version 1.9, 2002/11/01 06:47:41 |
version 1.10, 2002/11/22 07:32:10 |
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/* $OpenXM: OpenXM_contrib2/asir2000/engine/Fgfs.c,v 1.8 2002/11/01 05:43:35 noro Exp $ */ |
/* $OpenXM: OpenXM_contrib2/asir2000/engine/Fgfs.c,v 1.9 2002/11/01 06:47:41 noro Exp $ */ |
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#include "ca.h" |
#include "ca.h" |
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void cont_pp_mv_sf(VL vl,VL rvl,P p,P *c,P *pp); |
void cont_pp_mv_sf(VL vl,VL rvl,P p,P *c,P *pp); |
void gcdsf_main(VL vl,P *pa,int m,P *r); |
void gcdsf_main(VL vl,P *pa,int m,P *r); |
void ugcdsf(P *pa,int m,P *r); |
void ugcdsf(P *pa,int m,P *r); |
void head_monomial(V v,P p,P *coef,P *term); |
void head_monomial(VL vl,V v,P p,P *coef,P *term); |
void sqfrsfmain(VL vl,P f,DCP *dcp); |
void sqfrsfmain(VL vl,P f,DCP *dcp); |
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); |
Line 351 void gcdsf_main(VL vl,P *pa,int m,P *r) |
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Line 351 void gcdsf_main(VL vl,P *pa,int m,P *r) |
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for ( i = 0; i < m; i++ ) { |
for ( i = 0; i < m; i++ ) { |
reorderp(nvl,vl,pa[i],&t); |
reorderp(nvl,vl,pa[i],&t); |
cont_pp_mv_sf(nvl,rvl,t,&pc[i],&ps[i]); |
cont_pp_mv_sf(nvl,rvl,t,&pc[i],&ps[i]); |
head_monomial(vmin,ps[i],&ph[i],&t); |
head_monomial(nvl,vmin,ps[i],&ph[i],&t); |
} |
} |
ugcdsf(pc,m,&cont); |
ugcdsf(pc,m,&cont); |
ugcdsf(ph,m,&hg); |
ugcdsf(ph,m,&hg); |
Line 377 void gcdsf_main(VL vl,P *pa,int m,P *r) |
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Line 377 void gcdsf_main(VL vl,P *pa,int m,P *r) |
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substp(nvl,ps[i],vmin,s,&ph[i]); |
substp(nvl,ps[i],vmin,s,&ph[i]); |
/* ge = GCD(ps[0]|x=s,...,ps[m-1]|x=s) */ |
/* ge = GCD(ps[0]|x=s,...,ps[m-1]|x=s) */ |
gcdsf(nvl,ph,m,&ge); |
gcdsf(nvl,ph,m,&ge); |
head_monomial(vmin,ge,&ce,&he); |
head_monomial(nvl,vmin,ge,&ce,&he); |
if ( NUM(he) ) { |
if ( NUM(he) ) { |
*r = cont; |
*r = cont; |
return; |
return; |
Line 444 void gcdsf_main(VL vl,P *pa,int m,P *r) |
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Line 444 void gcdsf_main(VL vl,P *pa,int m,P *r) |
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} |
} |
} |
} |
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void head_monomial(V v,P p,P *coef,P *term) |
void head_monomial(VL vl,V v,P p,P *coef,P *term) |
{ |
{ |
P t,s,u; |
P t,s,u; |
DCP dc; |
DCP dc; |
GFS one; |
GFS one; |
VL vl; |
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itogfs(1,&one); |
itogfs(1,&one); |
t = (P)one; |
t = (P)one; |
Line 480 void cont_pp_mv_sf(VL vl,VL rvl,P p,P *c,P *pp) |
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Line 479 void cont_pp_mv_sf(VL vl,VL rvl,P p,P *c,P *pp) |
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ps = (P *)ALLOCA(m*sizeof(P)); |
ps = (P *)ALLOCA(m*sizeof(P)); |
for ( t = BDY(dp), i = 0; t; t = NEXT(t), i++ ) |
for ( t = BDY(dp), i = 0; t; t = NEXT(t), i++ ) |
ps[i] = C(t); |
ps[i] = C(t); |
ugcdsf(ps,m,c); |
gcdsf(vl,ps,m,c); |
divsp(vl,p,*c,pp); |
divsp(vl,p,*c,pp); |
} |
} |
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Line 515 void mfctrsfmain(VL vl, P f, DCP *dcp) |
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Line 514 void mfctrsfmain(VL vl, P f, DCP *dcp) |
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P *l,*tl; |
P *l,*tl; |
P gcd,g,df,dfmin; |
P gcd,g,df,dfmin; |
P pa[2]; |
P pa[2]; |
P g0,pp0,spp0,c,c0,x,y,u,v,lcf,lcu,lcv,u0,v0,t,s; |
P f0,pp0,spp0,c,c0,x,y,u,v,lcf,lcu,lcv,u0,v0,t,s; |
P ype,yme; |
P ype,yme; |
GFS ev,evy; |
GFS ev,evy; |
P *fp0; |
P *fp0; |
Line 579 void mfctrsfmain(VL vl, P f, DCP *dcp) |
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Line 578 void mfctrsfmain(VL vl, P f, DCP *dcp) |
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} |
} |
NEXT(tvl) = 0; |
NEXT(tvl) = 0; |
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reorderp(nvl,vl,f,&g); |
reorderp(nvl,vl,f,&g); f = g; |
vx = nvl->v; |
vx = nvl->v; |
vy = NEXT(nvl)->v; |
vy = NEXT(nvl)->v; |
MKV(vx,x); |
MKV(vx,x); |
Line 588 void mfctrsfmain(VL vl, P f, DCP *dcp) |
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Line 587 void mfctrsfmain(VL vl, P f, DCP *dcp) |
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rvl = NEXT(NEXT(nvl)); |
rvl = NEXT(NEXT(nvl)); |
if ( !rvl ) { |
if ( !rvl ) { |
/* bivariate */ |
/* bivariate */ |
sfbfctr(g,vx,vy,getdeg(vx,g),&dc1); |
sfbfctr(f,vx,vy,getdeg(vx,f),&dc1); |
for ( dc0 = 0; dc1; dc1 = NEXT(dc1) ) { |
for ( dc0 = 0; dc1; dc1 = NEXT(dc1) ) { |
NEXTDC(dc0,dc); |
NEXTDC(dc0,dc); |
DEG(dc) = ONE; |
DEG(dc) = ONE; |
Line 602 void mfctrsfmain(VL vl, P f, DCP *dcp) |
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Line 601 void mfctrsfmain(VL vl, P f, DCP *dcp) |
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/* find good evaluation pt for X */ |
/* find good evaluation pt for X */ |
mev = (int *)CALLOC(n-2,sizeof(int)); |
mev = (int *)CALLOC(n-2,sizeof(int)); |
while ( 1 ) { |
while ( 1 ) { |
substvp_sf(nvl,rvl,g,mev,&g0); |
/* lcf(mev)=0 => invalid */ |
pa[0] = g0; |
substvp_sf(nvl,rvl,COEF(DC(f)),mev,&t); |
diffp(nvl,g0,vx,&pa[1]); |
if ( t ) { |
if ( pa[1] ) { |
substvp_sf(nvl,rvl,f,mev,&f0); |
gcdsf(nvl,pa,2,&gcd); |
pa[0] = f0; |
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diffp(nvl,f0,vx,&pa[1]); |
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if ( pa[1] ) { |
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gcdsf(nvl,pa,2,&gcd); |
/* XXX maybe we have to accept the case where gcd is a poly of y */ |
/* XXX maybe we have to accept the case where gcd is a poly of y */ |
if ( NUM(gcd) ) |
if ( NUM(gcd) ) |
break; |
break; |
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} |
} |
} |
/* XXX if generated indices exceed q of GF(q) => error in indextogfs */ |
/* XXX if generated indices exceed q of GF(q) => error in indextogfs */ |
next_evaluation_point(mev,n-2); |
next_evaluation_point(mev,n-2); |
} |
} |
/* g0 = g(x,y,mev) */ |
/* f0 = f(x,y,mev) */ |
/* separate content; g0 may have the content wrt x */ |
/* separate content; f0 may have the content wrt x */ |
cont_pp_sfp(nvl,g0,&c0,&pp0); |
cont_pp_sfp(nvl,f0,&c0,&pp0); |
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/* factorize pp0; pp0 = pp0(x,y+evy) = prod dc */ |
/* factorize pp0; pp0 = pp0(x,y+evy) = prod dc */ |
sfbfctr_shift(pp0,vx,vy,getdeg(vx,pp0),&evy,&spp0,&dc); pp0 = spp0; |
sfbfctr_shift(pp0,vx,vy,getdeg(vx,pp0),&evy,&spp0,&dc); pp0 = spp0; |
Line 671 void mfctrsfmain(VL vl, P f, DCP *dcp) |
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Line 674 void mfctrsfmain(VL vl, P f, DCP *dcp) |
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mulp(nvl,u0,fp0[win[i]],&t); u0 = t; |
mulp(nvl,u0,fp0[win[i]],&t); u0 = t; |
} |
} |
/* we have to consider the content */ |
/* we have to consider the content */ |
/* g0 = c0*u0*v0 */ |
/* f0 = c0*u0*v0 */ |
mulp(nvl,LC(u0),c0,&c); estimatelc_sf(nvl,rvl,c,lcfdc,&lcu); |
mulp(nvl,LC(u0),c0,&c); estimatelc_sf(nvl,rvl,c,lcfdc,&lcu); |
divsp(nvl,pp0,u0,&v0); |
divsp(nvl,pp0,u0,&v0); |
mulp(nvl,LC(v0),c0,&c); estimatelc_sf(nvl,rvl,c,lcfdc,&lcv); |
mulp(nvl,LC(v0),c0,&c); estimatelc_sf(nvl,rvl,c,lcfdc,&lcv); |
Line 709 void mfctrsfmain(VL vl, P f, DCP *dcp) |
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Line 712 void mfctrsfmain(VL vl, P f, DCP *dcp) |
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for ( i = 0, ++k; i < k; i++ ) |
for ( i = 0, ++k; i < k; i++ ) |
win[i] = i + 1; |
win[i] = i + 1; |
} |
} |
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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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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void next_evaluation_point(int *e,int n) |
void next_evaluation_point(int *e,int n) |
Line 833 void mfctrsf_hensel(VL vl,VL rvl,P f,P pp0,P u0,P v0,P |
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Line 835 void mfctrsf_hensel(VL vl,VL rvl,P f,P pp0,P u0,P v0,P |
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/* adjust coeffs */ |
/* adjust coeffs */ |
/* u0 = am x^m+ ... -> lcu*x^m + a(m-1)*(lcu(0)/am)*x^(m-1)+... */ |
/* u0 = am x^m+ ... -> lcu*x^m + a(m-1)*(lcu(0)/am)*x^(m-1)+... */ |
/* v0 = bm x^l+ ... -> lcv*x^l + b(l-1)*(lcv(0)/bl)*x^(l-1)+... */ |
/* v0 = bm x^l+ ... -> lcv*x^l + b(l-1)*(lcv(0)/bl)*x^(l-1)+... */ |
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/* f -> lcu*lcv*x^(m+l)+... */ |
adjust_coef_sf(vl,rvl,lcu,u0,&u); |
adjust_coef_sf(vl,rvl,lcu,u0,&u); |
adjust_coef_sf(vl,rvl,lcv,v0,&v); |
adjust_coef_sf(vl,rvl,lcv,v0,&v); |
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mulp(vl,lcu,lcv,&t); divsp(vl,t,LC(f),&m); mulp(vl,m,f,&t); f = t; |
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vx = vl->v; vy = NEXT(vl)->v; |
vx = vl->v; vy = NEXT(vl)->v; |
n = getdeg(vx,f); |
n = getdeg(vx,f); |
dy = getdeg(vy,f)+1; |
dy = getdeg(vy,f)+1; |
Line 843 void mfctrsf_hensel(VL vl,VL rvl,P f,P pp0,P u0,P v0,P |
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Line 848 void mfctrsf_hensel(VL vl,VL rvl,P f,P pp0,P u0,P v0,P |
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cv = (P *)ALLOCA((n+1)*sizeof(P)); |
cv = (P *)ALLOCA((n+1)*sizeof(P)); |
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/* ydy = y^dy */ |
/* ydy = y^dy */ |
ydy = C_UMALLOC(dy); DEG(ydy) = dy; COEF(ydy)[dy] = 1; |
ydy = C_UMALLOC(dy); DEG(ydy) = dy; COEF(ydy)[dy] = _onesf(); |
setmod_gfsn(ydy); |
setmod_gfsn(ydy); |
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/* (R[y]/(y^dy))[x,X] */ |
/* (R[y]/(y^dy))[x,X] */ |
poly_to_gfsn_poly(vl,f,vy,&t); ff = t; |
poly_to_gfsn_poly(vl,f,vy,&ff); |
poly_to_gfsn_poly(vl,u,vy,&t); u = t; |
poly_to_gfsn_poly(vl,u,vy,&t); u = t; |
poly_to_gfsn_poly(vl,v,vy,&t); v = t; |
poly_to_gfsn_poly(vl,v,vy,&t); v = t; |
substvp_sf(vl,rvl,u,0,&u0); |
substvp_sf(vl,rvl,u,0,&u0); |
Line 856 void mfctrsf_hensel(VL vl,VL rvl,P f,P pp0,P u0,P v0,P |
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Line 861 void mfctrsf_hensel(VL vl,VL rvl,P f,P pp0,P u0,P v0,P |
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/* compute a(x,y), b(x,y) s.t. a*u0+b*v0 = 1 mod y^dy */ |
/* 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]); |
extended_gcd_modyk(u0,v0,vx,vy,dy,&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 */ |
/* dv0 = LC(v0)^(-1)*v0 mod y^dy */ |
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); |
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 */ |
/* cu[i]*u0+cv[i]*v0 = x^i mod y^dy */ |
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/* (x*cu[i])*u0+(x*cv[i])*v0 = x^(i+1) */ |
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/* x*cu[i] = q*dv0+r => cu[i+1] = r */ |
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/* cv[i+1]*v0 = x*cv[i]*v0+q*u0*dv0 = (x*cv[i]+q*u0*inv)*v0 */ |
for ( i = 1; i <= n; i++ ) { |
for ( i = 1; i <= n; i++ ) { |
mulp(vl,x,cu[i-1],&m); divsrp(vl,m,dv0,&q,&cu[i]); |
mulp(vl,x,cu[i-1],&m); divsrp(vl,m,dv0,&q,&cu[i]); |
mulp(vl,x,cv[i-1],&m); divsrp(vl,m,du0,&q,&cv[i]); |
mulp(vl,x,cv[i-1],&m); mulp(vl,q,(P)inv,&t); |
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mulp(vl,t,u0,&s); |
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addp(vl,m,s,&cv[i]); |
} |
} |
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#if 0 |
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/* XXX : check */ |
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for ( i = 0; i <= n; i++ ) { |
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mulp(vl,cu[i],u0,&m); mulp(vl,cv[i],v0,&s); |
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addp(vl,m,s,&w); |
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printexpr(vl,w); |
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fprintf(asir_out,"\n"); |
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} |
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#endif |
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dbd = dbound(vx,f)+1; |
dbd = dbound(vx,f)+1; |
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/* extract homogeneous parts */ |
/* extract homogeneous parts */ |
Line 878 void mfctrsf_hensel(VL vl,VL rvl,P f,P pp0,P u0,P v0,P |
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Line 897 void mfctrsf_hensel(VL vl,VL rvl,P f,P pp0,P u0,P v0,P |
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for ( nv = 0, tvl = rvl; tvl; tvl = NEXT(tvl), nv++ ); |
for ( nv = 0, tvl = rvl; tvl; tvl = NEXT(tvl), nv++ ); |
md = (int *)ALLOCA(nv*sizeof(int)); |
md = (int *)ALLOCA(nv*sizeof(int)); |
for ( i = 0, tvl = rvl; i < nv; tvl = NEXT(tvl), i++ ) |
for ( i = 0, tvl = rvl; i < nv; tvl = NEXT(tvl), i++ ) |
md[i] = getdeg(tvl->v,ff); |
md[i] = getdeg(tvl->v,f); |
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/* XXX for removing content of factor wrt vx */ |
/* XXX for removing content of factor wrt vx */ |
NEWVL(onevl); onevl->v = vx; NEXT(onevl) = 0; |
NEWVL(onevl); onevl->v = vx; NEXT(onevl) = 0; |
Line 892 void mfctrsf_hensel(VL vl,VL rvl,P f,P pp0,P u0,P v0,P |
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Line 911 void mfctrsf_hensel(VL vl,VL rvl,P f,P pp0,P u0,P v0,P |
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for ( i = 0, t = 0; i <= j; i++ ) { |
for ( i = 0, t = 0; i <= j; i++ ) { |
mulp(vl,uh[i],vh[j-i],&s); addp(vl,s,t,&w); t = w; |
mulp(vl,uh[i],vh[j-i],&s); addp(vl,s,t,&w); t = w; |
} |
} |
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/* s = degree j part of (f-uv) */ |
/* s = degree j part of (f-uv) */ |
exthpc(vl,vx,ff,j,&fj); subp(vl,fj,t,&s); |
exthpc(vl,vx,ff,j,&fj); subp(vl,fj,t,&s); |
for ( i = 0, wu = 0, wv = 0; i <= n; i++ ) { |
for ( i = 0, wu = 0, wv = 0; i <= n; i++ ) { |
if ( s ) |
if ( !s ) |
si = 0; |
si = 0; |
else if ( VR(s) == vx ) |
else if ( VR(s) == vx ) |
coefp(s,i,&si); |
coefp(s,i,&si); |
Line 904 void mfctrsf_hensel(VL vl,VL rvl,P f,P pp0,P u0,P v0,P |
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Line 924 void mfctrsf_hensel(VL vl,VL rvl,P f,P pp0,P u0,P v0,P |
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else |
else |
si = 0; |
si = 0; |
if ( si ) { |
if ( si ) { |
mulp(vl,si,cu[i],&m); addp(vl,wu,m,&t); wu = t; |
mulp(vl,si,cv[i],&m); addp(vl,wu,m,&t); wu = t; |
mulp(vl,si,cv[i],&m); addp(vl,wv,m,&t); wv = t; |
mulp(vl,si,cu[i],&m); addp(vl,wv,m,&t); wv = t; |
} |
} |
} |
} |
if ( !wu ) { |
if ( !wu ) { |
gfsn_poly_to_poly(vl,u,vy,&t); u = t; |
gfsn_poly_to_poly(vl,u,vy,&t); |
if ( divtp(vl,f,u,&q) ) { |
if ( divtp(vl,f,t,&q) ) { |
cont_pp_mv_sf(vl,onevl,u,&cont,up); |
cont_pp_mv_sf(vl,onevl,t,&cont,up); |
return; |
return; |
} |
} |
} |
} |
if ( !wv ) { |
if ( !wv ) { |
gfsn_poly_to_poly(vl,v,vy,&t); v = t; |
gfsn_poly_to_poly(vl,v,vy,&t); |
if ( divtp(vl,f,u,&q) ) { |
if ( divtp(vl,f,t,&q) ) { |
cont_pp_mv_sf(vl,onevl,q,&cont,up); |
cont_pp_mv_sf(vl,onevl,q,&cont,up); |
return; |
return; |
} |
} |