map(myeval,cdr(cdr(FT)))); -#endif - } - else if(G==0) R=myeval(FT[2]); -#ifdef USEMODULE - else R=call(G[0],map(os_md.myeval,cdr(cdr(FT)))|option_list=G[1]); -#else - else R=call(G[0],map(myeval,cdr(cdr(FT)))|option_list=G[1]); -#endif - V=mysubst(V,[FT[0],R]); - F=mysubst(cdr(F),[FT[0],R]); - } - return (type(V)<4)?eval(V):mtransbys(eval,V,[]); -} - -def mydeval(F) -{ - if(type(F)!=4) V=F; - else if(length(F)==1) V=car(F); - else for(V=car(F),F=cdr(F); F!=[]; ){ - FT=car(F); - if(type(G=FT[1])==2){ - if(length(FT)==3) R=(*G)(myeval(FT[2])); -#ifdef USEMODULE - else R=call(G,map(os_md.mydeval,cdr(cdr(FT)))); -#else - else R=call(G,map(mydeval,cdr(cdr(FT)))); -#endif - } - else if(G==0) R=mydeval(FT[2]); -#ifdef USEMODULE - else R=call(G[0],map(os_md.mydeval,cdr(cdr(FT)))|option_list=G[1]); -#else - else R=call(G[0],map(mydeval,cdr(cdr(FT)))|option_list=G[1]); -#endif - V=mysubst(V,[FT[0],R]); - F=mysubst(cdr(F),[FT[0],R]); - } - return (type(V)<4)?deval(V):mtransbys(deval,V,[]); -} - -def myfeval(F,X) -{ - if(type(X)==4){ - if(isvar(X[0])&&length(X)==2) - return mydeval(mysubst(F,[X[0],X[1]])); - if(type(X[0])==4&&isvar(X[0][0])&&length(X[0])==2){ - for(Y=X;Y!=[];Y=cdr(Y)) - F=mysubst(F,[car(Y)[0],car(Y)[1]]); - return myeval(F); - } - } - return myeval(mysubst(F,[x,X])); -} - -def myf2eval(F,X,Y) -{ - return myeval(mysubst(F,[[x,X],[y,Y]])); -} - -def myf3eval(F,X,Y,Z) -{ - return myeval(mysubst(F,[[x,X],[y,Y],[z,Z]])); -} - -def myfdeval(F,X) -{ - if(type(X)==4){ - if(isvar(X[0])&&length(X)==2) - return mydeval(mysubst(F,[X[0],X[1]])); - if(type(X[0])==4&&isvar(X[0][0])&&length(X[0])==2){ - for(Y=X;Y!=[];Y=cdr(Y)) - F=mysubst(F,[car(Y)[0],car(Y)[1]]); - return mydeval(F); - } - } - return mydeval(mysubst(F,[x,X])); -} - -def myf2deval(F,X,Y) -{ - return mydeval(mysubst(F,[[x,X],[y,Y]])); -} - -def myf3deval(F,X,Y,Z) -{ - return mydeval(mysubst(F,[[x,X],[y,Y],[z,Z]])); -} - -def df2big(F) -{ - AG=[[os_md.mysin,sin],[os_md.mycos,cos],[os_md.mytan,tan],[os_md.myasin,asin], - [os_md.acos,acos],[os_md,atan,atan],[os_md.myexp,exp],[os_md.mylog,log],[os_md.mypow,pow]]; - if(getopt(inv)!=1) return mysubst(F,AG); - else return mysubst(F,AG|inv=1); - -} - -def f2df(F) -{ - if(type(Opt=getopt(opt))!=1) Opt=0; - if(iand(Opt,1)){ - if(Opt>0) F=map(eval,F); - else F=map(deval,F); - } - Cpx=getopt(cpx); - if(type(F)==4 && iand(Opt,2)==0) return F; - K=getopt(level); - if(type(K)!=1) K=0; - AG=[sin,cos,tan,asin,acos,atan,exp,sinh,cosh,tanh,log,pow]; - AGd=[os_md.mysin,os_md.mycos,os_md.mytan,os_md.myasin,os_md.myacos, - os_md.myatan,os_md.myexp,os_md.myexp,os_md.myexp,os_md.myexp, - os_md.mylog,os_md.sqrt,os_md.myexp]; - for(R=[],I=0,Arg=vars(F);Arg!=[];Arg=cdr(Arg)){ - Fn=functor(car(Arg)); - if(vtype(Fn)!=3) continue; - V=args(car(Arg)); - for(PAG=AG,PAGd=AGd;PAG!=[];PAG=cdr(PAG),PAGd=cdr(PAGd)){ - if(Fn==car(PAG)){ - if(K==0) L="z__"; - else L="z"+rtostr(K)+"__"; - if(I==0) VC=makev([L]); - else VC=makev([L,I]); - I++; - VC0=VC; - if(Fn==sinh || Fn==cosh || Fn==tanh){ - VC=makev([L,I++]); - if(Fn==sinh) - R=cons([VC0,0,(VC^2-1)/(2*VC)],R); - else if(Fn==cosh) - R=cons([VC0,0,(VC^2+1)/(2*VC)],R); - else - R=cons([VC0,0,(VC^2-1)/(VC^2+1)],R); - } - if(Fn==pow && (V[1]!=1/2||Cpx==1)){ -#if 0 - R0=f2df(V[1]*((type(V[0])==1)?dlog(V[0]):log(V[0]))|level=K+1); - PAGd=cdr(PAGd); -#else - R=cons([VC,os_md.mypow,V[0],V[1]],R); - F=mysubst(F,[car(Arg),VC0]); - Arg=cons(0,vars(F)); - break; -#endif - }else R0=f2df(V[0]|level=K+1); - R=cons([VC,car(PAGd),R0],R); - F=mysubst(F,[car(Arg),VC0]); - Arg=cons(0,vars(F)); - break; - } - } - } - if(R==[]) return F; - if(Cpx==1){ - for(PAG=P,PAGd=AGd;PAG!=[];PAG=cdr(PAG),PAGd=cdr(PAGd)) - R=mysubst(R,[car(PADd),car(PAG)]); - } - return cons(F,reverse(R)); -} - -def todf(F,V) -{ - if(type(V)!=4) V=[V]; - for(R=[];V!=[];V=cdr(V)){ - R=cons(f2df(car(V)),R); - } - V=reverse(R); - Z=makenewv([F,V]); - return [Z,cons(Z,cons(F,V))]; -} - -def compdf(F,V,G) -{ - FL=["abs","floor","rint","zeta","gamma","arg","real","imag","conj"]; - FS=[os_md.abs,floor,rint,os_md.zeta,os_md.gamma,os_md.myarg,real,imag,conj]; - if(type(V)==4){ - for(;V!=[];V=cdr(V),G=cdr(G)) F=compdf(F,car(V),car(G)); - return F; - } - if(type(F)==7){ - if(str_str(F,"|")==0){ - F="abs("+str_cut(F,1,str_len(F)-2)+")"; - }else if(str_str(F,"[")==0){ - F="floor("+str_cut(F,1,str_len(F)-2)+")"; - } - I=str_str(F,"("); - Var=x; - if(I>0){ - J=str_pair(F,I+1,"(",")"); - if(J<0) return 0; - Var=eval_str(str_cut(F,I+1,J-1)); - Var=f2df(Var); - F0=str_cut(F,0,I-1); - } - if((I=findin(F0,FL))<0&&(I=findin(F,FL))<0) F=f2df(eval_str(F)); - else F=[z__,[z__,FS[I],Var]]; - } - if(type(F)!=4) F=f2df(F); - if(type(G)!=4) G=f2df(G); - VF=vars(F);VG=vars(G); - for(E=I=0;I<30;I++){ - for(J=0;J<30;J++){ - X=makev(["z__",I,J]); - if(findin(X,VF)<0 && findin(X,VG)<0){ - E=1;break; - } - } - if(E) break; - } - if(!E) return 0; - if(V==G) return F; /* subst(F(V),V,G) */ - if(type(G)<4) return mysubst(F,[V,G]); - if(type(F)<4) F=[F]; /* return compdf([X,[X,0,F]],V,G); */ - F=mysubst(F,[V,X]); - if(isvar(G[0])){ - G=mysubst(G,[G[0],X]); - if(length(G)==2&&type(G[1])==4&&G[1][0]==X) G=G[1]; - G=cons(G,cdr(F)); - } - else G=cons([X,0,G],cdr(F)); - return cons(car(F),G); -} - -def fzero(F,LX) -{ - if(length(LX)==3){ - V=LX[0];LX=cdr(LX); - }else V=x; - LX1=eval(LX[0]);LX2=eval(LX[1]); - if(getopt(zero)==1){ - if(getopt(cont)==1) CT=1; - else CT=0; - if(getopt(trans)!=1 && type(F)<4) F=f2df(F); - F=mysubst(F,[[@pi,deval(@pi)],[@e,deval(@e)]]); - if(type(Dev=getopt(dev))!=1 || Dev<2) Dev=16; - V1=myeval(mysubst(F,[V,X1=LX1])); - V2=myeval(mysubst(F,[V,X2=LX2])); - if(V1>0){ - V0=V1;V1=V2;V2=V0; - X0=X1;X1=X2;X2=X0; - } - if(V1<0 && V2>0){ - D=(V2-V1)*1024; - for(I=0; I<Dev; I++){ -/* mycat([D,X1,V1,X2,V2]) ; */ - if(iand(I,1)) X0=(X1+X2)/2; - else X0=(V2*X1-V1*X2)/(V2-V1); - V0=myeval(mysubst(F,[V,X0])); - if(V0==0||V0==V1||V0==V2) return [X0,V0]; - if(V0<0){ - if(!CT && V0+D<0) return []; - V1=V0;X1=X0; - }else{ - if(!CT && V0>D) return []; - V2=V0;X2=X0; - } - } - X0=(V2*X1-V1*X2)/(V2-V1); - return [X0,myeval(mysubst(F,[V,X0]))]; - } - if(V0==0) return [X0,V0]; - if(V1==0) return [X1,V1]; - return []; - } - if(type(F)<4) F=f2df(F); - F=mysubst(F,[[@pi,deval(@pi)],[@e,deval(@e)]]); - L=[]; - if(type(F)<4){ - if(type(F)==3) F=nm(red(F)); - if((Deg=deg(F,V))<=2){ - if(Deg==2){ - D=(C1=coef(F,1,V))^2-4*(C2=coef(F,2,V))*coef(F,0,V); - if(D>=0){ - R=dsqrt(D); - if((S=(-C1+R)/(2*C2))>=LX1&&S<=LX2) L=[[S,mysubst(F,[V,S])]]; - if(D!=0 && (S=(-C1-R)/(2*C2))>=LX1&&S<=LX2) L=cons([S,mysubst(F,[V,S])],L); - } - L=qsort(L); - }else if(Deg==1&&(S=-coef(F,0,V)/coef(F,1,V))>=LX1&&S<=LX2) - L=[[S,mysubst(F,[V,S])]]; - return L; - } - for(L=[];S!=[];S=cdr(S)) - if(car(S)>=LX1&&car(S)<=LX2) L=cons([car(S),mysubst(F,[V,car(S)])],L); - return qsort(L); - } - if(type(Div=getopt(mesh))!=1 || Div<=0) - Div = 2^(10); - W=(LX2-LX1)/Div; - for(I=V2=0;I<=Div;I++){ - X1=X2;X2=LX1+I*W;V1=V2; - if((V2=myeval(mysubst(F,[V,X2])))==0) - L=cons([X2,V2],L); - if(V1*V2<0){ - L0=fzero(F,[V,X1,X2]|zero=1,trans=1); - if(L0!=[]) L=cons(L0,L); - } - } - return reverse(L); -} - -def fmmx(F,LX) -{ - if(length(LX)==3){ - V=LX[0];LX=cdr(LX); - }else V=x; - LX1=eval(LX[0]);LX2=eval(LX[1]); - FT=F; - if(getopt(trans)!=1 && type(F)<4) FT=f2df(FT); - FT=mysubst(FT,[[@pi,eval(@pi)],[@e,eval(@e)]]); - if(type(G=getopt(dif))>=1){ - if(G==1) G=os_md.mydiff(F,V); - L=fzero(G,[V,LX1,LX2]|option_list=getopt()); - R=[[LX1,myeval(mysubst(FT,[V,LX1]))]]; - for(I=0;L!=[];L=cdr(L),I++){ - X=car(L)[0]; - if(X==LX1) continue; - R=cons([X,myeval(mysubst(FT,[V,X]))],R); - } - if(X!=LX2) R=cons([LX2,myeval(mysubst(FT,[V,LX2]))],R); - if(getopt(mmx)!=1) return reverse(R); - for(Mi=Ma=car(R);R!=[];R=cdr(R)){ - if(car(R)[1]>Ma[1]) Ma=car(R); - else if(car(R)[1]<Mi[1]) Mi=car(R); - } - return [Mi,Ma]; - } - if(type(Div=getopt(mesh))!=1 || Div<=0) - Div = 2^(10); - if(type(Dev=getopt(dev))!=1 || Dev<2) Dev=16; - W=(LX2-LX1)/Div; - for(I=V2=V3=0;I<=Div;I++){ - X1=X2;X2=X3;X3=LX1+I*W;V1=V2;V2=V3; - V3=myeval(mysubst(FT,[V,X3])); - if(I==0) L=[[X3,V3]]; - if(I<2) continue; - if((V1-V2)*(V2-V3)<0){ - X02=X2;V02=V2;X03=X3;V03=V3; - for(J=0; J<Dev && X1!=X3; J++){ - X12=(X1+X2)/2;V12=myeval(mysubst(FT,[V,X12])); - if((V1-V12)*(V12-V2)<=0){ - X3=X2;V3=V2;X2=X12;V2=V12;continue; - } - X23=(X2+X3)/2;V23=myeval(mysubst(FT,[V,X23])); - if((V12-V2)*(V2-V23)<=0){ - X1=X12;V1=V12;X3=X23;V3=V23;continue; - } - if((V2-V23)*(V23-V3)<=0){ - X1=X2;V1=V2;X2=X23;V2=V23;continue; - } - } - L=cons([X2,V2],L); - X2=X02;V2=V02;X3=X03;V3=V03; - } - } - L=cons([LX2,myeval(mysubst(FT,[V,LX2]))],L); - if(getopt(mmx)!=1) return L; - for(Mi=Ma=car(L);L!=[];L=cdr(L)){ - if(car(L)[1]>Ma[1]) Ma=car(L); - else if(car(L)[1]<Mi[1]) Mi=car(L); - } - return [Mi,Ma]; -} - -def flim(F,L) -{ - FD=f2df(F); - Lim0=4;Lim=12;FS=1; - if(type(Pc=getopt(prec))==1){ - if((Pc>1&&Pc<31)||Pc>-5) Lim+=Pc; - } - if(type(Pc=getopt(init))==1 && Pc>0) FS*=Pc; - if(type(L)==7) L=[L]; - else if(type(L)<2){ - K=flim(F,["+",L]|option_list=getopt()); - if(K=="") return K; - K1=flim(F,["-",L]|option_list=getopt()); - if(K1=="") return K1; - if(type(K)==7||type(K1)==7){ - if(K!=K1) return ""; - return K; - } - if(abs(K)<10^(-5)){ - if(abs(K1)<10^(-5)) return (K1+K)/2; - else return ""; - } - if(abs((K1-K)/K)<10^(-4)) return (K1+K)/2; - return ""; - } - if(type(L)!=4||type(L[0])!=7) return ""; - if(L[0]=="-"||L[0]=="-infty"){ - FS=-FS; - }else if(L[0]!="+"&&L[0]!="infty") return ""; - FI=(length(L)==1)?1:0; - for(Inf=0,I=Lim0;I<Lim;I++){ - D1=FS*8^I;D2=8*D1; - if(FI==0){ - D1=1/D1;D2=1/D2; - } - if(D1>D2){ - D=D1;D1=D2;D1=D; - X1=D1;X2=D2; - } - if(FI==0){ - D1+=L[1];D2+=L[1]; - } - K=fmmx(FD,[D1,D2]|mmx=1,mesh=16,dev=4); - if(I>Lim0){ - if(DF<K[1][1]-K[0][1]&&DF>10^(-8)&&DF<10^7){ - if(I>Lim0+1){ - if(Inf==0) return ""; - }else Inf=1; - }else if(Inf==1) return ""; - } - DF=K[1][1]-K[0][1]; - } - if(Inf==1){ - if(K[0][1]>10^8) return "+"; - else if(K[1][1]<-10^8) return "-"; - return ""; - } - V=(myfeval(FD,D1)+1.0)-1.0; - if(V!=0 && abs(V)<10^(-9)) return 0; - return V; -} - -def fcont(F,LX) -{ - if(length(LX)==3){ - V=LX[0];LX=cdr(LX); - }else V=x; - LX1=eval(LX[0]);LX2=eval(LX[1]); - if(getopt(trans)!=1 && type(F)<4) FT=f2df(F); - if(type(Div=getopt(mesh))!=1 || Div<=0) - Div = 2^(10); - if(type(Dev=getopt(dev))!=1 || Dev<2) Dev=16; - W=(LX2-LX1)/Div; - if((Df=getopt(dif))!=1){ - Df=0; - }else{ - if(Dev==16) Dev=6; - WD=W/2^(Dev+1); - } - F=FT; - C=2; - for(I=V2=V3=0;I<=Div;I++){ - X1=X2;X2=X3;X3=LX1+I*W;V1=V2;V2=V3; - V3=myeval(mysubst(F,[V,X3])); - if(Df){ - if(I==Div) break; - V3=(myeval(mysubst(F,[V,X3+WD]))-V3)/WD; - } - if(I==0) L=[[X3,V3]]; - if(I<2) continue; - if(C*dabs(2*V2-V1-V3) > dabs(V1-V3)){ - X01=X1;V01=V1;X02=X2;V02=V2;X03=X3;V03=V3; - for(J=0; X01!=X03; J++){ - if(dabs(V01-V02)>dabs(V02-V03)){ - X03=X02;V03=V02; - }else{ - X01=X02;V01=V02; - } - if(J==Dev) break; - X02=(X01+X02)/2; - V02=myeval(mysubst(F,[V,X02])); - if(Df) V02=(myeval(mysubst(F,[V,WD]))-V02)/WD; - if(C*dabs(2*V02-V01-V03) < dabs(V01-V03)) break; - } - if(J==Dev||X01==X03) L=cons([X01,X03,V03-V01],L); - } - } - return reverse(L); -} - -def xygraph(F,N,LT,LX,LY) -{ - if((Proc=getopt(proc))!=1&&Proc!=2&&Proc!=3) Proc=0; - if(type(DV=getopt(dviout))==4){ - OL=delopt(getopt(),["dviout","shift","ext","cl"]); - OL=cons(["proc",1],OL); - R=xygraph(F,N,LT,LX,LY|option_list=OL); - OL=delopt(getopt(),["shift","ext","cl"]|inv=1); - return execdraw(R,DV|optilon_list=OL); - } - if(N==0) N=32; - if(N<0){ - N=-N; - N1=-1; N2=N+1; - }else{ - N1=0; N2=N; - } - if(length(LT)==3 && isvar(LT[0])==1){ - TT=LT[0]; LT=cdr(LT); - F=mysubst(F,[TT,x]); - } - if(LX==0) LX=LT; - if((Acc=getopt(Acc))!=1) Acc=0; - if(Acc){ - LX=[eval(LX[0]),eval(LX[1])]; - LY=[eval(LY[0]),eval(LY[1])]; - LT=[eval(LT[0]),eval(LT[1])]; - }else{ - LX=[deval(LX[0]),deval(LX[1])]; - LY=[deval(LY[0]),deval(LY[1])]; - LT=[deval(LT[0]),deval(LT[1])]; - } - TD=(LT[1]-LT[0])/N; - if(type(Mul=getopt(scale))!=1){ - if(type(Mul)==4){ - MulX=Mul[0]; MulY=Mul[1]; - }else MulX=MulY=1; - }else MulX=MulY=Mul; - if(type(Org=getopt(org))==4){ - Orgx=Org[0];Orgy=Org[1]; - }else Orgx=Orgy=0; - if(type(F)!=4 || (getopt(para)!=1 && length(F)>1 && type(F[0])<4 && type(F[1])==4)) { - if(getopt(rev)!=1){ - F1=x; /* LX[0]+(LX[1]-LX[0])*(x-LT[0])/(TD*N); */ - F2=F; - }else{ - F1=F; - F2=x; /* LY[0]+(LY[1]-LY[0])*(x-LT[0])/(TD*N); */ - } - }else{ - F1=F[0]; F2=F[1]; - } - if(F1==0 || F2==0) LT=[]; - if(length(LT)==2){ - if(Acc){ - for(LTT=[],I=N2;I>=N1;I--) - LTT=cons(eval(LT[0]+I*(LT[1]-LT[0])/N),LTT); - }else{ - for(LTT=[],I=N2;I>=N1;I--) - LTT=cons(deval(LT[0]+I*(LT[1]-LT[0])/N),LTT); - } - LT=LTT; - } - Cpx=getopt(cpx); - if(Cpx!=1 && (str_str(rtostr(F1),"@i")>=0 || str_str(rtostr(F2),"@i")>=0)) - Cpx=1; - if(type(Cpx)<0) Cpx=0; - if(!Acc){ - if(type(F1)<4) F1=f2df(F1); - if(type(F2)<4) F2=f2df(F2); - } - if(type(Err=getopt(err))==1){ - F1=mysubst(F1,[x,x+Err*TD/1001.23]); - F2=mysubst(F2,[x,x+Err*TD/1001.23]); - } - if(type(F1)==4 || type(F2)==4){ - Dn=1; - }else Dn=dn(F1)*dn(F2); - for(V=[],PT=LT;PT!=[]; PT=cdr(PT)){ - T=car(PT); - if(myfeval(Dn,T)==0){ - V=cons(0,V); continue; - } - if(Cpx>0||Acc){ - X=myfeval(F1,T);Y=myfeval(F2,T); - }else{ - X=myfdeval(F1,T);Y=myfdeval(F2,T); - } - if((N1==0||(PT!=LT&&length(PT)!=1)) && (X<LX[0]||X>LX[1]||Y<LY[0]||Y>LY[1])) - V=cons(0,V); - else - V=cons([MulX*(X-Orgx),MulY*(Y-Orgy)],V); - } - V=reverse(V); - Gap0=Gap=Arg=0; - if(type(Prec=getopt(prec))<0) - Level=0; - else if(Prec==0) Level=4; - else if(type(Prec)==1){ - Level=Prec; - if(Level<0){ - Level=-Level; - Gap0=1; - } - }else if(type(Prec)==4){ - Level=Prec[0]; - if(length(Prec)>1) Arg=Prec[1]; - if(length(Prec)>2) Gap0=Prec[2]; - } - if(Level>0){ - if(Level>16) Level=16; - if(Arg<=0) Arg=30; - else if(Arg>120) Arg=120; - Arg=Acc?eval(@pi*Arg/180):deval(@pi*Arg/180); - SL=dcos(Arg); - } - if(Gap0>0){ - if(Gap0<2) Gap0=16; - else if(Gap0>512) Gap0=512; - Gap=((MulX*(LX[1]-LX[0]))^2+(MulY*(LY[1]-LY[0]))^2)/(Gap0^2); - } - for(I=0;I<Level;I++){ - for(F=K=G=0,NV=NLT=[],PLT=LT,PV=V;PLT!=[];K++,PLT=cdr(PLT),PV=cdr(PV)){ - TG=0;D0=D1;CLT0=CLT;CV0=CV;CV=car(PV);CLT=car(PLT); - if(length(PV)>1){ - if((CV1=car(cdr(PV)))!=0 && CV!=0) - D1=[CV[0]-CV1[0],CV[1]-CV1[1]]; - else D1=0; - }else K=-1; /* ? */ - if(K>0 &&(((D1==0||D0==0)&&(CV0!=0||CV!=0||CV1!=0)) || dvangle(D0,D1)<SL || - (Gap>0 && type(D0)==4 && (TG=(D0[0]^2+D0[1]^2-Gap)>0)))){ - G++;T1=(CLT0+CLT)/2; - if(F==0 && (CV0!=0 || CV!=0)){ - if(myfdeval(Dn,T1)==0){ - NV=cons(0,NV); NLT=cons(T1,NLT); - } - if(Cpx>0||Acc){ - X=myfeval(F1,T1);Y=myfeval(F2,T1); - }else{ - X=myfdeval(F1,T1);Y=myfdeval(F2,T1); - } - if(K==1 && N1<0){ - NV=[];NLT=[]; - } - if((K>1||N1==0)&&(X<LX[0]||X>LX[1]||Y<LY[0]||Y>LY[1])){ - NV=cons(0,NV);NLT=cons(T1,NLT);F=0; - }else{ - NV=cons([MulX*(X-Orgx),MulY*(Y-Orgy)],NV);NLT=cons(T1,NLT); - } - } - NV=cons(CV,NV);NLT=cons(CLT,NLT); - if(!TG&&(CV0!=0||CV1!=0)){ - T2=(car(cdr(PLT))+CLT)/2; - if(myfdeval(Dn,T2)==0){ - NV=cons(0,NV); NLT=cons(CLT,NLT); - } - if(Cpx>0||Acc){ - X=myfeval(F1,T2);Y=myfeval(F2,T2); - }else{ - X=myfdeval(F1,T2);Y=myfdeval(F2,T2); - } - if((N1==0||length(PV)!=2)&&(X<LX[0]||X>LX[1]||Y<LY[0]||Y>LY[1])){ - NV=cons(0,NV);NLT=cons(T1,NLT); - }else{ - NV=cons([MulX*(X-Orgx),MulY*(Y-Orgy)],NV);NLT=cons(T2,NLT); - } - } - if(length(PV)==2 && N1==-1) break; - F=1; - }else{ - F=0;NV=cons(CV,NV);NLT=cons(CLT,NLT); - } - } - V=reverse(NV);LT=reverse(NLT); - if(G==0) break; - } - if(Gap>0){ - for(NV=[],PV=V;PV!=[];PV=cdr(PV)){ - NV=cons(P0=car(PV),NV); - if(length(PV)>1 && P0!=0 && PV[1]!=0 - && (P0[0]-PV[1][0])^2+(P0[1]-PV[1][1])^2>Gap) NV=cons(0,NV); - } - V=reverse(NV); - } - if(getopt(raw)==1) return V; - OL=[["curve",1]];OLP=[]; - if(type(C=getopt(ratio))==1){ - OL=cons(["ratio",C],OL);OLP=cons(["ratio",C],OLP); - } - if(Acc==1) OL=cons(["Acc",1],OL); - if(N1<0) OL=cons(["close",-1],OL); - if(type(Opt=getopt(opt))!=7 && type(Opt)!=4){ - if(Opt==0) return xylines(V|option_list=cons(["opt",0],OL)); - } - OL=cons(["opt",(Proc)?0:Opt],OL); - if(type(Opt)>=0) OLP=cons(["opt",Opt],OLP); - if(type(Vb=getopt(verb))==1||type(Vb)==4){ - OL=cons(["verb",Vb],OL);OLP=cons(["verb",Vb],OL); - } - if(Proc){ - S=(Proc==1)? - [[0,[MulX*(LX[0]-Orgx),MulX*(LX[1]-Orgx)],[MulY*(LY[0]-Orgy),MulY*(LY[1]-Orgy)], - (TikZ)?1:1/10]]:[]; - S=cons([1,OLP,xylines(V|option_list=OL)],S); - if(Proc==3) return car(S); - }else S=xylines(V|option_list=OL); - if(type(Pt=getopt(pt))==4){ - if(type(Pt[0])!=4) Pt=[Pt]; - if(length(Pt)>1 && type(Pt[1])!=4) Pt=[Pt]; - for(PT=Pt;PT!=[];PT=cdr(PT)){ - PP=car(PT); - if(type(PP[0])!=4) PP=[PP]; - P=car(PP);PP=cdr(PP); - Qx=MulX*(P[0]-Orgx);Qy=MulY*(P[1]-Orgy); - if(length(PP)>0 && type(PP[0])==4){ /* draw line */ - P=car(PP); - Q1x=MulX*(P[0]-Orgx);Q1y=MulY*(P[1]-Orgy); - if(length(PP)<1 || car(PP)==0 || iand(car(PP),1)) - OL=["opt",(TikZ)?"-":"@{-}"]; - else OL=["opt",(TikZ)?".":"@{.}"]; - if(Proc) S=cons([1,OL,[[Qx,Qy],[Q1x,Q1y]]],S); - else S=S+xylines([[Qx,Qy],[Q1x,Q1y]]|optilon_list=OL); - continue; - } - if(length(PP)==0 || type(car(PP))!=7) SS="$\\bullet$"; - else SS=car(PP); - if(length(PP)<=1){ - if(Proc) S=cons([2,[],[Qx,Qy],[SS]],S); - else S=S+xyput([Qx,Qy,SS]); - }else{ - if(Proc) S=cons([2,[],[Qx,Qy],[[SS],"",PP[1]]],S); - S=S+xyput([Qx,Qy,SS,"",PP[1]]); - } - } - } - if(type(Ax=getopt(ax))==4){ /* draw axis */ - Adx0=Ady0=0; Adx1=Ady1=0.1; - if(!TikZ){ - if(!XYcm) Adx1=Ady1=1; - LOp="@{-}"; LxOp="+!U"; LyOp="+!R"; - }else{ - LOp="-"; LxOp="below"; LyOp="left"; - } - LOp0=LOp1=LOp; - LxOO=(Ax[1]==LY[0])?LxOp:(TikZ)?"below left":"+!UR"; - if(type(AxOp=getopt(axopt))>0){ - if(type(AxOp)==1){ - if(AxOp>0) Adx1=Ady1=AxOp; - else if(AxOp<0){ - Adx1=Ady1=0; Adx0=Ady0=AxOp; - } - }else if(type(AxOp)==4){ - if(type(T=car(AxOp))==4 && length(AxOp)>1){ - if(type(T)==7){ - LxOp=T; LyOp=AxOp[1]; - }else if(type(T)==4){ - Ay0=T[0]; Ay1=T[1]; Ax0=AxOp[1][0]; Ax1=AxOp[1][1]; - if(length(T)>2) LxOp=T[2]; - if(length(AxOp[1])>2) LyOp=AxOp[1][2]; - } - } - if(length(AxOp)>2 && type(AxOp[2])==7) LxOO=AxOp[2]; - if(length(AxOp)>3 && type(AxOp[3])==7) LOp0=AxOp[3]; - if(length(AxOp)>4 && type(AxOp[4])==7) LOp1=AxOp[4]; - } - if(type(AxOp)==7) LOp0=AxOp; - } - if(Ax[0]>=LX[0] && Ax[0]<=LX[1]){ /* draw marks on x-axis */ - if(Proc) S=cons([3,(type(LOp0)>=0)?[["opt",LOp0]]:[], - [MulX*(Ax[0]-Orgx),MulY*(LY[0]-Orgy)],[MulX*(Ax[0]-Orgx),MulY*(LY[1]-Orgy)]],S); - else S=S+xyarrow([MulX*(Ax[0]-Orgx),MulY*(LY[0]-Orgy)], - [MulX*(Ax[0]-Orgx),MulY*(LY[1]-Orgy)]|opt=LOp0); - if(length(Ax)>2){ - D=Ax[2]; - if(type(D)==1 && D>0){ - I0=ceil((LX[0]-Ax[0])/D); I1=floor((LX[1]-Ax[0])/D); - for(DD=[],I=I0; I<=I1; I++){ - if(length(Ax)<5) DD=cons(I*D,DD); - else if(Ax[4]==0) DD=cons([I*D,I*D+Ax[0]],DD); - else if(Ax[4]==1) DD=cons([I*D,I*D],DD); - else if(Ax[4]==2) DD=cons([I*D,I],DD); - } - D=DD; - } - if(type(D)==4){ - for(;D!=[]; D=cdr(D)){ - T=car(D); - if(type(T)==4) T=car(T); - X=MulX*(T+Ax[0]-Orgx); Y=MulY*(Ax[1]-Orgy); - if(T!=0){ - if(Proc) S=cons([3,(type(LOp1)>=0)?[["opt",LOp1]]:[],[X,Y+Ady0],[X,Y+Ady1]],S); - else S=S+xyarrow([X,Y+Ady0],[X,Y+Ady1]|opt=LOp1); - } - if(type(car(D))==4){ - Arg=[(T==0)?LxOO:LxOp,D[0][1]]; - if(Proc) S=cons([2,[],[X,Y+Ady0],[Arg]],S); - else S=S+xyput([X,Y+Ady0,Arg]); - } - } - } - } - } - if(Ax[1]>=LY[0] && Ax[1]<=LY[1]){ /* draw marks on y-axis */ - if(Proc) S=cons([3,[["opt",LOp0]], - [MulX*(LX[0]-Orgx),MulY*(Ax[1]-Orgy)], - [MulX*(LX[1]-Orgx),MulY*(Ax[1]-Orgy)]],S); - else S=S+xyarrow([MulX*(LX[0]-Orgx),MulY*(Ax[1]-Orgy)], - [MulX*(LX[1]-Orgx),MulY*(Ax[1]-Orgy)]|opt=LOp0); - if(length(Ax)>3){ - D=Ax[3]; - if(type(D)==1 && D>0){ - I0=ceil((LY[0]-Ax[1])/D); I1=floor((LY[1]-Ax[0])/D); - for(DD=[],I=I0; I<=I1; I++){ - if(length(Ax)<5) DD=cons(I*D,DD); - else if(I!=0){ - if(Ax[4]==0) DD=cons([I*D,I*D+Ax[1]],DD); - if(Ax[4]==1) DD=cons([I*D,I*D],DD); - if(Ax[4]==2) DD=cons([I*D,I],DD); - } - } - D=DD; - } - if(type(D)==4){ - for(;type(D)==4&&D!=[]; D=cdr(D)){ - T=car(D); - if(type(T)==4) T=car(T); - X=MulX*(Ax[0]-Orgx); Y=MulY*(T+Ax[1]-Orgy); - if(T!=0){ - if(Proc) S=cons([3,(type(LOp0)>=0)?[["opt",LOp1]]:[], - [X+Adx0,Y],[X+Adx1,Y]],S); - else S=S+xyarrow([X+Adx0,Y],[X+Adx1,Y]|opt=LOp1); - } - if(type(car(D))==4){ - if(Proc) S=cons([2,[],[X,Y+Ady0],[[LyOp,D[0][1]]]],S); - else S=S+xyput([X,Y+Ady0,[LyOp,D[0][1]]]); - } - } - } - } - } - } - if(Proc) return reverse(S); - if(getopt(dviout)!=1) return S; - xyproc(S|dviout=1); -} - -def xyarrow(P,Q) -{ - Cmd = ["fill","filldaw","shade","shadedraw","clip ","pattern","path ","node","coordinate"]; - if(type(P)<4) return "%\n"; - SS=getopt(opt); - if(!TikZ){ - if(type(Q)<4) return ""; - S="{"+xypos(P)+" \\ar"; - if(type(SS)==7) S=S+SS; - return S+" "+xypos(Q)+"};\n"; - } - if(type(SS)==4 && length(SS)>1){ - if(length(SS)>2) SU=SS[2]; - ST=SS[1]; - SS=SS[0]; - } - if(type(SS)!=7) SS="->"; - if(type(ST)!=7) ST=" -- "; - if(type(SU)!=7) SU=""; - if(type(S=getopt(cmd))==7) S="\\"+S; - else S="\\draw"; - if(type(Q)!=4){ - if(Q>0 && Q<=length(Cmd)) S="\\"+Cmd[Q-1]+""; - if(SS!="-") S=S+"["+SS+"]"; - if(SU!="") SU="["+SU+"]"; - return S+xypos(P)+ST+SU+";\n"; - } - if(SS!="-"&&SS!="") S=S+"["+SS+"]"; - if(length(P)<3 && length(Q)<3) - return S+xypos(P)+ST+xypos(Q)+SU+";\n"; - if(length(P)==2) P=[P[0],P[1],"","_0"]; - else if(length(P)==3 || (length(P)==4 && P[3]=="")) - P=[P[0],P[1],P[2],"_0"]; - else if(P[3]=="") - P=[P[0],P[1],P[2],"_0",P[4]]; - if(length(Q)==2) Q=[Q[0],Q[1],"","_1"]; - else if(length(Q)==3 || (length(Q)==4 && Q[3]=="")) - Q=[Q[0],Q[1],Q[2],"_1"]; - else if(Q[3]=="") - Q=[Q[0],Q[1],Q[2],"_1",Q[4]]; - return S+xypos(P)+" "+xypos(Q)+"("+P[3]+")"+ST+"("+Q[3]+")"+SU+";\n"; -} - -def xyarrows(P,Q,R) -{ - PQ=newvect(4); - PQ[0]=(type(P[0])!=4)?f2df(P[0]):P[0]; - PQ[1]=(type(P[1])!=4)?f2df(P[1]):P[1]; - PQ[2]=(type(Q[0])!=4)?f2df(Q[0]):Q[0]; - PQ[3]=(type(Q[1])!=4)?f2df(Q[1]):Q[1]; - if(type(R[0])!=4) R=[R]; - TR=R[0];NX=TR[2];X=X0=TR[0];DX=(TR[1]-TR[0])/NX; - if(length(R)==2){ - TR=R[1];NY=TR[2];Y=TR[0];DY=(TR[1]-TR[0])/NY; - }else{ - NY=1;Y=DY=0; - } - if(type(L=getopt(abs))!=1) L=0; - if(type(Sc=getopt(scale))!=1) Sc=0; - OL=[]; - if(type(Opt=getopt(opt))==7) OL=cons(["opt",Opt],OL); - Tb=str_tb(0,0); - for(J=0;J<NY;Y+=DY,J++){ - for(I=0,X=X0;I<NX;I++,X+=DX){ - PX=myf2eval(PQ[0],X,Y);PY=myf2eval(PQ[1],X,Y); - VX=myf2eval(PQ[2],X,Y);VY=myf2eval(PQ[3],X,Y); - if(L>0){ - C=dnorm([VX,VY]); - if(C!=0){ - VX*=L/C;VY*=L/C; - } - } - if(Sc){ - VX*=Sc;VY*=Sc; - } - if(VX||VY) str_tb(xyarrow([PX,PY],[PX+VX,PY+VY]|optilon_list=OL),Tb); - } - } - return str_tb(0,Tb); -} - -def polroots(L,V) -{ - INIT=1; - if(type(CF=getopt(comp))!=1) CF=0; - OL=getopt(); - if(CF>32){ - CF-=64; - INIT=0; - }else OL=cons(["comp",CF+64],delopt(OL,"comp")); - if(type(V)==4&&length(V)==1){ - L=L[0];V=V[0]; - } - Lim=Lim2=[]; - if(type(L)<4){ - if(type(Lim=getopt(lim))==4){ - if(type(Lim[0])!=4){ - if(!isvar(Lim[0])) Lim=cons(V,[Lim]); - Lim=[Lim]; - } - if(!isvar(Lim[0][0])) Lim=[cons(V,Lim)]; - Lim=delopt(Lim,V|inv=1); - if(Lim!=[]){ - Lim=Lim[0]; - if(length(Lim)==3) Lim2=Lim[2]; - Lim=Lim[1]; - } - }else{ - Lim=Lim2=[]; - } - if((CF==-2||CF==-1||CF==2)&&iscoef(L,os_md.israt)){ /* Rat+Comp, Rat+Real or Rat */ - S=(CF==-1)?getroot(L,V|cpx=1):getroot(L,V); - for(RR=[],F=x;S!=[];S=cdr(S)){ - if(findin(V,vars(C=car(S)))<0){ /* Rational solution */ - if(type(C)<2){ - if(Lim!=[]&&(real(C)<Lim[0]||real(C)>Lim[1])) continue; - if(Lim2!=[]&&(imag(C)<Lim2[0]||imag(C)>Lim2[1])) continue; - } - if(F!=C) RR=cons(F=C,RR); - }else if(CF<0){ /* Irrational solution */ - if((R=pari(roots,mysubst(C,[V,x])))!=0){ - for(R=vtol(R);R!=[];R=cdr(R)) - if((C=car(R))!=F && ntype(C)<CF+6){ - if(Lim!=[]&&(real(C)<Lim[0]||real(C)>Lim[1])) continue; - if(Lim2!=[]&&(imag(C)<Lim2[0]||imag(C)>Lim2[1])) continue; - RR=cons(F=C,RR); - } - } - } - } - return qsort(RR); - } - R=pari(roots,subst(L,V,x)); - if(R==0){ - R=[0]; - if(CF==1){ - for(R=[0],I=mydeg(L,V);I>1; I--) - R=cons(0,R); - } - return R; - } - if(CF==1){ /* Complex */ - if(Lim==[]&&Lim2==[]) return vtol(R); - for(L=[],I=length(R)-1;I>=0;I--){ - C=R[I]; - if(Lim!=[]&&(real(C)<Lim[0]||real(C)>Lim[1])) continue; - if(Lim2!=[]&&(imag(C)<Lim2[0]||imag(C)>Lim2[1])) continue; - L=cons(C,L); - } - return L; - } - for(L=[],F=x,I=length(R)-1;I>=0;I--){ /* Real */ - if(ntype(R[I])<4 && F!=R[I]){ - if(Lim!=[] && (R[I]<Lim[0]||R[I]>Lim[1])) continue; - L=cons(F=R[I],L); - } - } - return qsort(L); - } - if(SS==0&&INIT==1){ - SS=polroots(L,V|option_list=OL); - if(SS!=0) return SS; - for(C=0;SS==0&&C<4;C++){ - I=(C==0)?1:(iand(random(),0xff)-0x80); - for(LL=[],K=length(L)-1;K>=0;K--){ - for(Q=0,J=length(L)-1;J>=0;J--) - Q+=L[J]*(I+K)^J; - LL=cons(Q,LL); - } - SS=polroots(LL,V|option_list=OL); - if(SS!=0) return SS; - } - return SS; - } - C=2^(-32); - if(type(getopt(err))==1) C=err; - if((N=length(V))!=length(L)) return []; - if(N==1) return polroots(L[0],V[0]|option_list=OL); - for(L1=[],I=1;I<N;I++){ - Res=res(V[0],L[I-1],L[I]); - if(type(Res)<2) return Res; - L1=cons(res(V[0],L[I-1],L[I]),L1); - } - R=polroots(L1,V1=cdr(V)|option_list=OL); - if(type(R)<2) return R; - for(SS=[];R!=[];R=cdr(R)){ - RS=(N==2)?[car(R)]:car(R); - for(I=0,L0=L[0];I<N-1;I++) L0=mysubst(L0,[V1[I],RS[I]]); - if(L0==0) return 0; - S0=polroots(L0,V[0]|option_list=OL); - if(type(S0)<2) return S0; - for(S=S0;S!=[];S=cdr(S)){ - S0=cons(car(S),RS); - for(LT=cdr(L);LT!=[];LT=cdr(LT)){ - for(I=0,TV=car(LT);I<N;I++) TV=mysubst(TV,[V[I],S0[I]]); - if(abs(TV)>C) break; - } - if(LT==[]) SS=cons(S0,SS); - } - } - return reverse(SS); -} - -def ptcommon(X,Y) -{ - if(length(X)!=2 || length(Y)!=2) return 0; - if(type(X[1])==4){ /* X is a line */ - if((In=getopt(in))==-1||In==-2||In==-3){ - X0=(X[0][0]+X[1][0])/2;X1=(X[0][1]+X[1][1])/2; - X=[[X0,X1],[X0+X[1][1]-X[0][1],X1-X[1][0]+X[0][0]]]; - if(In==-1&&type(Y[1])==4) return ptcommon(Y,X|in=-2); - /* for the second line */ - if(In==-3) In=1; - else In=0; - }else if(In==2||In==3){ - X=(X[1][0]-X[0][0])+(X[1][1]-X[0][1])*@i; - if(X==0) return 0; - Y=(Y[1][0]-Y[0][0])+(Y[1][1]-Y[0][1])*@i; - X=myarg(Y/X); - return (In==2)?X:(X*180/deval(@pi)); - }else if(In!=1) In=0; - if(type(Y[0])<=3){ - if(In==1){ - return [(Y[1]*X[0][0]+Y[0]*X[1][0])/(Y[0]+Y[1]), - (Y[1]*X[0][1]+Y[0]*X[1][1])/(Y[0]+Y[1])]; - } - XX=X[1][0]-X[0][0];YY=X[1][1]-X[0][1]; - Arg=(length(Y)<2)?0:Y[1]; - Arg=deval(Arg); - if(Arg!=0){ - S=dcos(Arg)*XX-dsin(Arg)*YY; - YY=dsin(Arg)*XX+dcos(Arg)*YY; - XX=S; - } - S=dnorm([XX,YY]); - if(S!=0){ - XX*=Y[0]/S;YY*=Y[0]/S; - } - return [X[1][0]+XX,X[1][1]+YY]; - } - S=[X[0][0]+(X[1][0]-X[0][0])*x_,X[0][1]+(X[1][1]-X[0][1])*x_]; - if(type(Y[1])==4){ /* Y is a line */ - T=[Y[0][0]+(Y[1][0]-Y[0][0])*y_-S[0], - Y[0][1]+(Y[1][1]-Y[0][1])*y_-S[1]]; - R=lsol(T,[x_,y_]); - if(type(R[0])==4&&type(R[1])==4&&R[0][0]==x_&&R[1][0]==y_){ - if(!In || (R[0][1]>=0&&R[0][1]<=1&&R[1][1]>=0&&R[1][1]<=1) ) - return subst(S,x_,R[0][1],y_,R[1][1]); - } - if((type(R[0])>0&&type(R[0])<4)||(type(R[1])>0&&type(R[1])<4)) return 0; - if(!In) return 1; - I=(X[0][0]==X[1][0]&&Y[0][0]==Y[1][0]&&X[0][0]==Y[0][0])?1:0; - if(X[0][I]<=X[1][I]){ - X0=X[0][I];X1=X[1][I]; - }else{ - X1=X[0][I];X0=X[1][I]; - } - return ((Y[0][I]<X0 && Y[1][I]<X0)||(Y[0][I]>X1&&Y[1][I]>X1))?0:1; - }else if(Y[1]==0){ /* orth */ - T=[Y[0][0]+(X[1][1]-X[0][1])*y_-S[0], - Y[0][1]-(X[1][0]-X[0][0])*y_-S[1]]; - R=lsol(T,[x_,y_]); - if(type(R[0])==4&&type(R[1])==4&&R[0][0]==x_&&R[1][0]==y_){ - if(!In||(R[0][1]>=0&&R[0][1]<=1)) - return subst(S,x_,R[0][1],y_,R[1][1]); - } - return (X[0]==X[1])?0:1; - }else if(type(Y[1])==1 && Y[1]>0){ /* circle */ - T=(S[0]-Y[0][0])^2+(S[1]-Y[0][1])^2-Y[1]^2; - D=mycoef(T,1,x_)^2-4*mycoef(T,0,x_)*mycoef(T,2,x_); - if(D==0){ - V=mycoef(T,1,x_)/(2*mycoef(T,2,x_)); - if(!in||(V>=0&&V<=1)) return [subst(S,x_,V)]; - } - else if((type(D)==1&&D>0)){ - D=dsqrt(D); - V=-(mycoef(T,1,x_)+D)/(2*mycoef(T,2,x_)); - if(!In||(V>=0&&V<=1)) L=[subst(S,x_,V)]; - else L=[]; - V=(D-mycoef(T,1,x_))/(2*mycoef(T,2,x_)); - if(!In||(V>=0&&V<=1)) L=cons(subst(S,x_,V),L); - if(length(L)>0) return L; - } - } - return 0; - } - if(type(Y[1])==4 || X[1]==0) return ptcommon(Y,X); - /* X is a circle */ - if(Y[1]==0){ /* tangent line */ - if(Y[0][0]==X[0][0]+X[1] || Y[0][0]==X[0][0]-X[1]) L=[[Y[0][0],X[0][1]]]; - else L=[]; - P=(Y[0][0]+x_-X[0][0])^2+(Y[0][1]+x_*y_-X[0][1])^2-X[1]^2; - Q=mycoef(P,1,x_)^2-4*mycoef(P,2,x_)*mycoef(P,0,x_); - for(R=polroots(Q,y_);R!=[];R=cdr(R)){ - X0=-subst(mycoef(P,1,x_)/(2*mycoef(P,2,x_)),y_,car(R)); - L=cons([Y[0][0]+X0,Y[0][1]+car(R)*X0],L); - } - }else{ /* Y is a circle */ - P=(x_-X[0][0])^2+(y_-X[0][1])^2-X[1]^2; - Q=(x_-Y[0][0])^2+(y_-Y[0][1])^2-Y[1]^2; - V=(X[0][0]!=Y[0][0])?[x_,y_]:[y_,x_]; - R=subst(P,V[0],T=lsol(P-Q,V[0])); - if(type(T[0])<4) return (T[0]==0)?1:0; - S=polroots(R,V[1]); - for(L=[];S!=[];S=cdr(S)){ - R=subst(T,V[1],car(S)); - if(V[0]==x_) L=cons([R,car(S)],L); - else L=cons([S,R],L); - } - } - if(length(L)!=0) return L; - return 0; -} - -def tobezier(L) -{ - if((Div=getopt(div))==1||Div==2){ - if(length(L)!=4) return [tobezier(L|inv=[0,1/2]),tobezier(L|inv=[1/2,1])]; - if(type(L)==4) L=ltov(L); - if(type(L[0])==4) - L=[ltov(L[0]),ltov(L[1]),ltov(L[2]),ltov(L[3])]; - S=[(L[0]+3*L[1]+3*L[2]+L[3])/8]; - T=[L[3]]; - S=cons((L[0]+2*L[1]+L[2])/4,S); - T=cons((L[2]+L[3])/2,T); - S=cons((L[0]+L[1])/2,S); - T=cons((L[1]+2*L[2]+L[3])/4,T); - S=cons(L[0],S); - T=cons((L[0]+3*L[1]+3*L[2]+L[3])/8,T); - return [S,T]; - } - if(Div>2&&Div<257){ - L=tobezier(L); - for(R=[],I=Div-1;I>=0;I--) - R=cons(tobezier(L|inv=[I/Div,(I+1)/Div]),R); - return R; - } - if((V=getopt(inv))==1 || type(V)>3){ - if(type(L[0])>3 && type(V)>3) L=tobezier(L); - if(type(V)>3 && length(V)>2) V2=V[2]; - if(type(V2)!=2) V2=t; - if(type(V)>3) L=subst(L,V2,(V[1]-V[0])*V2+V[0]); - N=mydeg(L,V2); - for(R=[],I=0;I<=N;I++){ - RT=mycoef(L,I,V2); - R=cons(RT/binom(N,I),R); - L-=RT*V2^I*(1-V2)^(N-I); - } - return reverse(R); - }; - N=length(L)-1; - V=newvect(2); - for(I=0;I<=N;I++,L=cdr(L)){ - if(type(X=car(L))==4) X=ltov(X); - V+=X*binom(N,I)*t^I*(1-t)^(N-I); - } - return V; -} - -def cutf(F,X,VV) -{ - if(type(car(V=VV))==2){ - Y=[car(V),X]; - V=cdr(V); - }else Y=X; - if(type(X)>1){ - Y=(type(Y)==4)?Y[0]:x; - V1=makenewv(F); - if(X==Y||Y==x){ - V2=makenewv([F,V1]); - F=mysubst(F,[Y,V2]); - V=cons(V2,V); - } - return [V1,[V1,os_md.cutf,[F],X,[V]]]; - } - if(car(V)!=[] && X<car(V)[0]) return myfeval(car(V)[1],Y); - for(V=cdr(V); ;V=R){ - if((R=cdr(V))==[]){ - if(car(V)!=[] && car(V)[0]<X) return myfeval(car(V)[1],Y); - return myfeval(F,Y); - } - if(X>car(V)[0]) continue; - if(X==car(V)[0]) return car(V)[1]; - return myfeval(F,Y); - } -} - -def fsum(F,L) -{ - if(getopt(df)==1){ - F=f2df(F); - }else Sub=getopt(subst); - if(type(L[0])==2){ - X=L[0]; - L=cdr(L); - }else X=0; - V=(length(L)>2)?L[2]:1; - for(R=0,I=L[0];;I+=V){ - if(V==0||(I-L[1])*V>0) return R; - R+=(Sub==1)?subst(F,X?X:x,I):os_md.myfeval(F,X?[X,I]:I); - } -} - -def periodicf(F,L,X) -{ - if(type(L)==4) L=[eval(L[0]),eval(L[1])]; - else L=eval(L); - if(isvar(X)){ - Y=makenewv([X,V]); - Z=makenewv([X,Y,V]); - return [Z,[Z,os_md.periodicf,[mysubst(F,[x,Y])],(type(L)==4)?[L]:L,[[Y,X]]]]; - } - if(type(X)==4){ - V=X[0]; - X=X[1]; - }else V=x; - if(type(F)==5){ - X=eval(X); - return myfeval(F[floor(X/L)%length(F)],[V,X-floor(X/L)*L]); - } - if(type(L)==4){ - X-=floor((X-L[0])/(L[1]-L[0]))*(L[1]-L[0]); - return myfeval(F,[V,X]); - } -} - -def cmpf(X) -{ - if(type(X)>3){ - if(type(L)==7) return [S_Fc,Dx,S_Ic,S_Ec,S_EC,S_Lc]; - S_Lc=0; - if(type(S_Fc=X[0])!=4) S_Fc=f2df(S_Fc); - S_Ic=X[1]; - if(length(S_Ic)>2){ - S_Fc=mysubst(S_Fc,[S_Ic[0],x]); - S_Ic=cdr(S_Ic); - } - S_Dc=(type(S_Ic[0])==7)?1:0; - if(type(S_Ic[1])==7) S_Dc=ior(S_Dc,2); - if(type(S_Ec=getopt(exp))!=1) S_Ec=0; - if(S_Ec<=0){ - S_EC=-S_Ec; - if(S_EC==0) S_EC=1; - if(S_Dc==3) S_EC*=2; - else S_EC/=4; - if(type(F=X[0])==3&&vars(F)==[x]&&(D=deg(nm(F),x))==deg(dn(F),x)-2){ - S_Lc=S_EC*coef(nm(F),D,x)/coef(dn(F),D+2,x); - } - }else{ - S_EC=S_Ec; - if(S_Dc==3) S_EC*=12; - else S_EC/=6; - } - if(type(S_Fc)==3) S_Fc=red(S_Fc); - S_EC=1/S_EC; - return [z_,[z_,os_md.cmpf,x]]; - } - if(X<=0 && iand(S_Dc,1)) return S_Lc; - if(X>=1 && iand(S_Dc,2)) return S_Lc; - if(S_Dc==3){ - if(S_Ec>0){ - Y0=dexp(1/X)*S_EC; - Y1=dexp(1/(1-X))*S_EC; - return myfeval(S_Fc,Y1-Y0)*(Y0/X^2+Y1/(1-X)^2); - } - return myfeval(S_Fc,S_EC/(1-X)-S_EC/X)*(S_EC/(1-X)^2+S_EC/X^2); - } - if(S_Dc==1){ - if(S_Ec>0){ - Y=dexp(1-1/X); - R=myfeval(S_Fc,S_EC*(Y-1)+I[1])*Y; - } - else R=myfeval(S_Fc,I[1]+(1-1/X)*S_EC); - return R*S_EC/X^2; - } - if(S_Dc==2){ - if(S_Ec>0){ - Y=dexp(X/(1-X)); - R=myfeval(S_Fc,S_EC*(Y-1)+S_Ic[0])*Y; - }else R=myfeval(S_Fc,S_EC*X/(1-X)+S_Ic[0]); - return R*S_EC/(1-X)^2; - } - X=S_Ic[0]+(S_Ic[1]-S_Ic[0])*X; - return myfeval(S_Fc,X)/(S_Ic[1]-Ic[0]); -} - -def fresidue(P,Q) -{ - if(iscoef(Q,os_md.israt)) S=fctr(Q); - else S=[[Q,1]]; - for(R=[];S!=[];S=cdr(S)){ - T=car(S); - if((D=mydeg(T[0],z))==0) continue; - L=[]; - if(iscoef(T[0],os_md.iscrat)) L=getroot(T[0],z|cpx=2); - if(findin(z,vars(L))>=0) L=[]; - if(L==[]) L=polroots(T[0],z|comp=-1); - for(;L!=[];L=cdr(L)){ - QQ=Q; - for(I=T[1]; I>1;I--) QQ=mydiff(QQ,z); - for(U=0,W=I=T[1];I>0;I--,W++){ - QQ=diff(QQ,z); - U+=subst(QQ,z,L[0])*(z-L[0])^(W-T[1])/fac(W); - } - UD=mydiff(U,z); - for(I=T[1],K=1,PP=P; I>1;I--,K++) - PP=diff(PP,z)*U-K*PP*UD; - QQ=subst(PP,z,L[0])/subst(U,z,L[0])^K; -/* if(D==2) QQ=sqrt2rat(QQ); */ - R=cons([L[0],sqrt2rat(QQ)],R); - } - } - if(type(L=getopt(cond))==4){ - for(S=[];R!=[];R=cdr(R)){ - Z=car(R); - for(LL=L;LL!=[];LL=cdr(LL)){ - X=real(car(Z));Y=imag(car(Z)); - if(myf3eval(car(LL),X,Y,car(Z))<=0) break; - } - if(LL==[]) S=cons(Z,S); - } - R=reverse(S); - } - if((Sum=getopt(sum))==1||Sum==2){ - for(S=0;R!=[];R=cdr(R)) S+=car(R)[1]; - if(Sum==2) S*=2*@pi*@i; - return sqrt2rat(S); - } - return R; -} - -def fint(F,D,V) -{ - if(((L=length(V))==2 || (L==3&&isvar(V[0])<3)) - && (type(V[L-1])==7||(type(V[L-1])<3&&type(eval(V[L-1]))<2))) - /* real integral */ - return areabezier([F,D,V]|option_list=getopt()); - /* complex integral */ - if(L>1&&type(V[1])==4&&type(V[1][1])<4){ - if(type(V[0])==4&&type(V[0][0])<2){ - for(R=[],VT=car(V),VV=cdr(V);VV!=[];VV=cdr(VV),VT=VU){ - if((VU=car(VV))==-1) VU=car(V); - R=cons([ptcommon([VT,VU],[t,1-t]|in=1),[0,1]],R); - } - V=reverse(R); - } - else if(L==2) V=[V]; - } - Opt=cons(["cpx",1],getopt()); - for(R=0;V!=[];V=cdr(V)){ - VT=car(V); - X=car(VT)[0];XD=red(diff(X,t)); - Y=car(VT)[1];YD=red(diff(Y,t)); - F=mysubst(F,[[x,X],[y,Y],[z,X+@i*Y]]); - if(type(F)==4) - FF=cons(F[0]*(XD+@i*YD),cdr(F)); - else FF=red(F*(XD+@i*YD)); - R+=areabezier([FF,D,cons(t,VT[1])]|option_list=Opt); - } - return R; -} - -def areabezier(V) -{ - if(getopt(cpx)==1){ - Opt=delopt(getopt(),"cpx"); - F=V[0]; - if(!isvar(Var=V[2][0])) Var=x; - if(type(F)==3 && vars(F)==[Var] && imag(dn(F))!=0){ - F=(nm(F)*conj(dn(F)))/(dn(F)*conj(dn(F))); - V0=red(real(nm(F))/dn(F)); - R=areabezier([V0,V[1],V[2]]|option_list=Opt); - V0=red(imag(nm(F))/dn(F)); - return R+@i*areabezier([V0,V[1],V[2]]|option_list=Opt); - } - if(getopt(Acc)!=1) F=f2df(F); - V0=compdf([o,[o,real,o_]],o_,F); - R=areabezier([V0,V[1],V[2]]|option_list=Opt); - V0=compdf([o,[o,imag,o_]],o_,F); - return R+@i*areabezier([V0,V[1],V[2]]|option_list=Opt); - } - if(type(V[0])!=4 || vars(V[0][0])!=0){ - Mx=[-2.0^(512),2.0^(512)]; - I=length(V[2]); - if(type(V[2][I-1])==7||type(V[2][I-2])==7){ /* infinite interval */ - if(type(Ec=getopt(exp))==1) R=cmpf([V[0],V[2]]|exp=Ec); - else R=cmpf([V[0],V[2]]); - V=[R,V[1],[0,1]]; - } - if(type((Int=getopt(int)))==1 && type(V[0])<4 && (V1=V[1])>=0){ - if(Int==2&&iand(V1,1)) V1++; - if(!V1) V1=32; - Opt=cons(["raw",1],getopt()); - W=xygraph(V[0],V[1],V[2],Mx,Mx|option_list=Opt); - SS=W[0][1]; - for(S0=S1=0,I=0,L=W;L!=[] && I<=V1;I++, L=cdr(L)){ - if(iand(I,1)) S1+=car(L)[1]; - else S0+=car(L)[1]; - if (I==V1) SS+=car(L)[1]; - } - VV=deval(V[2][1]-V[2][0]); - if(Int==2) - return (2*S0+4*S1-SS)*VV/(3*V1); - else - return (2*S0+2*S1-SS)*VV/(2*V1); - } - Opt=cons(["opt",0],getopt()); - V=xygraph(V[0],V[1],V[2],Mx,Mx|option_list=Opt); - } - if(type(V[0][0])!=4) V=os_md.lbezier(V); - for(S=0; V!=[]; V=cdr(V)){ - B=tobezier(car(V)); - P=intpoly(B[1]*diff(B[0],t),t); - S+=mysubst(P,[t,1]); - } - return S; -} - -def velbezier(V,L) -{ - if(L==0) L=[t,0,1]; - else L=[(length(L)==3)?L[2]:t,L[0],L[1]]; - for(R=[],II=length(V)-1;II>=0;II--){ - S=fmmx(diff(V[II],L[0]|dif=1),L|dif=1); - for(U=0;S!=[];S=cdr(S)) if((T=abs(car(S)[1]))>U) U=T; - R=cons(U,R); - } - return R; -} - -def ptbezier(V,L) -{ - if(type(V[0])==4&&type(V[0][0])!=4) V=lbezier(V); - K=length(V); - if(type(L)<2){ - if(L<0) return K; - if(L>=K-1) L=[K-1,1]; - else{ - L0=floor(L); - if(L0>=K-1) L0=K-1; - L=[L0,L-L0]; - } - } - if(L[0]>=0) B=V[L[0]]; - else B=V[K+L[0]]; - B=tobezier(B); - BB=[diff(B[0],t),diff(B[1],t)]; - return [subst(B,t,L[1]),subst(BB,t,L[1])]; -} - -def ptcombezier(P,Q,T) -{ - if(type(T)<2){ - if(T<2) T=20; /* default */ - return ptcombezier(P,Q,[0,0,1,T]); - } - V=T[2]/2;; - PB=tobezier(P|div=1); - PP=[ptbbox(PB[0]),ptbbox(PB[1])]; - QB=tobezier(Q|div=1); - QQ=[ptbbox(QB[0]),ptbbox(QB[1])]; - for(L=[],I=0;I<2;I++){ - for(J=0;J<2;J++){ - if(!iscombox(PP[I],QQ[J])) continue; - if(T[3]<=1) return - [[T[0]+(I+0.5)*V,T[1]+(J+0.5)*V, - [(PP[I][0][0]+PP[I][0][1])/2,(PP[I][1][0]+PP[I][1][1])/2]]]; - else{ -#if 0 - U=PB[I][0];V=PB[I][length(PB[I])-1]; - if(abs(A=(U[0]-V[0]))>abs(B=(U[1]-V[I]))) - M=mat([1,0],[-B/A,1]); - else if(U!=V) - M=mat([1,-A/B],[0,1]); - else continue; - if(!iscombox(ptbox(ptaffine(M,PB[I])),ptbox(ptaffine(M,QB[J])))) continue; -#endif - - LN=ptcombezier(PB[I],QB[J],[T[0]+I*V,T[1]+J*V,V,T[3]-1]); -#if 0 - L=append(LN,L); -#else - if(LN!=[]){ - if(L==[]) L=LN; - else for(VV=3*V/2^T[3];LN!=[];LN=cdr(LN)){ - for(LT=L;LT!=[];LT=cdr(LT)){ - if(abs(car(LN)[0]-car(LT)[0])<VV&&abs(car(LN)[1]-car(LT)[1])<VV) break; - } - } - } - if(length(L)>32){ /* Too many points */ - I=J=2; - } -#endif - } - } - } - return L; -} - - -def ptcombz(P,Q,T) -{ - if(P==Q) Q=0; - if(type(P[0][0])!=4) P=P0=lbezier(P); - if(Q==0){ - Q=P;F=1; - } - else if(type(Q[0][0])!=4) Q=lbezier(Q); - for(R=[],I=0,Q0=Q;P!=[];P=cdr(P),I++){ - for(J=0,Q=Q0;Q!=[];Q=cdr(Q),J++){ - if(F==1&&I<J+2) break; - if((RT=ptcombezier(car(P),car(Q),T))!=[]){ - RT=cons([I,J],RT); - R=cons(RT,R); - } - } - } - if((Red=getopt(red))==1||Red==2){ - if(type(M=getopt(prec))!=1) M=12; - for(F=0,T=P0;T!=[];T=cdr(T)){ - for(S=car(T);S!=[];S=cdr(S)){ - if(type(ST=car(S))==4 && type(ST[0])<2){ - if(F++==0){ - X0=X1=ST[0];Y0=Y1=ST[1]; - }else{ - if(ST[0]<X0) X0=ST[0]; - if(ST[0]>X1) X1=ST[0]; - if(ST[1]<Y0) Y0=ST[1]; - if(ST[1]>Y1) Y1=ST[1]; - } - } - } - } - V0=(X1-X0)/2^M;V1=(Y1-Y2)/2^M; - for(RR=[],RT=R;RT!=[];RT=cdr(RT)) - for(S=cdr(car(RT));S!=[];S=cdr(S)) RR=cons(car(S)[2],RR); - RR=ltov(RR);L=length(RR); - for(I=0;I<L;I++) - for(K=1,J=I+1;K!=0&&J<L;J++) - if(abs(RR[I][0]-RR[J][0])<V0 && abs(RR[I][1]-RR[J][1])<V1) RR[I]=K=0; - R0=[]; - I=L-1; - if(Red==2){ - for(;I>=0;I--) if(RR[I]!=0) R0=cons(RR[I],R0); - }else{ - for(RT=R;RT!=[];RT=cdr(RT)){ - R00=[car(RT)[0]]; - for(S=cdr(car(RT));S!=[];S=cdr(S),I--) - if(RR[L-I-1]!=0) R00=cons(car(S),R00); - if(length(R00)>1) R0=cons(reverse(R00),R0); - } - } - return R0; - } - return reverse(R); -} - -def draw_bezier(ID,IDX,B) -{ - if(getopt(init)==1){ - S_FDot=0; - return; - } - if(type(Col=getopt(col))!=1&&Col!=0) Col=0; - Dot=0; - if(type(Opt=getopt(opt))==7){ - if(!Col){ - Col=drawopt(Opt,0); - if(Col==-1) Col=0; - } - T=drawopt(Opt,3); - if(iand(T,2)){ - M=iand(T,1)?1/8:1/4; - for(C=Col,Col=I=0;I<20;I+=8) - Col+=ishift(0xff-(floor((0xff-iand(0xff,ishift(C,I)))*M)),-I); - } - if(iand(T,4)) Dot=2; /* 2 or 3 or 4 or 6 */ - else if(iand(T,8)) Dot=4; - } - if(type(B)==4 && (type(B[0])==4||type(B[0])==5) && type(B[0][0])<2) B=lbezier(B); - else if(type(B)==5) B=[vtol(B)]; - for(;B!=[];B=cdr(B)){ - if(vars(F=car(B))==[]){ -#if 1 - if(length(F)<3&&!Dot){ /* line or point */ - if(length(F)>0){ - G=[rint(F[0][0]),rint(F[0][1])]; - if(length(F)==1) draw_obj(ID,IDX,G,Col); - else{ - G=[G[0],G[1],rint(F[1][0]),rint(F[1][1])]; - draw_obj(ID,IDX,G,Col); - } - } - continue; - } -#endif - if(length(F)<2) continue; - F=tobezier(F); - } - N=velbezier(F,0); - N=(N[0]>N[1])?N[0]:N[1]; - if(!N) N=1; - for(I=0;I<=N;I++,S_FDot++){ - if(Dot!=iand(S_FDot,Dot)) continue; - G=subst(F,t,I/N); - G=[rint(G[0]),rint(G[1])]; - if(G!=G0){ - draw_obj(ID,IDX,G,Col); - G0=G; - } - } - } - if(S_FDot-->=2^32) S_FDot=0; - return 0; -} - -def lbezier(L) -{ - if((In=getopt(inv))==1||In==2||In==3){ - for(F=0,R=[];L!=[];L=cdr(L)){ - LT=car(L); - if(F==car(LT)) R=cons(1,R); - else{ - if(R!=[]&&F!=0) R=cons(0,R); - R=cons(G=car(LT),R); - if(In==3) In==2; - } - for(LT=cdr(LT);LT!=[];LT=cdr(LT)) - R=cons(car(LT),R); - if((F=car(R))==G&&In==1){ - R=cons(-1,cdr(R)); - F=0; - } - } - if(In==3 && car(R)==G) R=cons(-1,cdr(R)); - return reverse(R); - } - for(F=0,RT=R=[];L!=[];L=cdr(L)){ - if(type(T=car(L))==4||type(T)==5){ - if(F==0){ - FT=T;F=1; - } - RT=cons(T,RT); - }else if(T==0){ - if(RT==[]) R=cons(reverse(RT),R); - RT=[];F=0; - }else if(T==1){ - if(RT!=[]){ - R=cons(reverse(RT),R); - RT=[car(RT)]; - }else{ - RT=[];F=0; - } - }else if(T==-1){ - RT=cons(FT,RT); - R=cons(reverse(RT),R); - RT=[];F=0; - } - } - if(RT!=[]) R=cons(reverse(RT),R); - return reverse(R); -} - - -def xybezier(L) -{ - if(L==0 || (LS=length(L))==0) return ""; - Out=str_tb(0,0); - if(type(VF=getopt(verb))==4){ - if(type(car(VF))>3){ - VFS=VF;VF=1; - }else{ - VFS=cdr(VF);VF=car(VF); - } - }else VFS=["$\\bullet$","$\\times$"]; - if(VF!=1 && VF!=2) VF=0; - if(!TikZ){ - if(VF) Ob=str_tb(0,0); - T="\n**\\crv{"; - if(type(Opt=getopt(opt))==7 && Opt!="") T=T+Opt; - L00=Q=L[I0=0];S=S1=""; - for(F=0,I=1;I<=LS;I++){ - P=Q;Q=(I==LS)?0:L[I]; - if(type(Q)==4){ - if(F==0){ - S1="";L0=P;F=1; - continue; - }else if(F==1) - F=2; - else if(F==2){ - S1=S1+"&"; - } - S1=S1+xypos(P); - if(VF&&length(VFS)>1) str_tb(xyput([P[0],P[1],VFS[1]]),Ob); - }else{ - if(Q==0){ - if(F>0){ - str_tb("{"+xypos(L0)+";"+xypos(P)+T+S1+"}};\n",Out); - if(VF){ - str_tb(xyput([L[0][0],L[0][1],VFS[0]]),Ob); - if(VF==1) str_tb(xyput([P[0],P[1],VFS[0]]),Ob); - } - F=0; - } - }else if(Q==1){ - str_tb("{"+xypos(L0)+";"+xypos(P)+T+S1+"}};\n",Out); - if(VF){ - str_tb(xyput([L[0][0],L[0][1],VFS[0]]),Ob); - if(VF==1) str_tb(xyput([P[0],P[1],VFS[0]]),Ob); - } - F=1; - }else if(Q==-1){ - if(F==2) - S1=S1+"&"; - str_tb("{"+xypos(L0)+";"+xypos(L00)+T+S1+xypos(P)+"}};\n",Out); - if(VF) str_tb(xyput([L[0][0],L[0][1],VFS[0]]),Ob); - F=0; - } - if(F==1){ - if(I<LS-1 && type(L[I+1])<2){ - if(L[I+1]==-1){ - str_tb("{"+xypos(P)+";"+xypos(L00)+T+"}};\n",Out); - } - if(VF) str_tb(xyput([P[0][0],P[0][1],VFS[0]]),Ob); - F=0; - } - } - while(++I<LS && type(L[I])<2); - if(I>=LS) break; - if(F==1){ - Q=P;I--;F=0; - }else L00=Q=L[I]; - } - } - }else{ - if(type(T=getopt(cmd))==7){ - if(T!="") T="\\"+T; - }else T="\\draw"; - if((Rel=getopt(relative))==1) VF=0; - if(VF) Ob=str_tb(0,0); - if(type(Opt=getopt(opt))==7 && Opt!="") T=T+"["+Opt+"]"; - Out=str_tb(T,0); - Q=L[0]; - for(F=M=0,I=1;I<=LS;I++){ - P=Q; Q=(I==LS)?0:L[I]; - if(++M>XYLim){ - str_tb("\n",Out);M=1; - } - if(type(Q)==4 || type(Q)==5 || type(Q)==7){ - if(F==0){ - str_tb(" ",Out); - F=1; - }else if(F==1){ - str_tb(" .. controls ",Out); - F=2; - }else if(F==2){ - str_tb(" and ",Out); - F=2; - } - PP=xypos(P); - if(Rel==1 && F==2) PP="+"+PP; - str_tb(PP,Out); - if(VF&&((F<2)||length(VFS)>1)) - str_tb(xyput([P[0],P[1],(F<2)?VFS[0]:VFS[1]]),Ob); - }else{ -/* if(I<LS-1) VF=0; */ - if(Q==0||Q==1){ - PP=xypos(P); - if(Rel==1) PP="+"+PP; - str_tb(((F==0)?" ":((F==1)?" -- ":" .. "))+PP,Out); - if(VF) str_tb(xyput([P[0],P[1],VFS[0]]),Ob); - F=Q; - }else if(Q==-1){ - PP=xypos(P); - if(Rel==1) PP="+"+PP; - if(F==1) - str_tb("..controls "+PP+" .. cycle",Out); - else if(F==2) - str_tb(" and "+PP+" .. cycle",Out); - if(VF&&length(VFS)>1) str_tb(xyput([P[0],P[1],VFS[1]]),Ob); - F=0; - } - if(F==1){ - if(I<LS-1){ - if(L[I+1]==-1){ - str_tb(" -- cycle",Out); - I=I+1; - F=0; - } - else if(type(L[I+1])<2) F=0; - } - } - while(++I<LS && type(L[I])<2); - if(I>=LS) break; - Q=L[I]; - } - } - str_tb(";\n",Out); - } - if(VF) str_tb(str_tb(0,Ob),Out); - return str_tb(0,Out); -} - -def xybox(L) -{ - K=length(L); - P=L[0];Q=L[1]; - if(K==2) - LL=[ P, [P[0],Q[1]], Q, [Q[0],P[1]] ]; - else{ - R=L[2]; - LL=[ P, R, Q, [P[0]+Q[0]-R[0],P[1]+Q[1]-R[1]] ]; - } - Opt=getopt(); - SS=getopt(opt); - FL=getopt(color); - if(TikZ&&type(SS)<1&&K==2){ - if(type(FL)==4){ - F=FL[0]; - if(length(FL)>1) CMD=FL[1]; - }else if(type(FL)==7) F=FL; - else F=""; - F=cons(F,["rectangle"]); - if(CMD) return xyarrow(P,Q|opt=F,cmd=CMD); - else return xyarrow(P,Q|opt=F); - } - if(type(SS)!=7&&!TikZ) Opt=cons(["opt","@{-}"],Opt); - Opt=cons(["close",1],Opt); - return xylines(LL|option_list=Opt); -} - -def xyang(S,P,Q,R) -{ - Opt=getopt(); - if(type(Prec=getopt(prec))!=1) Prec=0; - if(type(Q)>2){ - if(R==1||R==-1){ /* 直角 */ - P1=ptcommon([Q,P],[-S,0]); - S*=R; - P2=ptcommon([P,P1],[S,@pi/2]); - P3=ptcommon([P1,P2],[S,@pi/2]); - return xylines([P1,P2,P3]|option_list=Opt); - }else if((AR=abs(R))==0||AR==2||AR==3||AR==4){ /* 矢印 */ - Ang=myarg([Q[0]-P[0],Q[1]-P[1]]); - if(R<0) Ang+=3.14159; - ANG=[0.7854,0.5236,1.0472]; - X=(AR==0)?1.5708:ANG[AR-2]; - U=[P[0]+S*dcos(Ang+X),P[1]+S*dsin(Ang+X)]; - V=[P[0]+S*dcos(Ang-X),P[1]+S*dsin(Ang-X)]; /* 矢先 */ - V=(X==0)?[U,V]:[U,P,V]; - if(getopt(ar)==1) V=append([Q,P,0],V); /* 心棒 */ - return xylines(V|option_list=Opt); - }else if(AR>4&&AR<9){ - Ang=myarg([Q[0]-P[0],Q[1]-P[1]]); - ANG=[0.7854,0.5236,0.3927,0.2618]; - X=ANG[AR-5]; - U=[P[0]+S*dcos(Ang+X),P[1]+S*dsin(Ang+X)]; - V=[P[0]+S*dcos(Ang-X),P[1]+S*dsin(Ang-X)]; - W=ptcommon([P,U],[P,Q]|in=-2); - W1=[(U[0]+P[0]+W[0])/3,(U[1]+P[1]+W[1])/3]; - W2=[(V[0]+P[0]+W[0])/3,(V[1]+P[1]+W[1])/3]; - L=[U,W1,P,1,W2,V]; - if(getopt(ar)==1) L=append([Q,P,0],L); - if(type(Sc=getopt(scale))>0){ - if(type(Sc)==1) Sc=[Sc,Sc]; - L=ptaffine(diagm(2,Sc),L); - } - Opt=getopt(opt); - if(type(Opt)>0) OL=[["opt",Opt]]; - else OL=[]; - if(getopt(proc)==1) return append([2,OL],L); - S=xybezier(L|optilon_list=OL); - if(getopt(dviout)!=1) return S; - dviout(S); - return 1; - } - } - if(type(Q)<3){ - X=deval(Q); Y=deval(R); - }else{ - X=myarg([Q[0]-P[0],Q[1]-P[1]]); - Y=myarg([R[0]-P[0],R[1]-P[1]]); - } - if(Prec>2) N=8; - else if(Prec==2) N=6; - else if(Prec==1) N=4; - else N=3; - U=deval(@pi)*2/N; - if(X==Y||Y-X>6.28318){ - for(L=[],I=N-1;I>=0;I--) L=cons([P[0]+S*dcos(I*U),P[1]+S*dsin(I*U)],L); - return xylines(L|option_list=append([["curve",1],["close",1]],Opt)); - } - for(M=1;(Y-X)/M>U;M++); - for(L=[],I=M+1;I>-2;I--){ - Ang=X+(Y-X)*I/M; - L=cons([P[0]+S*dcos(Ang),P[1]+S*dsin(Ang)],L); - } - if(getopt(ar)!=1) return xylines(L|option_list=append([["curve",1],["close",-1]],Opt)); - OL=delopt(Opt,["dviout","opt","proc"]); - S=xylines(L|option_list=append([["curve",1],["close",-1],["opt",0]],OL)); - T=xylines([P,L[1]]|option_list=cons(["opt",0],OL)); - S=ptaffine("close",[S,T]); /* connect curves */ - if(getopt(opt)==0) return S; - OL=(type(SS=getopt(opt))>1)?[["opt",SS]]:[]; - if(type(T=getopt(proc))==1 && T>=1 && T<=3) return [1,OL,S]; - if(OL==[]) S=xybezier(S); - else S=(type(SS)==7)? xybezier(S|opt=SS):xybezier(S|opt=SS[0],cmd=SS[1]); - if(getopt(dviout)==1) return xyproc(S|dviout=1); - return S; -} - -def xyoval(P,L,R) -{ - if(type(Arg=getopt(arg))!=4 && type(Arg=getopt(deg))==4){ - if(length(Arg)>2) - Arg=[@pi*Arg[0]/180,@pi*Arg[1]/180,@pi*Arg[2]/180]; - else - Arg=[@pi*Arg[0]/180,@pi*Arg[1]/180]; - } - if(type(Arg)==4){ - Arg0=deval(Arg[0]); Arg1=deval(Arg[1]); - if(length(Arg)>2) Arg2=deval(Arg[2]); - if(Arg1<Arg0 || Arg0<-7) return 0; - } - if(type(Prec=getopt(prec))!=0) Prec=0; - if((Ar=getopt(ar))!=1) Ar=0; - L=xyang(L,[0,0],Arg0,Arg1|prec=Prec,opt=0,ar=Ar); - Sc=getopt(scale); - if(type(Sc=getopt(scale))<1) Sc=[1,1]; - else if(type(Sc)==1) Sc=[Sc,Sc]; - M=mat([1,0],[0,R]); - L=ptaffine(M,L|shift=P); - M=mat([Sc[0],0],[0,Sc[1]]); - L=ptaffine(M,L|arg=Arg2); - if((Opt=getopt(opt))==0) return L; - Opt=(type(Opt)>1)? [["opt2",Opt]]:[]; - if(getopt(proc)==1) return [1,Opt,L]; - S=xybezier(L|option_list=getopt()); - if(getopt(dviout)==1){ - xyproc(S|dviout=1); - return 1; - } - return S; -} - -def xycirc(P,R) -{ - ST=getopt(opt); - if(type(ST)<0) ST=""; - if(type(Arg=getopt(arg))!=4 && type(Arg=getopt(deg))==4){ - Arg=[@pi*Arg[0]/180,@pi*Arg[1]/180]; - } -/* Is it OK? - if(TikZ==0 && XYcm==1){ - R*=10; P=[P[0]*10,P[1]*10]; - } -*/ - if(type(Arg)==4){ - Arg0=deval(Arg[0]); Arg1=deval(Arg[1]); - if(Arg1<=Arg0 || Arg0<-7 || Arg1-Arg0>7) return 0; - if(type(ST)==7) - S=xygraph([R*cos(x)+P[0],R*sin(x)+P[1]],-4,[Arg0,Arg1],[P[0]-R-1,P[0]+R+1], - [P[1]-R-1,P[1]+R+1]|opt=ST); - else - S=xygraph([R*cos(x)+P[0],R*sin(x)+P[1]],-4,[Arg0,Arg1],[P[0]-R-1,P[0]+R+1], - [P[1]-R-1,P[1]+R+1]); - if(getopt(close)==1){ - S=S+xyline([0,0], - [deval(subst(R*cos(x)+P[0],x,Arg0)),deval(subst(R*sin(x)+P[0],x,Arg0))]); - S=S+xyline([0,0], - [deval(subst(R*cos(x)+P[0],x,Arg1)),deval(subst(R*sin(x)+P[0],x,Arg1))]); - } - return S; - } - if(TikZ){ - SP=""; - if(length(P)>2) SP=P[2]; - if(type(SP)!=7) SP="$"+my_tex_form(SP)+"$"; - if(R==0){ - if(ST!="") ST=ST+","; - return "\\node ["+ST+"circle,draw]"+xypos([P[0],P[1]])+ "{"+SP+"};\n"; - } - if(type(R)!=7) R=rtostr(deval(R)); - if(ST!="") ST="["+ST+"]"; - S="\\draw "+ST+xypos([P[0],P[1]])+" circle [radius="+R+"]"; - if(SP!="") S=S+" node at"+xypos([P[0],P[1]])+" {"+SP+"}"; - return S+";\n"; - } - S="{"+xypos([P[0],P[1]]); - if(length(P)>2){ - SP=P[2]; - if(type(P)!=7) SP=my_tex_form(SP); - S=S+" *+{"+SP+"}"; - } - S =S+" *\\cir"; - if(R!=0){ - R=deval(R); - S=S+"<"+rtostr(R)+((XYcm)?"cm>":"mm>"); - } - S = S+"{"; - if(type(ST)==7) S=S+ST; - return S+"}};\n"; -} - -def ptaffine(M,L) -{ - if(type(L)!=4&&type(L)!=5){ - erno(0);return L; - } - if(type(M)==7){ /* connect lists */ - if(M=="reverse"){ - for(LO=LR=[],F=0,LT=L; LT!=[]; LT=cdr(LT)){ - if(type(P=car(LT))==4 || type(P)==7){ - LR=cons(P,LR); - continue; - }else{ - if(P==-1){ - LL=reverse(LR); - LO=append(reverse(cons(-1,cdr(LL))),LO); - LO=cons(car(LL),LO); - LR=[]; - }else if(P==1){ - LR=cons(car(LR),cons(1,cdr(LR))); - }else if(P==0 || length(LT)==1){ - if(LO!=[] && car(LO)!=0 && (type(car(LO))==4 || car(LO)==1)) - LO=cons(0,LO); - LO=append(LR,LO); - if(length(LT)>1&&length(LO)>0&&car(LO)!=0) LO=cons(0,LO); - LR=[]; - } - } - } - return append(LR,LO); - } - if(type(L[0][0])!=4) L=[L]; - LO=[]; - if(M=="connect" || M=="close" || M=="loop"){ - Top=car(car(L)); - for(K=1,LL=L; LL!=[]; LL=cdr(LL)){ - for(F=0,LT=car(LL); LT!=[]; LT=cdr(LT),F++){ - if((LTT=car(LT))==0) LTT=1; - if(F==0 && LO!=[]){ - LO0=car(LO); - if(car(LO)!=1&&length(LO)>1) LO=cons(1,LO); - if(LTT==LO0) continue; - else LO=cons(1,cons(LTT, LO)); - }else LO=cons(LTT, LO); - } - } - if(M!="connect"){ - if(Top==car(LO) || car(LO)==1 || M=="loop") - LO=cons(-1,cdr(LO)); - else - LO=cons(-1,cons(1,LO)); - } - return reverse(LO); - } - if(M=="union"){ - for(LL=reverse(L); LL!=[]; LL=cdr(LL)){ - if(LO!=[]) LO=cons(0,LO); - LO=append(car(LL),LO); - } - L=LO; - } - return L; - } - if(type(Arg=getopt(deg))==1) - Arg=@pi*Arg/180; - else Arg=getopt(arg); - if(type(Arg)==2) Arg=deval(Arg); - if(type(Arg)==1) - M=M*mat([dcos(Arg),-dsin(Arg)],[dsin(Arg),dcos(Arg)]); - if(type(Sft=getopt(org))==4){ - Sft=ltov(Sft); - Sft-=M*Sft; - }else Sft=ltov([0,0]); - if(type(V=getopt(shift))==4) - Sft+=ltov(V); - if(getopt(proc)==1){ - if(Sft!=0&<ov(Sft)!=[0,0]) Sft=[["shift",vtol(Sft)]]; - else Sft=[]; - for(LO=[],LT=L;LT!=[];LT=cdr(LT)){ - if(type(car(T=car(LT)))<2){ - if((P=car(T))==0){ /* exedraw 0 */ - V=[[T[1][0],T[2][0]],[T[1][0],T[2][1]],[T[1][1],T[2][0]],[T[1][1],T[2][1]]]; - V=ptbbox(ptaffine(M,V|option_list=Sft)); - L1=cdr(cdr(cdr(T))); - LO=cons(append([0,V[0],V[1]],L1),LO); - continue; - }else if(P==1){ /* exedraw 1 */ - L1=[]; - for(TT=cdr(cdr(T));TT!=[];TT=cdr(TT)){ - D=car(TT); - if(type(D[0][0])==4){ - for(L2=[],DT=D;DT!=[];DT=cdr(DT)) - L2=cons(ptaffine(M,car(DT)|option_list=Sft),L2); - L1=cons(reverse(L2),L1); - }else L1=cons(ptaffine(M,D|option_list=Sft),L1); - } - LO=cons(append([1,T[1]],reverse(L1)),LO); - continue; - }else if(P>=2 && P<=5){ - L1=ptaffine(M,cdr(cdr(T))|optilon_list=Sft); - LO=cons(append([P,T[1]],L1),LO); - continue; - } - } - LO=cons(T,LO); - } - return reverse(LO); - } - F=0; - if(type(L)==4){ - for(LT=L; LT!=[]; LT=cdr(LT)){ - if((T=type(car(LT)))==4||T==5){ - F=1; break; - } - } - } - if(F==0) return (Sft==0)?ptaffine(M,[L])[0]:ptaffine(M,[L]|shift=vtol(Sft))[0]; - for(LO=[],LT=L; LT!=[]; LT=cdr(LT)){ - if(((T=type(P=car(LT)))!=4 && T!=5)||type(P[0])>3) LO=cons(P,LO); - else{ - if(T==4) P=ltov(P); - V=M*P; - if(Sft!=0) V+=Sft; - if(T==4) V=vtol(V); - LO=cons(V,LO); - } - } - return reverse(LO); -} - -def ptlattice(M,N,X,Y) -{ - if(type(S=getopt(scale))!=1) S=1; - if(type(Cond=getopt(cond))!=4) Cond=[]; - Line=getopt(line); - if(Line==1 || Line==2) F=newmat(M,N); - else Line=0; - if(type(Org=getopt(org))==4) Org=ltov(Org); - else Org=newvect(length(X)); - X=ltov(X); Y=ltov(Y); - for(L=[],I=M-1;I>=0;I--){ - for(P0=P1=0,J=N-1;J>=0;J--){ - P=Org+I*X+J*Y; - for(C=Cond; C!=[]; C=cdr(C)) - if(subst(car(C),x,P[0],y,P[1])<0) break; - if(C!=[]) continue; - if(Line) F[I][J]=1; - else L=cons(vtol(S*P),L); - } - } - if(Line==0) return L; - for(I=M-1;I>=0;I--){ - for(T0=0,T1=J=N-1;J>=0;J--){ - if((K=F[I][J])!=0){ - if(T0==0) T0=J; - else T1=J; - } - if(K==0 || T1==0){ - if(T1<T0){ - L=cons(vtol(S*(Org+I*X+T0*Y)), L); - L=cons(vtol(S*(Org+I*X+T1*Y)), L); - L=cons(0,L); - } - T0=0; T1=N-1; - } - } - } - for(J=N-1;J>=0;J--){ - for(T0=0,T1=I=M-1;I>=0;I--){ - if((K=F[I][J])!=0){ - if(T0==0) T0=I; - else T1=I; - } - if(K==0 || T1==0){ - if(T1<T0){ - L=cons(vtol(S*(Org+T0*X+J*Y)), L); - L=cons(vtol(S*(Org+T1*X+J*Y)), L); - L=cons(0,L); - } - T0=0; T1=M-1; - } - } - } - return cdr(L); -} - -def ptpolygon(N,R) -{ - if(type(S=getopt(scale))!=1) S=1; - if(type(Org=getopt(org))!=4) Org=[0,0]; - Pi=deval(@pi); - if(type(Arg=getopt(deg))==1) - Arg=Pi*Arg/180; - else Arg=getopt(arg); - if(type(Arg)==2) Arg=deval(Arg); - if(type(Arg)!=1) Arg=0; - Arg -= Pi*(1/2+1/N); - D=Pi*2/N; - for(L=[],I=N-1; I>=0; I--) - L=cons([S*(Org[0]+R*dcos(Arg+I*D)),S*(Org[1]+R*dsin(Arg+I*D))],L); - return L; -} - -def ptwindow(L,X,Y) -{ - if(type(S=getopt(scale))==1){ - X=[S*X[0],S*X[1]]; Y=[S*Y[0],S*Y[1]]; - } - for(R=[],LT=L;LT!=[];LT=cdr(LT)){ - P=car(LT); - if(P[0]<X[0] || P[0]>X[1] || P[1]<Y[0] || P[1]>Y[1]) - R=cons(0,R); - else R=cons(P,R); - } - return reverse(R); -} - -def lninbox(L,W) -{ - if(L[0]==L[1]) return 0; - R=newvect(2);C=newvect(2); - for(J=0;J<2;J++){ - C[J]=L[1][J]-L[0][J]; - if(C[J]!=0){ - R[J]=[(W[J][0]-L[0][J])/C[J],(W[J][1]-L[0][J])/C[J]]; - if(R[J][0]>R[J][1]) R[J]=[R[J][1],R[J][0]]; - } - } - if(R[0]==0) R[0]=R[1]; - if(R[1]==0) R[1]=R[0]; - S0=(R[0][0]<R[1][0])?R[1][0]:R[0][0]; - S1=(R[0][1]<R[1][1])?R[0][1]:R[1][1]; - if(getopt(in)==1){ - if(S0<0) S0=0; - if(S1>1) S1=1; - } - if(S0>S1) return 0; - return [[L[0][0]+C[0]*S0,L[0][1]+C[1]*S0],[L[0][0]+C[0]*S1,L[0][1]+C[1]*S1]]; -} - -def ptbbox(L) -{ - J=length(L[0]); - if((Box=getopt(box))==1){ - for(R=[],I=0;I<J;I++){ - P=car(LT=L)[I][0];Q=car(LT)[I][1]; - for(;LT!=[];LT=cdr(LT)){ - if((type(T=car(LT))==4 || type(T)==5) && length(T)==J){ - if(T[I][0]<P) P=T[I][0]; - if(T[I][1]>Q) Q=T[I][1]; - } - } - R=cons([P,Q],R); - } - }else if(type(Box)==4) return ptbbox([ptbbox(L),Box]|box=1); - else{ - for(R=[],I=0;I<J;I++){ - P=Q=car(LT=L)[I];LT=cdr(LT); - for(;LT!=[];LT=cdr(LT)){ - if((type(T=car(LT))==4||type(T)==5) && type(T[0])<2 && length(T)==J){ - if((V=T[I])<P) P=V; - else if(V>Q) Q=V; - } - } - R=cons([P,Q],R); - } - } - return reverse(R); -} - -def iscombox(S,T) -{ - for(;S!=[];S=cdr(S),T=cdr(T)) - if(car(S)[0]>car(T)[1] || car(S)[1]<car(T)[0]) return 0; - return 1; -} - -def ptcopy(L,V) -{ - if(type(V[0])!=4) V=[V]; - for(F=0,LL=[]; V!=[]; V=cdr(V)){ - if(F) LL=append(LL,[0]); - F++; - LL=append(LL,ptaffine(1,L|shift=car(V))); - } -} - -def average(L) -{ - L=os_md.m2l(L|flat=1); - M0=M1=car(L); - for(I=SS=0, LT=L; LT!=[]; LT=cdr(LT), I++){ - S+=(V=car(LT)); - SS+=V^2; - if(V<M0) M0=V; - else if(V>M1) M1=V; - } - SS=dsqrt(SS/I-S^2/I^2); - S=[deval(S/I),SS,I,M0,M1]; - if(isint(N=getopt(sint))) S=sint(S,N); - return S; -} - -def m2ll(M) -{ - for(R=[],I=size(M)[0]-1; I>=0; I--) - R=cons(vtol(M[I]),R); - return R; -} - -def madjust(M,W) -{ - if(type(Null=getopt(null))<0) Null=0; - if(type(M)==4 && type(M[0])==4){ - M=lv2m(M|null=Null); - return m2ll(madjust(M,W|null=Null)); - } - S=size(M); - if(W<0){ - W=-W; - T0=ceil(S[0]/W); - T1=S[1]*W; - N=newmat(T0,T1); - for(I=0; I<T0; I++){ - for(K=0; K<W; K++){ - II=K*T0+I; - for(J=0; J<S[1]; J++) - N[I][S[1]*K+J]=(II<S[0])?M[II][J]:Null; - } - } - }else{ - T1=W; - T0=S[0]*(D=ceil(S[1]/T1)); - N=newmat(T0,T1); - for(K=0; K<D; K++){ - for(J=0; J<W;J++){ - JJ=W*K+J; - for(I=0; I<S[0]; I++) - N[S[0]*K+I][J]=(JJ<S[1])?M[I][JJ]:Null; - } - } - } - return N; -} - -def texcr(N) -{ - if(!isint(N) || N<0 || N>127) return N; - S=(iand(N,8))? "\\allowdisplaybreaks":""; - if(iand(N,2)) S=S+"\\\\"; - if(iand(N,16)) S=S+"\\pause"; - if(iand(N,1)) S=S+"\n"; - if(iand(N,4)) S=S+"& "; - else if(!iand(N,1)) S=S+" "; - if(iand(N,64)) S=S+"="; - if(iand(N,32)) S=","+S; - return S; -} - -def ltotex(L) -{ - /* extern TeXLim; */ - - if(type(L)==5) - L = vtol(L); - if(type(L) != 4) - return my_tex_form(L); - Opt=getopt(opt); - Pre=getopt(pre); - if(type(Var=getopt(var))<1) Var=0; - Cr2="\n"; - if(type(Cr=getopt(cr))==4){ - Cr2=Cr[1];Cr=Cr[0]; - } - if(isint(Cr)) Cr=texcr(Cr); - if(type(Cr)!=7) Cr="\\\\\n & "; /* Cr=7 */ - if(type(Opt)==7) Opt=[Opt]; - if(type(Opt)!=4) - Op = -1; - else{ - Op=findin(Opt[0],["spt","GRS","Pfaff","Fuchs","vect","cr","text","spts","spts0", - "dform","tab", "graph","coord"]); - Opt=cdr(Opt); - } - if(Op==0){ /* spt */ - Out = str_tb("\\left\\{\n ",0); - for(CC=0; L!=[]; L=cdr(L), CC++){ - if(CC>0) str_tb(",\\, ",Out); - TP=car(L); - if(Op!=0) - str_tb(my_tex_form(TP),Out); - else if(TP[0]==1) - str_tb(my_tex_form(TP[1]),Out); - else - str_tb(["[", my_tex_form(TP[1]), "]_", rtotex(TP[0])],Out); - } - str_tb("%\n\\right\\}\n",Out); - }else if(Op==1){ /* GRS */ - Out = string_to_tb("\\begin{Bmatrix}\n"); - if(type(Pre)==7) str_tb(Pre,Out); - MC=length(M=ltov(L)); - for(ML=0, I=length(M); --I>=0; ){ - if(length(M[I]) > ML) ML=length(M[I]); - } - for(I=0; I<ML; I++){ - for(CC=J=0; J<MC; J++, CC++){ - if(length(M[J]) <= I){ - if(CC > 0) str_tb(" & ",Out); - }else if(M[J][I][0] <= 1){ - if(M[J][I][0] == 0) str_tb(" & ",Out); - else - str_tb([(!CC)?" ":" & ", my_tex_form(M[J][I][1])], Out); - }else - str_tb([((!CC)?" [":" & ["), my_tex_form(M[J][I][1]), "]_", - rtotex(M[J][I][0])], Out); - } - str_tb((I<ML-1)?"\\\\\n":"\n", Out); - } - str_tb("\\end{Bmatrix}",Out); - }else if(Op==2){ /* Pfaff */ - V=monototex(Opt[0]); - Out = string_to_tb("d"+V+"= \\Biggl("); - Opt=cdr(Opt); - II=length(Opt); - for(I=0; I<II; I++){ - str_tb([(I>0)?" + ":" ",mtotex(L[I]),"\\frac{d",monototex(Opt[I]),"}{", - my_tex_form(Opt[I]),(I==II-1)?"}\n":"}\n\\\\&\n"],Out); - } - str_tb(["\\Biggr)",V,"\n"],Out); - }else if(Op==3){ /* Fuchs */ - Out = string_to_tb("\\frac{d"); - V=my_tex_form(Opt[0]); - str_tb([V,"}{d",my_tex_form(Opt[1]),"}="] ,Out); - Opt=cdr(Opt); Opt=cdr(Opt); - II=length(Opt); - for(I=0; I<II; I++){ - str_tb([(I>0)?" +":"\\Biggl(", " \\frac{", - my_tex_form(L[I]),"}{", my_tex_form(Opt[I]),"}\n"],Out); - } - str_tb(["\\Biggr)",V,"\n"],Out); - }else if(Op==4){ /* vect */ - Out=str_tb(mtotex(matc(L)|lim=0,var=Var),0); - }else if(Op==5 || Op==6){ /* cr or text */ - Out = str_tb(0,0); - if(type(Lim=getopt(lim))!=1) Lim=0; - else if(Lim<30&&Lim>0) Lim=TeXLim; - Str=getopt(str); - if(length(Opt)==1 && (car(Opt)=="spts" || car(Opt)=="spts0") && type(Str)!=1) - Str=2; - for(K=I=0; L!=[]; I++, L=cdr(L)){ - LT=car(L); - if((!Lim||Op==6)&&I>0) str_tb((Op==5)?Cr:"\n",Out); - if(Op==6){ - if(type(LT)==7){ - str_tb([LT," "],Out); - I=-1; - continue; - } - str_tb("$",Out); - } - KK=0; - if(Str>0 && type(LT)==4 && Opt!=[]) - S=ltotex(LT|opt=car(Opt),lim=0,str=Str,cr=Cr2,var=Var); - else if(type(LT)==6){ - if(Lim>0){ - S=mtotex(LT|var=Var,lim=0,len=1); - KK=S[1]; - S=S[0]; - }else S=mtotex(LT|var=Var,lim=0); - }else if(type(LT)==3 || type(LT)==2) - S=fctrtos(LT|TeX=2,lim=0,var=Var); - else S=my_tex_form(LT); - if(Op!=6&&I>0&&Lim){ - if(Lim<0){ - if(I%(-Lim)==0) - str_tb((Op==5)?Cr:"\n",Out); - }else if((K+=(KK=(KK)?KK:texlen(S)))>Lim){ - str_tb((Op==5)?Cr:"\n",Out); - K=KK; - } - } - str_tb(S,Out); - if(Op==6) str_tb("$",Out); - } - }else if(Op==7||Op==8){ /* spts, spts0 */ - if(type(Lim=getopt(lim))!=1 || (Lim<30 && Lim!=0)) - Lim=TeXLim; - Str=getopt(str); - Out = str_tb(0,0); - for(K=0; L!=[]; L=cdr(L)){ - LT=car(L); - KK=0; - if(type(LT)==7 && Str==1) S=LT; - else if(type(LT)==3 || type(LT)==2) - S=fctrtos(LT|TeX=2,lim=0,var=Var); - else if(type(LT)==6){ - if(Lim){ - S=mtotex(LT|var=Var,lim=0,len=1); - KK=S[1]; - S=S[0]; - }else S=mtotex(LT|var=Var,lim=0); - }else - S=my_tex_form(LT); - if(Lim!=0){ - if(!KK) KK=texlen(S); - if(K>0 && K+KK>Lim){ - str_tb(Cr,Out); - K=0; - } - } - if(K>0){ - str_tb((Op==7)?"\\ ":" ",Out); - if(type(LT)>3 && type(LT)<7) str_tb("%\n",Out); - } - str_tb(S,Out); - K+=KK; - if(OP==7) K++; - } - }else if(Op==9){ /* dform */ - Out=str_tb(0,0); - for(I=0;L!=[];L=cdr(L),I++){ - for(J=0,LT=car(L); LT!=[]; LT=cdr(LT),J++){ - if(J==0){ - if((V=car(LT))==0) continue; - if(I>0){ - if(type(V)==1){ - if(V<0){ - str_tb("-",Out); - V=-V; - } - else str_tb("+",Out); - if(V==1 && length(LT)>1) continue; - str_tb(monototex(V),Out); - continue; - } - else str_tb("+",Out); - } - }else if(J>0) str_tb((J>1)?"\\wedge d":"\\,d",Out); - V=monototex(car(LT)); - if(V<"-" || V>=".") str_tb(V,Out); - else str_tb(["(",V,")"],Out); - } - } - }else if(Op==10 && type(L)==4 && type(car(L))==4){ /* tab */ - if(type(Null=getopt(null))<0) Null=""; - if(getopt(vert)==1){ - M=lv2m(L|null=Null); - L=m2ll(mtranspose(M)); - } - if(type(W=getopt(width))==1) - L=madjust(L,W|null=Null); - LV=ltov(L); - S=length(LV); -#if 1 - if(type(T=getopt(left))==4){ - T=str_times(T,S); - for(L=[],I=0;I<S;I++){ - L=cons(cons(car(T),LV[I]),L); - T=cdr(T); - } - LV=reverse(L); - } - if(type(T=getopt(right))==4){ - T=str_times(T,S); - for(L=[],I=0;I<S;I++){ - L=cons(append(LV[I],[car(T)]),L); - T=cdr(T); - } - LV=reverse(L); - } - for(I=CS=0; I<S; I++) - if(length(LV[I])>CS) CS=length(LV[I]); - if(type(T=getopt(top))==4){ - LV=cons(str_times(T,CS),vtol(LV)); - S++; - } - if(type(T=getopt(last))==4){ - LV=append(vtol(LV),[str_times(T,CS)]); - S++; - } -#else - for(I=CS=0; I<S; I++) - if(length(LV[I])>CS) CS=length(LV[I]); -#endif - if(type(Title=getopt(title))!=7) Title=""; - if(type(Vline=getopt(vline))!=4) Vline=[0,CS]; - else Vline=subst(Vline,z,CS); - for(VV=[],VT=Vline;VT!=[];VT=cdr(VT)){ - if(type(T=car(VT))==4 && T[1]>0){ - for(I=T[0];I<=CS;I+=T[1]) VV=cons(I,VV); - }else VV=cons(T,VV); - } - Vline=qsort(VV); - Out=str_tb("\\begin{tabular}{",0); - if(type(Al=getopt(align))==7 && str_len(Al)>1){ - str_tb(Al,Out); - }else{ - if(type(Al)!=7 || str_len(Al)<1) Al="r"; - for(I=0;I<=CS;I++){ - if(I!=0) str_tb(Al,Out); - while(Vline!=[] && car(Vline)==I){ - str_tb("|",Out); - Vline=cdr(Vline); - } - } - } - str_tb("}",Out); - if(Title!="") - str_tb("\n\\multicolumn{"+rtostr(CS)+"}{c}{"+Title+"}\\\\",Out); - if(type(Hline=getopt(hline))!=4) Hline=[0,S]; - else Hline=subst(Hline,z,S); - for(VV=[],VT=Hline;VT!=[];VT=cdr(VT)){ - if(type(T=car(VT))==4 && T[1]>0){ - for(I=T[0];I<=S;I+=T[1]) VV=cons(I,VV); - }else VV=cons(T,VV); - } - Hline=qsort(VV); - while(Hline!=[] && car(Hline)==0){ - str_tb(" \\hline\n",Out); - Hline=cdr(Hline); - } -/* - if(type(getopt(left))==4) CS++; - if(type(getopt(right))==4) CS++; - if(type(T=getopt(top))==4){ - LV=cons(str_times(T,CS),vtol(LV)); - S++; - } - if(type(T=getopt(last))==4){ - LV=append(vtol(LV),[str_times(T,CS)]); - S++; - } - if(type(T=getopt(left))==4){ - T=str_times(T,S); - for(L=[],I=0;I<S;I++){ - L=cons(cons(car(T),LV[I]),L); - T=cdr(T); - } - LV=reverse(L); - } - if(type(T=getopt(right))==4){ - T=str_times(T,S); - for(L=[],I=0;I<S;I++){ - L=cons(append(LV[I],[car(T)]),L); - T=cdr(T); - } - LV=reverse(L); - } -*/ - for(I=0; I<S; I++){ - for(C=0,LT=LV[I];C<CS; C++){ - if(LT!=[]){ - P=car(LT); - if(type(P)!=7) P="$"+my_tex_form(P)+"$"; - if(P!="") str_tb(P,Out); - LT=cdr(LT); - } - if(C<CS-1) str_tb("& ",Out); - } - str_tb("\\\\",Out); - while(Hline!=[] && car(Hline)==I+1){ - str_tb(" \\hline",Out); - Hline=cdr(Hline); - } - str_tb("\n",Out); - } - str_tb("\\end{tabular}\n",Out); - }else if(Op==11){ /* graph */ - if(type(Strip=getopt(strip))!=1) Strip=0; - if(type(MX=getopt(max))!=1) MX=0; - if(type(ML=getopt(mult))!=1) ML=0; - if((REL=getopt(relative))!=1) REL=0; - CL=getopt(color); - OL=delopt(getopt(),["color","strip","mult"]); - if(ML==1&&type(CL)==4){ - LL=L[1];L=L[0];K=length(L);S=T=""; - if(!MX){ - MX=vector(length(L[0])); - for(LT=L;LT!=[];LT=cdr(LT)){ - for(I=0,LTT=car(LT);LTT!=[];I++,LTT=cdr(LTT)){ - if(REL==1) MX[I]+=car(LTT); - else if(MX[I]<car(LTT)) MX[I]=car(LTT); - } - } - MX=lmax(MX); - OL=cons(["max",MX],OL); - } - if(REL==1) MX=newvect(length(L[0])); - for(I=0;I<K;I++){ - for(R=[],J=length(L[I]);--J>=0;){ - if(REL==1){ - R=cons([MX[J],V=MX[J]+L[I][J]],R); - MX[J]=V; - }else R=cons([(!I)?0:L[I-1][J],L[I][J]],R); - } - OP=cons(["color",CL[I]],OL); - S+=ltotex([R,LL]|option_list=cons(["value",0],cons(["strip",(!I)?1:2],OP))); - T+=ltotex([R,LL]|option_list=cons(["strip",3],OP)); - } - return(!Strip)?xyproc(S+T):(S+T); - }else if(!TikZ) CL=0; - if(type(Line=getopt(line))!=1){ - if(type(Line)==4){ - if(type(Line[0])==1 && (type(Line[1])==7 || type(Line[1])==1)){ - Opt=Line[1]; Line=Line[0]; - }else if(ML==1){ - OL=delopt(OL,"line"); - LL=L[1];L=L[0];K=length(L);S=""; - if(!MX){ - MX=newvect(length(L[0])); - for(LT=L;LT!=[];LT=cdr(LT)){ - for(I=0,LTT=car(LT);LTT!=[];I++,LTT=cdr(LTT)){ - if(REL==1) MX[I]+=car(LTT); - else if(MX[I]<car(LTT)) MX[I]=car(LTT); - } - } - MX=lmax(MX); - OL=cons(["max",MX],OL); - } - for(I=0;I<K;I++) - S+=ltotex([L[I],LL]|option_list - =cons(["line",Line[I]],cons(["strip",(!I)?1:2],OL))); - return(!Strip)?xyproc(S):S; - } - }else Line=0; - }else Opt="@{-}"; - Width=8; Hight=3; WRet=1/2; HMerg=(getopt(horiz)==1)?0.3:0.2; - if(!TikZ){ - Width*=10; Hight*=10; HMerg*=10; - } - VMerg=HMerg; - if(type(Shift=getopt(shift))!=1) - Shift=0; - if(type(V=getopt(size))==4){ - Width=V[0];Hight=V[1]; - if(length(V)>2) WRet=V[2]; - if(length(V)>3) VMerg=VMerg=V[3]; - if(length(V)>4) HMerg=V[4]; - } - Val=getopt(value); - if(!isint(Val)) Val=-1; - if(type(Line=getopt(line))!=1){ - if(type(Line)==4 && type(Line[0])==1 && (type(Line[1])==7 || type(Line[1])==1)){ - Opt=Line[1]; Line=Line[0]; - }else Line=0; - }else Opt="@{-}"; - if(type(car(L))==4){ - LL=L[1]; L=L[0]; - }else LL=[]; - if(Line==-1){ - for(Sum=0, LT=L; LT!=[]; LT=cdr(LT)){ - if((S=car(LT))<=0) return 0; - Sum+=S; - } - for(R=[],LT=L;LT!=[];LT=cdr(LT)) R=cons(car(LT)/Sum,R); - R=reverse(R); - Opt0=Opt*2/3; - Out=str_tb((Strip>0)?0:xyproc(1),0); - if(type(CL)!=4) str_tb(xylines(ptpolygon(6,Opt)|close=1,curve=1),Out); - for(S=0,RT=R,LT=LL;RT!=[];RT=cdr(RT)){ - SS=S+RT[0]; - if(type(CL)==4){ - str_tb(xyang(Opt,[0,0],(0.25-SS)*6.2832,(0.25-S)*6.2832|ar=1,opt=car(CL)),Out); - if(length(CL)>0) CL=cdr(CL); - }else str_tb(xyline([0,0],[Opt*dsin(S*6.2832),Opt*dcos(S*6.2832)]),Out); - T=(S+SS)/2; - S=SS; - if(LT!=[]){ - str_tb(xyput([Opt0*dsin(T*6.2832),Opt0*dcos(T*6.2832),car(LT)]),Out); - LT=cdr(LT); - } - } - if(!Strip) str_tb(xyproc(0),Out); - return str_tb(0,Out); - } - if(MX==0){ - for(MX=0,LT=L; LT!=[]; LT=cdr(LT)) - if(car(LT)>MX) MX=car(LT); - } - MX-=Shift; - S=length(L); - WStep=Width/S; - WWStep=WStep*WRet; - HStep=(Hight<0)?-Hight:Hight/MX; - if(LL!=[]&&length(LL)==S-1) WS2=WStep/2; - else WS2=0; - Out=str_tb((Strip>0)?0:xyproc(1),0); - Hori=getopt(horiz); - if(Strip<2){ - if(Hori==1) str_tb(xyline([0,0],[0,Width-WStep+WWStep]),Out); - else str_tb(xyline([0,0],[Width-WStep+WWStep,0]),Out); - } - for(I=0,LT=L;LT!=[]; LT=cdr(LT),I++){ - XP=WStep*I; XPM=XP+WWStep/2; - if(type(LTT=car(LT))==4){ - YP0=(car(LTT)-Shift)*HStep;YP=(LTT[1]-Shift)*HStep; - VL=LTT[1]; - if(REL) VL-=LTT[0]; - }else{ - YP0=0;YP=(LTT-Shift)*HStep;VL=LTT; - } - if(Hori==1){ - if(Line!=0){ - if(I>0) - str_tb(xyarrow([XPM,YP],[XPM-WStep,YPP]|opt=Opt),Out); - if(Val!=0) - str_tb(xyput([YP+HMerg, XPM,car(LT)]),Out); - if(Line==2) - str_tb(xyput([YP,XPM,"$\\bullet$"]),Out); - YPP=YP; - }else if(YP!=0 || Val==1){ - if(Strip!=3){ - if(CL) str_tb(xybox([[YP,XP+WWStep], [YP0,XP]]|color=CL),Out); - else str_tb(xybox([[YP,XP+WWStep],[YP0,XP]]),Out); - } - if(Val!=0) str_tb(xyput([(YP<0||REL==1)?(YP-HMerg):(YP+HMerg),XPM,VL]),Out); - } - if(LL!=[]&&I<length(LL)&&Strip<2) str_tb(xyput([-VMerg,XPM+WS2,LL[I]]),Out); - }else{ - if(Line!=0){ - if(I>0) - str_tb(xyarrow([XPM-WStep,YPP],[XPM,YP]|opt=Opt),Out); - if(Val!=0) - str_tb(xyput([XPM,YP+HMerg,car(LT)]),Out); - if(Line==2) - str_tb(xyput([XPM,YP,"$\\bullet$"]),Out); - YPP=YP; - }else if(YP!=0 || Val==1){ - if(Strip!=3){ - if(CL) str_tb(xybox([[XP,YP0],[XP+WWStep,YP]]|color=CL),Out); - else str_tb(xybox([[XP,YP0],[XP+WWStep,YP]]),Out); - } - if(Val!=0) str_tb(xyput([XPM,(YP<0||REL==1)?(YP-HMerg):(YP+HMerg),VL]),Out); - } - if(LL!=[]&&I<length(LL)&&Strip<2) str_tb(xyput([XPM+WS2,-VMerg,LL[I]]),Out); - } - } - if(!Strip)str_tb(xyproc(0),Out); - }else if(Op==12){ /* coord */ - Out=str_tb("(",0); - for(LT=L;;){ - X=car(LT); - if(type(X)>3 || imag(X)==0) str_tb(my_tex_form(X),Out); - else{ - XR=real(X);XI=imag(X); - S=monototex(imag(X)); - if(S=="1") S=""; - else if(S=="- 1") S="-"; - if(getopt(cpx)==2) S=S+"\\sqrt{-1}"; - else S=S+"i"; - if(XR!=0){ - if(str_char(S,0,"-")==0) S=monototex(XR)+S; - else S=monototex(XR)+"+"+S; - } - str_tb(S,Out); - } - if((LT=cdr(LT))==[]) break; - else str_tb(",",Out); - } - str_tb(")",Out); - } - else return my_tex_form(L); - S = str_tb(0,Out); - return (getopt(small)==1)?smallmattex(S):S; -} - - -def str_tb(L,TB) -{ - if(type(TB) == 0) TB = ""; - if(L == 0) - return (type(TB) == 7)?string_to_tb(TB):tb_to_string(TB); - if(type(L) == 7) - L = [L]; - else if(type(L) != 4){ - erno(0); - return 0; - } - if(type(TB) <= 7) - TB = string_to_tb((type(TB)==7)?TB:""); - for(; L != []; L = cdr(L)) - write_to_tb(car(L), TB); - return TB; -} - -/* -def redgrs(M,T) -{ - L = [zzz]; - for(I=S=0,Eq=[],MT=M; MT!=[]; I++, MT=cdr(MT)){ - for(J=LS=0, N=car(MT); N!=[]; N=cdr(N)){ - X = makev([z,I,z,J]); - L=cons(X,L); - LS += X; - S += car(N)[1]*X; - } - Eq = cons(LS-zzz,Eq); - } - Eq = cons(S-T,Eq); - Sol= lnsol(Eq,L); - for(LS=[],S=Sol; S!=[]; S=cdr(S)){ - T=car(S); - if(type(S)!=4) return 0; - LS=cons(car(S)[0],LS); - } -} -*/ - -/* T=0 : all reduction - =1 : construction procedure - =2 : connection coefficient - =3 : operator - =4 : series expansion - =5 : expression by TeX - =6 : Fuchs relation - =7 : All - =8 : basic - =9 : "" - =10: irreducible - =11: recurrence */ -def getbygrs(M, TT) -{ - /* extern TeXEq; */ - - if(type(M)==7) M=s2sp(M); - if(type(M) != 4 || TT =="help"){ - mycat( -["getbygrs(m,t) or getbygrs(m,[t,s_1,s_2,...]|perm=?,var=?,pt=?,mat=?)\n", -" m: generalized Riemann scheme or spectral type\n", -" t: reduction, construct, connection, series, operator, TeX, Fuchs, irreducible, basic, recurrence,\n", -" All\n", -" s: TeX dviout simplify short general operator irreducible top0 x1 x2 sft\n", -"Ex: getbygrs(\"111,21,111\", [\"All\",\"dviout\",\"operator\",\"top0\"])\n"]); - return 0; - } - if(type(TT) == 4){ - T = TT[0]; - T1 = cdr(TT); - }else{ - T = TT; - T1 = []; - } - if(type(T) == 7) - T = findin(T,["reduction","construct","connection", "operator", "series", - "TeX", "Fuchs", "All", "basic", "", "irreducible", "recurrence"]); - TeX = findin("TeX", T1); - Simp = findin("simplify", T1); - Short = findin("short", T1); - Dviout= findin("dviout", T1); - General=findin("general", T1); - Op =findin("operator", T1); - Irr =findin("irreducible", T1); - Top0 =findin("top0",T1); - X1 =findin("x1",T1); - X2 =findin("x2",T1); - Sft =findin("sft",T1); - Title = getopt(title); - Mat = getopt(mat); - if(Mat!=1 || T<0 ||(T!=0&&T!=1&&T!=5&&T!=6&&T!=8&&T!=10&&T!=9)) Mat = 0; - if(findin("keep",T1) >= 0) - Keep = Dviout = 1; - else Keep = 0; - if(Dviout >= 0 || T == 5) TeX = 1; - for(J = 0, MM = M; J == 0 && MM != []; MM = cdr(MM)){ - for(MI = car(MM); MI != []; MI = cdr(MI)){ - if(type(car(MI)) != 1 || car(MI) <= 0){ - J = 1; break; - } - } - } - - /* spectral type -> GRS */ - if(J == 0){ - for(R = [], S = J = 0, MM = M; MM != []; MM = cdr(MM), J++){ - MT = qsort(car(MM)); - R = cons(reverse(MT), R); - if(J == 1){ - S = length(MT)-1; - if(MT[S] > MT[0]) S = 0; - } - } - M = reverse(R); - R = getopt(var); - if(type(R)<1){ - for(R = [], I = J-1; I >= 0; I--) - R = cons(asciitostr([97+I]), R); - } - Sft=(Sft>=0)?1:0; - if(General < 0) - Sft=-Sft-1; - M = sp2grs(M,R,Sft|mat=Mat); - } - for(M0=[],MM=M;MM!=[];MM=cdr(MM)){ /* change "?" -> z_z */ - for(M1=[],Mm=car(MM);Mm!=[];Mm=cdr(Mm)){ - Mt=car(Mm); - if(type(Mt)==4 && Mt[1]=="?"){ - M1=cons([Mt[0],z_z],M1); - continue; - }else if(type(Mt)==7 && Mt=="?"){ - M1=cons(z_z,M1); - continue; - } - M1=cons(Mt,M1); - } - M0=cons(reverse(M1),M0); - } - M = fspt(reverse(M0),5); /* short -> long */ - if(findin(z_z,vars(M))>=0) - M=subst(M,z_z,lsol(chkspt(M|mat=Mat)[3],z_z)); /* Fuchs relation */ - NP = length(M); - Perm = getopt(perm); - if(type(Perm) == 4) - M = mperm(M,Perm,0); - if(T == 9){ /* "" */ - if(Short >= 0) - M = chkspt(M|opt=4,mat=Mat); - return M; - } - R = [0,M]; - ALL = [R]; - - while(type(R = redgrs(R[1]|mat=Mat)) == 4) - ALL = cons(R, ALL); - if(R < 0) - return 0; - - /* TeX */ - if(TeX >= 0 && !chkfun("print_tex_form", "names.rr")) - return 0; - if(Dviout >= 0 && type(Title) == 7) - dviout(Title|keep=1); - if(T == 7 && Dviout >= 0){ - S=["keep","simplify"]; - if(Top0 >= 0) - S = cons("top0",S); - getbygrs(M,cons(5,S)|title="\\noindent Riemann Scheme",mat=Mat); - Same = 0; - if(R > 0){ - MM = getbygrs(M,8|mat=Mat); /* basic GRS */ - MS = chkspt(MM|opt=0,mat=Mat); /* spectral type */ - if(M != MM) - getbygrs(MM,cons(5,S)|title="Basic Riemann Scheme",mat=Mat); - else{ - dviout("This is a basic Riemann Scheme.\n\n\\noindent"|keep=1); - Same = 1; - } - dviout(MS|keep=1); - } - if(chkspt(ALL[0][1]|mat=Mat)[3] != 0) - getbygrs(M,cons(6,S)|title="Fuchs condition",mat=Mat); - if(Same == 0){ - M1 = M[1]; - if(M1[length(M1)-1][0]==1 && Mat!=1){ - M1=M[2]; - if(M1[length(M1)-1][0] == 1){ - getbygrs(M,cons(2,S)|title="Connection formula"); - if(M1[length(M[0][0])-1][0] == 1 && R==0) - getbygrs(M,cons(11,S)|title="Recurrence relation shifting the last exponents at $\\infty$, 0, 1"); - } - getbygrs(M,cons(1,S)|title="Integral representation"); - getbygrs(M,cons(4,S)|title="Series expansion"); - } - if(Irr < 0){ - TI="Irreduciblity $\\Leftrightarrow$ any value of the following linear forms $\\notin\\mathbb Z$"; - if(R > 0) - TI += " + fundamental irreducibility"; - getbygrs(M,cons(10,S)|title=TI,mat=Mat); - dviout("which coorespond to the decompositions"|keep=1); - sproot(chkspt(M|opt=0),"pairs"|dviout=1,keep=1); - } - } - if(Op >= 0 && Mat!=1) getbygrs(M,cons(3,S)|title="Operator"); - dviout(" "); - return 1; - } - if(T == 0 && TeX >= 0){ - T = 1; TeX = 16; - } -/* Fuchs */ - Fuc = chkspt(ALL[0][1]|Mat=mat)[3]; - if(Fuc == 0) Simp = -1; - if(type(Fuc) == 1){ - print("Violate Fuchs condition"); - return 0; - } - if(T == 6){ - if(Dviout >= 0) dviout(Fuc|eq=0,keep=Keep); - return (TeX >= 0)?my_tex_form(Fuc):Fuc; - } - Fuc = [Fuc]; -/* Generelized Riemann scheme */ - if(T == 5){ - M = ltov(M); - for(ML=0, I=0; I<NP; I++){ - L = length(M[I]); - if(L > ML) ML = L; - } - Out = string_to_tb("P\\begin{Bmatrix}\nx="); - if(Top0 < 0) - write_to_tb("\\infty & ",Out); - Pt = getopt(pt); - if(type(Pt) == 4){ - for(J = 3; J < NP; J++){ - str_tb(["& ",rtotex(car(Pt))],Out); - Pt = cdr(Pt); - } - } - else if(X2>=0) - str_tb("0 & x_2",Out); - else - str_tb((X1>=0)?"x_1 & x_2":"0 & 1",Out); - for(J = 3; J < NP; J++) - str_tb(["& x_",rtotex(J)],Out); - if(Top0 >= 0) - write_to_tb("& \\infty",Out); - write_to_tb("\\\\\n",Out); - for(I = 0; I < ML; I++){ - for(CC = 0, J = (Top0 >= 0)?1:0; ; J++, CC++){ - if(J == NP){ - if(Top0 < 0) break; - J = 0; - } - if(length(M[J]) <= I){ - if(CC > 0) write_to_tb(" & ",Out); - }else if(M[J][I][0] <= 1){ - if(M[J][I][0] == 0) str_tb(" & ",Out); - else - str_tb([(!CC)?" ":" & ", my_tex_form(M[J][I][1])], Out); - }else{ - str_tb([((!CC)?"[":" & ["), my_tex_form(M[J][I][1]), - (Mat==1)?"]_{":"]_{("],Out); - str_tb([my_tex_form(M[J][I][0]),(Mat==1)?"}":")}"],Out); - } - if(Top0 >= 0 && J == 0) - break; - } - if(I == 0) - str_tb("&\\!\\!;x",Out); - str_tb("\\\\\n",Out); - } - str_tb("\\end{Bmatrix}",Out); - Out = str_tb(0,Out); - if(Dviout >= 0) - dviout(Out|eq=0,keep=Keep); - return Out; - } - -/* Reduction */ - if(T == 0){ - if(Simp >= 0) - ALL = simplify(ALL,Fuc,4); - return reverse(ALL); - } - LA = length(ALL) - 1; - NP = length(ALL[0][1]); - -/* irreducible */ - if(T == 10){ - for(IR=[], I = 0; I < LA; I++){ - AI = ALL[I]; AIT = AI[1]; - K = AI[0][0]; - P = -AIT[0][K][1]; - P -= cterm(P); - IR = cons(P, IR); - for(J = 0; J < NP; J++){ - K = AI[0][J]; - for(L = length(AIT[J]) - 1; L >= 0 ; L--){ - if(L == K || AIT[J][L][0] <= AIT[J][K][0]) - continue; - P = AIT[J][L][1] - AIT[J][K][1]; - Q = cterm(P); - if(dn(Q)==1) - P -= Q; - IR = cons(P,IR); - } - } - } - P=Fuc[0]; - Q=cterm(P); - if(type(Q)==1 && dn(Q)==1){ - for(F=0,V=vars(P);V!=[];V=cdr(V)){ - R=mycoef(P,1,car(V)); - if(type(R)!=1 || Q%R!=0){ - F=1; break; - } - } - if(F==0){ - P-=Q; - Simp=0; - } - } - if(Simp >= 0){ - IR=simplify(IR,[P],4); - for(R=[]; IR!=[]; IR=cdr(IR)){ - P=car(IR); - Q=cterm(P); - if(dn(Q)==1) P-=Q; - R=cons(P,R); - } - IR=R; - } - for(R=[]; IR!=[]; IR=cdr(IR)){ - P=car(IR); - if(str_len(rtostr(P)) > str_len(rtostr(-P))) - P = -P; - R = cons(P,R); - } - R = ltov(R); -#ifdef USEMODULE - R = qsort(R,os_md.cmpsimple); -#else - R = qsort(R,cmpsimple); -#endif - R = vtol(R); - if(TeX >= 0){ - Out = string_to_tb(""); - for(I=L=K=0; R!=[]; R=cdr(R),I++){ - K1 = K; - RS = my_tex_form(car(R)); - K = nmono(car(R)); - L += K; - if(I){ - if(K1 == K && L < 30) - str_tb("\\quad ",Out); - else{ - L = K; - str_tb((TeXEq==5)?["\\\\%\n &"]:["\\\\%\n "],Out); - } - } - str_tb(RS,Out); - } - R = Out; - if(Dviout>=0){ - dviout(R|eq=0,keep=Keep); - return 1; - } - } - return R; - } - - AL = []; SS = 0; - for(I = 0; I <= LA; I++){ - AI = ALL[I]; AIT = AI[1]; /* AIT: GRS */ - if(I > 0){ - for(S = J = 0; J < NP; J++){ - GE = AIT[J][AI0[J]][1]; - S += GE; - if(J == 0) - SS = []; - else - SS = cons(GE,SS); - } - SS = cons(1-Mat-S, reverse(SS)); - } - AI0 = AI[0]; - AL = cons([SS, cutgrs(AIT)], AL); - } - AL = reverse(AL); - AD = newvect(NP); - ALT = AL[0][1]; - for(J = 1; J < NP; J++){ - /* AD[J] = ALT[J][0][1]; [J][?][1] <- [J][?][0]: max */ - for(MMX=0, K = KM = length(ALT[J])-1; K >= 0; K--){ - if(MMX <= ALT[J][K][0]){ - if(J == 1 && MMX == ALT[J][K][0]) - continue; - KM = K; - MMX = ALT[J][K][0]; - } - } - AD[J] = ALT[J][KM][1]; - } - AL = cdr(AL); - AL = cons([vtol(AD), ALT], AL); - AL = cons([0, mcgrs(ALT, [vtol(-AD)]|mat=Mat)], AL); - if(Simp >= 0 && T != 3) - AL = simplify(AL,Fuc,4); -/* Basic */ - if(T == 8){ - ALT = AL[0][1]; - if(TeX >= 0){ - if(Dviout >= 0){ - return getbygrs(ALT,["TeX","dviout","keep"]); - } - return getbygrs(ALT,"TeX"); - } - if(Short >= 0) - ALT = chkspt(ALT|opt=4); - return ALT; - } - -/* Construct */ - if(T == 1){ - if(TeX >= 0){ - L = length(AL); - I = Done = 0; Out0=Out1=""; NM = DN = []; - if(TeX != 16){ - AL11=AL[L-1][1][1]; - AT = AL11[length(AL11)-1]; - if(type(AT) == 4){ - PW = (AT[0] > 1)?"":AT[1]; - }else PW = AT; - } - Out = string_to_tb(""); - while(--L >= 0){ - if(TeX == 16){ - if(Done) - write_to_tb(":\\ ", Out); - write_to_tb(getbygrs(AL[L][1],(Top0>=0)?["TeX", "top0"]:"TeX"|mat=Mat), Out); - Done = 1; - if(L != 0) write_to_tb((TeXEq==5)? - "\\\\%\n&\\leftarrow ":"\\\\%\n\\leftarrow ", Out); - } - ALT = AL[L][0]; - if(TeX != 16){ - V1 = (I==0)?"x":V2; - V2 = /* (I==0 && L<=2)?"s": */ - "s_"+rtotex(I); - }else V1=V2="x"; - JJ = (type(ALT) == 4)?length(ALT):0; - if(I > 0 && L > 0) - write_to_tb("\n ", Out); - for(Outt = "", J = 1; J < JJ; J++){ - if(ALT[J] == 0) continue; - if(J == 1) Outt += V1; - else if(J == 2) Outt += "(1-"+V1+")"; - else Outt += "(x_"+rtotex(J)+"-"+V1+")"; - Outt += "^"+ rtotex(ALT[J]); - } - if(TeX != 16) write_to_tb(Outt, Out); - else if(Outt != "") - str_tb(["\\mathrm{Ad}\\Bigl(",Outt,"\\Bigr)"], Out); - if(JJ == 0){ - if(I != 0) - Out1 = "ds_"+rtotex(I-1)+Out1; - continue; - } - if(ALT[0] == 0) continue; - Out0 += "\\int_p^{"+V1+"}"; - if(TeX == 16) - str_tb(["mc_",rtotex(ALT[0])], Out); - else{ - str_tb(["(",V1,"-",V2,")^",rtotex(-1+ALT[0])], Out); - AL11=AL[L-1][1][1]; - AT = AL11[length(AL11)-1]; - if(type(AT) == 4) AT = AT[1]; - DN = cons(ALT[0]+AT+1,DN); - NM = cons(AT+1,cons(ALT[0],NM)); - } - if(L != 2) Out1 += "d"+V2; - I++; - } - if(R){ - if(I == 0) Ov = "x"; - else Ov = "s_"+rtotex(I-1); - Out1 = "u_B("+Ov+")"+Out1; - } - if(TeX != 16){ - Out0 = string_to_tb(Out0); - str_tb([Out, Out1], Out0); - Out = Out0; - NM = simplify(NM, Fuc, 4); - DN = simplify(DN, Fuc, 4); - DNT = lsort(NM,DN,"reduce"); - NMT = DNT[0]; DNT = DNT[1]; - if(NMT != [] && PW != ""){ - write_to_tb((TeXEq==5)?"\\\\\n &\\sim\\frac{\n" - :"\\\\\n \\sim\\frac{\n", Out); - for(PT = NMT; PT != []; PT = cdr(PT)) - str_tb([" \\Gamma(",my_tex_form(car(PT)), ")\n"], Out); - write_to_tb(" }{\n", Out); - for(PT = DNT; PT != []; PT = cdr(PT)) - write_to_tb(" \\Gamma("+my_tex_form(car(PT))+")\n", Out); - write_to_tb(" }", Out); - if(R > 0) write_to_tb("C_0", Out); - write_to_tb("x^"+rtotex(PW) +"\\ \\ (p=0,\\ x\\to0)", Out); - } - }else - Out = str_tb(0, Out); - if(Dviout >= 0){ - dviout(Out|eq=0,keep=Keep); - return 1; - } - return O; - } - if(Short >= 0){ - for(ALL = [] ; AL != []; AL = cdr(AL)){ - AT = car(AL); - ALL = cons([AT[0], chkspt(AT[1]|opt=4)], ALL); - } - AL = reverse(ALL); - } - return AL; /* AL[0][1] : reduced GRS, R==0 -> rigid */ - } - - if(T == 2 || T == 4 || T == 11){ - for(I = (T==2)?2:1; I >= (T==11)?0:1; I--){ - ALT = M[I]; - if(ALT[length(ALT)-1][0] != 1){ - mycat(["multiplicity for",I,":",ALT[length(ALT)-1][1], - "should be 1"]); - return; - } - } - } - LA++; - NM = DN = []; - -/* Three term relation */ - if(T == 11){ - if(R > 0){ - print("This is not rigid\n"); - return 0; - } - for(I = 0; I <= LA; I++){ - if(I > 0){ - AI = AL[I][0]; /* operation */ - if(AI[0] != 0){ - DN = cons(simplify(AI1+1,Fuc,4),DN); - NM = cons(simplify(AI1+AI[0]+1,Fuc,4),NM); - } - } - ALT = AL[I][1][1]; AI1 = ALT[length(ALT)-1][1]; - } - DNT = lsort(NM,DN,"reduce"); - if(TeX < 0) return DNT; - NMT = DNT[0]; DNT = DNT[1]; - Out = str_tb("u_{0,0,0}-u_{+1,0,-1}=\\frac{",""); - for(PT = NMT; PT != []; PT = cdr(PT)) - str_tb(["(",my_tex_form(car(PT)),")"], Out); - str_tb(["}\n{"],Out); - for(PT = DNT; PT != []; PT = cdr(PT)) - str_tb(["(",my_tex_form(car(PT)),")"], Out); - write_to_tb("}u_{0,+1,-1}",Out); - if(Dviout >= 0){ - dviout(Out|eq=0,keep=Keep); - return 1; - } - return Out; - } - - AD=newvect(NP); - for(I = 0; I <= LA; I++){ - if(I > 0){ - AI = AL[I][0]; /* operation */ - if(T == 2 && AI[0] != 0){ - DN = cons(simplify(-AI2,Fuc,4), cons(simplify(AI1+1,Fuc,4),DN)); - NM = cons(simplify(-AI2-AI[0],Fuc,4), cons(simplify(AI1+AI[0]+1,Fuc,4), - NM)); - } - for(J = 1; J < NP; J++) - AD[J] += simplify(AI[J],Fuc,4); - } - if(T == 2){ - ALT = AL[I][1][1]; AI1 = ALT[length(ALT)-1][1]; - ALT = AL[I][1][2]; AI2 = ALT[length(ALT)-1][1]; - if(I == 0){ - C3 = AI1; C4 = AI2; - } - } - } - -/* Connection */ - if(T == 2){ - DNT = lsort(NM,DN,"reduce"); - NMT = DNT[0]; DNT = DNT[1]; - if(TeX < 0) return [NMT,DNT,AD]; - C0 = M[1][length(M[1])-1][1]; - C1 = M[2][length(M[2])-1][1]; - M = AL[0][1]; - C3 = M[1][length(M[1])-1][1]; - C4 = M[2][length(M[2])-1][1]; - Out = str_tb(["c(0\\!:\\!", my_tex_form(C0), - " \\rightsquigarrow 1\\!:\\!", my_tex_form(C1),")"], ""); - if(R > 0 && AMSTeX == 1 && (TeXEq == 4 || TeXEq == 5)){ - write_to_tb("\\\\\n", Out); - if(TeXEq == 5) write_to_tb(" &", Out); - } - write_to_tb("=\\frac{\n",Out); - for(PT = NMT; PT != []; PT = cdr(PT)) - write_to_tb(" \\Gamma("+my_tex_form(car(PT))+")\n", Out); - write_to_tb(" }{\n",Out); - for(PT = DNT; PT != []; PT = cdr(PT)) - write_to_tb(" \\Gamma("+my_tex_form(car(PT))+")\n",Out); - write_to_tb(" }", Out); - for(J = 3; J < length(AD); J++){ - if(AD[J] == 0) continue; - str_tb(["\n (1-x_", rtotex(J), "^{-1})^", rtotex(AD[J])], Out); - } - if(R != 0) - str_tb(["\n c_B(0\\!:\\!", my_tex_form(C3), - " \\rightsquigarrow 1\\!:\\!", my_tex_form(C4), ")"], Out); - Out = tb_to_string(Out); - if(Dviout >= 0){ - dviout(Out|eq=0,keep=Keep); - return 1; - } - return Out; - } - -/* Series */ - if(T == 4){ - AL11 = AL[0][1][1]; - V = AL11[length(AL11)-1][1]; - S00 = -V; S01 = (R==0)?[]:[[0,0]]; - S1 = S2 = []; - for(Ix = 1, ALL = cdr(AL); ALL != []; ){ - ALT = ALL[0][0]; - if(ALT[0] != 0){ /* mc */ - for(Sum = [], ST = S01; ST != []; ST = cdr(ST)) - Sum = cons(car(ST)[0], Sum); - S1 = cons(cons(S00+1,Sum), S1); - S2 = cons(cons(S00+1+ALT[0],Sum),S2); - S00 += ALT[0]; - } - ALL = cdr(ALL); - for(I = 1; I < length(ALT); I++){ /* addition */ - if(I == 1){ - S00 += ALT[1]; - if(ALL == []) - S00 = [S00]; - }else{ - if(ALT[I] == 0) - continue; - if(ALL != []){ - S1 = cons([-ALT[I],Ix],S1); - S2 = cons([1,Ix],S2); - S01= cons([Ix,I],S01); - Ix++; - }else - S00 = cons([ALT[I],I],S00); - } - } - } - S00 = reverse(S00); - S01 = qsort(S01); S1 = qsort(S1); S2 = qsort(S2); - if(Simp >= 0){ - S00 = simplify(S00,Fuc,4); - S01 = simplify(S01,Fuc,4); - S1 = simplify(S1,Fuc,4); - S2 = simplify(S2,Fuc,4); - SS = lsort(S1,S2,"reduce"); - S1 = SS[0]; S2 = SS[1]; - } - - if(TeX >= 0){ - /* Top linear power */ - TOP = Ps = Sm = ""; - for(TOP = Ps = Sm = "", ST = cdr(S00); ST != []; ST = cdr(ST)){ - SP = car(ST); - if(SP[0] != 0){ - if(SP[1] == 2) - TOP += "(1-x)^"+rtotex(SP[0]); - else - TOP += "(1-x/x_"+rtotex(SP[1])+")^"+rtotex(SP[0]); - } - } - /* Top power */ - PW = my_tex_form(car(S00)); - if(PW == "0") - PW = ""; - NP = length(AL[0][1]); - PWS = newvect(NP); - for(I = 0; I < NP; I++) - PWS[I] = ""; - for(S = S01, I = 0; S != []; S = cdr(S), I++){ - SI = rtotex(car(S)[0]); - if(I > 0) Sm += ",\\ "; - Sm += "n_"+SI+"\\ge0"; - if(PW != "") - PW += "+"; - PW += "n_"+SI; - if(car(S)[1] > 2) - PWS[car(S)[1]] += "-n_"+rtotex(car(S)[0]); - else if(car(S)[1] == 0) - Ps = "C_{n_0}"+Ps; - } - for(I = 3; I < NP; I++){ - if(PWS[I] != "") - Ps += "x_"+rtotex(I)+"^{"+PWS[I]+"}"; - } - Out = str_tb([TOP, Ps, "x^{", PW, "}"], ""); - /* Gamma factor */ - for(I = 0, SS = S1; I <= 1; I++, SS = S2){ - PW = string_to_tb(""); - for(PW1=""; SS != [] ; SS = cdr(SS)){ - for(J = 0, SST = car(SS); SST != []; SST = cdr(SST), J++){ - if(J == 0){ - JJ = (car(SST) == 1)?((length(SST)==2)?(-1):0):1; - if(JJ > 0) - str_tb(["(", my_tex_form(car(SST)), ")_{"], PW); - else if(JJ == 0) - PW1 = "("; - }else{ - if(JJ > 0){ - if(J > 1) write_to_tb("+", PW); - str_tb(["n_", rtotex(car(SST))], PW); - }else{ - if(J > 1) PW1 += "+"; - PW1 += "n_"+rtotex(car(SST)); - } - } - } - if(JJ > 0) write_to_tb("}", PW); - else PW1 += (JJ == 0)?")!":"!"; - } - if(I == 0) - Out0 = "\\frac"; - Out0 += "{"+tb_to_string(PW)+PW1+"}"; - PW = string_to_tb(""); PW1 = ""; - } - if(Out0 == "\\frac{}{}") - Out0 = ""; - Out = "\\sum_{"+Sm+"}"+Out0 + Top + tb_to_string(Out); - if(length(S01) == 1){ - Out = str_subst(Out, "{n_"+SI+"}", "n"); - Out = str_subst(Out, "n_"+SI, "n"); - } - if(Dviout >= 0) - dviout(Out|eq=0,keep=Keep); - return Out; - } - return [cons(S00, S01), S1, S2]; - } - -/* Operator */ - if(T==3){ - Fuc0 = car(Fuc); - if(Fuc0 != 0){ /* Kill Fuchs relation */ - for(V = vars(Fuc0); V != []; V = cdr(V)){ - VT = car(V); - if(deg(Fuc0,VT) == 1){ - AL = mysubst(AL, [VT, -red(coef(Fuc0,0,VT)/coef(Fuc0,1,VT))]); - break; - } - } - if(V == []){ - print("Fuchs condition has no variable with degree 1"); - return 0; - } - } - L = newvect(NP); - Pt = getopt(pt); - for(I = NP-1; I >= 1; I--){ - if(type(Pt) == 4) - L[I] = Pt[I-1]; - else if(I >= 3 || X1 >= 0 || (X2 >= 0 && I >= 2)) - L[I] = makev(["x_", I]); - else L[I] = I-1; - } - if(R){ /* non-rigid basic */ - MM = AL[0][1]; /* Riemann scheme */ - for(OD = 0, MT = car(MM); MT != []; MT = cdr(MT)) - OD += car(MT)[0]; - for(V = DN = [], M = MM; M != []; M = cdr(M)){ - MT = car(M); /* exponents */ - for(K = KM = 0, NT = []; ; K++){ - for(J = 0, P = 1, MTT = MT; MTT != []; MTT = cdr(MTT)){ - if(J == 0 && car(MTT)[1] == 0) - KM = car(MTT)[0]; - for(KK = car(MTT)[0] - K -1; KK >= 0; KK--) - P *= (dx-car(MTT)[1]-KK); - } - if(P == 1) break; - NT = cons(P,NT); - } - V = cons(reverse(NT), V); - DN = cons(KM, DN); - } - V = ltov(reverse(V)); /* conditions for GRS */ - DN = ltov(reverse(DN)); /* dims of local hol. sol. */ - for(J = OD; J >= 0; J--){ - for(I = Q = 1; I < NP; I++){ - if(J > DN[I]) - Q *= (x-L[I])^(J-DN[I]); - } - K = mydeg(Q,x); - if(J == OD){ - P = Q*dx^J; - DM = K; - }else{ - for(I = DM-OD+J-K; I >= 0; I--){ - X = makev(["r",J,"_",I]); - P += Q*x^I*X*dx^J; - } - } - } - for(R = [], I = 0; I < NP; I++){ - Q = toeul(P, [x,dx], (I==0)?"infty":L[I]); /* Euler at I-th pt */ - for(VT = V[I], J=0; VT != [] ; VT = cdr(VT), J++){ - if(car(VT) != 0) - R = cons(rpdiv(coef(Q,J,x), car(VT), dx)[0], R); /* equations */ - } - } - for(RR = RRR = [], I = OD-1; I>=0; I--){ - RR = []; - for(RT = R; RT != [] ; RT = cdr(RT)){ - if( (VT = mycoef(car(RT), I, dx)) != 0) - RR = cons(VT, RR); /* real linear eqs */ - } - J = mydeg(mycoef(P,I,dx),x); - for(S = 0, VVV = []; J >= 0; J--){ - X = makev(["r",I,"_",J]); - VVV = cons(X, VVV); /* unknowns */ - } - RR = lsol(RR,VVV); - LN = length(RR); - for(K=0; K<LN; K++){ - RRT = RR[K]; - if(type(RRT) != 4) continue; - R = mysubst(R,RRT); - P = mysubst(P,RRT); - } - } - }else /* Rigid case */ - P = dx^(AL[0][1][0][0][0]); - /* additions and middle convolutions */ - for(ALT = AL; ALT != []; ALT = cdr(ALT)){ - AI = car(ALT)[0]; - if(type(AI) != 4) continue; - V = ltov(AI); - if(V[0] != 0) P = mc(P,x,V[0]); - for(I = 1; I < NP; I++){ - if(V[I] != 0) - P = sftexp(P,x,L[I],-V[I]); - } - } - P = (Simp>=0)? simplify(P,Fuc,4|var=[dx]):simplify(P,Fuc,4); - if(TeX >= 0){ - Val = 1; - if(mydeg(P,dx) > 2 && AMSTeX == 1 && TeXEq > 3) - Val = (TeXEq==5)?3:2; - Out = fctrtos(P|var=[dx,"\\partial"],TeX=Val); - if(Dviout < 0) return Out; - dviout(Out|eq=0,keep=Keep); - return 1; - } - return P; - } - return 0; -} - -def mcop(P,M,S) -{ - for(V=[],ST=S;ST!=[];ST=cdr(ST)) - if(isvar(VT=car(ST))) V=cons(vweyl(VT),V); - V=reverse(V); - N=length(V); - for(MT=M;MT!=[];MT=cdr(MT)){ - T=car(MT); - if(T[0]!=0) - P=mc(P,V[0],T[0]); - for(TT=cdr(T),ST=cdr(S);ST!=[];TT=cdr(TT),ST=cdr(ST)) - if(car(TT)!=0) P=sftpexp(P,V,S[0]-ST[0],-car(TT)); - } - return P; -} - -/* option: zero, all, raw */ -def shiftop(M,S) -{ - if(type(M)==7) M=s2sp(M); - if(type(S)==7) S=s2sp(S); - Zero=getopt(zero); - NP=length(M); - for(V=L=[],I=NP-1; I>=0; I--){ - V=cons(strtov(asciitostr([97+I])),V); - if(I>2) L=cons(makev(["y_", I-1]),L); - else L=cons(I-1,L); - } - if(type(M[0][0])==4){ - F=1;RS=M;SS=S; - R=chkspt(M); - if(R[2]!=2 || R[3]!=0){ - mycat("GRS is not valid!");return 0; - } - for(; S!=[]; S=cdr(S)){ - if(nmono(S[0][0])!=1) break; - if(isint(S[0][1]-S[0][0])==0) break; - } - if(S!=[]){ - mycat("Error in shift!"); return 0; - } - }else{ - F=0; - RS=sp2grs(M,V,[1,length(M[0]),1]); - for(SS=S0=[],I=0; I<NP; I++){ - for(J=F=0; J<length(M[I]); J++){ - if(I==0 && J==length(M[0])-1) break; - if((U=S[I][J])!=0){ - if(isint(U)!=1){ - mycat("Error in shift!"); return 0; - } - VT=RS[I][J][1]; - SS=cons([VT,VT+U],SS); - }else if(I>0 && Zero==1 && F==0){ - RS=mysubst(RS,[RS[I][J][1],0]); - F=J+1; - } - } - if((F>0 && J==2) || (I==0 && J==1)){ - J=(I==0)?0:2-F; VT=RS[I][J][1]; - S0=cons([VT,strtov(asciitostr([strtoascii(rtostr(VT))[0]]))],S0); - } - } - } - RS1=mysubst(RS,SS); - if(F==1){ - R=chkspt(RS1); - if(R[2]!=2 || R[3]!=0){ - mycat("Error in shift!"); - return 0; - } - } - R=getbygrs(RS,1); R1=getbygrs(RS1,1); - RT=R[0][1][0]; - if(length(RT)!=1 || RT[0][0]!=1){ - mycat("Not rigid!"); - return 0; - } - P=dx;Q=Q1=1; - for(RT = R, RT1=R1; RT != []; RT = cdr(RT), RT1=cdr(RT1)){ - V=car(RT)[0]; V1=car(RT1)[0]; - if(type(V) != 4) continue; - - if(V[0] != 0){ - P = mc(P,x,V[0]); /* middle convolution */ - QT = mc(Q,x,V[0]); - }else QT=Q; - D0=mydeg(Q,dx);D0T=mydeg(QT,dx); - C0=red(mycoef(Q,D0,dx)/mycoef(QT,D0T,dx)); - if(C0!=1) QT=red(C0*QT); - - if(V1[0] != 0) Q1T = mc(Q1,x,V1[0]); - else Q1T=Q1; - D1=mydeg(Q1,dx);D1T=mydeg(Q1T,dx); - C1=red(mycoef(Q1,D1,dx)/mycoef(Q1T,D1T,dx)); - if(C1!=1) Q1T=red(C1*Q1T); - DD=(V[0]-V1[0])+(D0-D0T)-(D1-D1T); - if(DD>0){ - QT=muldo(dx^DD,QT,[x,dx]); - D0T+=DD; - }else if(DD<0){ - Q1T=muldo(dx^(-DD),Q1T,[x,dx]); - D1T-=DD; - } - C=mylcm(dn(QT),dn(Q1T),x); - if(C!=1){ - QT=red(C*QT); Q1T=red(C*Q1T); - } - Q=QT;Q1=Q1T; - for(I = 1; I < NP; I++){ - if(V[I]!=0){ - P = sftexp(P,x,L[I],-V[I]); /* addition u -> (x-L[I])^V[I]u */ - QT = sftexp(QT,x,L[I],-V[I]); - } - if(V1[I]!=0) - Q1T = sftexp(Q1T,x,L[I],-V1[I]); - } - C=red(mycoef(QT,D0T,dx)*mycoef(Q1,D1T,dx)/(mycoef(Q,D0T,dx)*mycoef(Q1T,D1T,dx))); - Q=red(dn(C)*QT);Q1=red(nm(C)*Q1T); - for(I = 1; I < NP; I++){ - if((J=V[I]-V1[I])!=0){ - if(J>0) Q1*=(x-L[I])^J; - else Q*=(x-L[I])^(-J); - } - while((QT=tdiv(Q,x-L[I]))!=0){ - if((Q1T=tdiv(Q1,x-L[I]))!=0){ - Q=QT;Q1=Q1T; - }else break; - } - } - } - P1=mysubst(P,SS); - if(type(S0)==4 && S0!=[]){ - P=mysubst(P,S0); Q=mysubst(Q,S0); - P1=mysubst(P1,S0); Q1=mysubst(Q1,S0); - RS=mysubst(RS,S0); RS1=mysubst(RS1,S0); - } - R=mygcd(Q1,P1,[x,dx]); - if(findin(dx,vars(R[0]))>=0){ - mycat("Some error!"); - return 0; - } - Q=muldo(R[1]/R[0],Q,[x,dx]); - R=divdo(Q,P,[x,dx]); - Q=red(R[1]/R[2]); - R=fctr(nm(Q)); - QQ=Q/R[0][0]; - R1=fctr(dn(QQ)); - for(RR=cdr(R1); RR!=[]; RR=cdr(RR)){ - VT=vars(car(RR)[0]); - if(findin(x,VT)<0 && findin(dx,VT)<0){ - for(I=car(RR)[1];I>0;I--) QQ=red(QQ*car(RR)[0]); - } - } - Raw=getopt(raw); - Dviout=getopt(dviout); - if(Dviout==1) Raw=4; - if(Raw!=1){ - for(RR=cdr(R); RR!=[]; RR=cdr(RR)){ - VT=vars(car(RR)[0]); - if(findin(x,VT)<0 && findin(dx,VT)<0){ - for(I=car(RR)[1];I>0;I--) QQ=red(QQ/car(RR)[0]); - } - } - } - if(Raw==2||Raw==3||Raw==4){ - R=mygcd(QQ,P,[x,dx]); /* R[0]=R[1]*QQ + R[2]*P */ - Q1=red(R[0]/R[2]); - for(Q=1,RR=cdr(fctr(nm(Q1))); RR!=[]; RR=cdr(RR)){ - VT=vars(car(RR)[0]); - if(findin(x,VT)<0){ - for(I=car(RR)[1];I>0;I--) Q*=car(RR)[0]; - } - } - if(Raw==3) QQ=[QQ,Q]; - else if(Raw==4) /* Q=Q*R[1]/R[0]*QQ+Q/R[0]*P */ - QQ=[QQ,Q,red(R[1]*Q/R[0])]; - else QQ=Q; - } - F=getopt(all); - if(Dviout==1){ - Pre = " x=\\infty & 0 & 1"; - for(I=3; I<NP; I++) Pre = Pre+"& "+rtostr(L[I]); - Pre = Pre+"\\\\\n"; - PW=str_tb(ltotex(RS|opt="GRS",pre=Pre),0); - str_tb( -"=\\{u\\mid Pu=0\\}\\\\\n&\\underset{Q_2}{\\overset{Q_1}{\\rightleftarrows}}\n",PW); - str_tb([ltotex(RS1|opt="GRS",pre=Pre),"\\\\\n"],PW); - R=fctrtos(QQ[0]|TeX=3,var=[dx,"\\partial"]); - if(type(R)==4) R="\\frac1{"+R[1]+"}"+R[0]; - str_tb(["Q_1&=",R,"\\\\\n"],PW); - R=fctrtos(QQ[2]|TeX=3,var=[dx,"\\partial"]); - if(type(R)==4) R="\\frac1{"+R[1]+"}"+R[0]; - str_tb(["Q_2&=",R,"\\\\\n"],PW); - str_tb(["Q_2Q_1&\\equiv ",fctrtos(QQ[1]|TeX=3),"\\mod W(x)P"],PW); - if(F==1) - str_tb(["\\\\\nP&=",fctrtos(P|TeX=3,var=[dx,"\\partial"])],PW); - dviout(str_tb(0,PW)|eq=0,title="Shift Operator"); - } - if(F==1) return [QQ,P,RS,P1,RS1]; - else if(F==0) return QQ; - return [QQ,P,RS]; -} - -def conf1sp(M) -{ - if(type(M)==7) M=s2sp(M); - L0 = length(M); - L1 = length(M[L0-1]); - X2 = getopt(x2); - Conf= getopt(conf); - if(Conf != 0) - Conf = -1; - if((X2==1 || X2==-1) && Conf != 0){ - X1 = 0; - X = x_1; - }else{ - X1 = 1; - X = x_2; - } - G = sp2grs(M,a,[L0,L1]); - for(I = 0; I < L0-1; I++){ - V = makev([a,I-Conf,0]); - G = subst(G,V,0); - } - L2 = length(M[1]); - for(I=J=S0=S1=0; I < L2; I++){ - S1 += G[1][I][0]; - while(S0 < S1){ - S0 += G[0][J][0]; - if((V=G[0][J][1]) != 0) - G = mysubst(G,[V,V-G[1][I][1]]); - J++; - } - if(S0 > S1){ - print("Error in data!"); - return 0; - } - } - if(Conf==0){ - for(L=[], I=L0-2; I>=0; I--) - L=cons(I,L); - L=cons(L0-1,L); - P = getbygrs(G,["operator","x2"]|perm=L); - }else if(X1) - P = getbygrs(mperm(G,[[1,2]],[]), ["operator","x2"]); - else - P = getbygrs(G,["operator","x1"]); - if(Conf==0) - P=nm(mysubst(P,[X,c])); - else{ - P = nm(mysubst(P,[X,1/c])); - if(X2==-1){ - for(I=2; I<L0; I++){ - V=makev(["x_",I]); VC=makev([c,I]); - P = nm(mysubst(P,[V,1/VC])); - } - } - } - for(I = 1; I < L2; I++){ - X = G[1][I][1]; - P = nm(mysubst(P,[X,X/c])); - } - VS = vars(P); - while(VS!=[]){ - V = car(VS); - if(str_chr(rtostr(V),0,"r")==0){ - CV = mycoef(P,1,V); - D = mymindeg(CV,c); - if(D > 0) P = mysubst(P,[V,V/c^D]); - CV = mycoef(P,1,V); - DD = mydeg(CV,dx); - CVV = mycoef(CV,DD,dx); - CD1 = mydeg(CVV,x); - CD = (X==x1)?0:CD1; - while(CD>=0 && CD<=CD1){ - CC = mycoef(CVV,CD,x); - if(type(CC)==1){ - VT = mycoef(mycoef(mycoef(P,DD,dx),CD,x),0,V)/CC; - if(VT != 0) P = mysubst(P,[V,V-VT]); - break; - } - if(X==x1) CD++; - else CD--; - } - while(subst(P,c,0,V,0) == 0) - P = red(mysubst(P,[V,c*V])/c); - } - VS =cdr(VS); - } - return P; -} - -def pgen(L,VV) -{ - if(type(L[0])<4) L=[L]; - if(type(L)==4) L=ltov(L); - K=length(L); - V=newvect(K); - if(type(Sum=getopt(sum))!=1) Sum=0; - if((Num=getopt(num))!=1) Num=0; - if((Sep=getopt(sep))!=1) Sep=0; - if(type(Shift=getopt(shift))!=1) Shift=0; - for(;;){ - for(PP=1,R=[],II=K-1; II>=0; II--){ - R=cons(V[II]+Shift,R); - if(II>0 && Sep==1) R=cons("_",R); - PP*=L[II][0]^V[II]; - } - P+=makev(cons(VV,R)|num=Num)*PP; - for(I=0;I<K;){ - if(++V[I]<=L[I][1]){ - if(Sum>0){ - for(S=II=0;II<K;) S+=V[II++]; - if(S>Sum){ - V[I++]=0; - continue; - } - } - }else{ - V[I++]=0; - continue; - } - break; - } - if(I>=K) return P; - } -} - -def diagm(M,A) -{ - return mgen(M,0,A,1); -} - -def mgen(M,N,A,S) -{ - if(M==0 && N==0){ - mycat([ -"mgen(m,n,a,s|sep=1) : generate a matrix of size m x n\n", -" n : a number or \"diagonal\", \"highdiag\", \"lowdiag\",\"skew\",\"symmetric\",\"perm\" = 0,-1,-2,..\n", -" a : a symbol or list (ex. a, [a], [a,b,c], [1,2,3])\n", -" s : 0 or 1 (shift of suffix)\n" - ]); - return 0; - } - if(type(N)==7) N=-findin(N,["diag","highdiag","lowdiag","skew","symmetric","perm"]); - Sep=(getopt(sep)==1)?1:0; - if(S < 0 || S > 2) - S = 0; - if(M+S > 30 || N+S > 30){ - erno(1); - return; - } - if(N==-5){ - NM=newmat(M,M); - for(I=0;I<M;I++,A=cdr(A)) NM[I][car(A)-S]=1; - return NM; - } - if(type(A) == 4) - L = length(A)-1; - else - L = -1; - if(N <= 0 && N >= -2){ - MM = newmat(M,M); - J = K = 0; - if(N == -1){ - K = 1; M--; - }else if(N == -2){ - J = 1; M--; - } - for(I = 0; I < M; I++){ - if(L >= 0) - MM[I+J][I+K] = A[(I > L)?L:I]; - else if(type(A)==7 || isvar(A)) - MM[I+J][I+K] = makev([A,S+I]|sep=Sep); - else - MM[I+J][I+K] = A; - } - return MM; - } - K = N; - if(K < 0) N = M; - MM = newmat(M,N); - for(I = 0; I < M; I++){ - if(L >= 0) - AA = rtostr(A[(I > L)?L:I]); - else - AA = rtostr(A)+rtostr(I+S); - if(AA>="0" && AA<=":"){ - erno(0); return; - } - for(J = 0; J < N; J++){ - if(K < 0){ - if(I > J) continue; - if(K == -3 && I == J) continue; - } - MM[I][J] = makev([AA,J+S]|sep=Sep); - } - } - if(K < 0){ - for(I = 0; I < M; I++){ - for(J = 0; J < I; J++) - MM[I][J] = (K == -4)?MM[J][I]:-MM[J][I]; - } - } - return MM; -} - -def newbmat(M,N,R) -{ - S = newvect(M); - T = newvect(N); - IM = length(R); - for(I = 0; I < IM; I++){ - RI = R[I]; - JM = length(RI); - for(J = 0; J < JM; J++){ - RIJ = RI[J]; - if(type(RIJ) == 6){ - S[I] = size(RIJ)[0]; - T[J] = size(RIJ)[1]; - } - } - } - for(I = K = 0; I < M; I++){ - if(S[I] == 0) - S[I] = 1; - K += S[I]; - } - for(J = L = 0; J < N; J++){ - if(T[J] == 0) - T[J] = 1; - L += T[J]; - } - M = newmat(K,L); - if(type(Null=getopt(null))>0){ - for(I=0;I<K;I++){ - for(J=0;J<L;J++) M[I][J]=Null; - } - } - for(I0 = II = 0; II < IM; I0 += S[II++]){ - RI = R[II]; - JM = length(RI); - for(J0 = JJ = 0; JJ < JM; J0 += T[JJ++]){ - if((RIJ = RI[JJ]) == 0) - continue; - Type = type(RIJ); - for(I = 0; I < S[II]; I++){ - for(J = 0; J < T[JJ]; J++){ - if(Type == 6) - M[I0+I][J0+J] = RIJ[I][J]; - else if(Type == 4 || Type == 5) - M[I0+I][J0+J] = (I>0)?RIJ[I]:RIJ[J]; - else - M[I0+I][J0+J] = RIJ; - } - } - } - } - return M; -} - -def unim(S) -{ - if(!Rand++) random(currenttime()); - if(!isint(Wt=getopt(wt))||Wt<0||Wt>10) Wt=2; - if(!isint(Xa=getopt(abs)) || Xa<1) - Xa=9; - if((Xaa=Xa)>10) Xaa=10; - if(Xaa%2) Xaa++; - Xh=Xaa/2; - if(type(S0=SS=S)==4){ - Int=(getopt(int)==1)?1:0; - U=[1,1,1,1,1,1,1,1,1,1,1,1,2,2,3,4]; - M=newmat(S[0],S[1]); - SS=cdr(S);SS=cdr(SS); - if(Rk=length(SS)) L=SS; - else{ - L=[0]; - I=(S[0]>S[1])?S[1]:S[0]; - if(I<=2) return 0; - if(!isint(Rk=getopt(rank))||Rk<1||Rk>S[0]||Rk>S[1]) - Rk=random()%(I-1)+2; - for(I=1;I<Rk;){ - P=random()%(S[1]+Wt)-Wt; - if(P<=0) P=1; - if(findin(P,L)!=0){ - L=cons(P,L); - I++; - } - } - } - L=ltov(qsort(L)); - M[0][L[0]]=1; - for(I=1;I<Rk;I++){ - P=Int?1:U[random()%length(U)]; - if(P>Xa) P=Xa; - M[I][L[I]]=(random()%2)?P:(-P); - } - for(I=0;I<Rk;I++){ - if(I!=0&&abs(M[I][L[I]])>1) M[K=random()%I][KK=L[I]]=1; - I0=(I==0)?1:L[I]+1; - I1=(I==Rk-1)?S[1]:L[I+1]; - for(J=I0;J<I1;J++){ - for(K=1;K<=Xa;K++){ - P=random()%(I+1); - if((random()%2)==1) M[P][J]++; - else M[P][J]--; - } - } - } - S=M; - Res=(getopt(res)==1)?dupmat(S):0; - } - Conj=0; - if(type(S)<2){ - if(S<2||S>20) return 0; - if(getopt(conj)==1){ - M=S+Wt; - if(M>15) M=10; - M0=floor((M-1)/2); - for(R=[],I=0;I<S;I++) R=cons(random()%M-M0,R); - R=qsort(R); - M=diagm(S,R); - if(getopt(diag)!=1){ - for(I=1;I<S;I++) - if(M[I-1][I-1]==M[I][I] && random()%2) M[I-1][I]=1; - } - if(M[0][0]==M[S-1][S-1]){ - for(I=1;I<S;I++) if(M[I-1][I]==1) break; - if(I==S){ - if(M[0][0]>0) M[0][0]--; - else M[S-1][S-1]++; - } - } - if(getopt(res)==1) RR=diagm(S,[1]); - S1=S; - Res=dupmat(S=M); - if(isint(I=getopt(int))&&I>1&&random()%I==0){ - K=S[0][0];L=K+1; - for(I=1;I<S1;I++){ - if(S[I][I]>L && S[I-1][I]==0 && (I==S1-1||S[I][I+1]==0)){ - L=S[I][I]; - if(RR){ - RR[I][I]=L-K;RR[0][I]=1; - } - S[0][I]=1; - if(!(random()%3)) break; - } - } - if(random()%3==0){ - for(I=0;I<S1-1;I++){ - if(iand(S[I][I],1)&&S[I][I+1]==1){ - for(J=I+2;J<S1&&S[I][J]==0;J++); - if(J<S1) continue; - for(J=I-1;J>=0&&S[J][I]==0;J--); - if(J>=0) continue; - S[I][I+1]=2; - for(J=0;J<S1;J++) RR[I][J]*=2; - break; - } - } - } - } - }else{ - M=diagm(S,[1]); - S1=S; - } - } - if(type(S)==6){ - M=dupmat(S); - S=size(S); - S1=S[1];S=S[0]; - Nt=1; - if(getopt(conj)==1&&S==S1) Conj=1; - } - if(!isint(Ct=getopt(time))) - Ct=(S>3||S1>3)?100:200; - if(getopt(both)==1){ - OL=delopt(getopt(),"both"); - M=unim(mtranspose(M)|option_list=OL); - M=mtranspose(M); - } - Mx=20; - for(I=K=LL=0;I<Ct+Mx;I++){ - P=random()%S;Q=random()%S; - if(3*K>Ct) T=random()%Xaa-Xh; - else if(5*K<Ct) T=random()%2-1; - else T=random()%4-2; - if(T>=0) T++; - if(P==Q) continue; - for(G=0,J=S1-1;J>=0;J--){ - if((H=abs(M[Q][J]+M[P][J]*T))>Xa&&(!Conj||J!=P)) break; - if(K<Mx&&!Conj) G=igcd(G,H); - } - if(K<Mx && G>1) J=1; - if(J>0) continue; - if(J<0&&Conj==1){ - for(J=S1-1;J>=0;J--) - if(J!=Q&&abs(M[J][P]-M[J][Q]*T)>Xa) break; - if(J<0&&abs(M[Q][P]-M[Q][Q]*T+M[P][P]*T-M[P][Q]*T^2)>Xa) J=1; - if(J<0&&M[P][P]==M[Q][Q]){ - LF=0; - for(L=S1-1;J>=0;J--) if(L!=Q&&M[J][Q]!=0) LF++; - for(L=S1-1;J>=0;J--) if(L!=P&&M[P][J]!=0) LF++; - if(!LF) J=1; - } - } - if(J<0){ - for(J=S1-1;J>=0;J--) - M[Q][J]+=M[P][J]*T; - if(Conj==1) - for(J=S1-1;J>=0;J--) M[J][P]-=M[J][Q]*T; - if(RR) for(J=S1-1;J>=0;J--) RR[Q][J]+=RR[P][J]*T; - K++; - } - if(K%5==0){ - if(!Nt) M=mtranspose(M); - else if(!Conj&&K%2==0){ - for(F=0;F<S;F++){ - if((V=lgcd(M[F]))>1){ - for(L=0;L<S1;L++) M[F][L]/=V; - } - } - } - } - if(I>Ct){ - for(L=S-1;L>=0;L--){ - for(F=0,J=S1-1;J>=0;J--) - if(M[L][J]!=0) F++; - if(F<2){ - F=-1;break; - } - else F=0; - } - if(F<0 && LL++<5){ - I=(CT-CT%2)/2;K=1; - } - if(I>Ct) break; - } - } - if(RR){ - for(I=F=0;I<S1;I++){ - V=Res[I][I]; - for(J=I+1;J<S1;J++){ - if(Res[J][J]!=V) break; - for(LP=0;LP<2;LP++){ - if(J==S1-1||Res[J][J+1]==0){ - if(I==0||Res[I-1][I]==0){ - for(VL=VS=[],K=0;K<S1;K++){ - VL=cons(RR[K][J],VL);VS=cons(RR[K][I],VS); - } - VR=ldev(VL,VS); - if(VR[0]){ - for(K=S1-1,VN=VR[1];K>=0;K--,VN=cdr(VN)) - RR[K][J]=car(VN); - F=1; - } - } - } - K=I;I=J;J=K; - } - } - if(F&&I==S1-1){ - F=0;I=-1; - } - } - if(getopt(int)==1){ - N=mtranspose(M); - for(F=I=0;I<S1;I++) if(lgcd(M[I])>1||lgcd(N[I])>1) F++; - if(F){ - for(F=I=0;I<S1;I++){ - if(Res[I][I]==-1) F=ior(F,1); - else if(Res[I][I]==1) F=ior(F,2); - } - C=0; - if(!iand(F,1)) C=1; - else if(!iand(F,2)) C=-1; - if(C){ - for(I=0;I<S1;I++){ - M[I][I]+=C;Res[I][I]+=C; - } - } - } - } - if(getopt(rep)!=1){ - for(Lp=0;Lp<5;Lp++){ - F=(M==Res||abs(lmax(RR))>Xa*10||abs(lmin(RR))>Xa*10)?1:0; - for(I=0;!F&&I<S1&&Lp<4;I++){ - for(K=L=J=0;J<S1;J++){ - if(M[I][J]) K++; - if(M[J][I]) L++; - } - if(K<2||L<2) F=1; - } - if(!F) break; - R=unim(S0|option_list=cons(["rep",1],getopt())); - M=R[0];Res=R[1];RR=R[3]; - } - } - } - if(Res==0) return M; - if(RR){ - for(I=K=V=0;I<S1;I++){ - for(J=0;J<S1;J++){ - if(RR[J][I]>0) V++; - else if(RR[J][I]<0) V--; - } - if(I<S1-1&&Res[I][I+1]!=0) continue; - if(V<0){ - for(;K<=I;K++) RR=colm(RR,K,-1); - } - K=I+1;V=0; - } - } - if(getopt(rep)!=1){ - if((F=getopt(dviout))==1){ - if(getopt(conj)==1){ - if(RR) show([Res,"=",myinv(RR),M,RR]|opt="spts0",str=1,lim=200); - }else{ - if(type(Lim=getopt(lim))==1) - mtoupper(M,0|step=1,opt=7,dviout=1,pages=1,lim=Lim); - else mtoupper(M,0|step=1,opt=7,dviout=1,pages=1); - } - }else if(F==-1){ - if(getopt(conj)==1){ - if(RR) return ltotex([Res,"=",myinv(RR),M,RR]|opt="spts0",str=1,lim=200); - }else{ - if(type(Lim=getopt(lim))==1) - return mtoupper(M,0|step=1,opt=7,pages=1,lim=Lim,dviout=-1); - else return mtoupper(M,0|step=1,opt=7,pages=1,dviout=-1); - } - } - } - if(RR==0) return[M,Res]; - return [M,Res,myinv(RR),RR]; -} - -def pfrac(F,X) -{ - F = red(F); - FN = nm(F); - FD = dn(F); - if(mydeg(FD,X) == 0) - return [[F,1,1]]; - R = rpdiv(FN,FD,X); - FN = R[0]/R[1]; - R0 = R[2]/R[1]; - FC = fctr(FD); - RT=[]; - if(getopt(root)==2){ - for(FE=[],FT=FC;FT!=[];FT=cdr(FT)){ - if(mydeg(P=car(FT)[0],X)==4 && vars(P)==[X] && pari(issquare,C=mycoef(P,4,X))){ - if((S=mycoef(P,3,X)/4/C)!=0) P=subst(P,X,X-S); - if(mycoef(P,1,X)==0 && pari(issquare,C0=mycoef(P,0,X))){ - C=sqrtrat(C);C0=sqrtrat(C0);C1=2*C*C0-mycoef(P,2,X); - if(C1>0){ - FE=cons([C*(X+S)^2-C1^(1/2)*(X+S)+C0,car(FT)[1]],FE); - FE=cons([C*(X+S)^2+C1^(1/2)*(X+S)+C0,car(FT)[1]],FE); - RT=cons(C1,RT); - continue; - } - } - } - FE=cons(car(FT),FE); - } - FC=reverse(FE); - } - N = Q = 0; - L = []; - for(I = length(FC)-1; I >= 0; I--){ - if((D = mydeg(FC[I][0],X)) == 0) continue; - for(K=1; K<=FC[I][1]; K++){ - for(J=P=0; J < D; J++){ - V = makev(["zz_",++N]); - P = P*X + V; - L = cons(V,L); - } - Q += P/(FC[I][0]^K); - Q = red(Q); - } - } - L=reverse(L); - Q = nm(red(red(Q*FD)-FN)); - Q = ptol(Q,X); - S = lsol(Q,L); - R = (R0==0)?[]:[[R0,1,1]]; - for(N=0,I=length(FC)-1; I >= 0; I--){ - if((D = mydeg(FC[I][0],X)) == 0) continue; - for(K=1; K<=FC[I][1]; K++){ - for(P=J=0; J < D; N++,J++) - P = P*X + S[N][1]; - if(P!=0) R = cons([P,FC[I][0],K],R); - } - } - for(;RT!=[];RT=cdr(RT)){ - RTT=car(RT); - R=mtransbys(os_md.substblock,R,[RTT^(1/2),(RTT^(1/2))^2,RTT]); - } - TeX=getopt(TeX); - if((Dvi=getopt(dviout))==1||TeX==1){ - V=strtov("0"); - for(S=L=0,RR=R;RR!=[];RR=cdr(RR),L++){ - RT=car(RR); - S+=(RT[0]/RT[1]^RT[2])*V^L; - } - if(TeX!=1) fctrtos(S|var=[V,""],dviout=1); - else return fctrtos(S|var=[V,""],TeX=3); - } - return reverse(R); -} - -def cfrac(X,N) -{ - F=[floor(X)]; - if(N<0){ - Max=N=-N; - } - X-=F[0]; - if(Max!=1) - M=mat([F[0],1],[1,0]); - for(;N>0 && X!=0;N--){ - X=1/X; - F=cons(Y=floor(X),F); - X-=Y; - if(Max){ - M0=M[0][0];M1=M[1][0]; - M=M*mat([Y,1],[1,0]); - if(M[0][0]>Max) return M0/M1; - } - } - return (Max==0)?reverse(F):M[0][0]/M[1][0]; -} - -def sqrt2rat(X) -{ - if(type(X)>3) return X; - X=red(X); - if(getopt(mult)==1){ - for(V=vars(X);V!=[];V=cdr(V)){ - T=funargs(F=car(V)); - if(type(T)==4&&length(T)>1){ - Y=T[1]; - Z=sqrt2rat(Y); - if(Y!=Z){ - if(length(T)==2){ - T0=T[0]; - X=subst(X,F,T0(Z)); - }else if(T[0]==pow) - X=subst(X,F,Y^T[2]); - } - } - } - } - for(V=vars(X);V!=[];V=cdr(V)){ /* r(x)^(1/2+n) -> r(x)^n*r(x)^(1/2) */ - T=args(Y=car(V)); - if(functor(Y)==pow&&T[1]!=1/2&&isint(T2=2*T[1])){ - if(iand(T2,1)){ - R=(T[0])^(1/2);T2--; - }else R=1; - R*=T[0]^(T2/2); - X=red(subst(X,Y,R)); - } - } - D=dn(X);N=nm(X); - if(imag(D)!=0){ - N*=conj(D); - D*=conj(D); - return sqrt2rat(N/D); - } - for(V=vars(N);V!=[];V=cdr(V)){ /* (r(x)^(n/m))^k */ - T=args(Y=car(V)); - if(functor(Y)==pow&&(T[1]==0||(type(T[1])==1&&ntype(T[1])==0))){ - Dn=dn(T[1]);Nm=nm(T[1]); - N=substblock(N,Y,Y^Dn,T[0]^Nm); - } - } - for(V=vars(D);V!=[];V=cdr(V)){ - T=args(Y=car(V)); - if(functor(Y)==pow&&(T[1]==0||(type(T[1])==1&&ntype(T[1])==0))){ - Dn=dn(T[1]);Nm=nm(T[1]); - D=substblock(D,Y,Y^Dn,T[0]^Nm); - } - } - for(V=vars(D);V!=[];V=cdr(V)){ - T=args(Y=car(V)); - if(functor(Y)==pow&&T[1]==1/2&&mydeg(D,Y)==1){ - N*=mycoef(D,0,Y)-mycoef(D,1,Y)*Y; - N=mycoef(N,0,Y)+mycoef(N,1,Y)*Y+mycoef(N,2,Y)*T[0]; - D=mycoef(D,0,Y)^2-mycoef(D,1,Y)^2*T[0]; - X=red(N/D); - D=dn(X);N=nm(X); - break; - } - } - X=red(N/D); - D=dn(X);N=nm(X); - for(V=vars(D);V!=[];V=cdr(V)){ - T=args(Y=car(V)); - if(functor(Y)==pow&&T[1]==1/2) - D=substblock(D,T[0]^T[1],(T[0]^T[1])^2,T[0]); - } - for(V=vars(N);V!=[];V=cdr(V)){ - T=args(Y=car(V)); - if(functor(Y)==pow&&T[1]==1/2) - N=substblock(N,T[0]^T[1],(T[0]^T[1])^2,T[0]); - } - for(V=vars(N);V!=[];V=cdr(V)){ - T=args(Y=car(V)); - if(functor(Y)==pow&&T[1]==1/2){ - Ag=T[0]; - R=S=1; - An=fctr(nm(Ag)); - CA=An[0][0]; - if(CA<0){ - CA=-CA;R=-1; - } - if(type(I=sqrtrat(CA))<2) S=I; - else R*=CA; - for(An=cdr(An);An!=[];An=cdr(An)){ - Pw=car(An)[1];I=iand(Pw,1); - if(I) R*=car(An)[0]; - if((Q=(Pw-I)/2)>0) S*=car(An)[0]^Q; - } - for(An=fctr(dn(Ag));An!=[];An=cdr(An)){ - Pw=car(An)[1];I=iand(Pw,1); - if(I) R/=car(An)[0]^I; - if((Q=(Pw-I)/2)>0) S/=car(An)[0]^Q; - } - if(S!=1) N=subst(N,Y,R^(1/2)*S); - } - } - for(V=vars(N);V!=[];V=cdr(V)){ - T=args(Y=car(V)); - if(functor(Y)==pow&&T[1]==1/2){ - C=mycoef(N,1,Y); - for(VC=vars(C);VC!=[];VC=cdr(VC)){ - TC=args(YC=car(VC)); - if(functor(YC)==pow&&TC[1]==1/2){ - Ag=red(T[0]*TC[0]); - R=S=1; - An=fctr(nm(Ag)); - CA=An[0][0]; - if(CA<0){ - CA=-CA;R=-1; - } - if(type(I=sqrtrat(CA))<2) S=I; - else R*=CA; - for(An=cdr(An);An!=[];An=cdr(An)){ - Pw=car(An)[1];I=iand(Pw,1); - if(I) R*=car(An)[0]; - if((Q=(Pw-I)/2)>0) S*=car(An)[0]^Q; - } - for(An=fctr(dn(Ag));An!=[];An=cdr(An)){ - Pw=car(An)[1];I=iand(Pw,1); - if(I) R/=car(An)[0]^I; - if((Q=(Pw-I)/2)>0) S/=car(An)[0]^Q; - } - CC=mycoef(C,1,YC); - N=N-CC*YC*Y+CC*R^(1/2)*S; - } - } - } - } - return red(N/D); -} - -def cfrac2n(X) -{ - if(type(L=getopt(loop))==1&&L>0) - C=x; - else{ - C=0;L=0; - } - if(L>1){ - for(Y=[];L>1;L--){ - Y=cons(car(X),Y); - X=cdr(X); - } - if(X!=[]){ - P=cfrac2n(X|loop=1); - for(V=P,Y=reverse(Y);Y!=[];Y=cdr(Y)) - V=sqrt2rat(car(Y)+1/V); - return V; - }else{ - C=0;X=reverse(Y); - } - } - for(V=C,X=reverse(X);X!=[];X=cdr(X)){ - if(V!=0) V=1/V; - V+=car(X); - } - if(C!=0){ - V=red(V);P=dn(V)*x-nm(V); - S=getroot(P,x|cpx=2); - T=map(eval,S); - V=(T[0]>0)?S[0]:S[1]; - } - return V; -} - -def s2sp(S) -{ - if(getopt(short)==1){ - if(type(F=getopt(std))==1) S=s2sp(S|std=F); - if(type(S)!=7) S=s2sp(S); - L=strtoascii(S); - for(LS=[],F=C=0;L!=[];L=cdr(L)){ - if((G=car(L))!=F){ - LS=cons(G,LS);C=0; - }else if(C<3){ - LS=cons(G,LS); - }else if(C==3){ - LS=cdr(LS);LS=cdr(LS); - LS=cons(94,LS);LS=cons(52,LS); - }else if(C==9){ - LS=cdr(LS);LS=cons(97,LS); - }else{ - K=car(LS);LS=cdr(LS);LS=cons(K+1,LS); - } - C++;F=G; - } - return asciitostr(reverse(LS)); - } - if(type(F=getopt(std))==1){ - F=(F>0)?1:-1; - if(type(S)==7) S=s2sp(S); - for(L=[];S!=[];S=cdr(S)) - L=cons(os_md.msort(car(S),[-1,0]),L); - return os_md.msort(L,[F,2]); - } - if(type(S)==7){ - S = strtoascii(S); - if(type(S) == 5) S = vtol(S); - for(N=0,R=TR=[]; S!=[]; S=cdr(S)){ - if(car(S)==45) /* - */ - N=1; - else if(car(S)==47) /* / */ - N=2; - if(N>0){ - while(car(S)<48&&car(S)!=40) S=cdr(S); - } - if((T=car(S))>=48 && T<=57) TR=cons(T-48,TR); - else if(T>=97) TR=cons(T-87,TR); - else if(T>=65 && T<=90) TR=cons(T-29,TR); /* A-Z */ - else if(T==44){ - R=cons(reverse(TR),R); - TR=[]; - }else if(T==94){ /* ^ */ - S=cdr(S); - if(car(S)==40){ /* ( */ - S=cdr(S); - for(T=0; car(S)!=41 && S!=[]; S=cdr(S)){ - V=car(S)-48; - if(V>=10) V-=39; - T=10*T+V; - } - }else{ - while(car(S)<48) S=cdr(S); - T=car(S)-48; - if(T>=10) T-=39; - } - while(--T>=1) TR=cons(car(TR),TR); - }else if(T==40){ /* ( */ - S=cdr(S); - if(N==1){ - N=0; NN=1; - }else NN=0; - if(car(S)==45){ /* - */ - S=cdr(S); - NN=1-NN; - } - for(I=0; I<2; I++){ - for(V=0; (SS=car(S))!=41 && SS!=47 && S!=[]; S=cdr(S)){ - T=SS-48; - if(T>=10) T-=39; - V=10*V+T; - } - if(NN==1){ - V=-V; NN=0; - } - TR=cons(V,TR); - if(SS!=47) break; - else{ - N=2; S=cdr(S); - } - } - }else if(T==60){ - for(V=[],S=cdr(S);S!=[]&&car(S)!=62;S=cdr(S)) - V=cons(car(S),V); - if(car(S)!=62) continue; - TR=cons(eval_str(asciitostr(reverse(V))),TR); - }else if(T<48) continue; - if(N==1){ - T = car(TR); - TR=cons(-T,cdr(TR)); - N=0; - }else if(N==2){ - T=car(TR); TR=cdr(TR); - TR=cons(car(TR)/T,cdr(TR)); - N=0; - } - } - return reverse(cons(reverse(TR),R)); - }else if(type(S)==4){ - Num=getopt(num); - for(R=[]; ; ){ - if(type(TS=car(S))!=4) return; - for(; TS!=[]; TS=cdr(TS)){ - V=car(TS); - if(type(V)>1||(type(V)==1&&ntype(V)>0)){ - V="<"+rtostr(V)+">"; - R=append(reverse(strtoascii(V)),R); - continue; - } - if(dn(V)>1){ - P=reverse(strtoascii(rtostr(V))); - R=append(P,cons(40,R)); - R=cons(41,R); - continue; - } - if(V<0 && V>-10){ - V=-V; - R=cons(45,R); - } - if(V<0 || V>35 || (V>9 && Num==1)){ - P=reverse(strtoascii(rtostr(V))); - R=append(P,cons(40,R)); - V=41; - }else if(V<10) V+=48; - else V+=87; - R=cons(V,R); - } - if((S=cdr(S))==[]) break; - R=cons(44,R); - } - return asciitostr(reverse(R)); - } - return 0; -} - -def sp2grs(M,A,L) -{ - MM = []; - T0 = 0; - Mat=getopt(mat); - if(Mat!=1) Mat=0; - if(type(M)==7) M=s2sp(M); - if((LM = length(M)) > 10 && type(A) < 4) - CK = 1; - Sft = (type(L)==1)?L:0; - if(type(L)==4 && length(L)>=3) - Sft = L[2]; - if(Sft < 0){ - T0 = 1; - Sft = -Sft-1; - } - for(I = LM-1; I >= 0; I--){ - MI = M[I]; MN = []; - if(CK == 1 && length(MI) > 10){ - erno(1); - return; - } - if(type(A) == 4) - AA = rtostr(A[I]); - else - AA = rtostr(A)+rtostr(I); - for(J = LM = length(MI)-1; J >= 0; J--){ - V = MI[J]; - if(type(V) > 3) - V = V[0]; - if(T0 == 0 || I == 0) - MN = cons([V, makev([AA,J+Sft])], MN); - else{ - if(LM == 1) - MN = cons([V, (J==0)?0:makev([AA])], MN); - else if(I == 1 && Mat == 0) - MN = cons([V, (J==length(MI)-1)?0:makev([AA,J+Sft])], MN); - else - MN = cons([V, (J==0)?0:makev([AA,J])], MN); - } - } - MM = cons(MN, MM); - } - if(type(L) == 4 && length(L) >= 2){ - R = chkspt(MM|mat=Mat); /* R[3]: Fuchs */ - AA = var(MM[L[0]-1][L[1]-1][1]); - if(AA==0) AA=var(R[3]); - if(AA!=0 && (P = mycoef(R[3],1,AA))!=0){ - P = -mycoef(R[3], 0, AA)/P; - MM = mysubst(MM,[AA,P]); - } - } - return MM; -} - -def intpoly(F,X) -{ - if((T=ptype(F,X))<4){ - if(T<3){ /* polynomial */ - if(type(C=getopt(cos))>0){ - V=vars(F); - Z=makenewv(V); - W=makenewv(cons(Z,V)); - Q=intpoly(F,X|exp=Z); - Q=(subst(Q,Z,@i*C)*(Z+@i*W)+subst(Q,Z,-@i*C)*(Z-@i*W))/2; - return [mycoef(Q,1,Z),mycoef(Q,1,W)]; - } - if(type(C=getopt(sin))>0){ - Q=intpoly(F,X|cos=C); - return [-Q[1],Q[0]]; - } - if(type(C=getopt(log))>0){ - Q=intpoly(F,X); - if(C[0]==0) return [Q,0]; - if(length(C)<3) C=[C[0],C[1],1]; - Q-=subst(Q,X,-C[1]/C[0]); - if(iscoef(Q,os_md.israt)) Q=red(Q); - if(C[2]==0) return [Q]; - S=subst(-Q*C[0]*C[2],X,X-C[1]/C[0]); - for(R=0,D=mydeg(S,X);D>0;D--) R+=mycoef(S,D,X)*X^(D-1); - R=subst(R,X,X+C[1]/C[0]); - return cons(Q,intpoly(R,X|log=[C[0],C[1],C[2]-1])); - } - if(type(C=getopt(exp))>0){ - D = mydeg(F,X); - for(P=Q=F/C;D>=0;D--){ - Q=-mydiff(Q,X)/C; - P+=Q; - } - return P; - } - for(P=0,I=mydeg(F,X);I >= 0;I--) - P += mycoef(F,I,X)*X^(I+1)/(I+1); - return P; - } - R=pfrac(F,X|root=2); /* rational */ - for(P=0;R!=[];R=cdr(R)){ - if(type(V=getopt(dumb))==5){ - for(PF=[],RR=R;RR!=[];RR=cdr(RR)) - PF=cons(RR[0][0]/RR[0][1]^RR[0][2],PF); - PF=[cons(X,reverse(PF))]; - if(P) PF=cons([1,P],PF); - V[0]=cons(PF,V[0]); - } - RT=car(R); - if(mydeg(RT[1],X)==0) P+=intpoly(RT[0]*RT[2],X); - else if((Deg=mydeg(RT[1],X))==1){ - if(RT[2]>1) P+=RT[0]*RT[1]^(1-RT[2])/(1-RT[2])/mycoef(RT[1],1,X); - else P+=RT[0]*log(RT[1])/mycoef(RT[1],1,X); - P=red(P); - }else if(Deg==2){ - D1=diff(RT[1],X);C1=mycoef(D1,1,X); - B=2*C1*mycoef(RT[1],0,X)-mycoef(RT[1],1,X)^2; /* ax^2+bx+c => B=4ac-b^2 */ - B=sqrt2rat(B); - N=RT[0]; - for(I=RT[2];I>0&&N!=0;I--){ - C0=mycoef(N,1,X)/C1;N-=C0*D1; - if(C0){ - if(I>1) P-=C0/RT[1]^(I-1)/(I-1); - else P+=C0*log(RT[1]); - } - if(I>1){ - BB=B/C1; - P+=N*X/RT[1]^(I-1)/(I-1)/BB; - N*=(2*I-3)/(I-1)/BB; - }else{ - if(type(BR=sqrtrat(B))>3){ - mycat(["Cannot obtain sqare root of ",B]); - return []; - } - if(real(nm(BR))!=0){ - P+=(2*N/BR)*atan(sqrt2rat(D1/BR|mult=1)); - }else{ - BR*=@i;BRI=sqrt2rat(1/BR); - R1=(-mycoef(RT[1],1,X)+BR)/C1; - R2=(-mycoef(RT[1],1,X)-BR)/C1; - P+=N*BRI*log( /* sqrt2rat */((x-R1)/(x-R2))); - } - } - P=red(P); - } - P=sqrt2rat(P); - }else{ - mycat(["Cannot get an indefinite integral of ",F]); - return []; - } - } - Q=simplog(P,X); - if(type(V)==5&&nmono(P)!=nmono(Q)) V[0]=cons([[1,red(P)]],V[0]); - return red(Q); - } - return []; -} - -def fshorter(P,X) -{ - Q=sqrt2rat(P); - R=trig2exp(Q,X|inv=1); - if(str_len(fctrtos(R))<str_len(fctrtos(Q))) Q=R; - Var=pfargs(Q,X|level=1); - for(C=F=0,R=1,V=Var;V!=[];V=cdr(V)){ - if(findin(car(V)[1],[cos,sin,tan])>=0){ - if(!C){ - F=car(V)[2]; - }else{ - R=red(car(V)[2]/F); - if(type(R)!=1) break; - F/=dn(R); - } - C++; - } - } - if(getopt(period)==1) return F; - if(!isint(Log=getopt(log))) Log=0; - if(V==[]&&F!=0){ - if(iand(Log,1)){ - H=append(cdr(fctr(nm(Q))),cdr(fctr(dn(Q)))); - for(L=0;H!=[];H=cdr(H)) - L+=str_len(rtostr(car(H)[0])); - }else L=str_len(fctrtos(Q)); - S=trig2exp(P,X); - for(T=[sin(F),tan(F),cos(F),sin(F/2),cos(F/2),tan(F/2)];T!=[];T=cdr(T)){ - R=trig2exp(S,X|inv=car(T)); - if(iand(Log,1)){ - H=append(cdr(fctr(nm(R))),cdr(fctr(dn(R)))); - for(K=0;H!=[];H=cdr(H)) - K+=str_len(rtostr(car(H)[0])); - }else K=str_len(fctrtos(R)); - if(K<L){ - Q=R;L=K; - } - } - } - return Q; -} - -def isshortneg(P) -{ - return(str_len(rtostr(P))>str_len(rtostr(-P)))?1:0; -} - -def simplog(R,X) -{ - for(V=[],Var=pfargs(R,X);Var!=[];Var=cdr(Var)){ - VT=car(Var); - if(VT[1]==log && ptype(R,VT[0])==2 && mydeg(R,VT[0])==1) - V=cons([VT[0],VT[2],mycoef(R,1,VT[0])],V); - } - for(;V!=[];V=cdr(V)){ - VT=car(V); - for(V2=cdr(V);V2!=[];V2=cdr(V2)){ - Dn=1; - if((C=red(car(V2)[2]/VT[2]))!=1&&C!=-1){ - if(getopt(mult)==1&&type(C)==1&&ntype(C)==0){ - Dn=dn(C);C*=Dn; - }else continue; - } - Log=red(VT[1]^Dn*car(V2)[1]^(Dn*C)); - L=str_len(rtostr(dn(Log)))-str_len(rtostr(nm(Log))); - if(L>0 || (L==0&&isshortneg(VT[2])) ){ - Dn=-Dn;Log=1/Log; - } - R=mycoef(R,0,VT[0]);R=mycoef(R,0,car(V2)[0]); - return(R+VT[2]*log(Log)/Dn); - } - } - return R; -} - -def integrate(P,X) -{ - Dvi=getopt(dviout); - if(type(I=getopt(I))==4){ - if((R=integrate(P,X))==[]) II="?"; - else if(type(I[0])>3||type(I[1])>3){ - R=subst(R,X,x); - V=flim(R,I[0]);VV=flim(R,I[1]); - if(V==""||VV=="") II="?"; - else if(type(V)==7||type(VV)==7){ - if(V==VV) II="?"; - else II=(VV=="+"||V=="-")?"\\infty":"-\\infty"; - }else{ - II=VV-V; - if(II>10^10) II="\\infty"; - else if(II<-10^10) II="-\\infty"; - } - }else{ - V=subst(R,X,I[1])-subst(R,X,I[0]); - VV=myval(V); - II=(type(VV)>=2||ntype(VV)<1)?VV:evalred(V); - } - if(type(Dvi)!=1) return II; - I=ltov(I); - for(J=0;J<2;J++){ - if(type(I[J])>3){ - if(type(I[J])==4&&length(I[J])>1) I[J]=I[J][1]; - else I[J]=(J==0)?"-\\infty":"\\infty"; - } - if(type(I[J])<4) I[J]=my_tex_form(I[J]); - } - S=(type(II)==7)?II:my_tex_form(II); - S="\\int_{"+I[0]+"}^{"+I[1]+"}"+monototex(P)+"\\,d"+my_tex_form(X)+"&="+S; - if(Dvi==1) dviout(texbegin("align",S)); - return S; - } - if(isint(Dvi)==1){ - if(Dvi==2||getopt(dumb)==-1){ - V=newvect(1);V[0]=[]; - }else V=0; - if((RR=integrate(P,X|dumb=V))==[]) return R; - S=fshorter(RR,X); - VV=[X]; - if(V!=0){ - R=cons([[1,RR]],V[0]); - if(S!=RR) R=cons([[1,RR=S]],R); - for(V=FR=[];R!=[];R=cdr(R)) - if(car(R)!=FR) V=cons(FR=car(R),V); - Var=varargs(V|all=1)[1]; - for(S0=[x0,x1,x2,x3],S=[t,s,u,v,w];S0!=[]&&S!=[];){ - if(findin(car(S0),Var)<0){ - S0=cdr(S0); continue; - } - if(findin(car(S),Var)>=0){ - S=cdr(S); continue; - } - V=subst(V,[car(S0),car(S)]);S0=cdr(S0);S=cdr(S); - } - if(Dvi==-2) return V; - S1="\\,dx&"; - }else{ - V=[[],[[1,RR=S]]]; - S1="\\,dx"; - } - if(type(P)>2){ - if(type(nm(P))<2){ - P=P*dx;S1=V?"&":""; - } - S=fctrtos(P|TeX=2,lim=0);SV0=my_tex_form(P); - if(str_len(SV0)<str_len(S)) S=SV0; - }else S=monototex(P); - if(Dvi!=-2) S="\\int "+S+S1; - else S=""; - for(L=[],V=cdr(V);V!=[];V=cdr(V)){ - CL=car(V);S0=["="]; /* a line */ - for(FL=0;CL!=[];CL=cdr(CL),FL++){ - CT=car(CL); /* a term */ - if((Y=CT[0])==0){ /* a variable */ - CT=cdr(CT); - if(length(CT)>2) CT=cdr(CT); - S0=["\\qquad(",CT[0],"=",CT[1],")"]; - break; - }else{ - for(FT=0,S2=[],CT=cdr(CT);CT!=[];CT=cdr(CT),FT++){ - SV=fctrtos(car(CT)|TeX=2,lim=0);SV0=my_tex_form(car(CT)); - if(str_len(SV0)<str_len(SV)) SV=SV0; - if(FL||FT||(F&&type(Y)<2)) SV=minustos(SV); - S2=append(["+",SV],S2); - } - S2=reverse(cdr(S2)); - if(type(Y)>1){ - if(length(S2)>1){ - S1="\\int\\left(";S3="\\right)\\,d"; - }else{ - S1="\\int";S3="\\,d"; - } - S2=cons(S1,append(S2,[S3,Y])); - if(findin(Y,VV)<0) VV=cons(Y,VV); - } - if(FL) S0=append(S0,cons("+",S2)); - else S0=append(S0,S2); - } - } - L=append([S0],L); - }; - V=pfargs(RR,X|level=1); - for(Var=[];V!=[];V=cdr(V)) Var=cons(car(V)[0],Var); - Var=reverse(Var); - if(!isint(J=getopt(frac))) J=0;; - if(!iand(J,4)&&(!iand(J,2)||length(Var)==1)&&(iand(J,8)==8||ptype(RR,Var)==2)){ - F=1; - if(iand(J,1)){ - K=str_len(fctrtos(RR)); - I=str_len(fctrtos(RR|var=Var)); - if(I>=K) F=0; - } - if(F){ - V=[fctrtos(RR|var=Var,TeX=2)]; - if(Dvi!=-2) V=cons("=",V); - if(length(L)>0) L=cdr(L); - L=append([V],L); - } - }else if(ptype(RR,X)==2){ - L=cdr(L); - V=[fctrtos(RR|var=X,TeX=2)]; - if(Dvi!=-2) V=cons("=",V); - L=append([V],L); - } - S=texket(S+ltotex(reverse(L)|opt=["cr","spts0"],str=1)); - if(getopt(log)!=1){ - for(V=[];VV!=[];VV=cdr(VV)) - V=cons(strtoascii(my_tex_form(car(VV))),V); - S1=strtoascii("\\log"); - for(F=1;F;){ /* log(log(x)) */ - F=FT=0; - S0=strtoascii(S); /* log(x) -> log|x| */ - L=length(S0); - S2=str_tb(0,0); - for(I=0;;){ - if(I>=L||(J=str_str(S0,S1|top=I+FT))<0){ - S=str_tb(0,S2)+str_cut(S0,I,100000); - break; - } - if((K=str_str(S0,40|top=J+4))<0 - ||(K!=J+4&&K!=J+9)||(N=str_pair(S0,K+1,40,41))<0){ - FT=J-I+4;continue; - } - FT=0; - if(str_str(S0,V|top=K+1,end=N-1)[0]<0) S2=str_tb(str_cut(S0,I,N),S2); - else{ - /* log(a) -> log(a) */ - F=1; - if(N<L-1&&S0[N+1]==94){ /* log(x)^2 -> (log|x|)^2 */ - S2=str_tb([str_cut(S0,I,J-1),"\\left(",str_cut(S0,J,K-1), - "|",str_cut(S0,K+1,N-1),"|\\right)"],S2); - } - else S2=str_tb([str_cut(S0,I,K-1),"|",str_cut(S0,K+1,N-1),"|"],S2); - } - I=N+1; - } - } - } - if(Dvi>0){ - dviout(texbegin("align*",S)); - return 1; - } - return S; - } /* end of dviout */ - SM=["Cannot integrate",P,"at present"]; - P=sqrt2rat(P|mult=1); - Dumb2=1;Dumb3=0;W=newvect(1);W[0]=[]; - if(type(Dumb=getopt(dumb))==5){ - Dumb2=Dumb3=Dumb;D2=W; - }else if(!isint(Dumb)) Dumb=0; - if(Dumb==-1){ - Dumb2=Dumb3=-1; - } - if(type(Dumb)!=5) D2=Dumb2; - if(!isint(Mul=getopt(mult))) Mul=0; - else Mul++; - if(type(VAR=getopt(var))!=4) VAR=[]; - if(type(P)>4) return []; - if(iand(T=ptype(P=red(P),X),63)>3||Mul>4){ - if(Dumb!=1) mycat(SM); - return []; - } - if(Dumb==-1) mycat(["integrate", P]); - else if(type(Dumb)==5) Dumb[0]=cons([[X,P]],Dumb[0]); - if(T<4 && (T<3||iscoef(P,os_md.israt))){ - if(Dumb==-1) mycat(["rational function",P]); - else if(type(Dumb)==5) Dumb[0]=cons([[X,P]],Dumb[0]); - return intpoly(P,X|dumb=Dumb); /* rational function */ - } - Var=pfargs(P,X); - for(F=0,VV=Var;VV!=[];VV=cdr(VV)){ - /* p(x)*log(x^2-1), @e^x, a^x, f(x)^(m/n) etc.->simplify */ - V=car(VV); - if(V[1]==log && (T=ptype(V[2],X))>1 && T<4){ - if(mydeg(dn(V[2]),X)>0||mydeg(nm(V[2]),X)>1){ - FC=pfctr(V[2],X);RV=1; - if(length(FC)>2){ - RR=0;RV=1; - if((F0=car(FC)[0])!=1){ - if(type(F0)!=1 && F0<0){ - for(FT=cdr(FT);FT!=[];FT=cdr(FT)){ - if(iand(car(FT)[1],1)){ - RV=-1;F0=-F0;break; - } - } - } - } - if(F0!=1) RR=log(F0); - for(FC=cdr(FC);FC!=[];FC=cdr(FC)){ - if(RV==-1&&iand(car(FC)[1],1)==1){ - RR+=car(FC)[1]*log(-car(FC)[0]); - RV=1; - }else - RR+=car(FC)[1]*log(car(FC)[0]); - } - P=subst(P,V[0],RR); - F=1; - } - } - F=1; - }else if(V[1]==pow){ - if(ptype(V[2],X)==1){ - F=1; - if(V[2]==@e){ /* @e^(f(x)) */ - P=subst(P,V[0],exp(V[3])); - }else P=subst(P,V[0],exp(log(V[2])*V[3])); - }else if(type(V[3])<=1 && ntype(V[3])==0){ /* r(x)^(m/n) */ - if((Pw=floor(V[3]))!=0){ - R=V[2]^Pw; - if((PF=V[3]-Pw)!=0) R*=V[2]^PF; - P=subst(P,V[0],R); - F=1; - V=[V[2]^PF,V[1],V[2],PF]; - } - if(ptype(nm(V[2]),X)<2&&V[3]>0){ /* (1/p(x))^(m/n) */ - P=subst(P,V[0],V[2]*red(1/V[2])^(1-V[3])); - F=0;VV=cons(0,Var=pfargs(P,X));continue; - } - if(ptype(V[2],X)<4&&(K=dn(V[3]))>1){ - V2=red(V[2]); - DN=mydeg(nm(V2),X);DD=mydeg(dn(V2),X); - if(DN+DD>1){ - VF=pfctr(V2,X); - R=car(VF)[0]^(car(VF)[1]);RR=0; - for(VF=cdr(VF);VF!=[];VF=cdr(VF)){ - TV=car(VF);TM=TV[1]; - while(abs(TM)>=K){ - RR=1; - if(TM>0){ - TM-=K; - RR*=TV[0]^nm(V[3]); - }else{ - TM+=K; - RR/=TV[0]^nm(V[3]); - } - } - if(TM!=0) R*=TV[0]^TM; - } - if(RR){ - P=subst(P,V[0],RR*red(R)^(V[3]));F=1; - F=0;VV=cons(0,Var=pfargs(P,X));continue; - } - } - } - } - } - } - if(F){ - P=sqrt2rat(P|mult=1); - Var=pfargs(P=red(P),X);T=ptype(P,X); - if(T<4 && (T<3||iscoef(P,os_md.israt))){ - if(Dumb==-1) mycat(["rational function",P]); - else if(type(Dumb)==5){ - Dumb[0]=cons([[X,P]],Dumb[0]); - return intpoly(P,X|dumb=Dumb3); - } - return intpoly(P,X); /* rational function */ - } - } -#if 1 - for(P0=P,V=pfargs(P,X|level=1);V!=[];V=cdr(V)) /* P:tan(x) -> P0:sin(x)/cos(x) */ - if(car(V)[1]==tan) P0=red(subst(P0,car(V)[0],sin(car(V)[2])/cos(car(V)[2]))); - if(iand(ptype(P0,X),128)){ /* (log f)'=f'/f */ - for(Df=cdr(fctr(dn(P0)));Df!=[];Df=cdr(Df)){ - if(!iand(ptype(car(Df)[0],X),64)) continue; - Q=car(Df)[0]^(car(Df)[1]);QQ=red(dn(P0)/Q); - DQ=red(diff(Q,X)*QQ); - if(type(C=DQ/nm(P0))<2&&C!=0){ - PP=0;DN=[1]; - }else for(DN=cdr(fctr(DQ));DN!=[];DN=cdr(DN)){ - Y=car(DN)[0]; - if(!iand(ptype(Y,X),64)||(I=mydeg(nm(P0),Y))!=mydeg(DQ,Y) - || ptype((C=red(mycoef(nm(P0),I,Y)/mycoef(DQ,I,Y))),X)>1||C==0) continue; - PP=red(P0-C*diff(Q,X)/Q); - if(nmono(P0)>nmono(PP)) break; - } - if(DN!=[]){ - R=C*log(Q); - if(PP==0){ - if(P!=P0&&type(Dumb)==5) Dumb[0]=cons([[X,P0]],Dumb[0]); - return R; - } - W[0]=[]; - S=integrate(PP,X|dumb=D2); - if(S!=[]){ - if(type(Dumb)==5){ - Dumb[0]=cons([[X,red(P0-PP),PP]],Dumb[0]); - TD=W[0]; - for(W0=[],TD=reverse(TD);TD!=[];TD=cdr(TD)){ - if(car(TD)[0][0]){ - WL=cons([1,R],car(TD)); - Dumb[0]=cons(WL,Dumb[0]); - } - else Dumb[0]=cons(car(TD),Dumb[0]); - } - } - return red(R+S); - } - } - } - } -#endif - if((length(Var)==1||getopt(exe)==1) && /* p(x)*atan(q(x))^m+r(x), etc */ - findin((VT=car(Var))[1],[atan,asin,acos,log])>=0 && ptype(P,VT[0])==2 && - (VT[1]!=log||(T!=65&&T!=66)||mydeg(VT[2],X)!=1)){ /* exclude x*log(x+1)^2 */ - for(R=0,D=mydeg(P,VT[0]);D>=0;D--){ - Q=S=mycoef(P,D,VT[0]); - if(S){ - if(D>0){ - if((Q=integrate(S,X|mult=Mul))==[]) return Q; - }else{ - W[0]=[]; - if((Q=integrate(S,X|dumb=D2,var=VAR,mult=Mul))==[]) return Q; - if(type(Dumb)==5){ - TD=W[0]; - for(W0=[],TD=reverse(TD);TD!=[];TD=cdr(TD)){ - if(car(TD)[0][0]){ - WL=cons([1,R],car(TD)); - Dumb[0]=cons(WL,Dumb[0]); - } - else Dumb[0]=cons(car(TD),Dumb[0]); - } - if(car(Dumb[0])!=[[1,R],[1,Q]]) - Dumb[0]=cons([[1,R,Q]],Dumb[0]); - } - return red(R+Q); - } - }else if(D>0) continue; - if(D==0){ - if(Q!=0&&type(Dumb)==5) Dumb[0]=cons([[1,R,Q]],Dumb[0]); - return red(Q+R); - } - R0=Q*VT[0]^D; - P=(P0=P)-S*VT[0]^D-Q*diff(VT[0]^D,X); - if(mydeg(P,VT[0])>=D){ /* (x+1)*log(x)/x^2 */ - if(mydeg(P,VT[0])==D && - ptype(C=red(mycoef(P,D,VT[0])/diff(VT[0],X)),VT[0])<2){ - P=P0-(S*VT[0]^D+Q*diff(VT[0]^D,X)+C*diff(VT[0]^(D+1),X)/(D+1)); - R0+=C*VT[0]^(D+1)/(D+1); - }else{ - P=P0; - if(Dumb!=1) mycat(SM); - return []; - } - } - if(type(Dumb)==5){ - if(P) Dumb[0]=cons([R?[1,R,R0]:[1,R0],[X,P]],Dumb[0]); - else if(R!=0) Dumb[0]=cons([[1,R,R0]],Dumb[0]); - } - R+=R0; - } - } - if(length(Var)==1 && (VT=car(Var))[1]==pow && mydeg(P,VT[0])==1 && (PT=ptype(VT[2],X))<4){ - PR=mycoef(P,0,VT[0]); - if(RR!=0){ - RR=integrate(RR,X|dumb=Dumb3,var=Var); - if(RR==[]) return RR; - } - PW=VT[3]; - if((D=mydeg(nm(V2=VT[2]),X))==2&&PT==2){ /* f(x)*(ax^2+bx+c)^(m/2)+r(x) */ - if(isint(2*PW)){ - C2=mycoef(V20=V2,2,X);F=1; - if((C21=sqrtrat(C2))==[]) return []; - if(imag(C21)!=0){ - if(real(C21)!=0) return []; - C21=C21/@i;F=-1; - } - if(type(C21)>3) return []; - P=subst(P,X,X/C21);VT=mysubst(VT,[X,X/C21]);V2=VT[2]; - C1=mycoef(V2,1,X)/F/2; - if(C1!=0){ - P=subst(P,X,X-C1);VT=mysubst(VT,[X,X-C1]);V2=VT[2]; - } - C0=mycoef(V2,0,X); - if((C01=sqrtrat(C0))==[]) return []; - if(imag(nm(C01))!=0){ - if(real(nm(C01))!=0) return []; - C01=C01/@i;G=-1; - }else G=1; - if(type(C01)>3||(F==-1&&G==-1)) return []; - Y=makenewv([P,VAR]|var=x); - if(F==-1){ /* (c^2-x^2)^(1/2) */ - Q=subst(P,VT[0],(C01*cos(Y))^(2*PW),X,YX=C01*sin(Y)) - *C01*cos(Y)/C21; - SY=(C21*X+C1);CY=V20;YY=asin(sqrt2rat((C21*X+C1)/C01|mult=1)); - }else if(G==-1){ /* (x^2-c^2)^(1/2) */ - Q=subst(P,VT[0],(C01*sin(Y)/cos(Y))^(2*PW),X,YX=C01/cos(Y)) - *C01*sin(Y)/cos(Y)^2/C21; - SY=V20;CY=1/(C21*X+C1);YY=acos(sqrt2rat(C01*(C21*X+C1)|mult=1)); - }else{ /* (x^2+c^2)^(1/2) */ - Q=subst(P,VT[0],(C01/cos(Y))^(2*PW),X,YX=C01*sin(Y)/cos(Y)) - *C01/cos(Y)^2/C21; - CY=V20; YY=atan(sqrt2rat((C21*X+C1)/C01|mult=1)); - } - if(Dumb==-1) mycat([C21*X+C1,"=",YX]); - else if(type(Dumb)==5) Dumb[0]=cons([[0,Y,C21*X+C1,YX]],Dumb[0]); - Q=sqrt2rat(Q); - QQ=red(substblock(nm(Q),sin(Y),sin(Y)^2,1-cos(Y)^2) - /substblock(dn(Q),sin(Y),sin(Y)^2,1-cos(Y)^2)); - if(cmpsimple(QQ,Q|comp=2)<0) Q=QQ; - QQ=red(substblock(nm(Q),cos(Y),cos(Y)^2,1-sin(Y)^2) - /substblock(dn(Q),cos(Y),cos(Y)^2,1-sin(Y)^2)); - if(cmpsimple(QQ,Q|comp=2)<0) Q=QQ; - if((Q=integrate(Q,Y|dumb=Dumb2,var=cons(X,Var)))==[]) return []; - Q=trig2exp(Q,Y|inv=cos(Y)); - for(V=vars(Q);V!=[];V=cdr(V)){ - FA=funargs(car(V)); - if(type(FA)==4&&FA[0]==log){ - QQ=trig2exp(FA[1],Y|inv=cos(Y)); - Q=mycoef(Q,0,car(V))+mycoef(Q,1,car(V))*log(QQ); - } - } - if(type(Dumb)==5) Dumb[0]=cons([[1,Q]],Dumb[0]); - if(F==-1) Q=subst(Q,sin(Y),SY/C01,cos(Y),CY^(1/2)/C01,Y,YY); - else if(G==-1){ - Q=red(subst(Q,sin(Y),SY^(1/2)*cos(Y)/C01)); - Q=red(subst(Q,cos(Y),C01*CY,Y,YY)); - }else{ - Q=red(subst(Q,sin(Y),(C21*X+C1)*cos(Y)/C01)); - Nm=substblock(nm(Q),cos(Y),C01^2/CY,cos(Y)^2); - Nm=subst(Nm,cos(Y),C01/CY^(1/2)); - Dn=substblock(dn(Q),cos(Y),C01^2/CY,cos(Y)^2); - Dn=subst(Dn,cos(Y),C01/CY^(1/2)); - Q=red(subst(Nm/Dn,Y,YY)); - } - if(findin(Y,vars(Q))>=0) return []; - for(R=[],Var=vars(Q);Var!=[];Var=cdr(Var)){ - VT=funargs(V=car(Var)); - if(type(VT)==4&&VT[0]==log&&ptype(VT[1],X)>60&&mydeg(Q,V)==1) - R=cons([mycoef(Q,1,V),V],R); - } - if(length(R)==2 && (R[0][0]==R[1][0]||R[0][0]+R[1][0]==0)){ - R0=args(R[0][1])[0];R1=args(R[1][1])[0]; - if(R[0][0]==R[1][0]) S=R0*R1; - else S=R1/R0; - Q=mycoef(Q,0,R[0][1]);Q=mycoef(Q,0,R[1][1]); - Q+=R[1][0]*log(red(S)); - } - for(Var=vars(Q);Var!=[];Var=cdr(Var)){ - VT=funargs(car(Var)); - if(type(VT)==4&&VT[0]==log&&ptype(VT[1],X)>60){ - S=trig2exp(VT[1],X|inv=cos(X),arc=1); - if(ptype(dn(S),X)<2 && mydeg(Q,car(Var))==1 - && ptype(mycoef(Q,1,car(Var)),X)<2){ - S=nm(S); - SF=fctr(S); - S/=SF[0][0]; - } - if(cmpsimple(S,-S)>0) S=-S; - Q=subst(Q,car(Var),log(S)); - } - } /* x/(1-x^2)^(1/2) */ - if(type(Q=red(Q+RR))==2&&type(Dumb)!=5) Q-=cterm(Q); - if(Dumb==-1) mycat(["->",Q]); - else if(type(Dumb)==5) Dumb[0]=cons([[1,Q]],Dumb[0]); - return Q; - } - }else if(D==1 && mydeg(Dn=dn(V2),X)<2 && type(PW)==1 && ntype(PW)==0 && - (V2!=X||ptype(mycoef(P,1,VT[0]),X)>2)){ /* p(x)((ax+b)/(cx+d))^(m/n) */ - PN=nm(PW);PD=dn(PW); - Y=makenewv([P,VAR]|var=x);Q=Y^PD*Dn-nm(V2);F=-mycoef(Q,0,X)/mycoef(Q,1,X); - Q=red(subst(P,VT[0],Y^PN,X,F)*diff(F,Y)); - if(Dumb==-1) mycat([Y,"=",V2^(1/PD)]); - else if(type(Dumb)==5) Dumb[0]=cons([[0,Y,V2^(1/PD)]],Dumb[0]); - if((Q=integrate(Q,Y|dumb=Dumb3,var=cons(X,Var)))==[]) return []; - Q=red(Q); - QN=subst(substblock(nm(Q),Y,Y^PD,V2),Y,V2^(1/PD)); - QD=subst(substblock(dn(Q),Y,Y^PD,V2),Y,V2^(1/PD)); - Q=red(QN/QD+RR); - if(Dumb==-1) mycat(["->",Q]); - else if(type(Dumb)==5) Dumb[0]=cons([[1,Q]],Dumb[0]); - return Q; - } - }else if(length(Var)==2 && /* r(x,(ax+b)^(1/2),(cx+d)^(1/2)) */ - (VT=car(Var))[1]==pow && ptype(VT[2],X)==1 && mydeg(VT[2],X)==1 && VT[3]==1/2 && - (VS=car(car(Var)))[1]==pow && ptype(VS[2],X)==1 && mydeg(VS[2],X)==1 && VS[3]==1/2){ - Y=makenewv([P,VAR]|var=x);R=(Y^2-myceof(VS[0],0,X))/(C=mycoef(VS[0],1,X)); - if(Dumb==-1) mycat([Y,"=",VS[0]]); - else if(type(Dumb)==5) Dumb[0]=cons([[0,Y,VD[0]]],Dumb[0]); - R=integrate(subst(P,VS[0],Y,X,R)*2*Y/C,Y|dumb=Dumb3,var=cons(X,Var)); - if(R!=[]){ - R=subst(substblock(R,Y,VS[0],Y^2),Y,VS[0]); - if(Dumb==-1) mycat(["->",R]); - else if(type(Dumb)==5) Dumb[0]=cons([[1,R]],Dumb[0]); - } - return R; - } - if(T==65||T==66){ /* polynomial including sin, exp etc */ - for(F=0,VT=Var;VT!=[];VT=cdr(VT)){ - VTT=car(VT); - if(ptype(VTT[2],X)>2||mydeg(VTT[2],X)>1) F=ior(F,256); /* compos. or rat. or nonlin. */ - K=findin(VTT[1],[cos,sin,tan,exp,log,pow]); - F=ior(F,2^(K+1)); /* 1:other,2:cos,4:sin,8:tan,16:exp,32:log,64:pow */ - if((Deg=mydeg(P,VTT[0]))>1&&K!=4) F=ior(F,1024); /* nonlinear */ - if(K==5 && (ptype(VTT[3],X)!=0 || VTT[2]!=x||Deg>1)) F=ior(F,8192); /* pow */ - for(;Deg>0;Deg--){ /* coef */ - if(ptype(mycoef(P,Deg,VTT[0]),X)>2){ - if(K==4||K==5) F=ior(F,2048); /* exp, log */ - else F=ior(F,4096); - } - } - } - if(!iand(F,1+8+64+256+512+2048+8192)){ /* cos,sin,exp,log^n,x^c */ - if(iand(F,1024+4096)&&!iand(F,32+64)){ /* cos,sin,exp */ - if(type(Dumb)==5){ - S=trig2exp(P,X|inv=1); - if(P!=S) Dumb[0]=cons([[X,S]],Dumb[0]); - } - R=integrate(trig2exp(P,X),X); - if(R!=[]) S=trig2exp(R,X|inv=1); - R=fshorter(S,X); - if(type(Dumb)==5&&R!=S){ - Dumb[0]=cons([[1,S]],Dumb[0]); - } - return R; - } - for(R=0,VT=Var;VT!=[];VT=cdr(VT)){ - CV=car(VT); - C0=mycoef(CV[2],0,X);C1=mycoef(CV[2],1,X); - Q=mycoef(P,1,CV[0]); - if(CV[1]==sin||CV[1]==cos){ - TR=(CV[1]==sin)?intpoly(Q,X|sin=C1):intpoly(Q,X|cos=C1); - R+=TR[0]*cos(CV[2])+TR[1]*sin(CV[2]); - }else if(CV[1]==exp){ - QT=exp(CV[2]); - for(V2=vars(C1);V2!=[];V2=cdr(V2)){ /* exp(2*log(a)*x) => a^(2*x) */ - if(vtype(VA=car(V2))==2&&functor(VA)==log){ - if(ptype(C1,VA)!=2||mydeg(C1,VA)==1&&mycoef(C1,0,VA)==0){ - QT=args(VA)[0]^(red(C1/VA)*X); - if(C0!=0) QT*=exp(C0); - break; - } - } - } - R+=intpoly(Q,X|exp=C1)*QT; - }else if(CV[1]==pow) - R+=intpoly(Q,X|pow=CV[2])*x^CV[2]; - else if(CV[1]==log){ - for(Deg=mydeg(P,CV[0]);Deg>0; Deg--){ - Q=mycoef(P,Deg,CV[0]); - TR=intpoly(Q,X|log=[C1,C0,Deg]); - for(I=0;TR!=[];I++,TR=cdr(TR)){ - if(I==Deg) R+=car(TR)-subst(car(TR),X,0); - else R+=car(TR)*CV[0]^(Deg-I); - } - } - } - P=mycoef(P,0,CV[0]); - } - R+=intpoly(P,X); - return R; - } - } - for(K=0,VX=[],VT=Var;VT!=[];VT=cdr(VT)){ /* contain only both pow and trig */ - VTT=car(VT); - if(findin(VTT[1],[cos,sin,tan])>=0){ - if(ptype(VTT[2],X)!=2||mydeg(VTT[2],X)!=1) break; - VX=cons(VTT,VX); - }else if(VTT[1]==pow) K=1; - else break; - } - if(VT==[]&&K==1&&VX!=[]){ - D=VX[0][2]; - if(VX[0][1]==tan) D*=2; - for(VT=cdr(VX);VT!=[];VT=cdr(VT)){ - K=VT[0][2]/D; - if(VT[0][1]==tan) K*=2; - if(type(K)!=1||ntype(K)!=0) break; - D/=dn(K); - } - if(VT==[]){ - Y=makenewv([P,VAR]|var=x); - for(Q=P,VT=VX;VT!=[];VT=cdr(VT)){ - VTT=car(VT); - if(VTT[1]==cos||VTT[1]==sin){ - VV=trig2exp(VTT[0],X|inv=cos(D)); - VV=subst(VV,cos(D),(1-Y^2)/(1+Y^2),sin(D),2*Y/(Y^2+1)); - }else if(VTT[1]==tan){ - VV=trig2exp(VTT[0],X|inv=tan(D/2)); - VV=subst(VV,tan(D),Y); - } - Q=subst(Q,VTT[0],VV); - } - Q*=2/(Y^2+1); - if(diff(Q,X)==0){ - if(Dumb==-1) mycat([Y,"=",tan(D/2)]); - else if(type(Dumb)==5) Dumb[0]=cons([[0,Y,tan(D/2)]],Dumb[0]); - R=integrate(Q,Y|dumb=Dumb2,var=cons(X,Var)); - if(R!=[]){ - if(Dumb==-1) mycat(["->",R]); - else if(type(Dumb)==5) Dumb[0]=cons([[1,R]],Dumb[0]); - return sqrt2rat(subst(R,Y,tan(D/2))|mult=1); - } - } - } - } - if(T>65||iand(F,8)){ /* rational for functions or tan */ - if(findin(X,vars(P))<0){ - for(XV=XE=0,VT=Var;VT!=[];VT=cdr(VT)){ - VTT=car(VT); - if(mydeg(VTT[2],X)!=1) break; - if(VTT[1]==cos||VTT[1]==sin||VTT[1]==tan){ - K=red(VTT[2]/X); - if(type(K)>1||ntype(K)>0) break; - if(XV==0) XV=K; - else XV/=dn(K/XV); - if(VTT[1]==tan) P=red(subst(P,VTT[0],sin(VTT[2])/cos(VTT[2]))); - }else if(VTT[1]==exp){ - K=red(VTT[2]/X); - if(type(K)>1||ntype(K)>0) break; - if(XE==0) XE=K; - else XE/=dn(K/XE); - }else break; - } - if(VT==[]&&XE*XV==0){ - if(XE){ - if(XE<0) XE=-XE; - Y=makenewv([P,VAR]|var=x); - for(F=0,VT=Var;VT!=[];VT=cdr(VT),F++){ - VTT=car(VT);C=red(VTT[2]/X/XE); - P=subst(P,VTT[0],Y^C); - if(!F){ - if(Dumb==-1) mycat([Y^C,"=",VTT[0]]); - else if(type(Dumb)==5) Dumb[0]=cons([[0,Y^C,VTT[0]]],Dumb[0]); - } - } - P/=XE*Y; - Q=integrate(P,Y|dumb=Dumb3,var=cons(X,VAR)); - if(Q==[]) return []; - Q=subst(Q,Y,exp(XE*X)); - Q=trig2exp(Q,X); - if(Dumb==-1) mycat(["->",Q]); - else if(type(Dumb)==5) Dumb[0]=cons([[1,Q]],Dumb[0]); - return Q; - } - P=trig2exp(nm(P),X|inv=cos(XV*X))/trig2exp(dn(P),X|inv=cos(XV*X)); - Y=makenewv([P,VAR]|var=x); - Q=red(subst(P,sin(XV*X),Y*cos(XV*X))); - Q=substblock(nm(Q),cos(XV*X),cos(XV*X)^2,1/(Y^2+1))/ - (substblock(dn(Q),cos(XV*X),cos(XV*X)^2,1/(Y^2+1))*(Y^2+1)); - Q=red(Q); - if(ptype(Q,X)<2){ - XV*=2;P=Q; - }else{ - P=subst(P,cos(XV*X),(1-Y^2)/(1+Y^2),sin(XV*X),2*Y/(1+Y^2))*2/K/(1+Y^2); - P=red(P); - } - if(Dumb==-1){ - mycat([Y,"=",tan(XV*X/2)]); - mycat(["integrate",P]); - }else if(type(Dumb)==5) Dumb[0]=cons([[Y,P]],cons([[0,Y,tan(XV*X/2)]],Dumb[0])); - R=intpoly(P,Y|dumb=Dumb); - if(R==[]) return R; - if(Dumb==-1) mycat(["->",R]); - else if(type(Dumb)==5) Dumb[0]=cons([[1,R]],Dumb[0]); - for(Log=1,K=0,Var=pfargs(RR=R,Y);Var!=[];Var=cdr(Var)){ - VTT=car(Var); - if(VTT[1]==log){ - C=mycoef(R,1,VTT[0]); - VT2=VTT[2]; - if(K==0){ - K=C;Log=VT2; - if(K<0){ - K=-K;Log=1/Log; - } - }else{ - if((V=red(C/K))<0){ - VT2=1/VT2;V=-V; - } - if(type(V)>1||ntype(V)>0){ - Log=1;break; - } - if(isint(V)) Log*=VT2^V; - else{ - D=dn(V);K/=D; - Log=Log^D*VT2^nm(V); - } - } - RR=mycoef(RR,0,VTT[0]); - } - } - if(Log!=1){ - R=RR; - if(type(Dumb)==5){ - if(RR) Dumb[0]=cons([[1,K*log(Log),RR]],Dumb[0]); - else Dumb[0]=cons([[1,K*log(Log)]],Dumb[0]); - } - Log=red(subst(red(Log),Y,sin(XV*X/2)/cos(XV*X/2))); - Log=fshorter(Log,X|log=1); /* log(cos(2*x)+1)=-2*log(cos(x)) */ - Nm=fctr(nm(Log)); - for(T=[];Nm!=[];Nm=cdr(Nm)){ - if(ptype(car(Nm)[0],X)>1) T=cons(car(Nm),T); - } - Nm=fctr(dn(Log)); - for(;Nm!=[];Nm=cdr(Nm)){ - if(ptype(car(Nm)[0],X)>1) T=cons([car(Nm)[0],-car(Nm)[1]],T); - } - for(I=0,Nm=T;T!=[];T=cdr(T)){ - if(I=0) I=abs(car(T)[1]); - else I=igcd(I,car(T)[1]); - } - for(Log=1;Nm!=[];Nm=cdr(Nm)) Log*=car(Nm)[0]^(car(Nm)[1]/I); - K*=I; - if(cmpsimple(nm(Log),dn(Log))<0){ - K=-K;Log=red(1/Log); - } - Log=K*log(Log); - if(type(Dumb)==5){ - if(RR) Dumb[0]=cons([[1,Log,RR]],Dumb[0]); - else Dumb[0]=cons([[1,Log]],Dumb[0]); - } - }else Log=0; - for(Atan=0,Var=pfargs(RR=R,Y);Var!=[];Var=cdr(Var)){ - VTT=car(Var); - if(VTT[1]==atan){ - W=subst(VTT[2],Y,sin(XV*X/2)/cos(XV*X/2)); - W=trig2exp(W,X|inv=1); - V2=funargs(dn(W)); - if(type(V2)==4&&length(V2)==2){ - V3=V2[1]*mycoef(R,1,VTT[0]); - Z=0; - if(V2[0]==cos) - Z=red(W*cos(V2[1])/sin(V2[1])); - else if(V2[0]==sin){ - Z=red(W*sin(V2[1])/cos(V2[1])); - V3=-V3; - } - if(Z==1){ - Atan+=V3;W=0; - }else if(Z==-1){ - Atan-=V3;W=0; - } - } - R0=mycoef(R,0,VTT[0]); - if(W!=0) Atan+=subst(R-R0,VTT[0],atan(W)); /* atan(W); */ - R=R0; - } - } - if(R!=0){ - R=subst(R,Y,sin(XV*X/2)/cos(XV*X/2)); - R=red(R); - R=trig2exp(nm(R),X|inv=1)/trig2exp(dn(R),X|inv=1); - } - if(type(Dumb)==5){ - F=0;WL=[]; - if(R){ - WL=cons(R,WL); - F++; - } - if(Atan){ - WL=cons(Atan,WL); - F++; - } - if(Log){ - WL=cons(Log,WL); - F++; - } - WL=cons(1,WL); - if(F>1) Dumb[0]=cons([WL],Dumb[0]); - } - R=red(R+Log+Atan); - if(Dumb==-1) mycat(["->",R]); - else if(type(Dumb)==5) Dumb[0]=cons([[1,R]],Dumb[0]); - return fshorter(R,X); - } - } - } - VT=pfargs(Q=P,X|level=1); - V=(iand(ptype(P,X),7)<3)?[X]:[]; - for(;VT!=[];VT=cdr(VT)) - if(ptype(P,car(VT)[0])<3) V=cons(car(VT)[0],V); - if(length(V)>0){ /* 1/x+tan(x)+... etc.: sums */ - for(R=0;V!=[];V=cdr(V)){ - T=mycoef(Q,0,car(V)); - W[0]=[]; - S=integrate(TD=red(Q-T),X|dumb=D2,mult=Mul,exe=1); - if(S==[]) continue; - if(type(Dumb)==5){ - WL=0; - if(T!=0) WL=[[X,TD,T]]; - if(R!=0) WL=cons([1,R],WL); - if(WL) Dumb[0]=cons(WL,Dumb[0]); - TD=W[0]; - if(R!=0||T!=0){ - for(W0=[],TD=reverse(TD);TD!=[];TD=cdr(TD)){ - if(car(TD)[0][0]){ - WL=(!T)?[]:[[X,T]]; - WL=append(car(TD),WL); - if(R!=0) WL=cons([1,R],WL); - }else WL=car(TD); - Dumb[0]=cons(WL,Dumb[0]); - } - }else Dumb[0]=append(TD,Dumb[0]); - } - R+=S;Q=T; - if(!Q) return red(R); - } - W[0]=[]; - if(P!=Q&&type(S=integrate(Q,X|dumb=D2,mult=Mul))<4){ - RR=red(R+S); - if(type(Dumb)==5){ - TD=W[0]; - for(W0=[],TD=reverse(TD);TD!=[];TD=cdr(TD)){ - if(car(TD)[0][0]){ - WL=cons([1,R],car(TD)); - Dumb[0]=cons(WL,Dumb[0]); - } - else Dumb[0]=append(TD,Dumb[0]); - } - if(nmono(R)+nmono(S)!=nmono(RR)) Dumb[0]=cons([[1,R,S]],Dumb[0]); - } - return RR; - } - } - if(Dumb!=1) mycat(SM); - return []; -} - -def fimag(P) -{ - for(V=vars(P);V!=[];V=cdr(V)){ - Q=[]; - if(vtype(VF=car(V))==2){ - VAA=args(VF); - if(VAA==[]) continue; - VA=sqrt2rat(VAA[0]); - if(functor(VF)==exp){ - if(imag(VA)!=0){ - R=(real(VA)!=0)?exp(real(VA)):1; - Q=subst(P,VF,R*(cos(imag(VA))+sin(imag(VA))*@i)); - } - }else if(functor(VF)==pow){ - VA=sqrt2rat(VAA[1]); - if(imag(VA)!=0){ - R=(real(VA)!=0)?VAA[0]^(real(VA)):1; - L=(VAA[0]!=@e)?log(VAA[0]):1; - Q=subst(P,VAA[0]^(VAA[1]),R*(cos(L*imag(VA))+sin(L*imag(VA))*@i)); - }else if(VAA[1]!=(V0=fimag(VA))) - Q=subst(P,VAA[0]^(VAA[1]),VAA[0]^(V0)); - } - V0=VA; - if(length(VAA)==1&&(VAA[0]!=V0||VA!=(V0=fimag(VA)))) - Q=subst(P,VF,subst(VF,VAA[0],V0)); - } - if(Q!=[]&&P!=Q){ - P=Q;V=cons(0,vars(P)); - } - } - return P; -} - - -def trig2exp(P,X) -{ - if(iand(ptype(P,X),128)){ - OL=getopt(); - Nm=trig2exp(nm(P),X|option_list=OL); - Dn=trig2exp(dn(P),X|option_list=OL); - R=red(Nm/Dn); - if(getopt(arc)==1) return sqrt2rat(R); - } - if((Inv=getopt(inv))==1||type(Inv)==2){ - for(VT=T=vars(P);T!=[];T=cdr(T)){ - if(findin(functor(car(T)),[cos,sin,tan])>=0){ - P=trig2exp(P,X);VT=vars(P);break; - } - } - for(;VT!=[];VT=cdr(VT)){ - if(functor(CT=car(VT))==exp){ - if((Re=real(args(CT)[0]))!=0){ - if(isint(Re)) S=@e^Re; - else S=exp(Re); - }else S=1; - if((Im=imag(args(CT)[0]))!=0){ - Q=nm(Im);Q=mycoef(Q,mydeg(Q,X),X); - if(-Q>Q) S*=cos(-Im)-@i*sin(-Im); - else S*=cos(Im)+@i*sin(Im); - } - P=subst(P,CT,S); - } - } - P=red(P); - U=vars(Inv); - if(length(U)!=1||((F=functor(car(U)))!=sin&&F!=cos&&F!=tan)) return P; - XX=args(car(U))[0]; - if(mydeg(XX,X)!=1) return P; - if(!isvar(XX)) P=subst(P,X,(X-mycoef(XX,0,X))/mycoef(XX,1,X)); - for(VT=vars(P);VT!=[];VT=cdr(VT)){ - if(vtype(CT=car(VT))<2) continue; - TX=args(CT)[0]; - if(mydeg(TX,X)!=1) continue; - if(!isint(C1=mycoef(TX,1,X))) continue; - if((C0=mycoef(TX,0,X))==0){ - CC=1;CS=0; - }else if(vars(C0)==[@pi]){ - CC=myval(cos(C0)); - if(CC!=0&&type(CC)==1&&ntype(CC)!=0){ - CC=cos(C0);CS=sin(C0); - }else CS=myval(sin(C0)); - }else{ - CC=cos(C0);CS=sin(C0); - } - K=C1; - if(K<0) K=-K; - for(CC1=0,I=K;I>=0;I-=2) CC1+=(-1)^((K-I)/2)*binom(K,I)*cos(X)^I*sin(X)^(K-I); - for(CS1=0,I=K-1;I>=0;I-=2) CS1+=(-1)^((K-I-1)/2)*binom(K,I)*cos(X)^I*sin(X)^(K-I); - if(C1<0) CS1=-CS1; - if((TF=functor(CT))==cos) P=subst(P,cos(TX),CC1*CC-CS1*CS); - else if(TF==sin) P=subst(P,sin(TX),CS1*CC+CC1*CS); - } - if(F==sin) - P=substblock(P,cos(X),cos(X)^2,1-sin(X)^2); - else{ - P=substblock(P,sin(X),sin(X)^2,1-cos(X)^2); - if(F==tan){ - P=subst(P,sin(X),cos(X)*tan(X)); - P=substblock(P,cos(X),cos(X)^2,1/(tan(X)^2+1)); - } - } - if(!isvar(XX)) P=subst(P,X,XX); - - if(getopt(arc)==1){ - for(VT=vars(P);VT!=[];VT=cdr(VT)){ - FA=funargs(car(VT)); - if(type(FA)==4&&(FA[0]==cos||FA[0]==sin)&&ptype(FA[1],X)>60){ - VTT=vars(FA[1]); - if(type(FA[1])!=2||length(VTT)!=1) break; - FB=funargs(VTT[0]); - if(type(FB)!=4||(FF=findin(FB[0],[asin,acos,atan]))<0) break; - if(!isint(2*(C=mycoef(FA[1],1,VTT[0])))||mycoef(FA[1],0,VTT[0])!=0) break; - if(C==1/2){ - if(FF==1){ - U=(FA[0]==cos)?(1+FB[1])/2:(1-FB[1])/2; - P=subst(P,car(VT),red(U)^(1/2)); - }else if(FF==2){ - if(FA[0]==sin){ - FB1=red(FB[1]); - Nm=nm(FB1);CC=fctr(Nm)[0][0];Dn=dn(FB1); - if(CC<0) CC=-CC; - Nm/=CC;Dn/=CC; - NN=Nm^2+Dn^2; - P=subst(P,car(VT),((NN)^(1/2)-Dn)/Nm*cos(FA[1])); - } - } - P=red(P); - }else if(C==1){ - if(FF==1){ - if(FA[0]==cos) P=subst(P,car(VT),FB[1]); - else P=subst(P,car(VT),(1-FB[1])^(1/2)); - }else if(FF==0){ - if(FA[0]==sin) P=subst(P,car(VT),FB[1]); - else P=subst(P,car(VT),(1-FB[1])^(1/2)); - } - P=red(P); - } - } - } - P=sqrt2rat(P); - } - return red(P); - } - Var=pfargs(P,X); - for(VT=Var;VT!=[];VT=cdr(VT)){ - CT=car(VT); - if(CT[1]==cos) - P=subst(P,CT[0],exp(CT[2]*@i)/2+exp(-CT[2]*@i)/2); - else if(CT[1]==sin) - P=subst(P,CT[0],exp(-CT[2]*@i)*@i/2-exp(CT[2]*@i)*@i/2); - else if (CT[1]==tan) - P=subst(P,CT[0],(exp(-CT[2]*@i)*@i-exp(CT[2]*@i)*@i)/(exp(CT[2]*@i)+exp(-CT[2]*@i))); - else if(CT[1]==pow){ - if(ptype(CT[2],X)>1) continue; - if(CT[2]==@e) P=subst(P,CT[0],exp(CT[3])); - else P=subst(P,CT[0],exp(log(CT[2])*exp(CT[3]))); - } - } - P=red(P); - for(PP=1,Lp=(dn(P)==1)?1:0;Lp<2;Lp++){ - PP=1/PP; - U=(Lp==0)?dn(P):nm(P); - if(U==1) continue; - Var=vars(U); - for(R=[],VT=Var;VT!=[];VT=cdr(VT)) - if(functor(car(VT))==exp) R=cons(car(VT),R); - RR=os_md.terms(U,R); - for(Q=0,RRT=RR;RRT!=[];RRT=cdr(RRT)){ - for(S=0,CT=cdr(car(RRT)),CR=R,UT=U;CR!=[];CR=cdr(CR),CT=cdr(CT)){ - UT=mycoef(UT,car(CT),car(CR));S+=car(CT)*args(car(CR))[0]; - } - if(S==0) Q+=UT; - else Q+=UT*exp(S); - } - PP*=Q; - } - return PP; -} - -def powsum(N) -{ - if (N < 0) return 0; - if (N == 0) return x; - P = intpoly(N*powsum(N-1),x); - C = subst(P,x,1); - return P+(1-C)*x; -} - -def bernoulli(N) -{ - return mydiff(powsum(N),x) - N*x^(N-1); -} - -/* linfrac01([x,y]) */ -/* linfrac01(newvect(10,[0,1,2,3,4,5,6,7,8,9]) */ -/* 0:x=0, 1:x=y, 2:x=1, 3:y=0, 4:y=1, 5:x=\infty, 6:y=\infty, 7:x=y=0, 8:x=y=1, 9:x=y=\infty - 10:y_2=0, 11:y_2=x, 12:y_2=y, 13: y_2=1, 14: y_2=\infty - 15:y_3=0, 16:y_3=x, 17:y_3=y, 18: y_3=y_2, 19: y_3=1, 20:y_3=\infty - X[0],X[11],X[2],X[10],X[13],X[5],X[14],X[7],X[8],X[9], - X[3],X[1],X[12],X[4],X[6] - - T=0 (x_2,x_1,x_3,x_4,...) - T=-j (x_1,x_2,..,x_{j-1},x_{j+1},x_j,x_{j+2},...) - T=1 (1-x_1,1-x_2,1-x_3,1-x_4,...) - T=2 (1/x_1,1/x_2,1/x_3,1/x_4,...) - T=3 (x_1,x_1/x_2,x_1/x_3,x_1/x_4,...) -*/ - -def lft01(X,T) -{ - MX=getopt(); - if(type(X)==4){ - K=length(X); - if(K>=1) D=1; - } - if(type(X)==5){ - K=length(X); - for(J=5, F=K-10; F>0; F-=J++); - if(F==0) D=2; - } - if(D==0) return 0; - if(T==0){ /* x <-> y */ - if(D==1){ - R=cdr(X); R=cdr(R); - R=cons(X[0],R); - return cons(X[1],R); - } - R=newvect(K,[X[3],X[1],X[4],X[0],X[2],X[6],X[5]]); - for(I=7;I<K;I++) R[I]=X[I]; - for(I=11,J=5; I<K; I+=J++){ - R[I]=X[I+1]; R[I+1]=X[I]; - } - return R; - } - if(T==1){ - if(D==1){ - for(R=[];X!=[];X=cdr(X)) R=cons(1-car(X),R); - return reverse(R); - } - R=newvect(K,[X[2],X[1],X[0],X[4],X[3],X[5],X[6],X[8],X[7],X[9]]); - for(I=11;I<K;I++) R[I]=X[I]; - for(I=10, J=5; I<K; I+=J++){ - R[I]=X[I+J-2]; R[I+J-2]=X[I]; - } - return R; - } - if(T==2){ - if(D==1){ - for(R=[]; X!=[]; X=cdr(X)) R=cons(red(1/car(X)),R); - return reverse(R); - } - R=newvect(K,[X[5],X[1],X[2],X[6],X[4],X[0],X[3],X[9],X[8],X[7]]); - for(I=11;I<K;I++) R[I]=X[I]; - for(I=10,J=5; I<K; I+=J++){ - R[I]=X[I+J-1]; R[I+J-1]=X[I]; - } - return R; - } - if(T==3){ - if(D==1){ - T=car(X); - for(R=[T],X=cdr(X); X!=[]; X=cdr(X)) - R=cons(red(T/car(X)),R); - return reverse(R); - } - R=newvect(K,[X[7],X[4],X[2],X[6],X[1],X[9],X[3],X[0],X[8],X[5]]); - for(I=10,J=5; I<K; I+=J++){ - R[I]=X[I+J-1]; R[I+1]=X[I+J-2]; R[I+J-2]=X[I+1]; R[I+J-1]=X[I]; - } - return R; - } - if(T==-1){ - if(D==1){ - return append([X[1],X[2],X[0]],cdr(cdr(cdr(X)))); - } - R=newvect(K,[X[0],X[11],X[2],X[10],X[13],X[5],X[14],X[7],X[8],X[9], - X[3],X[1],X[12],X[4],X[6]]); - for(I=11;I<K;I++) R[I]=X[I]; - for(I=17,J=5; I<K; I+=J++){ - R[I]=X[I+1]; R[I+1]=X[I]; - } - return R; - } - if(T<0){ - if(D==1){ - for(R=[],I=0; X!=[]; X=cdr(X),I--){ - if(I==T){ - R=cons(X[1],R); - R=cons(X[0],R); - X=cdr(X); - } - else R=cons(car(X),R); - } - return reverse(R); - } - T=3-T; - R=newvect(K); - for(I=0;I<K;I++) R[I]=X[I]; - for(I=10,J=5;J<T;I+=J++); - for(II=0; II<J-2; II++){ - R[I]=X[I+J]; R[I+J]=R[I]; - } - for( ; II<J; II++){ - R[I]=X[I+J+1]; R[I+J+1]=X[I]; - } - return R; - } - return 0; -} - -def linfrac01(X) -{ - if(type(X)==4) K=length(X)-2; - else if(type(X)==5){ - L=length(X); - for(K=0,I=10,J=5; I<L; K++,I+=J++); - if(I!=L) return 0; - } - if(K>3 && getopt(over)!=1) return(-1); - II=(K==-1)?3:4; - for(CC=C=1,L=[X]; C!=0; CC+=C){ - for(F=C,C=0,R=L; F>0; R=cdr(R), F--){ - P=car(R); - for(I=-K; I<II; I++){ - S=lft01(P,I); - if(findin(S,L) < 0){ - C++; L=cons(S,L); - } - } - } - } - return L; -} - - -def varargs(P) -{ - if((All=getopt(all))!=1) All=0; - V=vars(P); - for(Arg=FC=[];V!=[];V=cdr(V)){ - if(vtype(CV=car(V))==0&&All==1){ - Arg=lsort([CV],Arg,0); - } - if(vtype(CV)!=2) continue; - if(findin(F=functor(CV),FC)<0) FC=cons(F,FC); - for(AT=vars(args(CV));AT!=[];AT=cdr(AT)){ - if(vtype(X=car(AT))<2){ - if(findin(X,Arg)<0) Arg=cons(X,Arg); - }else if(vtype(X)==2){ - R=varargs(X); - if(R[1]!=[]){ - Arg=lsort(R[1],Arg,0); - FC=lsort(R[0],FC,0); - } - } - } - } - return [FC,Arg]; -} - -def pfargs(P,X) -{ - if(type(L=getopt(level))!=1) L=0; - for(Var=[],V=vars(P);V!=[];V=cdr(V)){ - if(vtype(car(V))==2){ - VT=funargs(car(V)); - if(length(VT)>1){ - if(L<2 &&(ptype(VT[1],X)>1 || (length(VT)>2 && ptype(VT[2],X)>1))) - Var=cons(cons(car(V),VT),Var); - if(L!=1 && (R=pfargs(VT[1],X|level=L-1))!=[]) Var=append(R,Var); - } - } - } - return reverse(Var); -} - -def ptype(P,L) -{ - if((T=type(P))<2 || T>3) return T; - if(type(L)!=4) L=[L]; - F=0; - if(lsort(L,varargs(dn(P))[1],2)!=[]) F=128; - if(lsort(L,varargs(nm(P))[1],2)!=[]) F+=64; - if(lsort(L,vars(dn(P)),2)!=[]) return F+3; - return (lsort(L,vars(nm(P)),2)==[])?(F+1):(F+2); -} - -def nthmodp(X,N,P) -{ - X=X%P; - for(Z=1;;){ - if((W=iand(N,1))==1) Z=(Z*X)%P; - if((N=(N-W)/2)<=0) return Z; - X=irem(X*X,P); - } -} - -def issquaremodp(X,P) -{ - N=getopt(power); - if(!isint(N)) N=2; - if(P<=1 || !isint(P) || !pari(ispsp,P) || !isint(X) || !isint(N) || N<1){ - errno(0); - return -2; - } - M=(P-1)/igcd(N,P-1); - if((X%=P) == 0) return 0; - if(X==1 || M==P-1) return 1; - return (nthmodp(X,M,P)==1)?1:-1; -} - -def iscoef(P,F) -{ - if(P==0) return 1; - if(type(P)==1) return F(P); - if(type(P)==2) { - X=var(P); - for(I=deg(P,X); I>=0; I--){ - if(!iscoef(mycoef(P,I,X),F)) return 0; - } - }else if(type(P)==3){ - if(!iscoef(nm(P),F)||!iscoef(dn(P),F)) return 0; - }else if(type(P)==4){ - for(;P!=[];P=cdr(P)) if(!iscoef(P,F)) return 0; - }else if(type(P)>4 && type(P)<7) return iscoef(m2l(PP),F); - else return 0; - return 1; -} - -def rootmodp(X,P) -{ - X%=P; - if(X==0) return [0]; - N=getopt(power); - PP=pari(factor,P); - P0=PP[0][0]; P1=PP[0][1]; - P2=pari(phi,P); - if(!isint(N)) N=2; - N%=P2; - if(P0==2 || size(PP)[0]>1){ - for(I=1,R=[]; I<P2; I++) - if(nthmodp(I,N,P)==X) R=cons(I,R); - return qsort(R); - } - Y=primroot(P); - if(Y==0) return 0; - Z=nthmodp(Y,N,P); - G=igcd(N,P2); - P3=P2/G; - for(I=0, W=1; I<P3;I++){ - if(W==X) break; - W=(W*Z)%P; - } - if(I==P3) return []; - W=nthmodp(Y,I,P); - Z=nthmodp(Y,P3,P); - for(I=0,R=[];;){ - R=cons(W,R); - if(++I>=G) break; - W=(W*Z)%P; - } - return qsort(R); -} - -def primroot(P) -{ - PP=pari(factor,P); - P0=PP[0][0]; P1=PP[0][1]; - S=size(PP); - if(S[0]>1 || !isint(P) || P0<=2){ - print("Not odd prime(power)!"); - return 0; - } - if(isint(Ind=getopt(ind))){ - Ind %= P; - if(Ind<=0 || igcd(Ind,P)!=1 || (Z=primroot(P))==0){ - print("Not exist!"); - return 0; - } - P2=P0^(P1-1)*(P0-1); - for(I=1,S=1; I<P2; I++) - if((S = (S*Z)%P) == Ind) return I; - return 0; - } - if(getopt(all)==1){ - I=primroot(P); - P2=P0^(P1-1)*(P0-1); - for(L=[],J=1; J<P2; J++){ - if(P1>1 && igcd(P0,J)!=1) continue; - if(igcd(P0-1,J)!=1) continue; - L=cons(nthmodp(I,J,P),L); - } - return qsort(L); - } - if(PP[0][1]>1){ - I=primroot(P0); - P2=P0^(P1-2)*(P0-1); - if(nthmodp(I,P2,P)==1) I+=P0; - return I; - } - F=pari(factor,P-1); - SF=size(F)[0]; - for(I=2; I<P; I++){ - for(J=0; J<SF; J++) - if(nthmodp(I,(P-1)/F[J][0],P)==1) break; - if(J==SF) return I; - } -} - -def rabin(P,X) -{ - for(M=0,Q=P-1;iand(Q,1)==0;M++,Q/=2); - Z=nthmodp(X,Q,P); - for(N=M;M>0&&Z!=1&&Z!=P-1;M--,Z=(Z*Z)%P); - return (M<N&&(M==0||Z==1))?0:1; -} - -def powprimroot(P,N) -{ - if(P<3) P=3; - FE=getopt(exp); - if(FE!=1) FE=0; - if((Log=getopt(log))==1||Log==2) FE=-1; - else if(Log==3){ - FE=-2; - for(PP=1, L0=["$r$","$p/a$"];;){ - PP=pari(nextprime,PP+1); - if(PP>=P) break; - L0=cons(PP, L0); - } - L0=reverse(L0); - } - if(FE==0) All=getopt(all); - for(I=0, PP=P, LL=[]; I<N; I++,PP++){ - PP=pari(nextprime,PP); - if(All==1){ - PR=primroot(PP|all=1); - LL=cons(cons(PP,PR),LL); - continue; - } - PR=primroot(PP); - if(FE==-2){ /* log=3 */ - LT=cdr(L0);LT=cdr(L0); - for(L=[PP];LT!=[];LT=cdr(LT)) - L=cons(primroot(PP|ind=car(LT)),L); - LL=cons(reverse(L),LL); - if(I<N-1) L0=append(L0,[PP]); - }else if(FE){ - for(J=1, L=[PP], K=1; J<PP; J++){ - if(FE==-1){ /* log=1,2 */ - K=primroot(PP|ind=J); - if(K==0 && Log==2) K=PP-1; - } - else K=(K*PR)%PP; /* exp=1 */ - L=cons(K,L); - } - LL=cons(reverse(L),LL); - }else - LL=cons([PP,PR],LL); /* default */ - } - LL=reverse(LL); - if(!FE) return LL; - PP--; - if(FE==-2) return append(LL,[L0]); - for(I=1,L=["$p$"];I<PP; I++) L=cons(I,L); - return cons(reverse(L),LL); -} - -def ntable(F,II,D) -{ - F=f2df(F|opt=-1); - Df=getopt(dif); - Str=getopt(str); - if(Df!=1) Df=0; - L=[]; - if(type(D)==4){ - if(type(II[0])==4){ - T1=II[0][1]-II[0][0];T2=II[1][1]-II[1][0]; - for(L0=[],I=0;I<D[0];I++){ - for(R=[],J=0;J<D[1];J++) - R=cons(myf2eval(F,II[0][0]+I*T1/D[0],II[1][0]+J*T2/D[1]),R); - L=cons(reverse(R),L);L0=cons(II[0][0]+I*T1/D[0],L0); - } - }else{ - for(T=II[1]-II[0],L0=[],I=0;I<D[0];I++){ - for(R=[],J=0;J<D[1];J++) - R=cons(myfdeval(F,II[0]+I*T/D[0]+J*T/D[0]/D[1]),R); - L=cons(reverse(R),L);L0=cons(II[0]+I*T/D[0],L0); - } - } - L=reverse(L);L0=reverse(L0); - if(type(Str)==4){ - L0=mtransbys(os_md.sint,L0,[Str[0]]|str=1,zero=0); - L=mtransbys(os_md.sint,L,[Str[1]]|str=1,zero=0); - if(Df==1){ - for(DT=[],RT=L,I=0;RT!=[];){ - for(LT=[],TT=car(RT);TT!=[];TT=cdr(TT)){ - VV=car(TT); - if((J=str_char(VV,0,"."))>=0){ - if(J==0) VV=str_cut(VV,1,10000); - else VV=str_cut(VV,0,J-1)+str_cut(VV,J+1,10000); - } - V1=eval_str(VV); - if(I++) LT=cons(V1-V0,LT); - V0=V1; - } - DT=cons(LT,DT); - if((RT=cdr(RT))==[]){ - VE=rint(myfdeval(F,II[1])*10^Str[1]); - DT=cons([VE-V0],DT); - } - } - for(I=0,D=[],TT=DT;TT!=[];TT=cdr(TT)){ - if(!I++) V=car(TT)[0]; - else{ - T1=reverse(cons(V,car(TT))); - V=car(T1); - if(length(TT)>1) T1=cdr(T1); - D=cons(T1,D); - } - } - for(DD=[],TT=D;TT!=[];TT=cdr(TT)) - DD=cons([os_md.lmin(car(TT)),os_md.lmax(car(TT))],DD); - DD=reverse(DD); - L=lsort(L,DD,"append"); - } - } - L=lsort(L,L0,"cons"); - if(type(Top=getopt(top))==4||getopt(TeX)==1){ - if(type(Top)==4){ - K=length(L[0])-length(Top); - if(K>0&&K<4){ - if(K>1){ - Top=append(Top,["",""]); - K-=2; - } - if(K) Top=cons("",Top); - } - L=cons(Top,L); - } - if(type(H=getopt(hline))!=4) H=[0,1,z]; - if(type(V=getopt(vline))!=4) V=[0,1,(DF)?z-2:z]; - if(type(T=getopt(title))!=7) Out=ltotex(L|opt="tab",hline=H,vline=V); - else Out=ltotex(L|opt="tab",hline=H,vline=V,title=T); - if(Df) Out=str_subst(Out,"\\hline","\\cline{1-"+rtostr(length(L[0])-2)+"}"); - return Out; - } - return L; - } - for(L=[],I=0;I<=D;I++){ - X=II[0]+I*T/D; - L=cons([X,myfdeval(F,X)],L); - } - if(Df==1){ - for(LD=[],LL=L;LL!=[];LL=cdr(LL)){ - if(LD==[]) LD=cons([car(LL)[0],car(LL)[1],0],LD); - else LD=cons([car(LL)[0],car(LL)[1],abs(car(LL)[1]-car(LD)[1])],LD); - } - L=reverse(LD); - } - if(type(Str)==4){ - if(length(Str)==1) Str=[Str[0],Str[0]]; - if(Df==1 && length(Str)==2) Str=[Str[0],Str[1],Str[1]]; - for(S=Str,Str=[];S!=[];S=cdr(S)){ - if(type(car(S))!=4) Str=cons([car(S),3],Str); - else Str=cons(car(S),Str); - } - Str=reverse(Str); - for(LD=[],LL=L;LL!=[];LL=cdr(LL)){ - for(K=[],J=length(Str); --J>=0; ) - K=cons(sint(car(LL)[J],Str[J][0]|str=Str[J][1]),K); - LD=cons(K,LD); - } - L=LD; - }else - L=reverse(L); - if(type(M=getopt(mult))==1){ - Opt=[["opt","tab"],["vline",[[0,2+Df]]],["width",-M]]; - if(type(T=getopt(title))==7) - Opt=cons(["title",T],Opt); - if(type(Tp=getopt(top))==4) - Opt=cons(["top",Tp],Opt); - L=ltotex(L|option_list=Opt); - } - return L; -} - -def distpoint(L) -{ - L=m2l(L|flat=1); - if(getopt(div)==5) Div=5; - else Div=10; - V=newvect(100/Div); - for(LT=L,LL=[],N=0; LT!=[]; LT=cdr(LT)){ - if(type(K=car(LT))>1||K<0){ - N++; continue; - } - LL=cons(K,LL); - T=idiv(K,Div); - if(Div==10 && T>=9) T=9; - else if(Div==5 && T>=19) T=19; - V[T]++; - } - V=vtol(V); - if((Opt=getopt(opt))=="data") return V; - Title=getopt(title); - OpList=[["opt","tab"]]; - if(type(Title=getopt(title)) == 7) - OpList=cons(["title",Title],OpList); - if(Opt=="average"){ - T=isMs()?["平均点","標準偏差","最低点","最高点","受験人数"]: - ["average","deviation","min","max","examinees"]; - L=average(LL); - L=[sint(L[0],1),sint(L[1],1),L[3],L[4],L[2]]; - if(N>0){ - T=append(T,[isMs()?"欠席者":"absentees"]);L=append(L,[N]); - } - OpList=cons(["align","c"],OpList); - return ltotex([T,L]|option_list=OpList); - } - - if(getopt(opt)=="graph"){ - Mul=getopt(size); - if(Div==5){ - V0=["00","05","10","15","20","25","30","35","40","45","50","55", - "60","65","70","75","80","85","90","95"]; - if(type(Mul)!=4){ - Size = (TikZ)?[12,3,1/2,0.2]:[120,30,1/2,2]; - } - }else{ - V0=["00-","10-","20-","30-","40-","50-","60-","70-","80-","90-"]; - if(type(Mul)!=4){ - Size = (TikZ)?[8,3,1/2,0.2]:[80,30,1/2,2]; - } - } - return ltotex([V,V0]|opt="graph",size=Size); - } - if(Div==5) - V0=["00--04","05--09","10--14","15--19", "20--24", "25--29", "30--34", "35-39", - "40--44", "45--49","50--54", "55--59","60--64", "65--69", - "70--74", "75--79","80--84", "85--89","90--94", "95--100"]; - else - V0=["00--09","10--19","20--29","30--39","40--49","50--59","60--69", - "70--79","80--89","90--100"]; - Title=getopt(title); - return ltotex([V0,V]|option_list=OpList); -} - -def keyin(S) -{ - print(S,2); - purge_stdin(); - S=get_line(); - L=length(S=strtoascii(S)); - if(L==0) return ""; - return str_cut(S,0,L-2); -} - -def init() { - LS=["DIROUT","DVIOUTA","DVIOUTB","DVIOUTH","DVIOUTL","TeXLim","TeXEq","TikZ", - "XYPrec","XYcm","Canvas"]; - if(!access(get_rootdir()+"/help/os_muldif.dvi")||!access(get_rootdir()+"/help/os_muldif.pdf")) - mycat(["Put os_muldif.dvi and os_muldif.pdf in", get_rootdir()+(isMs()?"\\help.":"/help.")]); - if(!isMs()){ - DIROUT="%HOME%/asir/tex"; - DVIOUTA=str_subst(DVIOUTA,[["\\","/"],[".bat",".sh"]],0); - DVIOUTB=str_subst(DVIOUTB,[["\\","/"],[".bat",".sh"]],0); - DVIOUTL=str_subst(DVIOUTL,[["\\","/"],[".bat",".sh"]],0); - DVIOUTH="%ASIRROOT%/help/os_muldif.pdf"; - } - Home=getenv("HOME"); - if(type(Home)!=7) Home=""; - for(Id=-7, F=Home; Id<-1;){ - G = F+"/.muldif"; - if(access(G)) Id = open_file(G); - else Id++; - if(Id==-6) F+="/asir"; - else if(Id==-5) F=get_rootdir(); - else if(Id==-4) F+="/bin"; - else if(Id==-3) F=get_rootdir()+"/lib-asir-contrib"; - } - if(Id>=0){ - while((S=get_line(Id))!=0){ - if(type(P=str_str(S,LS))==4 && (P0=str_char(S,P[1]+5,"="))>0){ - if(P[0]<5){ - P0=str_chr(S,P0+1,"\""); - if(P0>0){ - for(P1=P0;(P2=str_char(S,P1+1,"\""))>0; P1=P2); - if(P1>P0+1){ - SS=str_cut(S,P0+1,P1-1); - SS=str_subst(SS,["\\\\","\\\""],["\\","\""]); - if(P[0]==0) DIROUT=SS; - else if(P[0]==1) DVIOUTA=SS; - else if(P[0]==2) DVIOUTB=SS; - else if(P[0]==3) DVIOUTH=SS; - else if(P[0]==4) DVIOUTL=SS; - } - } - if(P0<0 || P1<P0+2) mycat(["Error! Definiton of", LS[P[0]], - "in .muldif"]); - }else{ - SV=eval_str(str_cut(S,P0+1,str_len(S)-1)); - if(P[0]==5) TeXLim=SV; - else if(P[0]==6) TeXEq=SV; - else if(P[0]==7) TikZ=SV; - else if(P[0]==8) XYPrec=SV; - else if(P[0]==9) XYcm=SV; - else if(P[0]==10) XYcm=Canvas; - } - } - } - close_file(Id); - } - chkfun(1,0); -} - -#ifdef USEMODULE -endmodule; -os_md.init()$ -#else -init()$ -#endif - -end$ |