/* $OpenXM: OpenXM_contrib2/asir2000/engine/Hgfs.c,v 1.1 2001/06/20 09:32:13 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;
{
unsigned int n;
int i;
n = ((unsigned int)random()) % d; DEG(p) = n; COEF(p)[n] = _onesf();
for ( i = 0; i < (int)n; i++ )
COEF(p)[i] = _randomsf();
}
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 spwrum0sf(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)); spwrum0sf(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 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;
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();
STON(q,n1); pwrn(n1,d,&n2); subn(n2,ONEN,&n3);
STON(2,n4); divsn(n3,n4,&n5);
while ( 1 ) {
randsfum(2*d,t); spwrum0sf(f,t,n5,s);
subsfum(s,o,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;
}
}
}
}