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diff --git a/texmf-dist/scripts/ketcindy/ketlib/oshima/os_muldif.rr b/texmf-dist/scripts/ketcindy/ketlib/oshima/os_muldif.rr
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+/* The latest version will be at ftp://akagi.ms.u-tokyo.ac.jp/pub/math/muldif
+ scp os_muldif.[dp]* ${USER}@lemon.math.kobe-u.ac.jp:/home/web/OpenXM/Current/doc/other-docs
+*/
+#define USEMODULE 1
+/* #undef USEMODULE */
+
+/* os_muldif.rr (Library for Risa/Asir)
+ * Toshio Oshima (Nov. 2007 - Aug. 2017)
+ *
+ * For polynomials and differential operators with coefficients
+ * in rational funtions (See os_muldif.pdf)
+ *
+ * "Tab = 4 column" is best
+ */
+
+ord([zz,dz,dy,dx])$
+
+#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 orthpoly$
+localf schurpoly$
+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 sgn$
+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 addIL$
+localf xy2curve$
+localf xygrid$
+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="00170825"$
+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=varargs(L|all=2);
+ 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){
+ if(type(DIROUTD)!=7){
+ DIROUTD=str_subst(DIROUT,["%HOME%","%ASIRROOT%","\\"],
+ [getenv("HOME"),get_rootdir(),"/"])+"/";
+ if(isMs()) DIROUTD=str_subst(DIROUTD,"/","\\"|sjis=1);
+ }
+ if(S==-1) return;
+ 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;
+ }
+ R=output(S);
+ print(X);
+ output();
+ if(getopt(exe)==1) shell("\""+S+"\"");
+ return R;
+}
+
+def mycat0(L,T)
+{
+ Opt = getopt(delim);
+ Del = (type(Opt) >= 0)?Opt:"";
+ if(type(L)!=4) L=[L];
+ 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(ptype(dn(P),X)<2)
+ 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;
+ Pr=getopt(prec);
+ if(type(L)!=4){
+ if(L==2){
+ L=(Pr!=1)?
+ [[[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]]]:
+ [[[1,2,1/50],[2,5,1/20],[5,10,1/10], [10,20,1/5],[20,50,1/2],[50,100,1]],
+ [[1,5,1/10],[5,10,1/2], [10,20,1],[50,100,5]],
+ [[1,5,1/2],[5,10,1], [10,50,5],[50,100,10]]];
+ LS=2;
+ }else if(L==3){
+ L=(Pr!=1)?
+ [[[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]]]:
+ [[[1,2,1/50],[2,5,1/20],[5,10,1/10],[10,20,1/5],[20,50,1/2],[50,100,1],
+ [100,200,2],[200,500,5],[500,1000,10]],
+ [[1,5,1/10],[5,10,1/2], [10,50,1],[50,100,5], [100,500,10],[500,1000,50]],
+ [[1,5,1/2],[5,10,1], [10,50,5],[50,100,10], [100,500,50],[500,1000,100]]];
+ LS=3;
+ }else{
+ L=(Pr!=1)?
+ [[[1,2,1/50],[2,5,1/20],[5,10,1/10]],
+ [[1,5,1/10],[5,10,1/2]],
+ [[1,5,1/2],[5,10,1]]]:
+ [[[1,2,1/100],[2,5,1/50],[5,10,1/20]],
+ [[1,2,1/20],[2,10,1/10]],
+ [[1,2,1/10],[2,10,1/2]]];
+ }
+ }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(SC)==1){
+ S0=SC;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=M0=[],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 M0=cons(V+D0,M0);
+ }
+ if(S1==0) M=cons(reverse(M0),M);
+ }
+ if(S1!=0) M=cdr(M);
+ if(S1==0||getopt(TeX)!=1) return M;
+ M=reverse(M);
+ if(type(U=getopt(line))==4)
+ M=cons([U[0]+D0,D1],cons([U[1]+D0,D1],cons(0,M)));
+ if(type(Col=getopt(col))<1) S=xylines(M);
+ else S=xylines(M|opt=Col);
+ if(type(Mes=getopt(mes))==4){
+ S3=car(Mes);
+ if(type(S3)==4){
+ Col=S3[1];
+ S3=car(S3);
+ }else Col=0;
+ 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=car(Mes);M!=[];M=cdr(M),V=cdr(V)){
+ VT=deval(car(V));
+ if(Col!=0) VT=[Col,VT];
+ S+=xyput([car(M),S3,VT]);
+ }
+ }
+ return S;
+}
+
+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(type(X)==4){
+ if(getopt(deg)==1)
+ X=[deval(@pi*X[0]/180),deval(@pi*X[1]/180),deval(@pi*X[2]/180)];
+ if(getopt(conj)==1)
+ return mrot([-X[2],-X[1],0])*mrot([X[0],X[1],X[2]]);
+ if(X[1]==0){
+ X=[X[0]+X[2],0,0];
+ if(X[0]==0) return diagm(3,[1]);
+ }
+ if(X[0]!=0){
+ M=mat([dcos(X[0]),-dsin(X[0]),0],[dsin(X[0]),dcos(X[0]),0],[0,0,1]);
+ if(X[1]==0) return M;
+ }
+ N=mat([dcos(X[1]),0,-dsin(X[1])],[0,1,0],[dsin(X[1]),0,dcos(X[1])]);
+ if(X[0]!=0) N=M*N;
+ if(X[2]==0) return N;
+ return N*mrot([X[2],0,0]);
+ }
+ 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(N==0) return 1;
+ 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 sgn(X)
+{
+ if(X==0) return 0;
+ if(type(X)==1){
+ return (X>0)?1:-1;
+ }
+ if(type(X)==5) X=vtol(X);
+ if(type(X)==4){
+ for(W=0,Y=X;Y!=[];Y=cdr(Y))
+ for(Z=cdr(Y);Z!=[];Z=cdr(Z))
+ if(car(Y)>car(Z)) W++;
+ if(getopt(val)==1) return W;
+ return (iand(W,1))?-1:1;
+ }
+}
+
+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){
+ fcat(-1,0);
+ 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)
+{
+ 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 xygrid(X,Y)
+{
+ for(RR=[],I=0,Z=X;I<2;I++){
+ U=Z[2];L=LL=[];M=Z[3];
+ if(Z[1]==1||Z[1]==-1){
+ if(type(M)==4) L=M;
+ else{
+ if(U*(-dlog(1-1/20)/dlog(10))>=M){
+ L=cons([1,2,1/10],L);
+ LL=cons([1,2,1/2],LL);
+ }else if(U*(-dlog(1-1/10)/dlog(10))>=M)
+ L=cons([1,2,1/5],L);
+ else if(U*(-dlog(1-1/4)/dlog(10))>=M)
+ L=cons([1,2,1/2],L);
+ if(U*(-dlog(1-1/50)/dlog(10))>=M){
+ L=cons([2,5,1/10],L);
+ LL=cons([2,5,1/2],LL);
+ }else if(U*(-dlog(1-1/25)/dlog(10))>=M)
+ L=cons([2,5,1/5],L);
+ else if(U*(-dlog(1-1/10)/dlog(10))>=M)
+ L=cons([2,5,1/2],L);
+ if(U*(-dlog(1-1/100)/dlog(10))>=M){
+ L=cons([5,10,1/10],L);
+ LL=cons([5,10,1/2],LL);
+ }
+ else if(U*(-dlog(1-1/50)/dlog(10))>=M)
+ L=cons([5,10,1/5],L);
+ else if(U*(-dlog(1-1/20)/dlog(10))>=M)
+ L=cons([5,10,1/2],L);
+ L=cons(L,cons(LL,[[[1,10,1]]]));
+ }
+ R=scale(L|scale=U);
+ if(Z[1]==-1){
+ for(LL=[];R!=[];R=cdr(R)){
+ for(L=[],T=car(R);T!=[];T=cdr(T)) L=cons(U-car(T),L);
+ LL=cons(reverse(L),LL);
+ }
+ R=reverse(LL);
+ }
+ }else if(Z[1]==0){
+ if(type(M)==4){
+ R=scale(M|f=x,scale=U);
+ }else{
+ V=0;
+ if(U/10>=M) V=1/10;
+ else if(U/5>=M) V=1/5;
+ else if(U/2>=M) V=1/2;
+ R=[];
+ if(V>0){
+ UU=U*V;
+ for(R=[],J=UU;J<U;J+=UU) R=cons(J,R);
+ }
+ if(V==1/10) L=[U/2];
+ else L=[];
+ R=cons(R,cons(L,[[0,U]]));
+ }
+ }else if(type(Z[1])==4){
+ R=Z[1];
+ if(length(R)==0||type(R[0])!=4) R=[[],[],R];
+ }else return 0;
+ K=length(R);
+ S=newvect(K);
+ for(J=0;J<K;J++){
+ for(S[J]=[],JJ=0;JJ<=Z[0];JJ+=U){
+ for(P=R[J];P!=[];P=cdr(P))
+ if(car(P)+JJ<=Z[0]) S[J]=cons(car(P)+JJ,S[J]);
+ }
+ }
+ for(J=0;J<K;J++) S[J]=lsort(S[J],[],1);
+ for(U=[],J=K-1;J>0;J--){
+ U=lsort(S[J],U,0);S[J-1]=lsort(S[J-1],U,1);
+ }
+ RR=cons(vtol(S),RR);
+ Z=Y;
+ }
+ if((Raw=getopt(raw))==1) return RR;
+ SS=[];
+ if(type(Sf=getopt(shift))==7){
+ Sx=Sf[0];Sy=Sf[1];
+ }else Sx=Sy=0;
+ for(I=0;I<2;I++){
+ for(S0=[],L=RR[I];L!=[];L=cdr(L)){
+ for(S=[],T=car(L);T!=[];T=cdr(T)){
+ if(S!=[]) S=cons(0,S);
+ if(I==0){
+ S=cons([X[0]+Sx,car(T)+Sy],S);
+ S=cons([Sx,car(T)+Sy],S);
+ }else{
+ S=cons([car(T)+Sx,Y[0]+Sy],S);
+ S=cons([car(T)+Sx,Sy],S);
+ }
+ }
+ S0=cons(S,S0);
+ }
+ SS=cons(reverse(S0),SS);
+ }
+ SS=reverse(SS);
+ if(Raw==2) return SS;
+ if(length(Y)<5) T=[["",""]];
+ else if(type(Y[4])==4) T=[Y[4]];
+ else T=[Y[4],Y[4]];
+ if(length(X[4])==4) T=cons([""],T);
+ else if(type(X[4])==4) T=cons(X[4],T);
+ else T=cons([X[4]],T);
+ for(Sx=Sy=[],I=0;I<2;I++){
+ TT=T[I];
+ for(V=SS[I];V!=[];V=cdr(V)){
+ Op=car(TT);
+ if(length(TT)>1) TT=cdr(TT);
+ if(car(V)==[]) continue;
+ if(Op=="") S=xylines(car(V));
+ else S=xylines(car(V)|opt=Op);
+ if(I==0) Sx=cons(S,Sx);
+ else Sy=cons(S,Sy);
+ }
+ }
+ for(S="",Sx=reverse(Sx), Sy=reverse(Sy);Sx!=[]&&Sy!=[];){
+ if(Sx!=[]){
+ S+=car(Sx);Sx=cdr(Sx);
+ }
+ if(Sy!=[]){
+ S+=car(Sy);Sy=cdr(Sy);
+ }
+ }
+ return S;
+}
+
+
+def addIL(I,L)
+{
+ if(I==0){
+ for(R=[];L!=[];L=cdr(L)) R=addIL(car(L),R);
+ return reverse(R);
+ }
+ if(type(In=getopt(in))==1){
+ if(In==-1){
+ J=JJ=I[1];I=I[0];
+ for(R=[];L!=[];L=cdr(L)){
+ J=lmin([car(L)[0],JJ]);
+ if(J>I) R=cons([I,J],R);
+ I=lmax([car(L)[1],I]);
+ }
+ if(I<JJ) R=cons([I,JJ],R);
+ return reverse(R);
+ }else{
+ for(;L!=[];L=cdr(L)){
+ if(car(L)[0]>I) return 0;
+ if(car(L)[1]>=I){
+ if(In==3) return car(L);
+ if(In==1||(I!=car(L)[0]&&I!=car(L)[1])) return 1;
+ return 2;
+ }
+ }
+ return 0;
+ }
+ }
+ I0=car(I);I1=I[1];
+ for(F=0,R=[];L!=[];L=cdr(L)){
+ if(I0>car(L)[1]){
+ R=cons(car(L),R);
+ continue;
+ }
+ if(I0<=car(L)[1]){
+ I0=lmin([I0,car(L)[0]]);
+ if(I1<car(L)[0]){
+ R=cons([I0,I1],R);
+ for( ;L!=[];L=cdr(L)) R=cons(car(L),R);
+ F=1;
+ break;
+ }
+ I1=lmax([I1,car(L)[1]]);
+ }
+ }
+ if(!F) R=cons([I0,I1],R);
+ return reverse(R);
+}
+
+def xy2curve(F,N,Lx,Ly,Lz,A,B)
+{
+ Raw=getopt(raw);
+ if(type(Gap=getopt(gap))==4){
+ MG=Gap[1];Gap=car(Gap);
+ }else MG=3;
+ if(type(Gap)!=1 && Gap!=0) Gap=0.7;
+ if(type(Dvi=getopt(dviout))<1) Dvi=0;
+ OL=[["dviout",Dvi]];
+ if(type(Opt=getopt(opt))<1) Opt=0;
+ else OL=cons(["opt",Opt],OL);
+ if(type(Sc=getopt(scale))!=1 && type(Sc)!=4) Sc=[1,1,1];
+ else if(type(Sc)!=4) Sc=[Sc,Sc,Sc];
+ else if(length(Sc)!=3) Sc=[Sc[0],Sc[1],Sc[1]];
+ M=diagm(3,Sc);
+ if(A!=0||B!=0){
+ if(type(A)!=6){ /* M=mrot([-A,B,0]|deg=1)*M; */
+ Pi=deval(@pi);
+ Ac=dcos(Pi*A/180);As=dsin(Pi*A/180);
+ M=mat([Ac,As,0],[-As,Ac,0],[0,0,1])*M;
+ Ac=dcos(Pi*B/180);As=dsin(Pi*B/180);
+ M=mat([Ac,0,As],[0,1,0],[-As,0,Ac])*M;
+ }else M=A;
+ V=M*newvect(3,[x,y,z]);
+ Fx=compdf(V[0],[x,y,z],F);Fy=compdf(V[1],[x,y,z],F);Fz=compdf(V[2],[x,y,z],F);
+ }else{
+ for(I=0;I<3;I++){
+ if(type(T=F[I])!=4) T=f2df(T);
+ if(type(T)==4) T=cons(car(T)*Sc[I],cdr(T));
+ else T*=Sc[I];
+ if(I==0) Fx=T;
+ else if(I==1) Fy=T;
+ else Fz=T;
+ }
+ }
+ if(Raw==5||!Gap)
+ return (Dvi||!Gap)? xygraph([Fy,Fz],N,Lx,Ly,Lz|option_list=OL):[Fx,Fy,Fz];
+ R=xygraph([Fy,Fz],N,Lx,Ly,Lz|raw=2);
+ R0=cdr(car(R));R1=R[1];
+ for(LT=[];R0!=[];R0=cdr(R0),R1=cdr(R1))
+ if(car(R0)!=0) LT=cons([R1[0],R1[1]],LT);
+ LT=reverse(LT);
+ if(N<0){
+ Be=xylines(car(R)|curve=1,proc=3,close=-1);
+ LT=reverse(cdr(LT));
+ LT=reverse(cdr(LT));
+ }
+ else Be=xylines(car(R)|curve=1,proc=3);
+ Be=cdr(cdr(Be));
+ Be=lbezier(car(Be));
+ if(Raw==4) return [Be,LT,Lx];
+ X=ptcombz(Be,0,0);
+ Var=(length(Lx)==3)?car(Lx):x;
+ if(type(Eq=getopt(eq))!=1) Eq=0.01;
+ if(TikZ==1){
+ Gap/=10;Eq/=10;
+ }
+ for(R=[],XT=X;XT!=[];XT=cdr(XT)){
+ V=car(XT);
+ U=LT[V[0][0]];
+ T=U[0]*V[1][0]+U[1]*(1-V[1][0]);
+ VV=myfdeval(Fx,[Var,T]);
+ U=LT[V[0][1]];
+ T=U[0]*V[1][1]+U[1]*(1-V[1][1]);
+ VV-=myfdeval(Fx,[Var,T]);
+ if(abs(VV)<Eq) continue;
+ I=(VV<0)?0:1;
+ R=cons([V[0][I],V[1][I],V[0][1-I],V[1][1-I]],R);
+ }
+ R=qsort(R);
+ if(Raw==3) return [Be,R];
+ Db=newvect(L=length(Be));
+ for(I=0;I<L;I++) Db[I]=[];
+ for(TR=R;TR!=[];TR=cdr(TR)){
+ V1=ptbezier(Be,[I=car(TR)[0],P=car(TR)[1]])[1];
+ V2=ptbezier(Be,[car(TR)[2],car(TR)[3]])[1];
+ T=dsqrt(1-dvangle(V1,V2)^2);
+ if(T<1/MG) T=MG;
+ GP=Gap/T;
+ W=GP/dnorm(V1);
+ Db[I]=addIL([P-W,P+W],Db[I]);
+ if(P-W<0 && I>0) Db[I-1]=addIL([P-W+1,1],Db[I-1]);
+ if(P+W>1 && I+1<L) Db[I+1]=addIL([0,P+W-1],Db[I+1]);
+ }
+ Db=vtol(Db);
+ for(Bf=[];Be!=[];Be=cdr(Be),Db=cdr(Db)){
+ if(car(Db)==[]) Bf=cons(car(Be),Bf);
+ else{
+ D=addIL([0,1],car(Db)|in=-1);
+ for(;D!=[];D=cdr(D))
+ Bf=cons(tobezier(car(Be)|inv=car(D)),Bf);
+ }
+ }
+ Bf=reverse(Bf);
+ if(Raw==2) return Bf;
+ OL=[];
+ if(Opt){
+ if(type(Opt)==4&&length(Opt)>1) OL=[["opt",Opt[0]],["cmd",Opt[1]]];
+ else OL=[["opt",Opt]];
+ }else OL=[];
+ S=xybezier(lbezier(Bf|inv=1)|option_list=OL);
+ if(Raw==1||!Dvi) return S;
+ return xyproc(S|dviout=Dvi);
+}
+
+def xy2graph(F0,N,Lx,Ly,Lz,A,B)
+{
+ /* (x,y,z) -> (z sin B + x cos A cos B + y sin A cos B,
+ -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 orthpoly(N)
+{
+ F=0;
+ if(type(P=getopt(pol))==7){
+ for(L=["Le","Ge","Tc","2T","Ja","He","La","Se"];L!=[];L=cdr(L),F++)
+ if(str_str(P,car(L)|end=2)==0) break;
+ }else P=0;
+ if(type(D=N)==4) D=N[0];
+ if(!isint(D)||D<0) return 0;
+ if(F==0) return seriesHG([-D,D+1],[1],(1-x)/2,D);
+ if(F==1) return red(seriesHG([-D,D+2*N[1]],[N[1]+1/2],(1-x)/2,D)*binom(D+2*N[1]-1,D));
+ if(F==2) return seriesHG([-D,D],[1/2],(1-x)/2,D);
+ if(F==3){
+ if(D==0) return 0;
+ return orthpoly([D-1,1]|pol="Ge");
+ }
+ if(F==4) return red(seriesHG([-D,D+N[1]],[N[2]],x,D));
+ if(F==5){
+ for(S=I=1;I<=D;I+=2) S*=I;
+ if(iand(D,1)) return seriesHG([-(D-1)/2],[3/2],x^2/2,D-1)*x*S*(-1)^((D-1)/2);
+ else return seriesHG([-D/2],[1/2],x^2/2,D)*S*(-1)^(D/2);
+ }
+ if(F==6){
+ NN=(type(N)==4)?N[1]:0;
+ return red(seriesHG([-D],[NN+1],x,D)*binom(D+NN,D));
+ }
+ if(F==7){
+ NN=N[1];
+ for(S=1,I=1;I<=D;I++) S+=(-1)^I*binom(D,I)*binom(D+I,I)*sftpow(x,I)/sftpow(NN,I);
+ return S;
+ }
+ return 0;
+}
+
+def schurpoly(L)
+{
+ N=length(L);
+ for(R=[],I=1;L!=[];L=cdr(L),I++) R=cons(car(L)+N-I,R);
+ L=reverse(R);
+ if(type(X=getopt(var))!=4){
+ V=(type(X)>1)?X:"x";
+ for(X=[],I=0;I<N;I++) X=cons(makev([V,N-I]),X);
+ }
+ M=newmat(N,N);
+ for(I=0;I<N;I++)
+ for(J=0;J<N;J++) M[I][J]=X[I]^L[J];
+ P=det(M);
+ for(I=0;I<N;I++)
+ for(J=I+1;J<N;J++) P=sdiv(P,X[I]-X[J]);
+ return P;
+}
+
+def fouriers(A,B,X)
+{
+ if((Y=getopt(y))==0||type(Y)>0) Y=deval(Y);
+ else Y=0;
+ if((V=getopt(const))==0||type(V)>0){
+ V=myfeval(V,Y);
+ K=1;
+ }else K=0;
+ if(A!=[]&&type(car(A))>1){
+ for(C=[],I=A[1];I>=K;I--) C=cons(myf2eval(car(A),I,Y),C);
+ if(K) C=cons(0,C);
+ A=C;
+ }
+ if(K){
+ if(A!=[]) A=cdr(A);
+ A=cons(V,A);
+ }
+ if(B!=[]&&type(car(B))>1){
+ for(C=[],I=B[1];I>0;I--) C=cons(myf2eval(car(B),I,Y),C);
+ B=C;
+ }
+ L=length(B)+1;
+ if(length(A)>=L) L=length(A)+1;
+ if(type(Sum=getopt(sum))>0){
+ if(Sum==1) Sum=1-x;
+ else if(Sum==2) Sum=[(z__)/(3.1416*x),[z__,os_md.mysin,3.1416*x]];
+ else Sum=f2df(Sum);
+ C=[];
+ if(A!=[]){
+ C=cons(car(A),C);
+ A=cdr(A);
+ }
+ for(I=1;A!=[];A=cdr(A),I++) C=cons(car(A)*myf2eval(Sum,I/L,L),C);
+ A=reverse(C);
+ for(C=[],I=1;B!=[];B=cdr(B),I++) C=cons(car(B)*myf2eval(Sum,I/L,L),C);
+ B=reverse(C);
+ }
+ 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+=S*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(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);
+ if(V==G) return F; /* subst(F(V),V,G) */
+ VF=vars(F);VG=vars(G);
+ if(type(V)==4){
+ for(VT=[],VV=V;VV!=[];VV=cdr(VV)){
+ if(findin(car(VV),VF)>=0){
+ X=makenewv(append(VF,VG));
+ VF=cons(X,VF);
+ F=mysubst(F,[car(VV),X]);
+ VT=cons(X,VT);
+ }else VT=cons(car(VV),VT);
+ }
+ for(V=reverse(VT);V!=[];V=cdr(V),G=cdr(G)) F=compdf(F,car(V),car(G));
+ return F;
+ }
+ 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(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((Raw=getopt(raw))==1) return V;
+ if(Raw==2) return [V,LT];
+ 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<5;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(car(V)==[]||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,F]);
+ Z=makenewv([X,Y,F]);
+ 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&&ltov(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=2);
+ 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!=2) All=0;
+ V=vars(P);
+ for(Arg=FC=[];V!=[];V=cdr(V)){
+ if(vtype(CV=car(V))==0&&All!=0){
+ 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);
+ }
+ }
+ }
+ }
+ Arg=reverse(Arg);
+ return (All==2)?Arg:[reverse(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]+4,"="))>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) Canvas=SV;
+ }
+ }
+ }
+ close_file(Id);
+ }
+ chkfun(1,0);
+}
+
+#ifdef USEMODULE
+endmodule;
+os_md.init()$
+#else
+init()$
+#endif
+
+end$