File: [local] / OpenXM_contrib2 / asir2000 / engine / Fgfs.c (download)
Revision 1.21, Sat Apr 3 05:52:56 2004 UTC (20 years, 5 months ago) by noro
Branch: MAIN
CVS Tags: R_1_3_1-2, RELEASE_1_3_1_13b, RELEASE_1_2_3_12, RELEASE_1_2_3, KNOPPIX_2006, DEB_REL_1_2_3-9 Changes since 1.20: +2 -2
lines
Fixed a bug in sffctr and sfsqfr.
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/* $OpenXM: OpenXM_contrib2/asir2000/engine/Fgfs.c,v 1.21 2004/04/03 05:52:56 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(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,int *mev,P *lcp);
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,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);
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 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) )
*c = f;
else
lex_lc(COEF(DC(f)),c);
}
DCP append_dc(DCP dc,DCP dct)
{
DCP dcs;
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;
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;
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;
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;
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;
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;
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;
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;
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);
/* 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]);
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;
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;
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;
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;
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);
/* 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);
/* 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;
/* 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);
/* 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++);
/* 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;
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;
}
}
/*
* dc : f1^E1*...*fk^Ek
* 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,int *mev,P *lcp)
{
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;
}
void substvp_sf(VL vl,VL rvl,P f,int *mev,P *r)
{
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;
}
/*
* f <- f(X+sgn*mev)
*/
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;
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;
}
/*
* pp(f(0)) = u0*v0
*/
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;
/* 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;
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);
/* (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]);
/* 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]);
}
#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 */
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);
/* 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;
}
/* 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;
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;
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);
}
}