version 1.4, 2002/09/30 06:13:07 |
version 1.7, 2002/10/30 08:07:11 |
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/* $OpenXM: OpenXM_contrib2/asir2000/engine/Fgfs.c,v 1.3 2002/09/27 08:40:48 noro Exp $ */ |
/* $OpenXM: OpenXM_contrib2/asir2000/engine/Fgfs.c,v 1.6 2002/10/25 02:43:40 noro Exp $ */ |
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#include "ca.h" |
#include "ca.h" |
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Line 10 void sqfrsfmain(VL vl,P f,DCP *dcp); |
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Line 10 void sqfrsfmain(VL vl,P f,DCP *dcp); |
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void pthrootsf(P f,Q m,P *r); |
void pthrootsf(P f,Q m,P *r); |
void partial_sqfrsf(VL vl,V v,P f,P *r,DCP *dcp); |
void partial_sqfrsf(VL vl,V v,P f,P *r,DCP *dcp); |
void gcdsf(VL vl,P *pa,int k,P *r); |
void gcdsf(VL vl,P *pa,int k,P *r); |
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void mfctrsfmain(VL vl, P f, DCP *dcp); |
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void next_evaluation_point(int *mev,int n); |
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void estimatelc_sf(VL vl,VL rvl,P c,DCP dc,P *lcp); |
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void mfctrsf_hensel(VL vl,VL rvl,P f,P pp0,P u0,P v0,P lcu,P lcv,P *up); |
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void substvp_sf(VL vl,VL rvl,P f,int *mev,P *r); |
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void shift_sf(VL vl, VL rvl, P f, int *mev, int sgn, P *r); |
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void adjust_coef_sf(VL vl,VL rvl,P lcu,P u0,P *r); |
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void extended_gcd_modyk(P u0,P v0,P *cu,P *cv); |
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void poly_to_gfsn_poly(VL vl,P f,V v,P *r); |
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void gfsn_poly_to_poly(VL vl,P f,V v,P *r); |
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void lex_lc(P f,P *c) |
void lex_lc(P f,P *c) |
{ |
{ |
Line 468 void cont_pp_mv_sf(VL vl,VL rvl,P p,P *c,P *pp) |
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Line 478 void cont_pp_mv_sf(VL vl,VL rvl,P p,P *c,P *pp) |
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ps[i] = C(t); |
ps[i] = C(t); |
ugcdsf(ps,m,c); |
ugcdsf(ps,m,c); |
divsp(vl,p,*c,pp); |
divsp(vl,p,*c,pp); |
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} |
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void mfctrsf(VL vl, P f, DCP *dcp) |
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{ |
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DCP dc0,dc,dct,dcs,dcr; |
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Obj obj; |
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simp_ff((Obj)f,&obj); f = (P)obj; |
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sqfrsf(vl,f,&dct); |
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dc = dc0 = dct; dct = NEXT(dct); NEXT(dc) = 0; |
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for ( ; dct; dct = NEXT(dct) ) { |
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mfctrsfmain(vl,COEF(dct),&dcs); |
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for ( dcr = dcs; dcr; dcr = NEXT(dcr) ) |
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DEG(dcr) = DEG(dct); |
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for ( ; NEXT(dc); dc = NEXT(dc) ); |
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NEXT(dc) = dcs; |
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} |
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*dcp = dc0; |
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} |
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/* f : sqfr, non const */ |
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void mfctrsfmain(VL vl, P f, DCP *dcp) |
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{ |
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VL tvl,nvl,rvl; |
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DCP dc,dc0,dc1,dc2,dct,lcfdc,dcs; |
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int imin,inext,i,j,n,k,np; |
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int *da; |
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V vx,vy; |
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V *va; |
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P *l,*tl; |
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P gcd,g,df,dfmin; |
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P pa[2]; |
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P g0,pp0,spp0,c,c0,x,y,u,v,lcf,lcu,lcv,u0,v0,t,s; |
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P ype,yme; |
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GFS ev,evy; |
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P *fp0; |
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int *mev,*win; |
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clctv(vl,f,&tvl); vl = tvl; |
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if ( !vl ) |
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error("mfctrsfmain : cannot happen"); |
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if ( !NEXT(vl) ) { |
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/* univariate */ |
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ufctrsf(f,&dc); |
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/* remove lc */ |
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*dcp = NEXT(dc); |
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return; |
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} |
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for ( n = 0, tvl = vl; tvl; tvl = NEXT(tvl), n++ ); |
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va = (V *)ALLOCA(n*sizeof(int)); |
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da = (int *)ALLOCA(n*sizeof(int)); |
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/* find v s.t. diff(f,v) is nonzero and deg(f,v) is minimal */ |
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imin = -1; |
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for ( i = 0, tvl = vl; i < n; tvl = NEXT(tvl), i++ ) { |
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va[i] = tvl->v; |
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da[i] = getdeg(va[i],f); |
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diffp(vl,f,va[i],&df); |
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if ( !df ) |
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continue; |
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if ( imin < 0 || da[i] < da[imin] ) { |
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dfmin = df; |
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imin = i; |
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} |
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} |
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/* find v1 neq v s.t. deg(f,v) is minimal */ |
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inext = -1; |
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for ( i = 0; i < n; i++ ) { |
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if ( i == imin ) |
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continue; |
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if ( inext < 0 || da[i] < da[inext] ) |
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inext = i; |
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} |
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pa[0] = f; |
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pa[1] = dfmin; |
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gcdsf_main(vl,pa,2,&gcd); |
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if ( !NUM(gcd) ) { |
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/* f = gcd * f/gcd */ |
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mfctrsfmain(vl,gcd,&dc1); |
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divsp(vl,f,gcd,&g); |
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mfctrsfmain(vl,g,&dc2); |
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for ( dct = dc1; NEXT(dct); dct = NEXT(dct) ); |
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NEXT(dct) = dc2; |
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*dcp = dc1; |
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return; |
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} |
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/* create vl s.t. vl[0] = va[imin], vl[1] = va[inext] */ |
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nvl = 0; |
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NEXTVL(nvl,tvl); tvl->v = va[imin]; |
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NEXTVL(nvl,tvl); tvl->v = va[inext]; |
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for ( i = 0; i < n; i++ ) { |
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if ( i == imin || i == inext ) |
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continue; |
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NEXTVL(nvl,tvl); tvl->v = va[i]; |
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} |
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NEXT(tvl) = 0; |
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reorderp(nvl,vl,f,&g); |
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vx = nvl->v; |
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vy = NEXT(nvl)->v; |
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MKV(vx,x); |
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MKV(vy,y); |
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/* remaining variables */ |
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rvl = NEXT(NEXT(nvl)); |
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if ( !rvl ) { |
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/* bivariate */ |
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sfbfctr(g,vx,vy,getdeg(vx,g),&dc1); |
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for ( dc0 = 0; dc1; dc1 = NEXT(dc1) ) { |
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NEXTDC(dc0,dc); |
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DEG(dc) = ONE; |
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reorderp(vl,nvl,COEF(dc1),&COEF(dc)); |
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} |
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NEXT(dc) = 0; |
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*dcp = dc0; |
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return; |
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} |
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/* n >= 3; nvl = (vx,vy,X) */ |
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/* find good evaluation pt for X */ |
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mev = (int *)CALLOC(n-2,sizeof(int)); |
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while ( 1 ) { |
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substvp_sf(nvl,rvl,g,mev,&g0); |
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pa[0] = g0; |
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diffp(nvl,g0,vx,&pa[1]); |
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if ( pa[1] ) { |
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gcdsf(nvl,pa,2,&gcd); |
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/* XXX maybe we have to accept the case where gcd is a poly of y */ |
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if ( NUM(gcd) ) |
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break; |
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} |
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/* XXX if generated indices exceed q of GF(q) => error in indextogfs */ |
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next_evaluation_point(mev,n-2); |
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} |
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/* g0 = g(x,y,mev) */ |
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/* separate content; g0 may have the content wrt x */ |
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cont_pp_sfp(nvl,g0,&c0,&pp0); |
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/* factorize pp0; pp0 = pp0(x,y+evy) = prod dc */ |
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sfbfctr_shift(pp0,vx,vy,getdeg(vx,pp0),&evy,&spp0,&dc); pp0 = spp0; |
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if ( !NEXT(dc) ) { |
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/* f is irreducible */ |
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NEWDC(dc); DEG(dc) = ONE; COEF(dc) = f; NEXT(dc) = 0; |
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*dcp = dc; |
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return; |
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} |
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/* ype = y+evy, yme = y-evy */ |
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addp(nvl,y,(P)evy,&ype); subp(nvl,y,(P)evy,&yme); |
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/* shift c0; c0 <- c0(y+evy) */ |
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substp(nvl,c0,vy,ype,&s); c0 = s; |
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/* shift f; f <- f(y+evy) */ |
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substp(nvl,f,vy,ype,&s); f = s; |
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/* now f(x,0,mev) = c0 * prod dc */ |
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/* factorize lc_x(f) */ |
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lcf = COEF(DC(f)); |
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mfctrsf(nvl,lcf,&dct); |
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/* skip the first element (= a number) */ |
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dct = NEXT(dct); |
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/* shift lcfdc; c <- c(X+mev) */ |
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for ( lcfdc = 0; dct; dct = NEXT(dct) ) { |
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NEXTDC(lcfdc,dcs); |
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DEG(dcs) = DEG(dct); |
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shift_sf(nvl,rvl,COEF(dct),mev,1,&COEF(dcs)); |
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} |
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NEXT(dcs) = 0; |
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/* np = number of bivariate factors */ |
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for ( np = 0, dct = dc; dct; dct = NEXT(dct), np++ ); |
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fp0 = (P *)ALLOCA((np+1)*sizeof(P)); |
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for ( i = 0, dct = dc; i < np; dct = NEXT(dct), i++ ) |
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fp0[i] = COEF(dct); |
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fp0[np] = 0; |
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l = tl = (P *)ALLOCA((np+1)*sizeof(P)); |
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win = W_ALLOC(np+1); |
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/* f <- f(X+mev) */ |
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shift_sf(nvl,rvl,f,mev,1,&s); f = s; |
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for ( k = 1, win[0] = 1, --np; ; ) { |
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itogfs(1,&u0); |
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/* u0 = product of selected factors */ |
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for ( i = 0; i < k; i++ ) { |
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mulp(nvl,u0,fp0[win[i]],&t); u0 = t; |
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} |
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/* we have to consider the content */ |
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/* g0 = c0*u0*v0 */ |
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mulp(nvl,LC(u0),c0,&c); estimatelc_sf(nvl,rvl,c,lcfdc,&lcu); |
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divsp(nvl,pp0,u0,&v0); |
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mulp(nvl,LC(v0),c0,&c); estimatelc_sf(nvl,rvl,c,lcfdc,&lcv); |
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mfctrsf_hensel(nvl,rvl,f,pp0,u0,v0,lcu,lcv,&u); |
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if ( u ) { |
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/* save the factor */ |
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reorderp(vl,nvl,u,&t); |
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/* x -> x-mev, y -> y-evy */ |
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shift_sf(vl,rvl,t,mev,-1,&s); substp(vl,s,vy,yme,tl++); |
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/* update f,pp0 */ |
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divsp(nvl,f,u,&t); f = t; |
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divsp(nvl,pp0,u0,&t); pp0 = t; |
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/* update win, fp0 */ |
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for ( i = 0; i < k-1; i++ ) |
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for ( j = win[i]+1; j < win[i+1]; j++ ) |
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fp0[j-i-1] = fp0[j]; |
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for ( j = win[k-1]+1; j <= np; j++ ) |
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fp0[j-k] = fp0[j]; |
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if ( ( np -= k ) < k ) break; |
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if ( np-win[0]+1 < k ) |
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if ( ++k <= np ) { |
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for ( i = 0; i < k; i++ ) |
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win[i] = i + 1; |
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continue; |
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} else |
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break; |
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else |
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for ( i = 1; i < k; i++ ) |
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win[i] = win[0] + i; |
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} else { |
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if ( ncombi(1,np,k,win) == 0 ) |
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if ( k == np ) break; |
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else |
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for ( i = 0, ++k; i < k; i++ ) |
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win[i] = i + 1; |
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} |
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reorderp(vl,nvl,f,&t); |
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/* x -> x-mev, y -> y-evy */ |
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shift_sf(vl,rvl,t,mev,-1,&s); substp(vl,s,vy,yme,tl++); |
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*tl = 0; |
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for ( dc0 = 0, i = 0; l[i]; i++ ) { |
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NEXTDC(dc0,dc); DEG(dc) = ONE; COEF(dc) = l[i]; |
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} |
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NEXT(dc) = 0; *dcp = dc0; |
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} |
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} |
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void next_evaluation_point(int *e,int n) |
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{ |
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int i,t,j; |
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for ( i = n-1; i >= 0; i-- ) |
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if ( e[i] ) break; |
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if ( i < 0 ) e[n-1] = 1; |
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else if ( i == 0 ) { |
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t = e[0]; e[0] = 0; e[n-1] = t+1; |
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} else { |
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e[i-1]++; t = e[i]; |
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for ( j = i; j < n-1; j++ ) |
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e[j] = 0; |
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e[n-1] = t-1; |
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} |
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} |
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/* |
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* dc : f1^E1*...*fk^Ek |
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* find e1,...,ek s.t. fi(0)^ei | c |
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* and return f1^e1*...*fk^ek |
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* vl = (vx,vy,rvl) |
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*/ |
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void estimatelc_sf(VL vl,VL rvl,P c,DCP dc,P *lcp) |
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{ |
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DCP dct; |
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P r,c1,c2,t,s,f; |
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int i,d; |
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Q q; |
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for ( dct = dc, r = (P)ONE; dct; dct = NEXT(dct) ) { |
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if ( NUM(COEF(dct)) ) |
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continue; |
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/* constant part */ |
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substvp_sf(vl,rvl,COEF(dct),0,&f); |
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d = QTOS(DEG(dct)); |
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for ( i = 0, c1 = c; i < d; i++ ) |
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if ( !divtp(vl,c1,f,&c2) ) |
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break; |
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else |
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c1 = c2; |
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if ( i ) { |
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STOQ(i,q); |
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pwrp(vl,COEF(dct),q,&s); mulp(vl,r,s,&t); r = t; |
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} |
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} |
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*lcp = r; |
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} |
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void substvp_sf(VL vl,VL rvl,P f,int *mev,P *r) |
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{ |
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int i; |
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VL tvl; |
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P g,t; |
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GFS ev; |
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for ( g = f, i = 0, tvl = rvl; tvl; tvl = NEXT(tvl), i++ ) { |
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if ( !mev ) |
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ev = 0; |
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else |
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indextogfs(mev[i],&ev); |
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substp(vl,g,tvl->v,(P)ev,&t); g = t; |
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} |
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*r = g; |
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} |
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/* |
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* f <- f(X+sgn*mev) |
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*/ |
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void shift_sf(VL vl, VL rvl, P f, int *mev, int sgn, P *r) |
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{ |
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VL tvl; |
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int i; |
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P x,g,t,s; |
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GFS ev; |
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for ( g = f, tvl = rvl, i = 0; tvl; tvl = NEXT(tvl), i++ ) { |
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if ( !mev[i] ) |
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continue; |
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indextogfs(mev[i],&ev); |
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MKV(tvl->v,x); |
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if ( sgn > 0 ) |
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addp(vl,x,(P)ev,&t); |
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else |
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subp(vl,x,(P)ev,&t); |
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substp(vl,g,tvl->v,t,&s); g = s; |
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} |
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*r = g; |
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} |
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/* |
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* pp(f(0)) = u0*v0 |
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*/ |
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void mfctrsf_hensel(VL vl,VL rvl,P f,P pp0,P u0,P v0,P lcu,P lcv,P *up) |
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{ |
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VL tvl,onevl; |
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P t,s,w,u,v,ff,si,wu,wv,fj,cont; |
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UM ydy; |
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V vx,vy; |
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int dy,n,i,dbd,nv,j; |
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int *md; |
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P *uh,*vh; |
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P x,du0,dv0,m,q,r; |
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P *cu,*cv; |
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GFSN inv; |
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/* adjust coeffs */ |
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/* u0 = am x^m+ ... -> lcu*x^m + a(m-1)*(lcu(0)/am)*x^(m-1)+... */ |
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/* v0 = bm x^l+ ... -> lcv*x^l + b(l-1)*(lcv(0)/bl)*x^(l-1)+... */ |
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adjust_coef_sf(vl,rvl,lcu,u0,&u); |
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adjust_coef_sf(vl,rvl,lcv,v0,&v); |
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vx = vl->v; vy = NEXT(vl)->v; |
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n = getdeg(vx,f); |
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dy = getdeg(vy,f)+1; |
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MKV(vx,x); |
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cu = (P *)ALLOCA((n+1)*sizeof(P)); |
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cv = (P *)ALLOCA((n+1)*sizeof(P)); |
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/* ydy = y^dy */ |
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ydy = C_UMALLOC(dy); COEF(ydy)[dy] = 1; |
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setmod_gfsn(ydy); |
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/* (R[y]/(y^dy))[x,X] */ |
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poly_to_gfsn_poly(vl,f,vy,&t); ff = t; |
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poly_to_gfsn_poly(vl,u,vy,&t); u = t; |
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poly_to_gfsn_poly(vl,v,vy,&t); v = t; |
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substvp_sf(vl,rvl,u,0,&u0); |
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substvp_sf(vl,rvl,v,0,&v0); |
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/* compute a(x,y), b(x,y) s.t. a*u0+b*v0 = 1 mod y^dy */ |
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extended_gcd_modyk(u0,v0,&cu[0],&cv[0]); |
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/* du0 = LC(u0)^(-1)*u0 mod y^dy */ |
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/* dv0 = LC(v0)^(-1)*v0 mod y^dy */ |
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invgfsn((GFSN)LC(u0),&inv); mulp(vl,u0,(P)inv,&du0); |
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invgfsn((GFSN)LC(v0),&inv); mulp(vl,v0,(P)inv,&dv0); |
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/* cu[i]*u0+cv[i]*v0 = x^i mod y^dy */ |
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for ( i = 1; i <= n; i++ ) { |
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mulp(vl,x,cu[i-1],&m); divsrp(vl,m,dv0,&q,&cu[i]); |
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mulp(vl,x,cv[i-1],&m); divsrp(vl,m,du0,&q,&cv[i]); |
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} |
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dbd = dbound(vx,f)+1; |
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/* extract homogeneous parts */ |
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W_CALLOC(dbd,P,uh); W_CALLOC(dbd,P,vh); |
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for ( i = 0; i <= dbd; i++ ) { |
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exthpc(vl,vx,u,i,&uh[i]); exthpc(vl,vx,v,i,&vh[i]); |
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} |
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/* register degrees in each variables */ |
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for ( nv = 0, tvl = rvl; tvl; tvl = NEXT(tvl), nv++ ); |
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md = (int *)ALLOCA(nv*sizeof(int)); |
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for ( i = 0, tvl = rvl; i < nv; tvl = NEXT(tvl), i++ ) |
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md[i] = getdeg(tvl->v,ff); |
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/* XXX for removing content of factor wrt vx */ |
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NEWVL(onevl); onevl->v = vx; NEXT(onevl) = 0; |
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for ( j = 1; j <= dbd; j++ ) { |
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for ( i = 0, tvl = rvl; i < nv; tvl = NEXT(tvl), i++ ) |
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if ( getdeg(tvl->v,u)+getdeg(tvl->v,v) > md[i] ) { |
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*up = 0; |
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return; |
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} |
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for ( i = 0, t = 0; i <= j; i++ ) { |
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mulp(vl,uh[i],vh[j-i],&s); addp(vl,s,t,&w); t = w; |
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} |
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/* s = degree j part of (f-uv) */ |
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exthpc(vl,vx,ff,j,&fj); subp(vl,fj,t,&s); |
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for ( i = 0, wu = 0, wv = 0; i <= n; i++ ) { |
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if ( s ) |
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si = 0; |
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else if ( VR(s) == vx ) |
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coefp(s,i,&si); |
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else if ( i == 0 ) |
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si = s; |
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else |
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si = 0; |
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if ( si ) { |
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mulp(vl,si,cu[i],&m); addp(vl,wu,m,&t); wu = t; |
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mulp(vl,si,cv[i],&m); addp(vl,wv,m,&t); wv = t; |
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} |
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} |
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if ( !wu ) { |
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gfsn_poly_to_poly(vl,u,vy,&t); u = t; |
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if ( divtp(vl,f,u,&q) ) { |
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cont_pp_mv_sf(vl,onevl,u,&cont,up); |
|
return; |
|
} |
|
} |
|
if ( !wv ) { |
|
gfsn_poly_to_poly(vl,v,vy,&t); v = t; |
|
if ( divtp(vl,f,u,&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; |
|
} |
|
} |
|
|
|
void adjust_coef_sf(VL vl,VL rvl,P lcu,P u0,P *r) |
|
{ |
|
P lcu0,cu; |
|
DCP dc0,dcu,dc; |
|
|
|
substvp_sf(vl,rvl,lcu,0,&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,P *cu,P *cv) |
|
{ |
|
} |
|
|
|
void poly_to_gfsn_poly(VL vl,P f,V v,P *r) |
|
{ |
|
} |
|
|
|
void gfsn_poly_to_poly(VL vl,P f,V v,P *r) |
|
{ |
} |
} |