OpenXM_contrib2/asir2000/engine/Fgfs.c - diff

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Diff for /OpenXM_contrib2/asir2000/engine/Fgfs.c between version 1.8 and 1.17

version 1.8, 2002/11/01 05:43:35

version 1.17, 2003/01/13 06:40:41

Line 1

/* $OpenXM: OpenXM_contrib2/asir2000/engine/Fgfs.c,v 1.7 2002/10/30 08:07:11 noro Exp $ */

/* $OpenXM: OpenXM_contrib2/asir2000/engine/Fgfs.c,v 1.16 2003/01/06 09:23:27 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);

void gcdsf(VL vl,P *pa,int k,P *r);

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

void next_evaluation_point(int *mev,int n);

void estimatelc_sf(VL vl,VL rvl,P c,DCP dc,P *lcp);

void estimatelc_sf(VL vl,VL rvl,P c,DCP dc,int *mev,P *lcp);

void mfctrsf_hensel(VL vl,VL rvl,P f,P pp0,P u0,P v0,P lcu,P lcv,P *up);

void mfctrsf_hensel(VL vl,VL rvl,P f,P pp0,P u0,P v0,P lcu,P lcv,int *mev,P *up);

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

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);

Line 25 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 monomialfctr_sf(VL vl,P p,P *pr,DCP *dcp)

{

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;

}

void lex_lc(P f,P *c)

{

if ( !f || NUM(f) )

Line 50 void sqfrsf(VL vl, P f, DCP *dcp)

Line 73 void sqfrsf(VL vl, P f, DCP *dcp)

{

DCP dc,dct;

Obj obj;

P t,s,c;

P t,s,c,cont;

VL tvl,nvl;

VL tvl,onevl;

simp_ff((Obj)f,&obj); f = (P)obj;

lex_lc(f,&c); divsp(vl,f,c,&t); f = t;

monomialfctr(vl,f,&t,&dc); 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) ) {

Line 65 void sqfrsf(VL vl, P f, DCP *dcp)

Line 89 void sqfrsf(VL vl, P f, DCP *dcp)

} else {

t = f;

for ( tvl = vl; tvl; tvl = NEXT(tvl) ) {

reordvar(vl,tvl->v,&nvl);

onevl->v = tvl->v;

cont_pp_mv_sf(vl,NEXT(nvl),t,&c,&s); t = s;

cont_pp_mv_sf(vl,onevl,t,&cont,&s); t = s;

sqfrsf(vl,c,&dct);

sqfrsf(vl,cont,&dct);

dc = append_dc(dc,NEXT(dct));

}

sqfrsfmain(vl,t,&dct);

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

Line 375 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 377 void gcdsf_main(VL vl,P *pa,int m,P *r)

Line 401 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 444 void gcdsf_main(VL vl,P *pa,int m,P *r)

Line 468 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 474 void cont_pp_mv_sf(VL vl,VL rvl,P p,P *c,P *pp)

Line 497 void cont_pp_mv_sf(VL vl,VL rvl,P p,P *c,P *pp)

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,&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);

ugcdsf(ps,m,c);

gcdsf(vl,ps,m,c);

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

initd(&currentspec);

}

void mfctrsf(VL vl, P f, DCP *dcp)

Line 515 void mfctrsfmain(VL vl, P f, DCP *dcp)

Line 544 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;

P ype,yme,fin;

GFS ev,evy;

P *fp0;

int *mev,*win;

Line 557 void mfctrsfmain(VL vl, P f, DCP *dcp)

Line 586 void mfctrsfmain(VL vl, P f, DCP *dcp)

}

pa[0] = f;

pa[1] = dfmin;

gcdsf_main(vl,pa,2,&gcd);

gcdsf(vl,pa,2,&gcd);

if ( !NUM(gcd) ) {

/* f = gcd * f/gcd */

mfctrsfmain(vl,gcd,&dc1);

Line 579 void mfctrsfmain(VL vl, P f, DCP *dcp)

Line 608 void mfctrsfmain(VL vl, P f, DCP *dcp)

}

NEXT(tvl) = 0;

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

fin = f;

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

vx = nvl->v;

vy = NEXT(nvl)->v;

MKV(vx,x);

Line 588 void mfctrsfmain(VL vl, P f, DCP *dcp)

Line 618 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 602 void mfctrsfmain(VL vl, P f, DCP *dcp)

Line 632 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;

if ( !NEXT(dc) ) {

/* f is irreducible */

NEWDC(dc); DEG(dc) = ONE; COEF(dc) = f; NEXT(dc) = 0;

NEWDC(dc); DEG(dc) = ONE; COEF(dc) = fin; NEXT(dc) = 0;

*dcp = dc;

return;

}

Line 642 void mfctrsfmain(VL vl, P f, DCP *dcp)

Line 676 void mfctrsfmain(VL vl, P f, DCP *dcp)

lcf = COEF(DC(f));

mfctrsf(nvl,lcf,&dct);

/* skip the first element (= a number) */

dct = NEXT(dct);

lcfdc = NEXT(dct);

/* shift lcfdc; c <- c(X+mev) */

for ( lcfdc = 0; dct; dct = NEXT(dct) ) {

NEXTDC(lcfdc,dcs);

DEG(dcs) = DEG(dct);

shift_sf(nvl,rvl,COEF(dct),mev,1,&COEF(dcs));

}

NEXT(dcs) = 0;

/* np = number of bivariate factors */

for ( np = 0, dct = dc; dct; dct = NEXT(dct), np++ );

fp0 = (P *)ALLOCA((np+1)*sizeof(P));

Line 661 void mfctrsfmain(VL vl, P f, DCP *dcp)

Line 687 void mfctrsfmain(VL vl, P f, DCP *dcp)

l = tl = (P *)ALLOCA((np+1)*sizeof(P));

win = W_ALLOC(np+1);

/* f <- f(X+mev) */

shift_sf(nvl,rvl,f,mev,1,&s); f = s;

for ( k = 1, win[0] = 1, --np; ; ) {

itogfs(1,&u0);

/* u0 = product of selected factors */

Line 671 void mfctrsfmain(VL vl, P f, DCP *dcp)

Line 694 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);

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,&lcv);

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

mfctrsf_hensel(nvl,rvl,f,pp0,u0,v0,lcu,lcv,&u);

mfctrsf_hensel(nvl,rvl,f,pp0,u0,v0,lcu,lcv,mev,&u);

if ( u ) {

/* save the factor */

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

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

/* y -> y-evy */

shift_sf(vl,rvl,t,mev,-1,&s); substp(vl,s,vy,yme,tl++);

substp(vl,t,vy,yme,tl++);

/* update f,pp0 */

divsp(nvl,f,u,&t); f = t;

Line 709 void mfctrsfmain(VL vl, P f, DCP *dcp)

Line 732 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);

/* 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)

Line 740 void next_evaluation_point(int *e,int n)

Line 762 void next_evaluation_point(int *e,int n)

* dc : f1^E1*...*fk^Ek

* find e1,...,ek s.t. fi(0)^ei | c

* find e1,...,ek s.t. fi(mev)^ei | c

* and return f1^e1*...*fk^ek

* vl = (vx,vy,rvl)

void estimatelc_sf(VL vl,VL rvl,P c,DCP dc,P *lcp)

void estimatelc_sf(VL vl,VL rvl,P c,DCP dc,int *mev,P *lcp)

{

DCP dct;

P r,c1,c2,t,s,f;

Line 756 void estimatelc_sf(VL vl,VL rvl,P c,DCP dc,P *lcp)

Line 778 void estimatelc_sf(VL vl,VL rvl,P c,DCP dc,P *lcp)

if ( NUM(COEF(dct)) )

continue;

/* constant part */

substvp_sf(vl,rvl,COEF(dct),0,&f);

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) )

Line 817 void shift_sf(VL vl, VL rvl, P f, int *mev, int sgn, P

Line 839 void shift_sf(VL vl, VL rvl, P f, int *mev, int sgn, P

* pp(f(0)) = u0*v0

void mfctrsf_hensel(VL vl,VL rvl,P f,P pp0,P u0,P v0,P lcu,P lcv,P *up)

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;

Line 826 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

int dy,n,i,dbd,nv,j;

int *md;

P *uh,*vh;

P x,du0,dv0,m,q,r;

P x,du0,dv0,m,q,r,fin;

P *cu,*cv;

GFSN inv;

/* adjust coeffs */

/* check the validity of lc's and adjust coeffs */

/* u0 = am x^m+ ... -> lcu*x^m + a(m-1)*(lcu(0)/am)*x^(m-1)+... */

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

/* v0 = bm x^l+ ... -> lcv*x^l + b(l-1)*(lcv(0)/bl)*x^(l-1)+... */

mulp(vl,lcu,lcv,&t);

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

if ( !divtp(vl,t,LC(f),&m) ) {

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

*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;

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

n = getdeg(vx,f);

dy = getdeg(vy,f)+1;

Line 843 void mfctrsf_hensel(VL vl,VL rvl,P f,P pp0,P u0,P v0,P

Line 878 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);

Line 856 void mfctrsf_hensel(VL vl,VL rvl,P f,P pp0,P u0,P v0,P

Line 891 void mfctrsf_hensel(VL vl,VL rvl,P f,P pp0,P u0,P v0,P

/* 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]);

/* 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 878 void mfctrsf_hensel(VL vl,VL rvl,P f,P pp0,P u0,P v0,P

Line 927 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 892 void mfctrsf_hensel(VL vl,VL rvl,P f,P pp0,P u0,P v0,P

Line 941 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 904 void mfctrsf_hensel(VL vl,VL rvl,P f,P pp0,P u0,P v0,P

Line 954 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) ) {

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

cont_pp_mv_sf(vl,onevl,u,&cont,up);

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); v = t;

gfsn_poly_to_poly(vl,v,vy,&t);

if ( divtp(vl,f,u,&q) ) {

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

if ( divtp(vl,fin,s,&q) ) {

cont_pp_mv_sf(vl,onevl,q,&cont,up);

return;

}

Line 929 void mfctrsf_hensel(VL vl,VL rvl,P f,P pp0,P u0,P v0,P

Line 981 void mfctrsf_hensel(VL vl,VL rvl,P f,P pp0,P u0,P v0,P

}

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

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

{

P lcu0,cu;

DCP dc0,dcu,dc;

substvp_sf(vl,rvl,lcu,0,&lcu0);

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 ) {

Line 980 void gfsn_univariate_to_sfbm(P f,int dy,BM *r)

Line 1032 void gfsn_univariate_to_sfbm(P f,int dy,BM *r)

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;

}

Line 1021 void poly_to_gfsn_poly_main(P f,V v,P *r)

Line 1075 void poly_to_gfsn_poly_main(P f,V v,P *r)

GFSN g;

DCP dc,dct,dc0;

if ( !f || NUM(f) )

if ( !f )

*r = f;

else if ( VR(f) == v ) {

else if ( NUM(f) || VR(f) == v ) {

d = getdeg(v,f);

u = UMALLOC(d);

ptosfum(f,u);

Line 1080 void gfsn_poly_to_poly_main(P f,V v,P *r)

Line 1134 void gfsn_poly_to_poly_main(P f,V v,P *r)

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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