File: [local] / OpenXM_contrib2 / asir2000 / engine / Hgfs.c (download)
Revision 1.3, Fri Jun 22 08:51:12 2001 UTC (23 years, 3 months ago) by noro
Branch: MAIN
Changes since 1.2: +233 -1
lines
Adding Hensel lifting related routines for bibariate factorization over
small finite field. (not completed)
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/* $OpenXM: OpenXM_contrib2/asir2000/engine/Hgfs.c,v 1.3 2001/06/22 08:51:12 noro Exp $ */
#include "ca.h"
struct p_pair {
UM p0;
UM p1;
struct p_pair *next;
};
void canzassf(UM,int,UM *);
void lnfsf(int,UM,UM,struct p_pair *,UM,UM);
void minipolysf(UM,UM,UM);
void czsfum(UM,UM *);
void gensqfrsfum(UM,DUM);
void fctrsf(p,dcp)
P p;
DCP *dcp;
{
int n,i,j,k;
DCP dc,dc0;
P lc;
P zp;
UM mp;
UM *tl;
struct oDUM *udc,*udc1;
simp_ff(p,&zp); p = zp;
if ( !p ) {
*dcp = 0; return;
}
mp = W_UMALLOC(UDEG(p));
ptosfum(p,mp);
if ( (n = DEG(mp)) < 0 ) {
*dcp = 0; return;
} else if ( n == 0 ) {
NEWDC(dc); COEF(dc) = p; DEG(dc) = ONE;
NEXT(dc) = 0; *dcp = dc;
return;
}
lc = COEF(DC(p));
if ( !_isonesf(COEF(mp)[n]) ) {
monicsfum(mp);
}
W_CALLOC(n+1,struct oDUM,udc);
gensqfrsfum(mp,udc);
tl = (UM *)ALLOCA((n+1)*sizeof(UM));
W_CALLOC(DEG(mp)+1,struct oDUM,udc1);
for ( i = 0,j = 0; udc[i].f; i++ )
if ( DEG(udc[i].f) == 1 ) {
udc1[j].f = udc[i].f; udc1[j].n = udc[i].n; j++;
} else {
bzero((char *)tl,(n+1)*sizeof(UM));
czsfum(udc[i].f,tl);
for ( k = 0; tl[k]; k++, j++ ) {
udc1[j].f = tl[k]; udc1[j].n = udc[i].n;
}
}
udc = udc1;
NEWDC(dc0); COEF(dc0) = lc; DEG(dc0) = ONE; dc = dc0;
for ( n = 0; udc[n].f; n++ ) {
NEWDC(NEXT(dc)); dc = NEXT(dc);
STOQ(udc[n].n,DEG(dc)); sfumtop(VR(p),udc[n].f,&COEF(dc));
}
NEXT(dc) = 0; *dcp = dc0;
}
void gensqfrsfum(p,dc)
UM p;
struct oDUM *dc;
{
int n,i,j,d,mod;
UM t,s,g,f,f1,b;
if ( (n = DEG(p)) == 1 ) {
dc[0].f = UMALLOC(DEG(p)); cpyum(p,dc[0].f); dc[0].n = 1;
return;
}
t = W_UMALLOC(n); s = W_UMALLOC(n); g = W_UMALLOC(n);
f = W_UMALLOC(n); f1 = W_UMALLOC(n); b = W_UMALLOC(n);
diffsfum(p,t); cpyum(p,s); gcdsfum(t,s,g);
if ( !DEG(g) ) {
dc[0].f = UMALLOC(DEG(p)); cpyum(p,dc[0].f); dc[0].n = 1;
return;
}
cpyum(p,b); cpyum(p,t); divsfum(t,g,f);
for ( i = 0, d = 0; DEG(f); i++ ) {
while ( 1 ) {
cpyum(b,t);
if ( divsfum(t,f,s) >= 0 )
break;
else {
cpyum(s,b); d++;
}
}
cpyum(b,t); cpyum(f,s); gcdsfum(t,s,f1);
divsfum(f,f1,s); cpyum(f1,f);
dc[i].f = UMALLOC(DEG(s)); cpyum(s,dc[i].f); dc[i].n = d;
}
mod = characteristic_sf();
if ( DEG(b) > 0 ) {
d = 1;
while ( 1 ) {
cpyum(b,t);
for ( j = DEG(t); j >= 0; j-- )
if ( COEF(t)[j] && (j % mod) )
break;
if ( j >= 0 )
break;
else {
DEG(s) = DEG(t)/mod;
for ( j = 0; j <= DEG(t); j++ )
COEF(s)[j] = COEF(t)[j*mod];
cpyum(s,b); d *= mod;
}
}
gensqfrsfum(b,dc+i);
for ( j = i; dc[j].f; j++ )
dc[j].n *= d;
}
}
void randsfum(d,p)
int d;
UM p;
{
int i;
for ( i = 0; i < d; i++ )
COEF(p)[i] = _randomsf();
for ( i = d-1; i >= 0 && !COEF(p)[i]; i-- );
p->d = i;
}
void pwrmodsfum(p,e,f,pr)
int e;
UM p,f,pr;
{
UM wt,ws,q;
if ( e == 0 ) {
DEG(pr) = 0; COEF(pr)[0] = _onesf();
} else if ( DEG(p) < 0 )
DEG(pr) = -1;
else if ( e == 1 ) {
q = W_UMALLOC(DEG(p)); cpyum(p,pr);
DEG(pr) = divsfum(pr,f,q);
} else if ( DEG(p) == 0 ) {
DEG(pr) = 0; COEF(pr)[0] = _pwrsf(COEF(p)[0],e);
} else {
wt = W_UMALLOC(2*DEG(f)); ws = W_UMALLOC(2*DEG(f));
q = W_UMALLOC(2*DEG(f));
pwrmodsfum(p,e/2,f,wt);
if ( !(e%2) ) {
mulsfum(wt,wt,pr); DEG(pr) = divsfum(pr,f,q);
} else {
mulsfum(wt,wt,ws);
DEG(ws) = divsfum(ws,f,q);
mulsfum(ws,p,pr);
DEG(pr) = divsfum(pr,f,q);
}
}
}
void spwrsfum(m,f,e,r)
UM f,m,r;
N e;
{
UM t,s,q;
N e1;
int a;
if ( !e ) {
DEG(r) = 0; COEF(r)[0] = _onesf();
} else if ( UNIN(e) )
cpyum(f,r);
else {
a = divin(e,2,&e1);
t = W_UMALLOC(2*DEG(m)); spwrsfum(m,f,e1,t);
s = W_UMALLOC(2*DEG(m)); q = W_UMALLOC(2*DEG(m));
mulsfum(t,t,s); DEG(s) = divsfum(s,m,q);
if ( a ) {
mulsfum(s,f,t); DEG(t) = divsfum(t,m,q); cpyum(t,r);
} else
cpyum(s,r);
}
}
void tracemodsfum(m,f,e,r)
UM f,m,r;
int e;
{
UM t,s,q,u;
int i;
q = W_UMALLOC(2*DEG(m)+DEG(f)); /* XXX */
t = W_UMALLOC(2*DEG(m));
s = W_UMALLOC(2*DEG(m));
u = W_UMALLOC(2*DEG(m));
DEG(f) = divsfum(f,m,q);
cpyum(f,s);
cpyum(f,t);
for ( i = 1; i < e; i++ ) {
mulsfum(t,t,u);
DEG(u) = divsfum(u,m,q); cpyum(u,t);
addsfum(t,s,u); cpyum(u,s);
}
cpyum(s,r);
}
void make_qmatsf(p,tab,mp)
UM p;
UM *tab;
int ***mp;
{
int n,i,j;
int *c;
UM q,r;
int **mat;
int one;
n = DEG(p);
*mp = mat = almat(n,n);
for ( j = 0; j < n; j++ ) {
r = W_UMALLOC(DEG(tab[j])); q = W_UMALLOC(DEG(tab[j]));
cpyum(tab[j],r); DEG(r) = divsfum(r,p,q);
for ( i = 0, c = COEF(r); i <= DEG(r); i++ )
mat[i][j] = c[i];
}
one = _onesf();
for ( i = 0; i < n; i++ )
mat[i][i] = _subsf(mat[i][i],one);
}
void nullsf(mat,n,ind)
int **mat;
int *ind;
int n;
{
int i,j,l,s,h,inv;
int *t,*u;
bzero((char *)ind,n*sizeof(int));
ind[0] = 0;
for ( i = j = 0; j < n; i++, j++ ) {
for ( ; j < n; j++ ) {
for ( l = i; l < n; l++ )
if ( mat[l][j] )
break;
if ( l < n ) {
t = mat[i]; mat[i] = mat[l]; mat[l] = t; break;
} else
ind[j] = 1;
}
if ( j == n )
break;
inv = _invsf(mat[i][j]);
for ( s = j, t = mat[i]; s < n; s++ )
t[s] = _mulsf(t[s],inv);
for ( l = 0; l < n; l++ ) {
if ( l == i )
continue;
u = mat[l]; h = _chsgnsf(u[j]);
for ( s = j; s < n; s++ )
u[s] = _addsf(_mulsf(h,t[s]),u[s]);
}
}
}
void null_to_solsf(mat,ind,n,r)
int **mat;
int *ind;
int n;
UM *r;
{
int i,j,k,l;
int *c;
UM w;
for ( i = 0, l = 0; i < n; i++ ) {
if ( !ind[i] )
continue;
w = UMALLOC(n);
for ( j = k = 0, c = COEF(w); j < n; j++ )
if ( ind[j] )
c[j] = 0;
else
c[j] = mat[k++][i];
c[i] = _chsgnsf(_onesf());
for ( j = n; j >= 0; j-- )
if ( c[j] )
break;
DEG(w) = j;
r[l++] = w;
}
}
/*
make_qmatsf(p,tab,mp)
nullsf(mat,n,ind)
null_to_solsf(ind,n,r)
*/
void czsfum(f,r)
UM f,*r;
{
int i,j;
int d,n,ord;
UM s,t,u,v,w,g,x,m,q;
UM *base;
n = DEG(f); base = (UM *)ALLOCA(n*sizeof(UM));
bzero((char *)base,n*sizeof(UM));
w = W_UMALLOC(2*n); q = W_UMALLOC(2*n); m = W_UMALLOC(2*n);
base[0] = W_UMALLOC(0); DEG(base[0]) = 0; COEF(base[0])[0] = _onesf();
t = W_UMALLOC(1); DEG(t) = 1; COEF(t)[0] = 0; COEF(t)[1] = _onesf();
ord = field_order_sf();
pwrmodsfum(t,ord,f,w);
base[1] = W_UMALLOC(DEG(w));
cpyum(w,base[1]);
for ( i = 2; i < n; i++ ) {
mulsfum(base[i-1],base[1],m);
DEG(m) = divsfum(m,f,q);
base[i] = W_UMALLOC(DEG(m)); cpyum(m,base[i]);
}
v = W_UMALLOC(n); cpyum(f,v);
DEG(w) = 1; COEF(w)[0] = 0; COEF(w)[1] = _onesf();
x = W_UMALLOC(1); DEG(x) = 1; COEF(x)[0] = 0; COEF(x)[1] = _onesf();
t = W_UMALLOC(n); s = W_UMALLOC(n); u = W_UMALLOC(n); g = W_UMALLOC(n);
for ( j = 0, d = 1; 2*d <= DEG(v); d++ ) {
for ( DEG(t) = -1, i = 0; i <= DEG(w); i++ )
if ( COEF(w)[i] ) {
mulssfum(base[i],COEF(w)[i],s);
addsfum(s,t,u); cpyum(u,t);
}
cpyum(t,w); cpyum(v,s); subsfum(w,x,t);
gcdsfum(s,t,g);
if ( DEG(g) >= 1 ) {
berlekampsf(g,d,base,r+j); j += DEG(g)/d;
divsfum(v,g,q); cpyum(q,v);
DEG(w) = divsfum(w,v,q);
for ( i = 0; i < DEG(v); i++ )
DEG(base[i]) = divsfum(base[i],v,q);
}
}
if ( DEG(v) ) {
r[j] = UMALLOC(DEG(v)); cpyum(v,r[j]); j++;
}
r[j] = 0;
}
int berlekampsf(p,df,tab,r)
UM p;
int df;
UM *tab,*r;
{
int n,i,j,k,nf,d,nr;
int **mat;
int *ind;
UM mp,w,q,gcd,w1,w2;
UM *u;
int *root;
n = DEG(p);
ind = ALLOCA(n*sizeof(int));
make_qmatsf(p,tab,&mat);
nullsf(mat,n,ind);
for ( i = 0, d = 0; i < n; i++ )
if ( ind[i] )
d++;
if ( d == 1 ) {
r[0] = UMALLOC(n); cpyum(p,r[0]); return 1;
}
u = ALLOCA(d*sizeof(UM *));
r[0] = UMALLOC(n); cpyum(p,r[0]);
null_to_solsf(mat,ind,n,u);
root = ALLOCA(d*sizeof(int));
w = W_UMALLOC(n); mp = W_UMALLOC(d);
w1 = W_UMALLOC(n); w2 = W_UMALLOC(n);
for ( i = 1, nf = 1; i < d; i++ ) {
minipolysf(u[i],p,mp);
nr = find_rootsf(mp,root);
for ( j = 0; j < nf; j++ ) {
if ( DEG(r[j]) == df )
continue;
for ( k = 0; k < nr; k++ ) {
cpyum(u[i],w1); cpyum(r[j],w2);
COEF(w1)[0] = _chsgnsf(root[k]);
gcdsfum(w1,w2,w);
if ( DEG(w) > 0 && DEG(w) < DEG(r[j]) ) {
gcd = UMALLOC(DEG(w));
q = UMALLOC(DEG(r[j])-DEG(w));
cpyum(w,gcd); divsfum(r[j],w,q);
r[j] = q; r[nf++] = gcd;
}
if ( nf == d )
return d;
}
}
}
}
void minipolysf(f,p,mp)
UM f,p,mp;
{
struct p_pair *list,*l,*l1,*lprev;
int n,d;
UM u,p0,p1,np0,np1,q,w;
list = (struct p_pair *)MALLOC(sizeof(struct p_pair));
list->p0 = u = W_UMALLOC(0); DEG(u) = 0; COEF(u)[0] = _onesf();
list->p1 = W_UMALLOC(0); cpyum(list->p0,list->p1);
list->next = 0;
n = DEG(p); w = UMALLOC(2*n);
p0 = UMALLOC(2*n); cpyum(list->p0,p0);
p1 = UMALLOC(2*n); cpyum(list->p1,p1);
q = W_UMALLOC(2*n);
while ( 1 ) {
COEF(p0)[DEG(p0)] = 0; DEG(p0)++; COEF(p0)[DEG(p0)] = _onesf();
mulsfum(f,p1,w); DEG(w) = divsfum(w,p,q); cpyum(w,p1);
np0 = UMALLOC(n); np1 = UMALLOC(n);
lnfsf(n,p0,p1,list,np0,np1);
if ( DEG(np1) < 0 ) {
cpyum(np0,mp); return;
} else {
l1 = (struct p_pair *)MALLOC(sizeof(struct p_pair));
l1->p0 = np0; l1->p1 = np1;
for ( l = list, lprev = 0, d = DEG(np1);
l && (DEG(l->p1) > d); lprev = l, l = l->next );
if ( lprev ) {
lprev->next = l1; l1->next = l;
} else {
l1->next = list; list = l1;
}
}
}
}
void lnfsf(n,p0,p1,list,np0,np1)
int n;
UM p0,p1;
struct p_pair *list;
UM np0,np1;
{
int inv,h,d1;
UM t0,t1,s0,s1;
struct p_pair *l;
cpyum(p0,np0); cpyum(p1,np1);
t0 = W_UMALLOC(n); t1 = W_UMALLOC(n);
s0 = W_UMALLOC(n); s1 = W_UMALLOC(n);
for ( l = list; l; l = l->next ) {
d1 = DEG(np1);
if ( d1 == DEG(l->p1) ) {
h = _divsf(COEF(np1)[d1],_chsgnsf(COEF(l->p1)[d1]));
mulssfum(l->p0,h,t0); addsfum(np0,t0,s0); cpyum(s0,np0);
mulssfum(l->p1,h,t1); addsfum(np1,t1,s1); cpyum(s1,np1);
}
}
}
int find_rootsf(p,root)
UM p;
int *root;
{
UM *r;
int i,j,n;
n = DEG(p);
r = ALLOCA((DEG(p))*sizeof(UM));
canzassf(p,1,r);
for ( i = 0; i < n; i++ )
root[i] = _chsgnsf(COEF(r[i])[0]);
return n;
}
void canzassf(f,d,r)
UM f,*r;
int d;
{
UM t,s,u,w,g,o;
N n1,n2,n3,n4,n5;
UM *b;
int n,m,i,q,ed;
if ( DEG(f) == d ) {
r[0] = UMALLOC(d); cpyum(f,r[0]);
return;
} else {
n = DEG(f); b = (UM *)ALLOCA(n*sizeof(UM));
bzero((char *)b,n*sizeof(UM));
t = W_UMALLOC(2*d);
s = W_UMALLOC(DEG(f)); u = W_UMALLOC(DEG(f));
w = W_UMALLOC(DEG(f)); g = W_UMALLOC(DEG(f));
o = W_UMALLOC(0); DEG(o) = 0; COEF(o)[0] = _onesf();
q = field_order_sf();
if ( q % 2 ) {
STON(q,n1); pwrn(n1,d,&n2); subn(n2,ONEN,&n3);
STON(2,n4); divsn(n3,n4,&n5);
} else
ed = d*extdeg_sf();
while ( 1 ) {
randsfum(2*d,t);
if ( q % 2 ) {
spwrsfum(f,t,n5,s); subsfum(s,o,u);
} else
tracemodsfum(f,t,ed,u);
cpyum(f,w);
gcdsfum(w,u,g);
if ( (DEG(g) >= 1) && (DEG(g) < DEG(f)) ) {
canzassf(g,d,r);
cpyum(f,w); divsfum(w,g,s);
canzassf(s,d,r+DEG(g)/d);
return;
}
}
}
}
/* Hensel related functions */
int sfberle(VL,P,int,GFS *,DCP *);
void sfgcdgen(P,ML,ML *);
void sfhenmain(LUM,ML,ML,ML *);
void ptosflum(int,P,LUM);
/* f = f(x,y) */
void sfhensel(count,f,x,listp)
int count;
P f;
V x;
ML *listp;
{
int i,j;
int fn,n,bound;
int *p;
int **pp;
ML blist,clist,rlist;
UM *b;
LUM fl,tl;
LUM *l;
VL vl,nvl;
V y;
int dx,dy;
GFS ev;
P f1,g,g0,t,yev,c;
DCP dc;
LUM gl;
clctv(CO,f,&vl);
if ( vl->v != x ) {
reordvar(vl,x,&nvl); reorderp(nvl,vl,f,&f1);
vl = nvl; f = f1;
}
y = vl->next->v;
dx = getdeg(x,f);
dy = getdeg(y,f);
if ( dx == 1 ) {
*listp = blist = MLALLOC(1); blist->n = 1; blist->c[0] = 0;
return;
}
fn = sfberle(vl,f,count,&ev,&dc);
if ( fn <= 1 ) {
/* fn == 0 => short of evaluation points */
*listp = blist = MLALLOC(1); blist->n = fn; blist->c[0] = 0;
return;
}
/* pass the the leading coeff. to the first element */
c = dc->c; dc = NEXT(dc);
mulp(vl,dc->c,c,&t); dc->c = t;
blist = MLALLOC(n);
blist->n = fn;
for ( i = 0; i < fn; i++, dc = NEXT(dc) ) {
blist->c[i] = W_UMALLOC(UDEG(dc->c));
ptosfum(dc->c,blist->c[i]);
}
/* f(x,y) -> g = f(x,y+ev) */
MKV(y,t); addp(vl,t,(P)ev,&yev);
substp(vl,f,y,yev,&g);
substp(vl,g,y,0,&g0);
sfgcdgen(g0,blist,&clist);
blist->bound = clist->bound = dy;
W_LUMALLOC(dx,bound,gl);
ptosflum(bound,g,gl);
sfhenmain(gl,blist,clist,listp);
}
/* main variable of f = x */
int sfberle(vl,f,count,ev,dcp)
VL vl;
P f;
int count;
GFS *ev;
DCP *dcp;
{
UM wf,wf1,wf2,wfs,gcd;
ML flist;
int fn,fn1,n;
GFS m,fm;
DCP dc,dct,dc0;
VL nvl;
V x,y;
P g,lc,lc0,f0;
int j,q1,index,i;
clctv(vl,f,&nvl); vl = nvl;
x = vl->v; y = vl->next->v;
simp_ff(f,&g); g = f;
n = QTOS(DEG(DC(f)));
wf = W_UMALLOC(n); wf1 = W_UMALLOC(n); wf2 = W_UMALLOC(n);
wfs = W_UMALLOC(n); gcd = W_UMALLOC(n);
q1 = field_order_sf()-1;
lc = DC(f)->c;
for ( j = 0, fn = n + 1, index = 0;
index < q1 && j < count && fn > 1; ) {
MKGFS(index,m);
substp(vl,lc,y,(P)m,&lc0);
if ( lc0 ) {
substp(vl,f,y,(P)m,&f0);
ptosfum(m,f,wf); cpyum(wf,wf1);
diffsfum(m,wf1,wf2); gcdsfum(m,wf1,wf2,gcd);
if ( DEG(gcd) == 0 ) {
fctrsf(f0,&dc);
for ( dct = NEXT(dc), i = 0; dct; dct = NEXT(dct), i++ );
if ( i < fn ) {
dc0 = dc; fn = i; fm = m;
}
j++;
}
}
}
if ( index == q1 )
return 0;
else if ( fn == 1 )
return 1;
else {
*dcp = dc0;
*ev = fm;
return fn;
}
}
void sfgcdgen(f,blist,clistp)
P f;
ML blist,*clistp;
{
int i;
int n,d,np;
UM wf,wm,wx,wy,wu,wv,wa,wb,wg,q,tum;
UM *in,*out;
ML clist;
n = UDEG(f); np = blist->n;
d = 2*n;
q = W_UMALLOC(d); wf = W_UMALLOC(d);
wm = W_UMALLOC(d); wx = W_UMALLOC(d);
wy = W_UMALLOC(d); wu = W_UMALLOC(d);
wv = W_UMALLOC(d); wg = W_UMALLOC(d);
wa = W_UMALLOC(d); wb = W_UMALLOC(d);
ptosfum(f,wf); DEG(wg) = 0; COEF(wg)[0] = _onesf();
*clistp = clist = MLALLOC(np); clist->n = np;
for ( i = 0, in = (UM *)blist->c, out = (UM *)clist->c; i < np; i++ ) {
divsfum(wf,in[i],q); tum = wf; wf = q; q = tum;
cpyum(wf,wx); cpyum(in[i],wy);
eucsfum(wx,wy,wa,wb); mulsfum(wa,wg,wm);
DEG(wm) = divsfum(wm,in[i],q); out[i] = UMALLOC(DEG(wm));
cpyum(wm,out[i]); mulsfum(q,wf,wu);
mulsfum(wg,wb,wv); addsfum(wu,wv,wg);
}
}
/*
sfhenmain(fl,bqlist,cqlist,listp)
*/
void sfhenmain(f,bqlist,cqlist,listp)
LUM f;
ML bqlist,cqlist,*listp;
{
int i,j,k;
int *px,*py;
int **pp,**pp1;
int n,np,bound,dr,tmp;
UM wt,wq0,wq,wr,wm,wm0,wa,q;
LUM wb0,wb1,tlum;
UM *b,*c;
LUM *l;
ML list;
n = DEG(f); np = bqlist->n; bound = bqlist->bound;
*listp = list = MLALLOC(n);
list->n = np; list->bound = bound;
W_LUMALLOC(n,bound,wb0); W_LUMALLOC(n,bound,wb1);
wt = W_UMALLOC(n); wq0 = W_UMALLOC(n); wq = W_UMALLOC(n);
wr = W_UMALLOC(n); wm = W_UMALLOC(2*n); wm0 = W_UMALLOC(2*n);
wa = W_UMALLOC(2*n); q = W_UMALLOC(2*n);
b = (UM *)bqlist->c; c = (UM *)cqlist->c; l = (LUM *)list->c;
for ( i = 0; i < np; i++ ) {
l[i] = LUMALLOC(DEG(b[i]),bound);
for ( j = DEG(b[i]), pp = COEF(l[i]), px = COEF(b[i]); j >= 0; j-- )
pp[j][0] = px[j];
}
for ( i = 1; i < bound; i++ ) {
mulsflum(i+1,l[0],l[1],wb0);
for ( j = 2; j < np; j++ ) {
mulsflum(i+1,l[j],wb0,wb1);
tlum = wb0; wb0 = wb1; wb1 = tlum;
}
for ( j = n, px = COEF(wt); j >= 0; j-- )
px[j] = 0;
for ( j = n, pp = COEF(f), pp1 = COEF(wb0); j >= 0; j-- )
COEF(wt)[j] = _subsf(pp[j][i],pp1[j][i]);
degum(wt,n);
for ( j = n, px = COEF(wq0); j >= 0; j-- )
px[j] = 0;
for ( j = 1; j < np; j++ ) {
mulsfum(wt,c[j],wm); dr = divsfum(wm,b[j],q);
for ( k = DEG(q), px = COEF(wq0), py = COEF(q); k >= 0; k-- )
px[k] = _addsf(px[k],py[k]);
for ( k = dr, pp = COEF(l[j]), px = COEF(wm); k >= 0; k-- )
pp[k][i] = px[k];
}
degum(wq0,n); mulsfum(wq0,b[0],wm);
mulsfum(wt,c[0],wm0); addsfum(wm,wm0,wa);
for ( j = DEG(wa), pp = COEF(l[0]), px = COEF(wa); j >= 0; j-- )
pp[j][i] = px[j];
for ( j = n, px = COEF(wq0); j >= 0; j-- )
px[j] = 0;
}
}
void ptosflum(bound,f,fl)
int bound;
P f;
LUM fl;
{
DCP dc;
int **pp;
int d;
UM t;
t = UMALLOC(bound);
for ( dc = DC(f), pp = COEF(fl); dc; dc = NEXT(dc) ) {
d = QTOS(DEG(dc));
ptosfum(COEF(dc),t);
bcopy(t->c,pp[d],(t->d+1)*sizeof(int));
}
}