=================================================================== RCS file: /home/cvs/OpenXM_contrib2/asir2000/engine/Fgfs.c,v retrieving revision 1.21 retrieving revision 1.22 diff -u -p -r1.21 -r1.22 --- OpenXM_contrib2/asir2000/engine/Fgfs.c 2004/04/03 05:52:56 1.21 +++ OpenXM_contrib2/asir2000/engine/Fgfs.c 2018/03/29 01:32:51 1.22 @@ -1,4 +1,4 @@ -/* $OpenXM: OpenXM_contrib2/asir2000/engine/Fgfs.c,v 1.20 2004/02/03 23:31:57 noro Exp $ */ +/* $OpenXM: OpenXM_contrib2/asir2000/engine/Fgfs.c,v 1.21 2004/04/03 05:52:56 noro Exp $ */ #include "ca.h" @@ -27,737 +27,737 @@ void sfbm_to_gfsn_univariate(BM f,V x,V y,P *r); void monomialfctr_sf(VL vl,P p,P *pr,DCP *dcp) { - VL nvl,avl; - Q d; - P f,t,s; - DCP dc0,dc; - Obj obj; + VL nvl,avl; + Q d; + P f,t,s; + DCP dc0,dc; + Obj obj; - clctv(vl,p,&nvl); - for ( dc0 = 0, avl = nvl, f = p; avl; avl = NEXT(avl) ) { - getmindeg(avl->v,f,&d); - if ( d ) { - MKV(avl->v,t); - simp_ff((Obj)t,&obj); t = (P)obj; - NEXTDC(dc0,dc); DEG(dc) = d; COEF(dc) = t; - pwrp(vl,t,d,&s); divsp(vl,f,s,&t); f = t; - } - } - if ( dc0 ) - NEXT(dc) = 0; - *pr = f; *dcp = dc0; + clctv(vl,p,&nvl); + for ( dc0 = 0, avl = nvl, f = p; avl; avl = NEXT(avl) ) { + getmindeg(avl->v,f,&d); + if ( d ) { + MKV(avl->v,t); + simp_ff((Obj)t,&obj); t = (P)obj; + NEXTDC(dc0,dc); DEG(dc) = d; COEF(dc) = t; + pwrp(vl,t,d,&s); divsp(vl,f,s,&t); f = t; + } + } + if ( dc0 ) + NEXT(dc) = 0; + *pr = f; *dcp = dc0; } void lex_lc(P f,P *c) { - if ( !f || NUM(f) ) - *c = f; - else - lex_lc(COEF(DC(f)),c); + if ( !f || NUM(f) ) + *c = f; + else + lex_lc(COEF(DC(f)),c); } DCP append_dc(DCP dc,DCP dct) { - DCP dcs; + DCP dcs; - if ( !dc ) - return dct; - else { - for ( dcs = dc; NEXT(dcs); dcs = NEXT(dcs) ); - NEXT (dcs) = dct; - return dc; - } + if ( !dc ) + return dct; + else { + for ( dcs = dc; NEXT(dcs); dcs = NEXT(dcs) ); + NEXT (dcs) = dct; + return dc; + } } void sqfrsf(VL vl, P f, DCP *dcp) { - DCP dc,dct; - Obj obj; - P t,s,c,cont; - VL tvl,onevl; + DCP dc,dct; + Obj obj; + P t,s,c,cont; + VL tvl,onevl; - simp_ff((Obj)f,&obj); f = (P)obj; - lex_lc(f,&c); divsp(vl,f,c,&t); f = t; - monomialfctr_sf(vl,f,&t,&dc); f = t; - clctv(vl,f,&tvl); vl = tvl; - NEWVL(onevl); NEXT(onevl)=0; - if ( !vl ) - ; - else if ( !NEXT(vl) ) { - sfusqfr(f,&dct); - dc = append_dc(dc,NEXT(dct)); - } else { - t = f; - for ( tvl = vl; tvl; tvl = NEXT(tvl) ) { - onevl->v = tvl->v; - cont_pp_mv_sf(vl,onevl,t,&cont,&s); t = s; - sqfrsf(vl,cont,&dct); - dc = append_dc(dc,NEXT(dct)); - } - sqfrsfmain(vl,t,&dct); - dc = append_dc(dc,dct); - } - NEWDC(dct); DEG(dct) = ONE; COEF(dct) = (P)c; NEXT(dct) = dc; - *dcp = dct; + simp_ff((Obj)f,&obj); f = (P)obj; + lex_lc(f,&c); divsp(vl,f,c,&t); f = t; + monomialfctr_sf(vl,f,&t,&dc); f = t; + clctv(vl,f,&tvl); vl = tvl; + NEWVL(onevl); NEXT(onevl)=0; + if ( !vl ) + ; + else if ( !NEXT(vl) ) { + sfusqfr(f,&dct); + dc = append_dc(dc,NEXT(dct)); + } else { + t = f; + for ( tvl = vl; tvl; tvl = NEXT(tvl) ) { + onevl->v = tvl->v; + cont_pp_mv_sf(vl,onevl,t,&cont,&s); t = s; + sqfrsf(vl,cont,&dct); + dc = append_dc(dc,NEXT(dct)); + } + sqfrsfmain(vl,t,&dct); + dc = append_dc(dc,dct); + } + NEWDC(dct); DEG(dct) = ONE; COEF(dct) = (P)c; NEXT(dct) = dc; + *dcp = dct; } void sqfrsfmain(VL vl,P f,DCP *dcp) { - VL tvl; - DCP dc,dct,dcs; - P t,s; - Q m,m1; - V v; + VL tvl; + DCP dc,dct,dcs; + P t,s; + Q m,m1; + V v; - clctv(vl,f,&tvl); vl = tvl; - dc = 0; - t = f; - for ( tvl = vl; tvl; tvl = NEXT(tvl) ) { - v = tvl->v; - partial_sqfrsf(vl,v,t,&s,&dct); t = s; - dc = append_dc(dc,dct); - } - if ( !NUM(t) ) { - STOQ(characteristic_sf(),m); - pthrootsf(t,m,&s); - sqfrsfmain(vl,s,&dct); - for ( dcs = dct; dcs; dcs = NEXT(dcs) ) { - mulq(DEG(dcs),m,&m1); DEG(dcs) = m1; - } - dc = append_dc(dc,dct); - } - *dcp = dc; + clctv(vl,f,&tvl); vl = tvl; + dc = 0; + t = f; + for ( tvl = vl; tvl; tvl = NEXT(tvl) ) { + v = tvl->v; + partial_sqfrsf(vl,v,t,&s,&dct); t = s; + dc = append_dc(dc,dct); + } + if ( !NUM(t) ) { + STOQ(characteristic_sf(),m); + pthrootsf(t,m,&s); + sqfrsfmain(vl,s,&dct); + for ( dcs = dct; dcs; dcs = NEXT(dcs) ) { + mulq(DEG(dcs),m,&m1); DEG(dcs) = m1; + } + dc = append_dc(dc,dct); + } + *dcp = dc; } void pthrootsf(P f,Q m,P *r) { - DCP dc,dc0,dct; - N qn,rn; + DCP dc,dc0,dct; + N qn,rn; - if ( NUM(f) ) - pthrootgfs(f,r); - else { - dc = DC(f); - dc0 = 0; - for ( dc0 = 0; dc; dc = NEXT(dc) ) { - NEXTDC(dc0,dct); - pthrootsf(COEF(dc),m,&COEF(dct)); - if ( DEG(dc) ) { - divn(NM(DEG(dc)),NM(m),&qn,&rn); - if ( rn ) - error("pthrootsf : cannot happen"); - NTOQ(qn,1,DEG(dct)); - } else - DEG(dct) = 0; - } - NEXT(dct) = 0; - MKP(VR(f),dc0,*r); - } + if ( NUM(f) ) + pthrootgfs(f,r); + else { + dc = DC(f); + dc0 = 0; + for ( dc0 = 0; dc; dc = NEXT(dc) ) { + NEXTDC(dc0,dct); + pthrootsf(COEF(dc),m,&COEF(dct)); + if ( DEG(dc) ) { + divn(NM(DEG(dc)),NM(m),&qn,&rn); + if ( rn ) + error("pthrootsf : cannot happen"); + NTOQ(qn,1,DEG(dct)); + } else + DEG(dct) = 0; + } + NEXT(dct) = 0; + MKP(VR(f),dc0,*r); + } } void partial_sqfrsf(VL vl,V v,P f,P *r,DCP *dcp) { - P ps[2]; - DCP dc0,dc; - int m; - P t,flat,flat1,g,df,q; + P ps[2]; + DCP dc0,dc; + int m; + P t,flat,flat1,g,df,q; - diffp(vl,f,v,&df); - if ( !df ) { - *dcp = 0; - *r = f; - return; - } - ps[0] = f; ps[1] = df; - gcdsf(vl,ps,2,&g); - divsp(vl,f,g,&flat); - m = 0; - t = f; - dc0 = 0; - while ( !NUM(flat) ) { - while ( divtp(vl,t,flat,&q) ) { - t = q; m++; - } - ps[0] = t; ps[1] = flat; - gcdsf(vl,ps,2,&flat1); - divsp(vl,flat,flat1,&g); - flat = flat1; - NEXTDC(dc0,dc); - COEF(dc) = g; - STOQ(m,DEG(dc)); - } - NEXT(dc) = 0; - *dcp = dc0; - *r = t; + diffp(vl,f,v,&df); + if ( !df ) { + *dcp = 0; + *r = f; + return; + } + ps[0] = f; ps[1] = df; + gcdsf(vl,ps,2,&g); + divsp(vl,f,g,&flat); + m = 0; + t = f; + dc0 = 0; + while ( !NUM(flat) ) { + while ( divtp(vl,t,flat,&q) ) { + t = q; m++; + } + ps[0] = t; ps[1] = flat; + gcdsf(vl,ps,2,&flat1); + divsp(vl,flat,flat1,&g); + flat = flat1; + NEXTDC(dc0,dc); + COEF(dc) = g; + STOQ(m,DEG(dc)); + } + NEXT(dc) = 0; + *dcp = dc0; + *r = t; } void gcdsf(VL vl,P *pa,int k,P *r) { - P *ps,*pl,*pm; - P **cp; - int *cn; - DCP *ml; - Obj obj; - int i,j,l,m; - P mg,mgsf,t; - VL avl,nvl,tvl,svl; + P *ps,*pl,*pm; + P **cp; + int *cn; + DCP *ml; + Obj obj; + int i,j,l,m; + P mg,mgsf,t; + VL avl,nvl,tvl,svl; - ps = (P *)ALLOCA(k*sizeof(P)); - for ( i = 0, m = 0; i < k; i++ ) { - simp_ff((Obj)pa[i],&obj); - if ( obj ) - ps[m++] = (P)obj; - } - if ( !m ) { - *r = 0; - return; - } - if ( m == 1 ) { - *r = ps[0]; - return; - } - pl = (P *)ALLOCA(m*sizeof(P)); - ml = (DCP *)ALLOCA(m*sizeof(DCP)); - for ( i = 0; i < m; i++ ) - monomialfctr(vl,ps[i],&pl[i],&ml[i]); - gcdmonomial(vl,ml,m,&mg); simp_ff((Obj)mg,&obj); mgsf = (P)obj; - for ( i = 0, nvl = vl, avl = 0; nvl && i < m; i++ ) { - clctv(vl,pl[i],&tvl); - intersectv(nvl,tvl,&svl); nvl = svl; - mergev(vl,avl,tvl,&svl); avl = svl; - } - if ( !nvl ) { - *r = mgsf; - return; - } - if ( !NEXT(avl) ) { - ugcdsf(pl,m,&t); - mulp(vl,mgsf,t,r); - return; - } - for ( tvl = nvl, i = 0; tvl; tvl = NEXT(tvl), i++ ); - for ( tvl = avl, j = 0; tvl; tvl = NEXT(tvl), j++ ); - if ( i == j ) { - /* all the pl[i]'s have the same variables */ - gcdsf_main(avl,pl,m,&t); - } else { - cp = (P **)ALLOCA(m*sizeof(P *)); - cn = (int *)ALLOCA(m*sizeof(int)); - for ( i = 0; i < m; i++ ) { - cp[i] = (P *)ALLOCA(lengthp(pl[i])*sizeof(P)); - cn[i] = pcoef(vl,nvl,pl[i],cp[i]); - } - for ( i = j = 0; i < m; i++ ) - j += cn[i]; - pm = (P *)ALLOCA(j*sizeof(P)); - for ( i = l = 0; i < m; i++ ) - for ( j = 0; j < cn[i]; j++ ) - pm[l++] = cp[i][j]; - gcdsf(vl,pm,l,&t); - } - mulp(vl,mgsf,t,r); + ps = (P *)ALLOCA(k*sizeof(P)); + for ( i = 0, m = 0; i < k; i++ ) { + simp_ff((Obj)pa[i],&obj); + if ( obj ) + ps[m++] = (P)obj; + } + if ( !m ) { + *r = 0; + return; + } + if ( m == 1 ) { + *r = ps[0]; + return; + } + pl = (P *)ALLOCA(m*sizeof(P)); + ml = (DCP *)ALLOCA(m*sizeof(DCP)); + for ( i = 0; i < m; i++ ) + monomialfctr(vl,ps[i],&pl[i],&ml[i]); + gcdmonomial(vl,ml,m,&mg); simp_ff((Obj)mg,&obj); mgsf = (P)obj; + for ( i = 0, nvl = vl, avl = 0; nvl && i < m; i++ ) { + clctv(vl,pl[i],&tvl); + intersectv(nvl,tvl,&svl); nvl = svl; + mergev(vl,avl,tvl,&svl); avl = svl; + } + if ( !nvl ) { + *r = mgsf; + return; + } + if ( !NEXT(avl) ) { + ugcdsf(pl,m,&t); + mulp(vl,mgsf,t,r); + return; + } + for ( tvl = nvl, i = 0; tvl; tvl = NEXT(tvl), i++ ); + for ( tvl = avl, j = 0; tvl; tvl = NEXT(tvl), j++ ); + if ( i == j ) { + /* all the pl[i]'s have the same variables */ + gcdsf_main(avl,pl,m,&t); + } else { + cp = (P **)ALLOCA(m*sizeof(P *)); + cn = (int *)ALLOCA(m*sizeof(int)); + for ( i = 0; i < m; i++ ) { + cp[i] = (P *)ALLOCA(lengthp(pl[i])*sizeof(P)); + cn[i] = pcoef(vl,nvl,pl[i],cp[i]); + } + for ( i = j = 0; i < m; i++ ) + j += cn[i]; + pm = (P *)ALLOCA(j*sizeof(P)); + for ( i = l = 0; i < m; i++ ) + for ( j = 0; j < cn[i]; j++ ) + pm[l++] = cp[i][j]; + gcdsf(vl,pm,l,&t); + } + mulp(vl,mgsf,t,r); } /* univariate gcd */ void ugcdsf(P *pa,int m,P *r) { - P *ps; - int i; - UM w1,w2,w3,w; - int d; - V v; + P *ps; + int i; + UM w1,w2,w3,w; + int d; + V v; - if ( m == 1 ) { - *r = pa[0]; - return; - } - for ( i = 0; i < m; i++ ) - if ( NUM(pa[i]) ) { - itogfs(1,r); - return; - } - ps = (P *)ALLOCA(m*sizeof(P)); - sort_by_deg(m,pa,ps); - v = VR(ps[m-1]); - d = getdeg(v,ps[m-1]); - w1 = W_UMALLOC(d); - w2 = W_UMALLOC(d); - w3 = W_UMALLOC(d); - ptosfum(ps[0],w1); - for ( i = 1; i < m; i++ ) { - ptosfum(ps[i],w2); - gcdsfum(w1,w2,w3); - w = w1; w1 = w3; w3 = w; - if ( !DEG(w1) ) { - itogfs(1,r); - return; - } - } - sfumtop(v,w1,r); + if ( m == 1 ) { + *r = pa[0]; + return; + } + for ( i = 0; i < m; i++ ) + if ( NUM(pa[i]) ) { + itogfs(1,r); + return; + } + ps = (P *)ALLOCA(m*sizeof(P)); + sort_by_deg(m,pa,ps); + v = VR(ps[m-1]); + d = getdeg(v,ps[m-1]); + w1 = W_UMALLOC(d); + w2 = W_UMALLOC(d); + w3 = W_UMALLOC(d); + ptosfum(ps[0],w1); + for ( i = 1; i < m; i++ ) { + ptosfum(ps[i],w2); + gcdsfum(w1,w2,w3); + w = w1; w1 = w3; w3 = w; + if ( !DEG(w1) ) { + itogfs(1,r); + return; + } + } + sfumtop(v,w1,r); } /* deg(HT(p),v), where p is considered as distributed poly over F[v] */ int gethdeg(VL vl,V v,P p) { - DCP dc; - Q dmax; - P cmax; + DCP dc; + Q dmax; + P cmax; - if ( !p ) - return -1; - else if ( NUM(p) ) - return 0; - else if ( VR(p) != v ) - /* HT(p) = HT(lc(p))*x^D */ - return gethdeg(vl,v,COEF(DC(p))); - else { - /* VR(p) = v */ - dc = DC(p); dmax = DEG(dc); cmax = COEF(dc); - for ( dc = NEXT(dc); dc; dc = NEXT(dc) ) - if ( compp(vl,COEF(dc),cmax) > 0 ) { - dmax = DEG(dc); cmax = COEF(dc); - } - return QTOS(dmax); - } + if ( !p ) + return -1; + else if ( NUM(p) ) + return 0; + else if ( VR(p) != v ) + /* HT(p) = HT(lc(p))*x^D */ + return gethdeg(vl,v,COEF(DC(p))); + else { + /* VR(p) = v */ + dc = DC(p); dmax = DEG(dc); cmax = COEF(dc); + for ( dc = NEXT(dc); dc; dc = NEXT(dc) ) + if ( compp(vl,COEF(dc),cmax) > 0 ) { + dmax = DEG(dc); cmax = COEF(dc); + } + return QTOS(dmax); + } } /* all the pa[i]'s have the same variables (=vl) */ void gcdsf_main(VL vl,P *pa,int m,P *r) { - int nv,i,i0,imin,d,d0,d1,d2,dmin,index; - V v,v0,vmin; - VL tvl,nvl,rvl,nvl0,rvl0; - P *pc, *ps, *ph,*lps; - P x,t,cont,hg,g,hm,mod,s; - P hge,ge,ce,he,u,cof1e,mode,mod1,adj,cof1,coadj,q; - GFS sf; + int nv,i,i0,imin,d,d0,d1,d2,dmin,index; + V v,v0,vmin; + VL tvl,nvl,rvl,nvl0,rvl0; + P *pc, *ps, *ph,*lps; + P x,t,cont,hg,g,hm,mod,s; + P hge,ge,ce,he,u,cof1e,mode,mod1,adj,cof1,coadj,q; + GFS sf; - for ( nv = 0, tvl = vl; tvl; tvl = NEXT(tvl), nv++); - if ( nv == 1 ) { - ugcdsf(pa,m,r); - return; - } - /* find v s.t. min(deg(pa[i],v)+gethdeg(pa[i],v)) is minimal */ - tvl = vl; - do { - v = tvl->v; - i = 0; - do { - d = getdeg(v,pa[i])+gethdeg(vl,v,pa[i]); - if ( i == 0 || (d < d0) ) { - d0 = d; i0 = i; v0 = v; - } - } while ( ++i < m ); - if ( tvl == vl || (d0 < dmin) ) { - dmin = d0; imin = i0; vmin = v0; - } - } while ( tvl = NEXT(tvl) ); + for ( nv = 0, tvl = vl; tvl; tvl = NEXT(tvl), nv++); + if ( nv == 1 ) { + ugcdsf(pa,m,r); + return; + } + /* find v s.t. min(deg(pa[i],v)+gethdeg(pa[i],v)) is minimal */ + tvl = vl; + do { + v = tvl->v; + i = 0; + do { + d = getdeg(v,pa[i])+gethdeg(vl,v,pa[i]); + if ( i == 0 || (d < d0) ) { + d0 = d; i0 = i; v0 = v; + } + } while ( ++i < m ); + if ( tvl == vl || (d0 < dmin) ) { + dmin = d0; imin = i0; vmin = v0; + } + } while ( tvl = NEXT(tvl) ); - /* reorder variables so that vmin is the last variable */ - for ( nvl0 = 0, rvl0 = 0, tvl = vl; tvl; tvl = NEXT(tvl) ) - if ( tvl->v != vmin ) { - NEXTVL(nvl0,nvl); nvl->v = tvl->v; - NEXTVL(rvl0,rvl); rvl->v = tvl->v; - } - /* rvl = remaining variables */ - NEXT(rvl) = 0; rvl = rvl0; - /* nvl = ...,vmin */ - NEXTVL(nvl0,nvl); nvl->v = vmin; NEXT(nvl) = 0; nvl = nvl0; - MKV(vmin,x); + /* reorder variables so that vmin is the last variable */ + for ( nvl0 = 0, rvl0 = 0, tvl = vl; tvl; tvl = NEXT(tvl) ) + if ( tvl->v != vmin ) { + NEXTVL(nvl0,nvl); nvl->v = tvl->v; + NEXTVL(rvl0,rvl); rvl->v = tvl->v; + } + /* rvl = remaining variables */ + NEXT(rvl) = 0; rvl = rvl0; + /* nvl = ...,vmin */ + NEXTVL(nvl0,nvl); nvl->v = vmin; NEXT(nvl) = 0; nvl = nvl0; + MKV(vmin,x); - /* for content and primitive part */ - pc = (P *)ALLOCA(m*sizeof(P)); - ps = (P *)ALLOCA(m*sizeof(P)); - ph = (P *)ALLOCA(m*sizeof(P)); - /* separate the contents */ - for ( i = 0; i < m; i++ ) { - reorderp(nvl,vl,pa[i],&t); - cont_pp_mv_sf(nvl,rvl,t,&pc[i],&ps[i]); - head_monomial(nvl,vmin,ps[i],&ph[i],&t); - } - ugcdsf(pc,m,&cont); - ugcdsf(ph,m,&hg); + /* for content and primitive part */ + pc = (P *)ALLOCA(m*sizeof(P)); + ps = (P *)ALLOCA(m*sizeof(P)); + ph = (P *)ALLOCA(m*sizeof(P)); + /* separate the contents */ + for ( i = 0; i < m; i++ ) { + reorderp(nvl,vl,pa[i],&t); + cont_pp_mv_sf(nvl,rvl,t,&pc[i],&ps[i]); + head_monomial(nvl,vmin,ps[i],&ph[i],&t); + } + ugcdsf(pc,m,&cont); + ugcdsf(ph,m,&hg); - /* for hg*pp (used in check phase) */ - lps = (P *)ALLOCA(m*sizeof(P)); - for ( i = 0; i < m; i++ ) - mulp(nvl,hg,ps[i],&lps[i]); + /* for hg*pp (used in check phase) */ + lps = (P *)ALLOCA(m*sizeof(P)); + for ( i = 0; i < m; i++ ) + mulp(nvl,hg,ps[i],&lps[i]); - while ( 1 ) { - g = 0; - cof1 = 0; - hm = 0; - itogfs(1,&mod); - index = 0; - for ( index = 0; getdeg(vmin,mod) <= d+1; index++ ) { - /* evaluation pt */ - indextogfs(index,&s); - substp(nvl,hg,vmin,s,&hge); - if ( !hge ) - continue; - for ( i = 0; i < m; i++ ) - substp(nvl,ps[i],vmin,s,&ph[i]); - /* ge = GCD(ps[0]|x=s,...,ps[m-1]|x=s) */ - gcdsf(nvl,ph,m,&ge); - head_monomial(nvl,vmin,ge,&ce,&he); - if ( NUM(he) ) { - *r = cont; - return; - } - divgfs((GFS)hge,(GFS)ce,&sf); t = (P)sf; - mulp(nvl,t,ge,&u); ge = u; - divsp(nvl,ph[imin],ge,&t); mulp(nvl,hge,t,&cof1e); - /* hm=0 : reset; he==hm : lucky */ - if ( !hm || !compp(nvl,he,hm) ) { - substp(nvl,mod,vmin,s,&mode); divsp(nvl,mod,mode,&mod1); - /* adj = mod/(mod|x=s)*(ge-g|x=s) */ - substp(nvl,g,vmin,s,&t); - subp(nvl,ge,t,&u); mulp(nvl,mod1,u,&adj); - /* coadj = mod/(mod|vmin=s)*(cof1e-cof1e|vmin=s) */ - substp(nvl,cof1,vmin,s,&t); - subp(nvl,cof1e,t,&u); mulp(nvl,mod1,u,&coadj); - if ( !adj ) { - /* adj == gcd ? */ - for ( i = 0; i < m; i++ ) - if ( !divtp(nvl,lps[i],g,&t) ) - break; - if ( i == m ) { - cont_pp_mv_sf(nvl,rvl,g,&t,&u); - mulp(nvl,cont,u,&t); - reorderp(vl,nvl,t,r); - return; - } - } else if ( !coadj ) { - /* ps[imin]/coadj == gcd ? */ - if ( divtp(nvl,lps[imin],cof1,&q) ) { - for ( i = 0; i < m; i++ ) - if ( !divtp(nvl,lps[i],q,&t) ) - break; - if ( i == m ) { - cont_pp_mv_sf(nvl,rvl,q,&t,&u); - mulp(nvl,cont,u,&t); - reorderp(vl,nvl,t,r); - return; - } - } - } - addp(nvl,g,adj,&t); g = t; - addp(nvl,cof1,coadj,&t); cof1 = t; - subp(nvl,x,s,&t); mulp(nvl,mod,t,&u); mod = u; - hm = he; - } else { - d1 = homdeg(hm); d2 = homdeg(he); - if ( d1 < d2 ) /* we use current hm */ - continue; - else if ( d1 > d2 ) { - /* use he */ - g = ge; - cof1 = cof1e; - hm = he; - subp(nvl,x,s,&mod); - } else { - /* d1==d2, but hm!=he => both are unlucky */ - g = 0; - cof1 = 0; - itogfs(1,&mod); - } - } - } - } + while ( 1 ) { + g = 0; + cof1 = 0; + hm = 0; + itogfs(1,&mod); + index = 0; + for ( index = 0; getdeg(vmin,mod) <= d+1; index++ ) { + /* evaluation pt */ + indextogfs(index,&s); + substp(nvl,hg,vmin,s,&hge); + if ( !hge ) + continue; + for ( i = 0; i < m; i++ ) + substp(nvl,ps[i],vmin,s,&ph[i]); + /* ge = GCD(ps[0]|x=s,...,ps[m-1]|x=s) */ + gcdsf(nvl,ph,m,&ge); + head_monomial(nvl,vmin,ge,&ce,&he); + if ( NUM(he) ) { + *r = cont; + return; + } + divgfs((GFS)hge,(GFS)ce,&sf); t = (P)sf; + mulp(nvl,t,ge,&u); ge = u; + divsp(nvl,ph[imin],ge,&t); mulp(nvl,hge,t,&cof1e); + /* hm=0 : reset; he==hm : lucky */ + if ( !hm || !compp(nvl,he,hm) ) { + substp(nvl,mod,vmin,s,&mode); divsp(nvl,mod,mode,&mod1); + /* adj = mod/(mod|x=s)*(ge-g|x=s) */ + substp(nvl,g,vmin,s,&t); + subp(nvl,ge,t,&u); mulp(nvl,mod1,u,&adj); + /* coadj = mod/(mod|vmin=s)*(cof1e-cof1e|vmin=s) */ + substp(nvl,cof1,vmin,s,&t); + subp(nvl,cof1e,t,&u); mulp(nvl,mod1,u,&coadj); + if ( !adj ) { + /* adj == gcd ? */ + for ( i = 0; i < m; i++ ) + if ( !divtp(nvl,lps[i],g,&t) ) + break; + if ( i == m ) { + cont_pp_mv_sf(nvl,rvl,g,&t,&u); + mulp(nvl,cont,u,&t); + reorderp(vl,nvl,t,r); + return; + } + } else if ( !coadj ) { + /* ps[imin]/coadj == gcd ? */ + if ( divtp(nvl,lps[imin],cof1,&q) ) { + for ( i = 0; i < m; i++ ) + if ( !divtp(nvl,lps[i],q,&t) ) + break; + if ( i == m ) { + cont_pp_mv_sf(nvl,rvl,q,&t,&u); + mulp(nvl,cont,u,&t); + reorderp(vl,nvl,t,r); + return; + } + } + } + addp(nvl,g,adj,&t); g = t; + addp(nvl,cof1,coadj,&t); cof1 = t; + subp(nvl,x,s,&t); mulp(nvl,mod,t,&u); mod = u; + hm = he; + } else { + d1 = homdeg(hm); d2 = homdeg(he); + if ( d1 < d2 ) /* we use current hm */ + continue; + else if ( d1 > d2 ) { + /* use he */ + g = ge; + cof1 = cof1e; + hm = he; + subp(nvl,x,s,&mod); + } else { + /* d1==d2, but hm!=he => both are unlucky */ + g = 0; + cof1 = 0; + itogfs(1,&mod); + } + } + } + } } void head_monomial(VL vl,V v,P p,P *coef,P *term) { - P t,s,u; - DCP dc; - GFS one; + P t,s,u; + DCP dc; + GFS one; - itogfs(1,&one); - t = (P)one; - while ( 1 ) { - if ( NUM(p) || VR(p) == v ) { - *coef = p; - *term = t; - return; - } else { - NEWDC(dc); - COEF(dc) = (P)one; DEG(dc) = DEG(DC(p)); - MKP(VR(p),dc,s); - mulp(vl,t,s,&u); t = u; - p = COEF(DC(p)); - } - } + itogfs(1,&one); + t = (P)one; + while ( 1 ) { + if ( NUM(p) || VR(p) == v ) { + *coef = p; + *term = t; + return; + } else { + NEWDC(dc); + COEF(dc) = (P)one; DEG(dc) = DEG(DC(p)); + MKP(VR(p),dc,s); + mulp(vl,t,s,&u); t = u; + p = COEF(DC(p)); + } + } } void cont_pp_mv_sf(VL vl,VL rvl,P p,P *c,P *pp) { - DP dp; - MP t; - int i,m; - P *ps; - struct order_spec *spec, *currentspec; - extern struct order_spec *dp_current_spec; + DP dp; + MP t; + int i,m; + P *ps; + struct order_spec *spec, *currentspec; + extern struct order_spec *dp_current_spec; - currentspec = dp_current_spec; - create_order_spec(0,0,&spec); - initd(spec); - ptod(vl,rvl,p,&dp); - for ( t = BDY(dp), m = 0; t; t = NEXT(t), m++ ); - ps = (P *)ALLOCA(m*sizeof(P)); - for ( t = BDY(dp), i = 0; t; t = NEXT(t), i++ ) - ps[i] = C(t); - gcdsf(vl,ps,m,c); - divsp(vl,p,*c,pp); - initd(currentspec); + currentspec = dp_current_spec; + create_order_spec(0,0,&spec); + initd(spec); + ptod(vl,rvl,p,&dp); + for ( t = BDY(dp), m = 0; t; t = NEXT(t), m++ ); + ps = (P *)ALLOCA(m*sizeof(P)); + for ( t = BDY(dp), i = 0; t; t = NEXT(t), i++ ) + ps[i] = C(t); + gcdsf(vl,ps,m,c); + divsp(vl,p,*c,pp); + initd(currentspec); } void mfctrsf(VL vl, P f, DCP *dcp) { - DCP dc0,dc,dct,dcs,dcr; - Obj obj; + DCP dc0,dc,dct,dcs,dcr; + Obj obj; - simp_ff((Obj)f,&obj); f = (P)obj; - sqfrsf(vl,f,&dct); - dc = dc0 = dct; dct = NEXT(dct); NEXT(dc) = 0; - for ( ; dct; dct = NEXT(dct) ) { - mfctrsfmain(vl,COEF(dct),&dcs); - for ( dcr = dcs; dcr; dcr = NEXT(dcr) ) - DEG(dcr) = DEG(dct); - for ( ; NEXT(dc); dc = NEXT(dc) ); - NEXT(dc) = dcs; - } - *dcp = dc0; + simp_ff((Obj)f,&obj); f = (P)obj; + sqfrsf(vl,f,&dct); + dc = dc0 = dct; dct = NEXT(dct); NEXT(dc) = 0; + for ( ; dct; dct = NEXT(dct) ) { + mfctrsfmain(vl,COEF(dct),&dcs); + for ( dcr = dcs; dcr; dcr = NEXT(dcr) ) + DEG(dcr) = DEG(dct); + for ( ; NEXT(dc); dc = NEXT(dc) ); + NEXT(dc) = dcs; + } + *dcp = dc0; } /* f : sqfr, non const */ void mfctrsfmain(VL vl, P f, DCP *dcp) { - VL tvl,nvl,rvl; - DCP dc,dc0,dc1,dc2,dct,lcfdc,dcs; - int imin,inext,i,j,n,k,np; - int *da; - V vx,vy; - V *va; - P *l,*tl; - P gcd,g,df,dfmin; - P pa[2]; - P f0,pp0,spp0,c,c0,x,y,u,v,lcf,lcu,lcv,u0,v0,t,s; - P ype,yme,fin; - GFS ev,evy; - P *fp0; - int *mev,*win; + VL tvl,nvl,rvl; + DCP dc,dc0,dc1,dc2,dct,lcfdc,dcs; + int imin,inext,i,j,n,k,np; + int *da; + V vx,vy; + V *va; + P *l,*tl; + P gcd,g,df,dfmin; + P pa[2]; + P f0,pp0,spp0,c,c0,x,y,u,v,lcf,lcu,lcv,u0,v0,t,s; + P ype,yme,fin; + GFS ev,evy; + P *fp0; + int *mev,*win; - clctv(vl,f,&tvl); vl = tvl; - if ( !vl ) - error("mfctrsfmain : cannot happen"); - if ( !NEXT(vl) ) { - /* univariate */ - ufctrsf(f,&dc); - /* remove lc */ - *dcp = NEXT(dc); - return; - } - for ( n = 0, tvl = vl; tvl; tvl = NEXT(tvl), n++ ); - va = (V *)ALLOCA(n*sizeof(V)); - da = (int *)ALLOCA(n*sizeof(int)); - /* find v s.t. diff(f,v) is nonzero and deg(f,v) is minimal */ - imin = -1; - for ( i = 0, tvl = vl; i < n; tvl = NEXT(tvl), i++ ) { - va[i] = tvl->v; - da[i] = getdeg(va[i],f); - diffp(vl,f,va[i],&df); - if ( !df ) - continue; - if ( imin < 0 || da[i] < da[imin] ) { - dfmin = df; - imin = i; - } - } - /* find v1 neq v s.t. deg(f,v) is minimal */ - inext = -1; - for ( i = 0; i < n; i++ ) { - if ( i == imin ) - continue; - if ( inext < 0 || da[i] < da[inext] ) - inext = i; - } - pa[0] = f; - pa[1] = dfmin; - gcdsf(vl,pa,2,&gcd); - if ( !NUM(gcd) ) { - /* f = gcd * f/gcd */ - mfctrsfmain(vl,gcd,&dc1); - divsp(vl,f,gcd,&g); - mfctrsfmain(vl,g,&dc2); - for ( dct = dc1; NEXT(dct); dct = NEXT(dct) ); - NEXT(dct) = dc2; - *dcp = dc1; - return; - } - /* create vl s.t. vl[0] = va[imin], vl[1] = va[inext] */ - nvl = 0; - NEXTVL(nvl,tvl); tvl->v = va[imin]; - NEXTVL(nvl,tvl); tvl->v = va[inext]; - for ( i = 0; i < n; i++ ) { - if ( i == imin || i == inext ) - continue; - NEXTVL(nvl,tvl); tvl->v = va[i]; - } - NEXT(tvl) = 0; + clctv(vl,f,&tvl); vl = tvl; + if ( !vl ) + error("mfctrsfmain : cannot happen"); + if ( !NEXT(vl) ) { + /* univariate */ + ufctrsf(f,&dc); + /* remove lc */ + *dcp = NEXT(dc); + return; + } + for ( n = 0, tvl = vl; tvl; tvl = NEXT(tvl), n++ ); + va = (V *)ALLOCA(n*sizeof(V)); + da = (int *)ALLOCA(n*sizeof(int)); + /* find v s.t. diff(f,v) is nonzero and deg(f,v) is minimal */ + imin = -1; + for ( i = 0, tvl = vl; i < n; tvl = NEXT(tvl), i++ ) { + va[i] = tvl->v; + da[i] = getdeg(va[i],f); + diffp(vl,f,va[i],&df); + if ( !df ) + continue; + if ( imin < 0 || da[i] < da[imin] ) { + dfmin = df; + imin = i; + } + } + /* find v1 neq v s.t. deg(f,v) is minimal */ + inext = -1; + for ( i = 0; i < n; i++ ) { + if ( i == imin ) + continue; + if ( inext < 0 || da[i] < da[inext] ) + inext = i; + } + pa[0] = f; + pa[1] = dfmin; + gcdsf(vl,pa,2,&gcd); + if ( !NUM(gcd) ) { + /* f = gcd * f/gcd */ + mfctrsfmain(vl,gcd,&dc1); + divsp(vl,f,gcd,&g); + mfctrsfmain(vl,g,&dc2); + for ( dct = dc1; NEXT(dct); dct = NEXT(dct) ); + NEXT(dct) = dc2; + *dcp = dc1; + return; + } + /* create vl s.t. vl[0] = va[imin], vl[1] = va[inext] */ + nvl = 0; + NEXTVL(nvl,tvl); tvl->v = va[imin]; + NEXTVL(nvl,tvl); tvl->v = va[inext]; + for ( i = 0; i < n; i++ ) { + if ( i == imin || i == inext ) + continue; + NEXTVL(nvl,tvl); tvl->v = va[i]; + } + NEXT(tvl) = 0; - fin = f; - reorderp(nvl,vl,f,&g); f = g; - vx = nvl->v; - vy = NEXT(nvl)->v; - MKV(vx,x); - MKV(vy,y); - /* remaining variables */ - rvl = NEXT(NEXT(nvl)); - if ( !rvl ) { - /* bivariate */ - sfbfctr(f,vx,vy,getdeg(vx,f),&dc1); - for ( dc0 = 0; dc1; dc1 = NEXT(dc1) ) { - NEXTDC(dc0,dc); - DEG(dc) = ONE; - reorderp(vl,nvl,COEF(dc1),&COEF(dc)); - } - NEXT(dc) = 0; - *dcp = dc0; - return; - } - /* n >= 3; nvl = (vx,vy,X) */ - /* find good evaluation pt for X */ - mev = (int *)CALLOC(n-2,sizeof(int)); - while ( 1 ) { - /* lcf(mev)=0 => invalid */ - substvp_sf(nvl,rvl,COEF(DC(f)),mev,&t); - if ( t ) { - substvp_sf(nvl,rvl,f,mev,&f0); - pa[0] = f0; - diffp(nvl,f0,vx,&pa[1]); - if ( pa[1] ) { - gcdsf(nvl,pa,2,&gcd); - /* XXX maybe we have to accept the case where gcd is a poly of y */ - if ( NUM(gcd) ) - break; - } - } - /* XXX if generated indices exceed q of GF(q) => error in indextogfs */ - next_evaluation_point(mev,n-2); - } - /* f0 = f(x,y,mev) */ - /* separate content; f0 may have the content wrt x */ - cont_pp_sfp(nvl,f0,&c0,&pp0); + fin = f; + reorderp(nvl,vl,f,&g); f = g; + vx = nvl->v; + vy = NEXT(nvl)->v; + MKV(vx,x); + MKV(vy,y); + /* remaining variables */ + rvl = NEXT(NEXT(nvl)); + if ( !rvl ) { + /* bivariate */ + sfbfctr(f,vx,vy,getdeg(vx,f),&dc1); + for ( dc0 = 0; dc1; dc1 = NEXT(dc1) ) { + NEXTDC(dc0,dc); + DEG(dc) = ONE; + reorderp(vl,nvl,COEF(dc1),&COEF(dc)); + } + NEXT(dc) = 0; + *dcp = dc0; + return; + } + /* n >= 3; nvl = (vx,vy,X) */ + /* find good evaluation pt for X */ + mev = (int *)CALLOC(n-2,sizeof(int)); + while ( 1 ) { + /* lcf(mev)=0 => invalid */ + substvp_sf(nvl,rvl,COEF(DC(f)),mev,&t); + if ( t ) { + substvp_sf(nvl,rvl,f,mev,&f0); + pa[0] = f0; + diffp(nvl,f0,vx,&pa[1]); + if ( pa[1] ) { + gcdsf(nvl,pa,2,&gcd); + /* XXX maybe we have to accept the case where gcd is a poly of y */ + if ( NUM(gcd) ) + break; + } + } + /* XXX if generated indices exceed q of GF(q) => error in indextogfs */ + next_evaluation_point(mev,n-2); + } + /* f0 = f(x,y,mev) */ + /* separate content; f0 may have the content wrt x */ + cont_pp_sfp(nvl,f0,&c0,&pp0); - /* factorize pp0; pp0 = pp0(x,y+evy) = prod dc */ - sfbfctr_shift(pp0,vx,vy,getdeg(vx,pp0),&evy,&spp0,&dc); pp0 = spp0; + /* factorize pp0; pp0 = pp0(x,y+evy) = prod dc */ + sfbfctr_shift(pp0,vx,vy,getdeg(vx,pp0),&evy,&spp0,&dc); pp0 = spp0; - if ( !NEXT(dc) ) { - /* f is irreducible */ - NEWDC(dc); DEG(dc) = ONE; COEF(dc) = fin; NEXT(dc) = 0; - *dcp = dc; - return; - } - /* ype = y+evy, yme = y-evy */ - addp(nvl,y,(P)evy,&ype); subp(nvl,y,(P)evy,&yme); + if ( !NEXT(dc) ) { + /* f is irreducible */ + NEWDC(dc); DEG(dc) = ONE; COEF(dc) = fin; NEXT(dc) = 0; + *dcp = dc; + return; + } + /* ype = y+evy, yme = y-evy */ + addp(nvl,y,(P)evy,&ype); subp(nvl,y,(P)evy,&yme); - /* shift c0; c0 <- c0(y+evy) */ - substp(nvl,c0,vy,ype,&s); c0 = s; + /* shift c0; c0 <- c0(y+evy) */ + substp(nvl,c0,vy,ype,&s); c0 = s; - /* shift f; f <- f(y+evy) */ - substp(nvl,f,vy,ype,&s); f = s; + /* shift f; f <- f(y+evy) */ + substp(nvl,f,vy,ype,&s); f = s; - /* now f(x,0,mev) = c0 * prod dc */ + /* now f(x,0,mev) = c0 * prod dc */ - /* factorize lc_x(f) */ - lcf = COEF(DC(f)); - mfctrsf(nvl,lcf,&dct); - /* skip the first element (= a number) */ - lcfdc = NEXT(dct); + /* factorize lc_x(f) */ + lcf = COEF(DC(f)); + mfctrsf(nvl,lcf,&dct); + /* skip the first element (= a number) */ + lcfdc = NEXT(dct); - /* np = number of bivariate factors */ - for ( np = 0, dct = dc; dct; dct = NEXT(dct), np++ ); - fp0 = (P *)ALLOCA((np+1)*sizeof(P)); - for ( i = 0, dct = dc; i < np; dct = NEXT(dct), i++ ) - fp0[i] = COEF(dct); - fp0[np] = 0; - l = tl = (P *)ALLOCA((np+1)*sizeof(P)); - win = W_ALLOC(np+1); + /* np = number of bivariate factors */ + for ( np = 0, dct = dc; dct; dct = NEXT(dct), np++ ); + fp0 = (P *)ALLOCA((np+1)*sizeof(P)); + for ( i = 0, dct = dc; i < np; dct = NEXT(dct), i++ ) + fp0[i] = COEF(dct); + fp0[np] = 0; + l = tl = (P *)ALLOCA((np+1)*sizeof(P)); + win = W_ALLOC(np+1); - for ( k = 1, win[0] = 1, --np; ; ) { - itogfs(1,&u0); - /* u0 = product of selected factors */ - for ( i = 0; i < k; i++ ) { - mulp(nvl,u0,fp0[win[i]],&t); u0 = t; - } - /* we have to consider the content */ - /* f0 = c0*u0*v0 */ - mulp(nvl,LC(u0),c0,&c); estimatelc_sf(nvl,rvl,c,lcfdc,mev,&lcu); - divsp(nvl,pp0,u0,&v0); - mulp(nvl,LC(v0),c0,&c); estimatelc_sf(nvl,rvl,c,lcfdc,mev,&lcv); - mfctrsf_hensel(nvl,rvl,f,pp0,u0,v0,lcu,lcv,mev,&u); - if ( u ) { - /* save the factor */ - reorderp(vl,nvl,u,&t); - /* y -> y-evy */ - substp(vl,t,vy,yme,tl++); + for ( k = 1, win[0] = 1, --np; ; ) { + itogfs(1,&u0); + /* u0 = product of selected factors */ + for ( i = 0; i < k; i++ ) { + mulp(nvl,u0,fp0[win[i]],&t); u0 = t; + } + /* we have to consider the content */ + /* f0 = c0*u0*v0 */ + mulp(nvl,LC(u0),c0,&c); estimatelc_sf(nvl,rvl,c,lcfdc,mev,&lcu); + divsp(nvl,pp0,u0,&v0); + mulp(nvl,LC(v0),c0,&c); estimatelc_sf(nvl,rvl,c,lcfdc,mev,&lcv); + mfctrsf_hensel(nvl,rvl,f,pp0,u0,v0,lcu,lcv,mev,&u); + if ( u ) { + /* save the factor */ + reorderp(vl,nvl,u,&t); + /* y -> y-evy */ + substp(vl,t,vy,yme,tl++); - /* update f,pp0 */ - divsp(nvl,f,u,&t); f = t; - divsp(nvl,pp0,u0,&t); pp0 = t; - /* update win, fp0 */ - for ( i = 0; i < k-1; i++ ) - for ( j = win[i]+1; j < win[i+1]; j++ ) - fp0[j-i-1] = fp0[j]; - for ( j = win[k-1]+1; j <= np; j++ ) - fp0[j-k] = fp0[j]; - if ( ( np -= k ) < k ) break; - if ( np-win[0]+1 < k ) - if ( ++k <= np ) { - for ( i = 0; i < k; i++ ) - win[i] = i + 1; - continue; - } else - break; - else - for ( i = 1; i < k; i++ ) - win[i] = win[0] + i; - } else { - if ( ncombi(1,np,k,win) == 0 ) - if ( k == np ) break; - else - for ( i = 0, ++k; i < k; i++ ) - win[i] = i + 1; - } - } - reorderp(vl,nvl,f,&t); - /* y -> y-evy */ - substp(vl,t,vy,yme,tl++); - *tl = 0; - for ( dc0 = 0, i = 0; l[i]; i++ ) { - NEXTDC(dc0,dc); DEG(dc) = ONE; COEF(dc) = l[i]; - } - NEXT(dc) = 0; *dcp = dc0; + /* update f,pp0 */ + divsp(nvl,f,u,&t); f = t; + divsp(nvl,pp0,u0,&t); pp0 = t; + /* update win, fp0 */ + for ( i = 0; i < k-1; i++ ) + for ( j = win[i]+1; j < win[i+1]; j++ ) + fp0[j-i-1] = fp0[j]; + for ( j = win[k-1]+1; j <= np; j++ ) + fp0[j-k] = fp0[j]; + if ( ( np -= k ) < k ) break; + if ( np-win[0]+1 < k ) + if ( ++k <= np ) { + for ( i = 0; i < k; i++ ) + win[i] = i + 1; + continue; + } else + break; + else + for ( i = 1; i < k; i++ ) + win[i] = win[0] + i; + } else { + if ( ncombi(1,np,k,win) == 0 ) + if ( k == np ) break; + else + for ( i = 0, ++k; i < k; i++ ) + win[i] = i + 1; + } + } + reorderp(vl,nvl,f,&t); + /* y -> y-evy */ + substp(vl,t,vy,yme,tl++); + *tl = 0; + for ( dc0 = 0, i = 0; l[i]; i++ ) { + NEXTDC(dc0,dc); DEG(dc) = ONE; COEF(dc) = l[i]; + } + NEXT(dc) = 0; *dcp = dc0; } void next_evaluation_point(int *e,int n) { - int i,t,j; + int i,t,j; - for ( i = n-1; i >= 0; i-- ) - if ( e[i] ) break; - if ( i < 0 ) e[n-1] = 1; - else if ( i == 0 ) { - t = e[0]; e[0] = 0; e[n-1] = t+1; - } else { - e[i-1]++; t = e[i]; - for ( j = i; j < n-1; j++ ) - e[j] = 0; - e[n-1] = t-1; - } + for ( i = n-1; i >= 0; i-- ) + if ( e[i] ) break; + if ( i < 0 ) e[n-1] = 1; + else if ( i == 0 ) { + t = e[0]; e[0] = 0; e[n-1] = t+1; + } else { + e[i-1]++; t = e[i]; + for ( j = i; j < n-1; j++ ) + e[j] = 0; + e[n-1] = t-1; + } } /* @@ -769,45 +769,45 @@ void next_evaluation_point(int *e,int n) void estimatelc_sf(VL vl,VL rvl,P c,DCP dc,int *mev,P *lcp) { - DCP dct; - P r,c1,c2,t,s,f; - int i,d; - Q q; + DCP dct; + P r,c1,c2,t,s,f; + int i,d; + Q q; - for ( dct = dc, r = (P)ONE; dct; dct = NEXT(dct) ) { - if ( NUM(COEF(dct)) ) - continue; - /* constant part */ - substvp_sf(vl,rvl,COEF(dct),mev,&f); - d = QTOS(DEG(dct)); - for ( i = 0, c1 = c; i < d; i++ ) - if ( !divtp(vl,c1,f,&c2) ) - break; - else - c1 = c2; - if ( i ) { - STOQ(i,q); - pwrp(vl,COEF(dct),q,&s); mulp(vl,r,s,&t); r = t; - } - } - *lcp = r; + for ( dct = dc, r = (P)ONE; dct; dct = NEXT(dct) ) { + if ( NUM(COEF(dct)) ) + continue; + /* constant part */ + substvp_sf(vl,rvl,COEF(dct),mev,&f); + d = QTOS(DEG(dct)); + for ( i = 0, c1 = c; i < d; i++ ) + if ( !divtp(vl,c1,f,&c2) ) + break; + else + c1 = c2; + if ( i ) { + STOQ(i,q); + pwrp(vl,COEF(dct),q,&s); mulp(vl,r,s,&t); r = t; + } + } + *lcp = r; } void substvp_sf(VL vl,VL rvl,P f,int *mev,P *r) { - int i; - VL tvl; - P g,t; - GFS ev; + int i; + VL tvl; + P g,t; + GFS ev; - for ( g = f, i = 0, tvl = rvl; tvl; tvl = NEXT(tvl), i++ ) { - if ( !mev ) - ev = 0; - else - indextogfs(mev[i],&ev); - substp(vl,g,tvl->v,(P)ev,&t); g = t; - } - *r = g; + for ( g = f, i = 0, tvl = rvl; tvl; tvl = NEXT(tvl), i++ ) { + if ( !mev ) + ev = 0; + else + indextogfs(mev[i],&ev); + substp(vl,g,tvl->v,(P)ev,&t); g = t; + } + *r = g; } /* @@ -816,23 +816,23 @@ void substvp_sf(VL vl,VL rvl,P f,int *mev,P *r) void shift_sf(VL vl, VL rvl, P f, int *mev, int sgn, P *r) { - VL tvl; - int i; - P x,g,t,s; - GFS ev; + VL tvl; + int i; + P x,g,t,s; + GFS ev; - for ( g = f, tvl = rvl, i = 0; tvl; tvl = NEXT(tvl), i++ ) { - if ( !mev[i] ) - continue; - indextogfs(mev[i],&ev); - MKV(tvl->v,x); - if ( sgn > 0 ) - addp(vl,x,(P)ev,&t); - else - subp(vl,x,(P)ev,&t); - substp(vl,g,tvl->v,t,&s); g = s; - } - *r = g; + for ( g = f, tvl = rvl, i = 0; tvl; tvl = NEXT(tvl), i++ ) { + if ( !mev[i] ) + continue; + indextogfs(mev[i],&ev); + MKV(tvl->v,x); + if ( sgn > 0 ) + addp(vl,x,(P)ev,&t); + else + subp(vl,x,(P)ev,&t); + substp(vl,g,tvl->v,t,&s); g = s; + } + *r = g; } /* @@ -841,325 +841,325 @@ void shift_sf(VL vl, VL rvl, P f, int *mev, int sgn, P void mfctrsf_hensel(VL vl,VL rvl,P f,P pp0,P u0,P v0,P lcu,P lcv,int *mev,P *up) { - VL tvl,onevl; - P t,s,w,u,v,ff,si,wu,wv,fj,cont; - UM ydy; - V vx,vy; - int dy,n,i,dbd,nv,j; - int *md; - P *uh,*vh; - P x,du0,dv0,m,q,r,fin; - P *cu,*cv; - GFSN inv; + VL tvl,onevl; + P t,s,w,u,v,ff,si,wu,wv,fj,cont; + UM ydy; + V vx,vy; + int dy,n,i,dbd,nv,j; + int *md; + P *uh,*vh; + P x,du0,dv0,m,q,r,fin; + P *cu,*cv; + GFSN inv; - /* check the validity of lc's and adjust coeffs */ - /* f -> lcu*lcv*x^(m+l)+... */ - mulp(vl,lcu,lcv,&t); - if ( !divtp(vl,t,LC(f),&m) ) { - *up = 0; return; - } - mulp(vl,m,f,&t); f = t; - /* u0 = am x^m+ ... -> lcu*x^m + a(m-1)*(lcu(mev)/am)*x^(m-1)+... */ - /* v0 = bm x^l+ ... -> lcv*x^l + b(l-1)*(lcv(mev)/bl)*x^(l-1)+... */ - adjust_coef_sf(vl,rvl,lcu,u0,mev,&u); - adjust_coef_sf(vl,rvl,lcv,v0,mev,&v); + /* check the validity of lc's and adjust coeffs */ + /* f -> lcu*lcv*x^(m+l)+... */ + mulp(vl,lcu,lcv,&t); + if ( !divtp(vl,t,LC(f),&m) ) { + *up = 0; return; + } + mulp(vl,m,f,&t); f = t; + /* u0 = am x^m+ ... -> lcu*x^m + a(m-1)*(lcu(mev)/am)*x^(m-1)+... */ + /* v0 = bm x^l+ ... -> lcv*x^l + b(l-1)*(lcv(mev)/bl)*x^(l-1)+... */ + adjust_coef_sf(vl,rvl,lcu,u0,mev,&u); + adjust_coef_sf(vl,rvl,lcv,v0,mev,&v); - /* f <- f(X+mev), u <- u(X+mev), v <- v(X+mev) */ - fin = f; - shift_sf(vl,rvl,f,mev,1,&s); f = s; - shift_sf(vl,rvl,u,mev,1,&s); u = s; - shift_sf(vl,rvl,v,mev,1,&s); v = s; + /* f <- f(X+mev), u <- u(X+mev), v <- v(X+mev) */ + fin = f; + shift_sf(vl,rvl,f,mev,1,&s); f = s; + shift_sf(vl,rvl,u,mev,1,&s); u = s; + shift_sf(vl,rvl,v,mev,1,&s); v = s; - vx = vl->v; vy = NEXT(vl)->v; - n = getdeg(vx,f); - dy = getdeg(vy,f)+1; - MKV(vx,x); - cu = (P *)ALLOCA((n+1)*sizeof(P)); - cv = (P *)ALLOCA((n+1)*sizeof(P)); + vx = vl->v; vy = NEXT(vl)->v; + n = getdeg(vx,f); + dy = getdeg(vy,f)+1; + MKV(vx,x); + cu = (P *)ALLOCA((n+1)*sizeof(P)); + cv = (P *)ALLOCA((n+1)*sizeof(P)); - /* ydy = y^dy */ - ydy = C_UMALLOC(dy); DEG(ydy) = dy; COEF(ydy)[dy] = _onesf(); - setmod_gfsn(ydy); + /* ydy = y^dy */ + ydy = C_UMALLOC(dy); DEG(ydy) = dy; COEF(ydy)[dy] = _onesf(); + setmod_gfsn(ydy); - /* (R[y]/(y^dy))[x,X] */ - poly_to_gfsn_poly(vl,f,vy,&ff); - poly_to_gfsn_poly(vl,u,vy,&t); u = t; - poly_to_gfsn_poly(vl,v,vy,&t); v = t; - substvp_sf(vl,rvl,u,0,&u0); - substvp_sf(vl,rvl,v,0,&v0); + /* (R[y]/(y^dy))[x,X] */ + poly_to_gfsn_poly(vl,f,vy,&ff); + poly_to_gfsn_poly(vl,u,vy,&t); u = t; + poly_to_gfsn_poly(vl,v,vy,&t); v = t; + substvp_sf(vl,rvl,u,0,&u0); + substvp_sf(vl,rvl,v,0,&v0); - /* compute a(x,y), b(x,y) s.t. a*u0+b*v0 = 1 mod y^dy */ - extended_gcd_modyk(u0,v0,vx,vy,dy,&cu[0],&cv[0]); + /* compute a(x,y), b(x,y) s.t. a*u0+b*v0 = 1 mod y^dy */ + extended_gcd_modyk(u0,v0,vx,vy,dy,&cu[0],&cv[0]); - /* dv0 = LC(v0)^(-1)*v0 mod y^dy */ - invgfsn((GFSN)LC(v0),&inv); mulp(vl,v0,(P)inv,&dv0); + /* dv0 = LC(v0)^(-1)*v0 mod y^dy */ + invgfsn((GFSN)LC(v0),&inv); mulp(vl,v0,(P)inv,&dv0); - /* cu[i]*u0+cv[i]*v0 = x^i mod y^dy */ - /* (x*cu[i])*u0+(x*cv[i])*v0 = x^(i+1) */ - /* x*cu[i] = q*dv0+r => cu[i+1] = r */ - /* cv[i+1]*v0 = x*cv[i]*v0+q*u0*dv0 = (x*cv[i]+q*u0*inv)*v0 */ - for ( i = 1; i <= n; i++ ) { - mulp(vl,x,cu[i-1],&m); divsrp(vl,m,dv0,&q,&cu[i]); - mulp(vl,x,cv[i-1],&m); mulp(vl,q,(P)inv,&t); - mulp(vl,t,u0,&s); - addp(vl,m,s,&cv[i]); - } + /* cu[i]*u0+cv[i]*v0 = x^i mod y^dy */ + /* (x*cu[i])*u0+(x*cv[i])*v0 = x^(i+1) */ + /* x*cu[i] = q*dv0+r => cu[i+1] = r */ + /* cv[i+1]*v0 = x*cv[i]*v0+q*u0*dv0 = (x*cv[i]+q*u0*inv)*v0 */ + for ( i = 1; i <= n; i++ ) { + mulp(vl,x,cu[i-1],&m); divsrp(vl,m,dv0,&q,&cu[i]); + mulp(vl,x,cv[i-1],&m); mulp(vl,q,(P)inv,&t); + mulp(vl,t,u0,&s); + addp(vl,m,s,&cv[i]); + } #if 0 - /* XXX : check */ - for ( i = 0; i <= n; i++ ) { - mulp(vl,cu[i],u0,&m); mulp(vl,cv[i],v0,&s); - addp(vl,m,s,&w); - printexpr(vl,w); - fprintf(asir_out,"\n"); - } + /* XXX : check */ + for ( i = 0; i <= n; i++ ) { + mulp(vl,cu[i],u0,&m); mulp(vl,cv[i],v0,&s); + addp(vl,m,s,&w); + printexpr(vl,w); + fprintf(asir_out,"\n"); + } #endif - dbd = dbound(vx,f)+1; + dbd = dbound(vx,f)+1; - /* extract homogeneous parts */ - W_CALLOC(dbd,P,uh); W_CALLOC(dbd,P,vh); - for ( i = 0; i <= dbd; i++ ) { - exthpc(vl,vx,u,i,&uh[i]); exthpc(vl,vx,v,i,&vh[i]); - } + /* extract homogeneous parts */ + W_CALLOC(dbd,P,uh); W_CALLOC(dbd,P,vh); + for ( i = 0; i <= dbd; i++ ) { + exthpc(vl,vx,u,i,&uh[i]); exthpc(vl,vx,v,i,&vh[i]); + } - /* register degrees in each variables */ - for ( nv = 0, tvl = rvl; tvl; tvl = NEXT(tvl), nv++ ); - md = (int *)ALLOCA(nv*sizeof(int)); - for ( i = 0, tvl = rvl; i < nv; tvl = NEXT(tvl), i++ ) - md[i] = getdeg(tvl->v,f); + /* register degrees in each variables */ + for ( nv = 0, tvl = rvl; tvl; tvl = NEXT(tvl), nv++ ); + md = (int *)ALLOCA(nv*sizeof(int)); + for ( i = 0, tvl = rvl; i < nv; tvl = NEXT(tvl), i++ ) + md[i] = getdeg(tvl->v,f); - /* XXX for removing content of factor wrt vx */ - NEWVL(onevl); onevl->v = vx; NEXT(onevl) = 0; + /* XXX for removing content of factor wrt vx */ + NEWVL(onevl); onevl->v = vx; NEXT(onevl) = 0; - for ( j = 1; j <= dbd; j++ ) { - for ( i = 0, tvl = rvl; i < nv; tvl = NEXT(tvl), i++ ) - if ( getdeg(tvl->v,u)+getdeg(tvl->v,v) > md[i] ) { - *up = 0; - return; - } - for ( i = 0, t = 0; i <= j; i++ ) { - mulp(vl,uh[i],vh[j-i],&s); addp(vl,s,t,&w); t = w; - } + for ( j = 1; j <= dbd; j++ ) { + for ( i = 0, tvl = rvl; i < nv; tvl = NEXT(tvl), i++ ) + if ( getdeg(tvl->v,u)+getdeg(tvl->v,v) > md[i] ) { + *up = 0; + return; + } + for ( i = 0, t = 0; i <= j; i++ ) { + mulp(vl,uh[i],vh[j-i],&s); addp(vl,s,t,&w); t = w; + } - /* s = degree j part of (f-uv) */ - exthpc(vl,vx,ff,j,&fj); subp(vl,fj,t,&s); - for ( i = 0, wu = 0, wv = 0; i <= n; i++ ) { - if ( !s ) - si = 0; - else if ( VR(s) == vx ) - coefp(s,i,&si); - else if ( i == 0 ) - si = s; - else - si = 0; - if ( si ) { - mulp(vl,si,cv[i],&m); addp(vl,wu,m,&t); wu = t; - mulp(vl,si,cu[i],&m); addp(vl,wv,m,&t); wv = t; - } - } - if ( !wu ) { - gfsn_poly_to_poly(vl,u,vy,&t); - shift_sf(vl,rvl,t,mev,-1,&s); - if ( divtp(vl,fin,s,&q) ) { - cont_pp_mv_sf(vl,onevl,s,&cont,up); - return; - } - } - if ( !wv ) { - gfsn_poly_to_poly(vl,v,vy,&t); - shift_sf(vl,rvl,t,mev,-1,&s); - if ( divtp(vl,fin,s,&q) ) { - cont_pp_mv_sf(vl,onevl,q,&cont,up); - return; - } - } - addp(vl,u,wu,&t); u = t; - addp(vl,uh[j],wu,&t); uh[j] = t; - addp(vl,v,wv,&t); v = t; - addp(vl,vh[j],wv,&t); vh[j] = t; - } - gfsn_poly_to_poly(vl,u,vy,&t); - shift_sf(vl,rvl,t,mev,-1,&s); - if ( divtp(vl,fin,s,&q) ) - cont_pp_mv_sf(vl,onevl,s,&cont,up); - else - *up = 0; + /* s = degree j part of (f-uv) */ + exthpc(vl,vx,ff,j,&fj); subp(vl,fj,t,&s); + for ( i = 0, wu = 0, wv = 0; i <= n; i++ ) { + if ( !s ) + si = 0; + else if ( VR(s) == vx ) + coefp(s,i,&si); + else if ( i == 0 ) + si = s; + else + si = 0; + if ( si ) { + mulp(vl,si,cv[i],&m); addp(vl,wu,m,&t); wu = t; + mulp(vl,si,cu[i],&m); addp(vl,wv,m,&t); wv = t; + } + } + if ( !wu ) { + gfsn_poly_to_poly(vl,u,vy,&t); + shift_sf(vl,rvl,t,mev,-1,&s); + if ( divtp(vl,fin,s,&q) ) { + cont_pp_mv_sf(vl,onevl,s,&cont,up); + return; + } + } + if ( !wv ) { + gfsn_poly_to_poly(vl,v,vy,&t); + shift_sf(vl,rvl,t,mev,-1,&s); + if ( divtp(vl,fin,s,&q) ) { + cont_pp_mv_sf(vl,onevl,q,&cont,up); + return; + } + } + addp(vl,u,wu,&t); u = t; + addp(vl,uh[j],wu,&t); uh[j] = t; + addp(vl,v,wv,&t); v = t; + addp(vl,vh[j],wv,&t); vh[j] = t; + } + gfsn_poly_to_poly(vl,u,vy,&t); + shift_sf(vl,rvl,t,mev,-1,&s); + if ( divtp(vl,fin,s,&q) ) + cont_pp_mv_sf(vl,onevl,s,&cont,up); + else + *up = 0; } void adjust_coef_sf(VL vl,VL rvl,P lcu,P u0,int *mev,P *r) { - P lcu0,cu; - DCP dc0,dcu,dc; + P lcu0,cu; + DCP dc0,dcu,dc; - substvp_sf(vl,rvl,lcu,mev,&lcu0); - divsp(vl,lcu0,LC(u0),&cu); - for ( dc0 = 0, dcu = DC(u0); dcu; dcu = NEXT(dcu) ) { - if ( !dc0 ) { - NEXTDC(dc0,dc); - COEF(dc) = lcu; - } else { - NEXTDC(dc0,dc); - mulp(vl,cu,COEF(dcu),&COEF(dc)); - } - DEG(dc) = DEG(dcu); - } - NEXT(dc) = 0; - MKP(VR(u0),dc0,*r); + substvp_sf(vl,rvl,lcu,mev,&lcu0); + divsp(vl,lcu0,LC(u0),&cu); + for ( dc0 = 0, dcu = DC(u0); dcu; dcu = NEXT(dcu) ) { + if ( !dc0 ) { + NEXTDC(dc0,dc); + COEF(dc) = lcu; + } else { + NEXTDC(dc0,dc); + mulp(vl,cu,COEF(dcu),&COEF(dc)); + } + DEG(dc) = DEG(dcu); + } + NEXT(dc) = 0; + MKP(VR(u0),dc0,*r); } void extended_gcd_modyk(P u0,P v0,V x,V y,int dy,P *cu,P *cv) { - BM g,h,a,b; + BM g,h,a,b; - gfsn_univariate_to_sfbm(u0,dy,&g); - gfsn_univariate_to_sfbm(v0,dy,&h); - sfexgcd_by_hensel(g,h,dy,&a,&b); - sfbm_to_gfsn_univariate(a,x,y,cu); - sfbm_to_gfsn_univariate(b,x,y,cv); + gfsn_univariate_to_sfbm(u0,dy,&g); + gfsn_univariate_to_sfbm(v0,dy,&h); + sfexgcd_by_hensel(g,h,dy,&a,&b); + sfbm_to_gfsn_univariate(a,x,y,cu); + sfbm_to_gfsn_univariate(b,x,y,cv); } /* (F[y])[x] -> F[x][y] */ void gfsn_univariate_to_sfbm(P f,int dy,BM *r) { - int dx,d,i; - BM b; - UM cy; - DCP dc; + int dx,d,i; + BM b; + UM cy; + DCP dc; - dx = getdeg(VR(f),f); - b = BMALLOC(dx,dy); - DEG(b) = dy; - for ( dc = DC(f); dc; dc = NEXT(dc) ) { - /* d : degree in x, cy : poly in y */ - d = QTOS(DEG(dc)); - cy = BDY((GFSN)COEF(dc)); - for ( i = DEG(cy); i >= 0; i-- ) - COEF(COEF(b)[i])[d] = COEF(cy)[i]; - } - for ( i = 0; i <= dy; i++ ) - degum(COEF(b)[i],dx); - *r = b; + dx = getdeg(VR(f),f); + b = BMALLOC(dx,dy); + DEG(b) = dy; + for ( dc = DC(f); dc; dc = NEXT(dc) ) { + /* d : degree in x, cy : poly in y */ + d = QTOS(DEG(dc)); + cy = BDY((GFSN)COEF(dc)); + for ( i = DEG(cy); i >= 0; i-- ) + COEF(COEF(b)[i])[d] = COEF(cy)[i]; + } + for ( i = 0; i <= dy; i++ ) + degum(COEF(b)[i],dx); + *r = b; } void sfbm_to_gfsn_univariate(BM f,V x,V y,P *r) { - P g; - VL vl; + P g; + VL vl; - sfbmtop(f,x,y,&g); - NEWVL(vl); vl->v = x; - NEWVL(NEXT(vl)); NEXT(vl)->v = y; - NEXT(NEXT(vl)) = 0; - poly_to_gfsn_poly(vl,g,y,r); + sfbmtop(f,x,y,&g); + NEWVL(vl); vl->v = x; + NEWVL(NEXT(vl)); NEXT(vl)->v = y; + NEXT(NEXT(vl)) = 0; + poly_to_gfsn_poly(vl,g,y,r); } void poly_to_gfsn_poly(VL vl,P f,V v,P *r) { - VL tvl,nvl0,nvl; - P g; + VL tvl,nvl0,nvl; + P g; - /* (x,y,...,v,...) -> (x,y,...,v) */ - for ( nvl0 = 0, tvl = vl; tvl; tvl = NEXT(tvl) ) { - if ( tvl->v != v ) { - NEXTVL(nvl0,nvl); - nvl->v = tvl->v; - } - } - NEXTVL(nvl0,nvl); - nvl->v = v; - NEXT(nvl) = 0; - reorderp(nvl0,vl,f,&g); - poly_to_gfsn_poly_main(g,v,r); + /* (x,y,...,v,...) -> (x,y,...,v) */ + for ( nvl0 = 0, tvl = vl; tvl; tvl = NEXT(tvl) ) { + if ( tvl->v != v ) { + NEXTVL(nvl0,nvl); + nvl->v = tvl->v; + } + } + NEXTVL(nvl0,nvl); + nvl->v = v; + NEXT(nvl) = 0; + reorderp(nvl0,vl,f,&g); + poly_to_gfsn_poly_main(g,v,r); } void poly_to_gfsn_poly_main(P f,V v,P *r) { - int d; - UM u; - GFSN g; - DCP dc,dct,dc0; + int d; + UM u; + GFSN g; + DCP dc,dct,dc0; - if ( !f ) - *r = f; - else if ( NUM(f) || VR(f) == v ) { - d = getdeg(v,f); - u = UMALLOC(d); - ptosfum(f,u); - MKGFSN(u,g); - *r = (P)g; - } else { - for ( dc0 = 0, dct = DC(f); dct; dct = NEXT(dct) ) { - NEXTDC(dc0,dc); - DEG(dc) = DEG(dct); - poly_to_gfsn_poly_main(COEF(dct),v,&COEF(dc)); - } - NEXT(dc) = 0; - MKP(VR(f),dc0,*r); - } + if ( !f ) + *r = f; + else if ( NUM(f) || VR(f) == v ) { + d = getdeg(v,f); + u = UMALLOC(d); + ptosfum(f,u); + MKGFSN(u,g); + *r = (P)g; + } else { + for ( dc0 = 0, dct = DC(f); dct; dct = NEXT(dct) ) { + NEXTDC(dc0,dc); + DEG(dc) = DEG(dct); + poly_to_gfsn_poly_main(COEF(dct),v,&COEF(dc)); + } + NEXT(dc) = 0; + MKP(VR(f),dc0,*r); + } } void gfsn_poly_to_poly(VL vl,P f,V v,P *r) { - VL tvl,nvl0,nvl; - P g; + VL tvl,nvl0,nvl; + P g; - gfsn_poly_to_poly_main(f,v,&g); - /* (x,y,...,v,...) -> (x,y,...,v) */ - for ( nvl0 = 0, tvl = vl; tvl; tvl = NEXT(tvl) ) { - if ( tvl->v != v ) { - NEXTVL(nvl0,nvl); - nvl->v = tvl->v; - } - } - NEXTVL(nvl0,nvl); - nvl->v = v; - NEXT(nvl) = 0; - reorderp(vl,nvl0,g,r); + gfsn_poly_to_poly_main(f,v,&g); + /* (x,y,...,v,...) -> (x,y,...,v) */ + for ( nvl0 = 0, tvl = vl; tvl; tvl = NEXT(tvl) ) { + if ( tvl->v != v ) { + NEXTVL(nvl0,nvl); + nvl->v = tvl->v; + } + } + NEXTVL(nvl0,nvl); + nvl->v = v; + NEXT(nvl) = 0; + reorderp(vl,nvl0,g,r); } void gfsn_poly_to_poly_main(P f,V v,P *r) { - DCP dc,dc0,dct; + DCP dc,dc0,dct; - if ( !f ) - *r = f; - else if ( NUM(f) ) { - if ( NID((Num)f) == N_GFSN ) - sfumtop(v,BDY((GFSN)f),r); - else - *r = f; - } else { - for ( dc0 = 0, dct = DC(f); dct; dct = NEXT(dct) ) { - NEXTDC(dc0,dc); - DEG(dc) = DEG(dct); - gfsn_poly_to_poly_main(COEF(dct),v,&COEF(dc)); - } - NEXT(dc) = 0; - MKP(VR(f),dc0,*r); - } + if ( !f ) + *r = f; + else if ( NUM(f) ) { + if ( NID((Num)f) == N_GFSN ) + sfumtop(v,BDY((GFSN)f),r); + else + *r = f; + } else { + for ( dc0 = 0, dct = DC(f); dct; dct = NEXT(dct) ) { + NEXTDC(dc0,dc); + DEG(dc) = DEG(dct); + gfsn_poly_to_poly_main(COEF(dct),v,&COEF(dc)); + } + NEXT(dc) = 0; + MKP(VR(f),dc0,*r); + } } void printsfum(UM f) { - int i; + int i; - for ( i = DEG(f); i >= 0; i-- ) { - printf("+("); - printf("%d",IFTOF(COEF(f)[i])); - printf(")*y^%d",i); - } + for ( i = DEG(f); i >= 0; i-- ) { + printf("+("); + printf("%d",IFTOF(COEF(f)[i])); + printf(")*y^%d",i); + } } void printsfbm(BM f) { - int i; + int i; - for ( i = DEG(f); i >= 0; i-- ) { - printf("+("); - printsfum(COEF(f)[i]); - printf(")*y^%d",i); - } + for ( i = DEG(f); i >= 0; i-- ) { + printf("+("); + printsfum(COEF(f)[i]); + printf(")*y^%d",i); + } }