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Diff for /OpenXM_contrib2/asir2000/engine/Fgfs.c between version 1.7 and 1.10

version 1.7, 2002/10/30 08:07:11

version 1.10, 2002/11/22 07:32:10

Line 1

/* $OpenXM: OpenXM_contrib2/asir2000/engine/Fgfs.c,v 1.6 2002/10/25 02:43:40 noro Exp $ */

/* $OpenXM: OpenXM_contrib2/asir2000/engine/Fgfs.c,v 1.9 2002/11/01 06:47:41 noro Exp $ */

#include "ca.h"

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 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 pthrootsf(P f,Q m,P *r);

void partial_sqfrsf(VL vl,V v,P f,P *r,DCP *dcp);

Line 17 void mfctrsf_hensel(VL vl,VL rvl,P f,P pp0,P u0,P v0,P

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);

void adjust_coef_sf(VL vl,VL rvl,P lcu,P u0,P *r);

void extended_gcd_modyk(P u0,P v0,P *cu,P *cv);

void extended_gcd_modyk(P u0,P v0,V x,V y,int dy,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);

void poly_to_gfsn_poly_main(P f,V v,P *r);

void gfsn_poly_to_poly_main(P f,V v,P *r);

void gfsn_univariate_to_sfbm(P f,int dy,BM *r);

void sfbm_to_gfsn_univariate(BM f,V x,V y,P *r);

void lex_lc(P f,P *c)

{

Line 347 void gcdsf_main(VL vl,P *pa,int m,P *r)

Line 351 void gcdsf_main(VL vl,P *pa,int m,P *r)

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(vmin,ps[i],&ph[i],&t);

head_monomial(nvl,vmin,ps[i],&ph[i],&t);

}

ugcdsf(pc,m,&cont);

ugcdsf(ph,m,&hg);

Line 373 void gcdsf_main(VL vl,P *pa,int m,P *r)

Line 377 void gcdsf_main(VL vl,P *pa,int m,P *r)

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(vmin,ge,&ce,&he);

head_monomial(nvl,vmin,ge,&ce,&he);

if ( NUM(he) ) {

*r = cont;

return;

Line 440 void gcdsf_main(VL vl,P *pa,int m,P *r)

Line 444 void gcdsf_main(VL vl,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)

{

P t,s,u;

DCP dc;

GFS one;

VL vl;

itogfs(1,&one);

t = (P)one;

Line 476 void cont_pp_mv_sf(VL vl,VL rvl,P p,P *c,P *pp)

Line 479 void cont_pp_mv_sf(VL vl,VL rvl,P p,P *c,P *pp)

ps = (P *)ALLOCA(m*sizeof(P));

for ( t = BDY(dp), i = 0; t; t = NEXT(t), i++ )

ps[i] = C(t);

ugcdsf(ps,m,c);

gcdsf(vl,ps,m,c);

divsp(vl,p,*c,pp);

}

Line 511 void mfctrsfmain(VL vl, P f, DCP *dcp)

Line 514 void mfctrsfmain(VL vl, P f, DCP *dcp)

P *l,*tl;

P gcd,g,df,dfmin;

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;

GFS ev,evy;

P *fp0;

Line 575 void mfctrsfmain(VL vl, P f, DCP *dcp)

Line 578 void mfctrsfmain(VL vl, P f, DCP *dcp)

}

NEXT(tvl) = 0;

reorderp(nvl,vl,f,&g);

reorderp(nvl,vl,f,&g); f = g;

vx = nvl->v;

vy = NEXT(nvl)->v;

MKV(vx,x);

Line 584 void mfctrsfmain(VL vl, P f, DCP *dcp)

Line 587 void mfctrsfmain(VL vl, P f, DCP *dcp)

rvl = NEXT(NEXT(nvl));

if ( !rvl ) {

/* bivariate */

sfbfctr(g,vx,vy,getdeg(vx,g),&dc1);

sfbfctr(f,vx,vy,getdeg(vx,f),&dc1);

for ( dc0 = 0; dc1; dc1 = NEXT(dc1) ) {

NEXTDC(dc0,dc);

DEG(dc) = ONE;

Line 598 void mfctrsfmain(VL vl, P f, DCP *dcp)

Line 601 void mfctrsfmain(VL vl, P f, DCP *dcp)

/* find good evaluation pt for X */

mev = (int *)CALLOC(n-2,sizeof(int));

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;

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);

}

/* 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);

/* factorize pp0; pp0 = pp0(x,y+evy) = prod dc */

sfbfctr_shift(pp0,vx,vy,getdeg(vx,pp0),&evy,&spp0,&dc); pp0 = spp0;

Line 667 void mfctrsfmain(VL vl, P f, DCP *dcp)

Line 674 void mfctrsfmain(VL vl, P f, DCP *dcp)

mulp(nvl,u0,fp0[win[i]],&t); u0 = t;

}

/* 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);

divsp(nvl,pp0,u0,&v0);

mulp(nvl,LC(v0),c0,&c); estimatelc_sf(nvl,rvl,c,lcfdc,&lcv);

Line 705 void mfctrsfmain(VL vl, P f, DCP *dcp)

Line 712 void mfctrsfmain(VL vl, P f, DCP *dcp)

for ( i = 0, ++k; i < k; i++ )

win[i] = i + 1;

}

reorderp(vl,nvl,f,&t);

/* x -> x-mev, y -> y-evy */

shift_sf(vl,rvl,t,mev,-1,&s); substp(vl,s,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;

}

reorderp(vl,nvl,f,&t);

/* x -> x-mev, y -> y-evy */

shift_sf(vl,rvl,t,mev,-1,&s); substp(vl,s,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)

Line 829 void mfctrsf_hensel(VL vl,VL rvl,P f,P pp0,P u0,P v0,P

Line 835 void mfctrsf_hensel(VL vl,VL rvl,P f,P pp0,P u0,P v0,P

/* adjust coeffs */

/* 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)+... */

/* f -> lcu*lcv*x^(m+l)+... */

adjust_coef_sf(vl,rvl,lcu,u0,&u);

adjust_coef_sf(vl,rvl,lcv,v0,&v);

mulp(vl,lcu,lcv,&t); divsp(vl,t,LC(f),&m); mulp(vl,m,f,&t); f = t;

vx = vl->v; vy = NEXT(vl)->v;

n = getdeg(vx,f);

dy = getdeg(vy,f)+1;

Line 839 void mfctrsf_hensel(VL vl,VL rvl,P f,P pp0,P u0,P v0,P

Line 848 void mfctrsf_hensel(VL vl,VL rvl,P f,P pp0,P u0,P v0,P

cv = (P *)ALLOCA((n+1)*sizeof(P));

/* ydy = y^dy */

ydy = C_UMALLOC(dy); COEF(ydy)[dy] = 1;

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,&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,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,&cu[0],&cv[0]);

extended_gcd_modyk(u0,v0,vx,vy,dy,&cu[0],&cv[0]);

/* du0 = LC(u0)^(-1)*u0 mod y^dy */

/* dv0 = LC(v0)^(-1)*v0 mod y^dy */

invgfsn((GFSN)LC(u0),&inv); mulp(vl,u0,(P)inv,&du0);

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); divsrp(vl,m,du0,&q,&cv[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");

}

#endif

dbd = dbound(vx,f)+1;

/* extract homogeneous parts */

Line 874 void mfctrsf_hensel(VL vl,VL rvl,P f,P pp0,P u0,P v0,P

Line 897 void mfctrsf_hensel(VL vl,VL rvl,P f,P pp0,P u0,P v0,P

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,ff);

md[i] = getdeg(tvl->v,f);

/* XXX for removing content of factor wrt vx */

NEWVL(onevl); onevl->v = vx; NEXT(onevl) = 0;

Line 888 void mfctrsf_hensel(VL vl,VL rvl,P f,P pp0,P u0,P v0,P

Line 911 void mfctrsf_hensel(VL vl,VL rvl,P f,P pp0,P u0,P v0,P

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 )

if ( !s )

si = 0;

else if ( VR(s) == vx )

coefp(s,i,&si);

Line 900 void mfctrsf_hensel(VL vl,VL rvl,P f,P pp0,P u0,P v0,P

Line 924 void mfctrsf_hensel(VL vl,VL rvl,P f,P pp0,P u0,P v0,P

else

si = 0;

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 ) {

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;

}

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);

return;

}

Line 946 void adjust_coef_sf(VL vl,VL rvl,P lcu,P u0,P *r)

Line 970 void adjust_coef_sf(VL vl,VL rvl,P lcu,P u0,P *r)

MKP(VR(u0),dc0,*r);

}

void extended_gcd_modyk(P u0,P v0,P *cu,P *cv)

void extended_gcd_modyk(P u0,P v0,V x,V y,int dy,P *cu,P *cv)

{

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);

}

/* (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;

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;

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;

/* (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;

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;

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;

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;

for ( i = DEG(f); i >= 0; i-- ) {

printf("+(");

printf("%d",IFTOF(COEF(f)[i]));

printf(")*y^%d",i);

}

void printsfbm(BM f)

{

int i;

for ( i = DEG(f); i >= 0; i-- ) {

printf("+(");

printsfum(COEF(f)[i]);

printf(")*y^%d",i);

}

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