/* $OpenXM: OpenXM_contrib2/asir2000/engine/Hgfs.c,v 1.33 2015/08/14 13:51:54 fujimoto Exp $ */
#include "ca.h"
#include "inline.h"
int debug_sfbfctr;
void lnfsf(int n,UM p0,UM p1,struct p_pair *list,UM np0,UM np1);
void extractcoefbm(BM f,int dx,UM r);
int comp_dum(DUM a,DUM b)
{
if ( DEG(a->f) > DEG(b->f) )
return -1;
else if ( DEG(a->f) < DEG(b->f) )
return 1;
else
return 0;
}
void ufctrsf(P p,DCP *dcp)
{
int n,i,j,k;
DCP dc,dc0;
P lc;
UM mp;
UM *tl;
Obj obj;
struct oDUM *udc,*udc1;
simp_ff((Obj)p,&obj); p = (P)obj;
if ( !p ) {
NEWDC(dc); COEF(dc) = 0; DEG(dc) = ONE;
NEXT(dc) = 0; *dcp = dc;
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;
for ( i = 0; udc[i].f; i++ );
qsort(udc,i,sizeof(struct oDUM),
(int (*)(const void *,const void *))comp_dum);
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(UM p,struct oDUM *dc)
{
int n,i,j,d,mod;
UM t,s,g,f,f1,b;
GFS u,v;
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++ ) {
iftogfs(COEF(t)[j*mod],&u);
pthrootgfs(u,&v);
COEF(s)[j] = v?FTOIF(CONT(v)):0;
}
cpyum(s,b); d *= mod;
}
}
gensqfrsfum(b,dc+i);
for ( j = i; dc[j].f; j++ )
dc[j].n *= d;
}
}
void randsfum(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(UM p,int e,UM f,UM 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(UM m,UM f,N e,UM r)
{
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(UM m,UM f,int e,UM r)
{
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(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(int **mat,int n,int *ind)
{
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(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(UM f,UM *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(UM p,int df,UM *tab,UM *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;
}
}
}
/* NOT REACHED */
error("berlekampsf : cannot happen");
return 0;
}
void minipolysf(UM f,UM p,UM 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(int n,UM p0,UM p1,struct p_pair *list,UM np0,UM np1)
{
int 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(UM p,int *root)
{
UM *r;
int i,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(UM f,int d,UM *r)
{
UM t,s,u,w,g,o;
N n1,n2,n3,n4,n5;
UM *b;
int n,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(V,V,P,int,GFS *,DCP *);
void sfgcdgen(P,ML,ML *);
void sfhenmain2(BM,UM,UM,int,BM *);
void ptosfbm(int,P,BM);
void sfhensel(int count,P f,V x,V y,int degbound,GFS *evp,P *sfp,ML *listp);
/* f = f(x,y) */
void sfhensel(int count,P f,V x,V y,int degbound,GFS *evp,P *sfp,ML *listp)
{
int i;
int fn;
ML rlist;
BM fl;
VL vl,nvl;
int dx,dy,bound;
GFS ev;
P f1,t,c,sf;
DCP dc,dct,dc0;
UM q,fm,hm;
UM *gm;
struct oEGT tmp0,tmp1,eg_hensel,eg_hensel_t;
clctv(CO,f,&vl);
if ( vl->v != x ) {
reordvar(vl,x,&nvl); reorderp(nvl,vl,f,&f1);
vl = nvl; f = f1;
}
if ( vl->next )
y = vl->next->v;
dx = getdeg(x,f);
dy = getdeg(y,f);
if ( dx == 1 ) {
*listp = rlist = MLALLOC(1); rlist->n = 1; rlist->c[0] = 0;
return;
}
fn = sfberle(x,y,f,count,&ev,&dc);
if ( fn <= 1 ) {
/* fn == 0 => short of evaluation points */
*listp = rlist = MLALLOC(1); rlist->n = fn; rlist->c[0] = 0;
return;
}
if ( degbound >= 0 ) {
/*
* reconstruct dc so that
* dc[1],... : factors satisfy degree bound
* dc[0] : product of others
*/
c = dc->c; dc = NEXT(dc);
dc0 = 0;
fn = 0;
while ( dc ) {
if ( getdeg(x,COEF(dc)) <= degbound ) {
dct = NEXT(dc); NEXT(dc) = dc0; dc0 = dc; dc = dct;
fn++;
} else {
mulp(vl,COEF(dc),c,&t); c = t;
dc = NEXT(dc);
}
}
if ( OID(c) == O_P ) {
NEWDC(dc); COEF(dc) = c; DEG(dc) = ONE; NEXT(dc) = dc0;
fn++;
} else {
mulp(vl,dc0->c,c,&t); dc0->c = t; dc = dc0;
}
} else {
/* pass the the leading coeff. to the first element */
c = dc->c; dc = NEXT(dc);
mulp(vl,dc->c,c,&t); dc->c = t;
}
/* convert mod y-a factors into UM */
gm = (UM *)ALLOCA(fn*sizeof(UM));
for ( i = 0; i < fn; i++, dc = NEXT(dc) ) {
gm[i] = W_UMALLOC(UDEG(dc->c));
ptosfum(dc->c,gm[i]);
}
/* set bound */
/* g | f, lc_y(g) = lc_y(f) => deg_y(g) <= deg_y(f) */
/* so, bound = dy is sufficient, but we use slightly large value */
bound = dy+2;
/* f(x,y) -> f(x,y+ev) */
fl = BMALLOC(dx,bound);
ptosfbm(bound,f,fl);
if ( ev ) shiftsfbm(fl,FTOIF(CONT(ev)));
/* sf = f(x+ev) */
sfbmtop(fl,x,y,&sf);
/* fm = fl mod y */
fm = W_UMALLOC(dx);
cpyum(COEF(fl)[0],fm);
hm = W_UMALLOC(dx);
q = W_UMALLOC(dx);
rlist = MLALLOC(fn); rlist->n = fn; rlist->bound = bound;
if ( debug_sfbfctr )
fprintf(asir_out,"%d candidates\n",fn);
init_eg(&eg_hensel);
for ( i = 0; i < fn-1; i++ ) {
if ( debug_sfbfctr )
fprintf(asir_out,"deg(fm) = %d, deg(gm[%d]) = %d\n",
DEG(fm),i,DEG(gm[i]));
init_eg(&eg_hensel_t);
get_eg(&tmp0);
/* fl = gm[i]*hm mod y */
divsfum(fm,gm[i],hm);
/* fl is replaced by the cofactor of gk mod y^bound */
/* rlist->c[i] = gk */
sfhenmain2(fl,gm[i],hm,bound,(BM *)&rlist->c[i]);
cpyum(hm,fm);
get_eg(&tmp1); add_eg(&eg_hensel_t,&tmp0,&tmp1);
add_eg(&eg_hensel,&tmp0,&tmp1);
if ( debug_sfbfctr) {
print_eg("Hensel",&eg_hensel_t);
fprintf(asir_out,"\n");
}
}
if ( debug_sfbfctr) {
print_eg("Hensel total",&eg_hensel);
fprintf(asir_out,"\n");
}
/* finally, fl must be the lift of gm[fn-1] */
rlist->c[i] = fl;
#if 0
/* y -> y-a */
mev = _chsgnsf(FTOIF(CONT(ev)));
for ( i = 0; i < fn; i++ )
shiftsfbm((BM)(rlist->c[i]),mev);
#endif
*evp = ev;
*sfp = sf;
*listp = rlist;
}
/* main variable of f = x */
int sfberle(V x,V y,P f,int count,GFS *ev,DCP *dcp)
{
UM wf,wf1,wf2,wfs,gcd;
int fn,n;
GFS m,fm;
DCP dc,dct,dc0;
VL vl;
P lc,lc0,f0;
Obj obj;
int j,q,index,i;
NEWVL(vl); vl->v = x;
NEWVL(NEXT(vl)); NEXT(vl)->v = y;
NEXT(NEXT(vl)) =0;
simp_ff((Obj)f,&obj); f = (P)obj;
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);
q = field_order_sf();
lc = DC(f)->c;
for ( j = 0, fn = n + 1, index = 0;
index < q && j < count && fn > 1; index++ ) {
indextogfs(index,&m);
substp(vl,lc,y,(P)m,&lc0);
if ( lc0 ) {
substp(vl,f,y,(P)m,&f0);
ptosfum(f0,wf); cpyum(wf,wf1);
diffsfum(wf1,wf2); gcdsfum(wf1,wf2,gcd);
if ( DEG(gcd) == 0 ) {
ufctrsf(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 == q )
return 0;
else if ( fn == 1 )
return 1;
else {
*dcp = dc0;
*ev = fm;
return fn;
}
}
void sfgcdgen(P f,ML blist,ML *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);
}
}
/* f = g0*h0 mod y -> f = gk*hk mod y^(dy+1), f is replaced by hk */
void sfhenmain2(BM f,UM g0,UM h0,int dy,BM *gp)
{
int i,k;
int dx;
UM wt,wa,wb,q,w1,w2,wh1,wg1,ws;
UM wc,wd,we,wz;
BM wb0,wb1;
int dg,dh;
BM fk,gk,hk;
if ( DEG(f) < dy )
error("sfhenmain2 : invalid input");
dx = degbm(f);
dg = DEG(g0);
dh = DEG(h0);
W_BMALLOC(dx,dy,wb0); W_BMALLOC(dx,dy,wb1);
wt = W_UMALLOC(dx); ws = W_UMALLOC(dx); q = W_UMALLOC(2*dx);
wg1 = W_UMALLOC(2*dx); wh1 = W_UMALLOC(2*dx);
/* fk = gk*hk mod y^k */
W_BMALLOC(dx,dy,fk);
cpyum(COEF(f)[0],COEF(fk)[0]);
gk = BMALLOC(dg,dy);
cpyum(g0,COEF(gk)[0]);
W_BMALLOC(dh,dy,hk);
cpyum(h0,COEF(hk)[0]);
wc = W_UMALLOC(2*dx); wd = W_UMALLOC(2*dx);
we = W_UMALLOC(2*dx); wz = W_UMALLOC(2*dx);
/* compute wa,wb s.t. wa*g0+wb*h0 = 1 mod y */
w1 = W_UMALLOC(dg); cpyum(g0,w1);
w2 = W_UMALLOC(dh); cpyum(h0,w2);
wa = W_UMALLOC(2*dx); wb = W_UMALLOC(2*dx); /* XXX */
eucsfum(w1,w2,wa,wb);
if ( debug_sfbfctr)
fprintf(stderr,"dy=%d\n",dy);
for ( k = 1; k <= dy; k++ ) {
if ( debug_sfbfctr)
fprintf(stderr,".");
/* at this point, f = gk*hk mod y^k */
/* clear wt */
clearum(wt,dx);
/* wt = (f-gk*hk)/y^k */
subsfum(COEF(f)[k],COEF(fk)[k],wt);
/* compute wf1,wg1 s.t. wh1*g0+wg1*h0 = wt */
mulsfum(wa,wt,wh1); DEG(wh1) = divsfum(wh1,h0,q);
mulsfum(wh1,g0,wc); subsfum(wt,wc,wd); DEG(wd) = divsfum(wd,h0,wg1);
/* check */
#if 0
if ( DEG(wd) >= 0 || DEG(wg1) > ng )
error("henmain2 : cannot happen(adj)");
mulsfum(wg1,h0,wc); mulsfum(wh1,g0,wd); addsfum(wc,wd,we);
subsfum(we,wt,wz);
if ( DEG(wz) >= 0 )
error("henmain2 : cannot happen");
#endif
/* fk += ((wg1*hk+wh1*gk)*y^k+wg1*wh1*y^(2*k) mod y^(dy+1) */
/* wb0 = wh1*y^k */
clearbm(dx,wb0);
cpyum(wh1,COEF(wb0)[k]);
/* wb1 = gk*wb0 mod y^(dy+1) */
clearbm(dx,wb1);
mulsfbm(gk,wb0,wb1);
/* fk += wb1 */
addtosfbm(wb1,fk);
/* wb0 = wg1*y^k */
clearbm(dx,wb0);
cpyum(wg1,COEF(wb0)[k]);
/* wb1 = hk*wb0 mod y^(dy+1) */
clearbm(dx,wb1);
mulsfbm(hk,wb0,wb1);
/* fk += wb1 */
addtosfbm(wb1,fk);
/* fk += wg1*wh1*y^(2*k) mod y^(dy+1) */
if ( 2*k <= dy ) {
mulsfum(wg1,wh1,wt); addsfum(COEF(fk)[2*k],wt,ws);
cpyum(ws,COEF(fk)[2*k]);
}
/* gk += wg1*y^k, hk += wh1*y^k */
cpyum(wg1,COEF(gk)[k]);
cpyum(wh1,COEF(hk)[k]);
}
if ( debug_sfbfctr)
fprintf(stderr,"\n");
*gp = gk;
DEG(f) = dy;
for ( i = 0; i <= dy; i++ )
cpyum(COEF(hk)[i],COEF(f)[i]);
}
/* a0*g+b0*h = 1 mod y -> a*g+b*h = 1 mod y^(dy+1) */
void sfexgcd_by_hensel(BM g,BM h,int dy,BM *ap,BM *bp)
{
int i,k;
int dx;
UM wt,wa,wb,q,w1,w2,ws;
UM wc,wd,we,wz,wa1,wb1;
BM wz0,wz1;
int dg,dh;
BM a,b,c;
dg = degbm(g);
dh = degbm(h);
dx = dg+dh;
a = BMALLOC(dh,dy);
b = BMALLOC(dg,dy);
/* c holds a*g+b*h-1 */
c = BMALLOC(dg+dh,dy);
W_BMALLOC(dx,dy,wz0); W_BMALLOC(dx,dy,wz1);
wt = W_UMALLOC(dx); ws = W_UMALLOC(dx); q = W_UMALLOC(2*dx);
wa1 = W_UMALLOC(2*dx); wb1 = W_UMALLOC(2*dx);
wc = W_UMALLOC(2*dx); wd = W_UMALLOC(2*dx);
we = W_UMALLOC(2*dx); wz = W_UMALLOC(2*dx);
/* compute wa,wb s.t. wa*g0+wb*h0 = 1 mod y */
w1 = W_UMALLOC(dg); cpyum(COEF(g)[0],w1);
w2 = W_UMALLOC(dh); cpyum(COEF(h)[0],w2);
wa = W_UMALLOC(2*dx); wb = W_UMALLOC(2*dx); /* XXX */
eucsfum(w1,w2,wa,wb);
cpyum(wa,COEF(a)[0]); cpyum(wb,COEF(b)[0]);
/* initialize c to a*g+b*h-1 */
mulsfbm(a,g,c); mulsfbm(b,h,wz0); addtosfbm(wz0,c);
COEF(COEF(c)[0])[0] = 0;
if ( debug_sfbfctr)
fprintf(stderr,"dy=%d\n",dy);
for ( k = 1; k <= dy; k++ ) {
if ( debug_sfbfctr)
fprintf(stderr,".");
/* at this point, a*g+b*h = 1 mod y^k, c = a*g+b*h-1 */
/* wt = -((a*g+b*h-1)/y^k) */
cpyum(COEF(c)[k],wt);
for ( i = DEG(wt); i >= 0; i-- )
COEF(wt)[i] = _chsgnsf(COEF(wt)[i]);
/* compute wa1,wb1 s.t. wa1*g0+wb1*h0 = wt */
mulsfum(wa,wt,wa1); DEG(wa1) = divsfum(wa1,COEF(h)[0],q);
mulsfum(wa1,COEF(g)[0],wc); subsfum(wt,wc,wd);
DEG(wd) = divsfum(wd,COEF(h)[0],wb1);
/* c += ((wa1*g+wb1*h)*y^k mod y^(dy+1) */
/* wz0 = wa1*y^k */
clearbm(dx,wz0);
cpyum(wa1,COEF(wz0)[k]);
/* wz1 = wz0*g mod y^(dy+1) */
clearbm(dx,wz1);
mulsfbm(g,wz0,wz1);
/* c += wz1 */
addtosfbm(wz1,c);
/* wz0 = wb1*y^k */
clearbm(dx,wz0);
cpyum(wb1,COEF(wz0)[k]);
/* wz1 = wz0*h mod y^(dy+1) */
clearbm(dx,wz1);
mulsfbm(h,wz0,wz1);
/* c += wz1 */
addtosfbm(wz1,c);
/* a += wa1*y^k, b += wb1*y^k */
cpyum(wa1,COEF(a)[k]);
cpyum(wb1,COEF(b)[k]);
}
if ( debug_sfbfctr)
fprintf(stderr,"\n");
DEG(a) = dy;
DEG(b) = dy;
*ap = a;
*bp = b;
}
/* fl->c[i] = coef_y(f,i) */
void ptosfbm(int dy,P f,BM fl)
{
DCP dc;
int d,i,dx;
UM t;
dx = QTOS(DEG(DC(f)));
if ( DEG(fl) < dy )
error("ptosfbm : invalid input");
DEG(fl) = dy;
clearbm(dx,fl);
t = UMALLOC(dy);
for ( dc = DC(f); dc; dc = NEXT(dc) ) {
d = QTOS(DEG(dc));
ptosfum(COEF(dc),t);
for ( i = 0; i <= DEG(t); i++ )
COEF(COEF(fl)[i])[d] = COEF(t)[i];
}
for ( i = 0; i <= dy; i++ )
degum(COEF(fl)[i],dx);
}
/* x : main variable */
void sfbmtop(BM f,V x,V y,P *fp)
{
UM *c;
int i,j,d,a,dy;
GFS b;
DCP dc0,dc,dct;
dy = DEG(f);
c = COEF(f);
d = degbm(f);
dc0 = 0;
for ( i = 0; i <= d; i++ ) {
dc = 0;
for ( j = 0; j <= dy; j++ ) {
if ( DEG(c[j]) >= i && (a = COEF(c[j])[i]) ) {
NEWDC(dct);
STOQ(j,DEG(dct));
iftogfs(a,&b);
COEF(dct) = (P)b;
NEXT(dct) = dc;
dc = dct;
}
}
if ( dc ) {
NEWDC(dct);
STOQ(i,DEG(dct));
MKP(y,dc,COEF(dct));
NEXT(dct) = dc0;
dc0 = dct;
}
}
if ( dc0 )
MKP(x,dc0,*fp);
else
*fp = 0;
}
void sfsqfr(P f,DCP *dcp)
{
Obj obj;
DCP dc;
VL vl;
simp_ff((Obj)f,&obj); f = (P)obj;
clctv(CO,f,&vl);
if ( !vl ) {
/* f is a const */
NEWDC(dc); DEG(dc) = ONE; COEF(dc) = f; NEXT(dc) = 0; *dcp = dc;
} else if ( !NEXT(vl) )
sfusqfr(f,dcp);
else
sqfrsf(vl,f,dcp);
}
void sfusqfr(P f,DCP *dcp)
{
DCP dc,dct;
struct oDUM *udc;
V x;
P lc;
int n,i;
UM mf;
x = VR(f);
n = getdeg(x,f);
mf = W_UMALLOC(n);
ptosfum(f,mf);
lc = COEF(DC(f));
if ( !_isonesf(COEF(mf)[n]) ) {
monicsfum(mf);
}
W_CALLOC(n+1,struct oDUM,udc);
gensqfrsfum(mf,udc);
for ( i = 0, dc = 0; udc[i].f; i++ ) {
NEWDC(dct); STOQ(udc[i].n,DEG(dct));
sfumtop(x,udc[i].f,&COEF(dct));
NEXT(dct) = dc; dc = dct;
}
NEWDC(dct); DEG(dct) = ONE; COEF(dct) = (P)lc; NEXT(dct) = dc;
*dcp = dct;
}
#if 0
void sfbsqfrmain(P f,V x,V y,DCP *dcp)
{
/* XXX*/
}
/* f is bivariate */
void sfbsqfr(P f,V x,V y,DCP *dcp)
{
P t,rf,cx,cy;
VL vl,rvl;
DCP dcx,dcy,dct,dc;
struct oVL vl0,vl1;
/* cy(y) = cont(f,x), f /= cy */
cont_pp_sfp(vl,f,&cy,&t); f = t;
/* rvl = [y,x] */
reordvar(vl,y,&rvl); reorderp(rvl,vl,f,&rf);
/* cx(x) = cont(rf,y), Rf /= cy */
cont_pp_sfp(rvl,rf,&cx,&t); rf = t;
reorderp(vl,rvl,rf,&f);
/* f -> cx*cy*f */
sfsqfr(cx,&dcx); dcx = NEXT(dcx);
sfsqfr(cy,&dcy); dcy = NEXT(dcy);
if ( dcx ) {
for ( dct = dcx; NEXT(dct); dct = NEXT(dct) );
NEXT(dct) = dcy;
} else
dcx = dcy;
if ( OID(f) == O_N )
*dcp = dcx;
else {
/* f must be bivariate */
sfbsqfrmain(f,x,y,&dc);
if ( dcx ) {
for ( dct = dcx; NEXT(dct); dct = NEXT(dct) );
NEXT(dct) = dc;
} else
dcx = dc;
*dcp = dcx;
}
}
#endif
void sfdtest(P,ML,V,V,DCP *);
/* if degbound >= 0 find factor s.t. deg_x(factor) <= degbound */
void sfbfctr(P f,V x,V y,int degbound,DCP *dcp)
{
ML list;
P sf;
GFS ev;
DCP dc,dct;
BM fl;
int dx,dy;
/* sf(x) = f(x+ev) = list->c[0]*list->c[1]*... */
sfhensel(5,f,x,y,degbound,&ev,&sf,&list);
if ( list->n == 0 )
error("sfbfctr : short of evaluation points");
else if ( list->n == 1 ) {
/* f is irreducible */
NEWDC(dc); DEG(dc) = ONE; COEF(dc) = f; NEXT(dc) = 0;
*dcp = dc;
return;
}
sfdtest(sf,list,x,y,&dc);
if ( ev ) {
dx = getdeg(x,sf);
dy = getdeg(y,sf);
W_BMALLOC(dx,dy,fl);
for ( dct = dc; dct; dct = NEXT(dct) ) {
ptosfbm(dy,COEF(dct),fl);
shiftsfbm(fl,_chsgnsf(FTOIF(CONT(ev))));
sfbmtop(fl,x,y,&COEF(dct));
}
}
*dcp = dc;
}
/* returns shifted f, shifted factors and the eval pt */
void sfbfctr_shift(P f,V x,V y,int degbound,GFS *evp,P *sfp,DCP *dcp)
{
ML list;
P sf;
GFS ev;
DCP dc,dct;
int dx,dy;
/* sf(x) = f(x+ev) = list->c[0]*list->c[1]*... */
sfhensel(5,f,x,y,degbound,&ev,&sf,&list);
if ( list->n == 0 )
error("sfbfctr_shift : short of evaluation points");
else if ( list->n == 1 ) {
/* f is irreducible */
NEWDC(dc); DEG(dc) = ONE; COEF(dc) = f; NEXT(dc) = 0;
*evp = 0;
*sfp = f;
*dcp = dc;
} else {
sfdtest(sf,list,x,y,dcp);
*evp = ev;
*sfp = sf;
}
}
/* f = f(x,y) = list->c[0]*list->c[1]*... mod y^(list->bound+1) */
void sfdtest(P f,ML list,V x,V y,DCP *dcp)
{
int np,dx,dy;
int i,j,k,bound;
int *win;
P g,lcg,factor,cofactor,lcyx;
P csum;
DCP dcf,dcf0,dc;
BM *c;
BM lcy;
UM lcg0,lcy0,w;
UM *d1c;
ML wlist;
struct oVL vl1,vl0;
VL vl;
int z,dt,dtok;
/* vl = [x,y] */
vl0.v = x; vl0.next = &vl1; vl1.v = y; vl1.next = 0; vl = &vl0;
/* setup various structures and arrays */
dx = getdeg(x,f);
dy = getdeg(y,f);
np = list->n;
win = W_ALLOC(np+1);
wlist = W_MLALLOC(np);
wlist->n = list->n;
bound = wlist->bound = list->bound;
c = (BM *)COEF(wlist);
bcopy((char *)COEF(list),(char *)c,(int)(sizeof(BM)*np));
lcg0 = W_UMALLOC(2*dy);
/* initialize g by f */
g = f;
/* initialize lcg */
mulp(vl,g,COEF(DC(g)),&lcg);
/* initialize lcg0 */
const_term(lcg,lcg0);
/* initialize csum = lcg(1) */
sfcsump(vl,lcg,&csum);
/* initialize lcy by LC(f) */
W_BMALLOC(0,dy,lcy);
NEWDC(dc); COEF(dc) = COEF(DC(g)); DEG(dc) = 0;
NEWP(lcyx); VR(lcyx) = x; DC(lcyx) = dc;
ptosfbm(dy,lcyx,lcy);
/* initialize lcy0 by LC(f) */
lcy0 = W_UMALLOC(bound);
ptosfum(COEF(DC(g)),lcy0);
/* ((d-1 coefs)*lcy0 */
d1c = (UM *)W_ALLOC(np*sizeof(UM));
w = W_UMALLOC(2*bound);
for ( i = 1; i < np; i++ ) {
extractcoefbm(c[i],degbm(c[i])-1,w);
d1c[i] = W_UMALLOC(2*bound);
mulsfum(w,lcy0,d1c[i]);
/* d1c[i] = d1c[i] mod y^(bound+1) */
if ( DEG(d1c[i]) > bound ) {
for ( j = DEG(d1c[i]); j > bound; j-- )
COEF(d1c[i])[j] = 0;
degum(d1c[i],bound);
}
}
if ( debug_sfbfctr)
fprintf(stderr,"np = %d\n",np);
dtok = 0;
for ( g = f, k = 1, dcf = dcf0 = 0, win[0] = 1, --np, z = 0; ; z++ ) {
if ( debug_sfbfctr && !(z % 1000) ) fprintf(stderr,".");
dt = sfdegtest(dy,bound,d1c,k,win);
if ( dt )
dtok++;
if ( dt && sfdtestmain(vl,lcg,lcg0,lcy,csum,wlist,
k,win,&factor,&cofactor) ) {
NEXTDC(dcf0,dcf); DEG(dcf) = ONE; COEF(dcf) = factor;
g = cofactor;
/* update lcg */
mulp(vl,g,COEF(DC(g)),&lcg);
/* update lcg0 */
const_term(lcg,lcg0);
/* update csum */
sfcsump(vl,lcg,&csum);
/* update dy */
dy = getdeg(y,g);
/* update lcy */
clearbm(0,lcy);
COEF(dc) = COEF(DC(g));
ptosfbm(dy,lcyx,lcy);
for ( i = 0; i < k - 1; i++ )
for ( j = win[i] + 1; j < win[i + 1]; j++ )
c[j-i-1] = c[j];
for ( j = win[k-1] + 1; j <= np; j++ )
c[j-k] = c[j];
if ( ( np -= k ) < k )
break;
if ( np - win[0] + 1 < k )
if ( ++k > np )
break;
else
for ( i = 0; i < k; i++ )
win[i] = i + 1;
else
for ( i = 1; i < k; i++ )
win[i] = win[0] + i;
/* update lcy0 */
ptosfum(COEF(DC(g)),lcy0);
/* update d-1 coeffs */
for ( i = 1; i <= np; i++ ) {
extractcoefbm(c[i],degbm(c[i])-1,w);
mulsfum(w,lcy0,d1c[i]);
/* d1c[i] = d1c[1] mod y^(bound+1) */
if ( DEG(d1c[i]) > bound ) {
for ( j = DEG(d1c[i]); j > bound; j-- )
COEF(d1c[i])[j] = 0;
degum(d1c[i],bound);
}
}
} else if ( !ncombi(1,np,k,win) )
if ( k == np )
break;
else
for ( i = 0, ++k; i < k; i++ )
win[i] = i + 1;
}
if ( debug_sfbfctr )
fprintf(stderr,"total %d, omitted by degtest %d\n",z,z-dtok);
NEXTDC(dcf0,dcf); COEF(dcf) = g;
DEG(dcf) = ONE; NEXT(dcf) = 0; *dcp = dcf0;
}
void extractcoefbm(BM f,int dx,UM r)
{
int j;
UM fj;
for ( j = DEG(f); j >= 0; j-- ) {
fj = COEF(f)[j];
if ( fj && DEG(fj) >= dx ) {
COEF(r)[j] = COEF(fj)[dx];
} else
COEF(r)[j] = 0;
}
degum(r,DEG(f));
}
/* deg_y(prod mod y^(bound+1)) <= dy ? */
int sfdegtest(int dy,int bound,UM *d1c,int k,int *in)
{
int i,j;
UM w,w1,wt;
BM t;
w = W_UMALLOC(bound);
w1 = W_UMALLOC(bound);
clearum(w,bound);
for ( i = 0; i < k; i++ ) {
addsfum(w,d1c[in[i]],w1); wt = w; w = w1; w1 = wt;
}
return DEG(w) <= dy ? 1 : 0;
}
/* lcy = LC(g), lcg = lcy*g, lcg0 = const part of lcg */
int sfdtestmain(VL vl,P lcg,UM lcg0,BM lcy,P csum,ML list,
int k,int *in,P *fp,P *cofp)
{
P fmul,csumg,q,cont;
V x,y;
x = vl->v;
y = vl->next->v;
if (!sfctest(lcg0,lcy,list,k,in))
return 0;
mulsfbmarray(UDEG(lcg),lcy,list,k,in,x,y,&fmul);
if ( csum ) {
sfcsump(vl,fmul,&csumg);
if ( csumg ) {
if ( !divtp(vl,csum,csumg,&q) )
return 0;
}
}
if ( divtp_by_sfbm(vl,lcg,fmul,&q) ) {
cont_pp_sfp(vl,fmul,&cont,fp);
cont_pp_sfp(vl,q,&cont,cofp);
return 1;
} else
return 0;
}
void const_term(P f,UM c)
{
DCP dc;
for ( dc = DC(f); dc && DEG(dc); dc = NEXT(dc) );
if ( dc )
ptosfum(COEF(dc),c);
else
DEG(c) = -1;
}
void const_term_sfbm(BM f,UM c)
{
int i,dy;
dy = DEG(f);
for ( i = 0; i <= dy; i++ )
if ( DEG(COEF(f)[i]) >= 0 )
COEF(c)[i] = COEF(COEF(f)[i])[0];
else
COEF(c)[i] = 0;
degum(c,dy);
}
/* lcy*(product of const part) | lcg0 ? */
int sfctest(UM lcg0,BM lcy,ML list,int k,int *in)
{
int dy,i,dr;
UM t,s,u,w;
BM *l;
dy = list->bound;
t = W_UMALLOC(2*dy);
s = W_UMALLOC(2*dy);
u = W_UMALLOC(2*dy);
const_term_sfbm(lcy,t);
if ( DEG(t) < 0 )
return 1;
l = (BM *)list->c;
for ( i = 0; i < k; i++ ) {
const_term_sfbm(l[in[i]],s);
mulsfum(t,s,u);
if ( DEG(u) > dy )
degum(u,dy);
w = t; t = u; u = w;
}
cpyum(lcg0,s);
dr = divsfum(s,t,u);
if ( dr >= 0 )
return 0;
else
return 1;
}
/* main var of f is x */
void mulsfbmarray(int dx,BM lcy,ML list,int k,int *in,V x,V y,P *g)
{
int dy,i;
BM wb0,wb1,t;
BM *l;
dy = list->bound;
W_BMALLOC(dx,dy,wb0); W_BMALLOC(dx,dy,wb1);
l = (BM *)list->c;
clearbm(dx,wb0);
mulsfbm(lcy,l[in[0]],wb0);
for ( i = 1; i < k; i++ ) {
clearbm(dx,wb1);
mulsfbm(l[in[i]],wb0,wb1);
t = wb0; wb0 = wb1; wb1 = t;
}
sfbmtop(wb0,x,y,g);
}
void sfcsump(VL vl,P f,P *s)
{
P t,u;
DCP dc;
for ( dc = DC(f), t = 0; dc; dc = NEXT(dc) ) {
addp(vl,COEF(dc),t,&u); t = u;
}
*s = t;
}
/* *fp = primitive part of f w.r.t. x */
void cont_pp_sfp(VL vl,P f,P *cp,P *fp)
{
V x,y;
int d;
UM t,s,gcd;
DCP dc;
GFS g;
x = vl->v;
y = vl->next->v;
d = getdeg(y,f);
if ( d == 0 ) {
itogfs(1,&g);
*cp = (P)g;
*fp = f; /* XXX */
} else {
t = W_UMALLOC(2*d);
s = W_UMALLOC(2*d);
gcd = W_UMALLOC(2*d);
dc = DC(f);
ptosfum(COEF(dc),gcd);
for ( dc = NEXT(dc); dc; dc = NEXT(dc) ) {
ptosfum(COEF(dc),t);
gcdsfum(gcd,t,s);
cpyum(s,gcd);
}
sfumtop(y,gcd,cp);
divsp(vl,f,*cp,fp);
}
}
int divtp_by_sfbm(VL vl,P f,P g,P *qp)
{
V x,y;
int fx,fy,gx,gy;
BM fl,gl,ql;
UM *cf,*cg,*cq;
UM hg,q,t,s;
int i,j,dr;
x = vl->v; y = vl->next->v;
fx = getdeg(x,f); fy = getdeg(y,f);
gx = getdeg(x,g); gy = getdeg(y,g);
if ( fx < gx || fy < gy )
return 0;
W_BMALLOC(fx,fy,fl); ptosfbm(fy,f,fl); cf = COEF(fl);
W_BMALLOC(gx,gy,gl); ptosfbm(gy,g,gl); cg = COEF(gl);
W_BMALLOC(fx-gx,fy-gy,ql); cq = COEF(ql);
hg = cg[gy];
q = W_UMALLOC(fx); t = W_UMALLOC(fx); s = W_UMALLOC(fx);
for ( i = fy; i >= gy; i-- ) {
if ( DEG(cf[i]) < 0 )
continue;
dr = divsfum(cf[i],hg,q);
if ( dr >= 0 )
return 0;
if ( DEG(q) > fx-gx )
return 0;
cpyum(q,cq[i-gy]);
for ( j = 0; j <= gy; j++ ) {
mulsfum(cg[j],q,t);
subsfum(cf[j+i-gy],t,s);
cpyum(s,cf[j+i-gy]);
}
}
for ( j = gy-1; j >= 0 && DEG(cf[j]) < 0; j-- );
if ( j >= 0 )
return 0;
sfbmtop(ql,x,y,qp);
return 1;
}
/* XXX generate an irreducible poly of degree n */
extern int current_gfs_q1;
extern int *current_gfs_ntoi;
void generate_defpoly_sfum(int n,UM *dp)
{
UM r,dr,t,g;
UM *f;
int *c,*w;
int max,i,j;
*dp = r = UMALLOC(n);
DEG(r) = n;
c = COEF(r);
c[n] = _onesf();
max = current_gfs_q1;
w = (int *)ALLOCA(n*sizeof(int));
bzero(w,n*sizeof(int));
dr = W_UMALLOC(n); t = W_UMALLOC(n); g = W_UMALLOC(n);
f = (UM *)ALLOCA((n+1)*sizeof(UM));
while ( 1 ) {
for ( i = 0; i < n && w[i] == max; i++ );
if ( i == n ) {
/* XXX cannot happen */
error("generate_defpoly_sfum : cannot happen");
}
for ( j = 0; j < i; j++ )
w[j] = 0;
w[i]++;
if ( !current_gfs_ntoi )
for ( i = 0; i < n; i++ )
c[i] = w[i]?FTOIF(w[i]):0;
else
for ( i = 0; i < n; i++ )
c[i] = w[i]?FTOIF(w[i]-1):0;
if ( !c[0] )
continue;
diffsfum(r,dr); cpyum(r,t); gcdsfum(t,dr,g);
if ( DEG(g) > 0 )
continue;
czsfum(r,f);
for ( i = 0; f[i]; i++ );
if ( i == 1 )
return;
}
}
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