Return to E.c CVS log

Up to [local] / OpenXM_contrib2 / asir2000 / engine

lprime() now returns arbitrary number of long primes.

/*
 * Copyright (c) 1994-2000 FUJITSU LABORATORIES LIMITED 
 * All rights reserved.
 * 
 * FUJITSU LABORATORIES LIMITED ("FLL") hereby grants you a limited,
 * non-exclusive and royalty-free license to use, copy, modify and
 * redistribute, solely for non-commercial and non-profit purposes, the
 * computer program, "Risa/Asir" ("SOFTWARE"), subject to the terms and
 * conditions of this Agreement. For the avoidance of doubt, you acquire
 * only a limited right to use the SOFTWARE hereunder, and FLL or any
 * third party developer retains all rights, including but not limited to
 * copyrights, in and to the SOFTWARE.
 * 
 * (1) FLL does not grant you a license in any way for commercial
 * purposes. You may use the SOFTWARE only for non-commercial and
 * non-profit purposes only, such as academic, research and internal
 * business use.
 * (2) The SOFTWARE is protected by the Copyright Law of Japan and
 * international copyright treaties. If you make copies of the SOFTWARE,
 * with or without modification, as permitted hereunder, you shall affix
 * to all such copies of the SOFTWARE the above copyright notice.
 * (3) An explicit reference to this SOFTWARE and its copyright owner
 * shall be made on your publication or presentation in any form of the
 * results obtained by use of the SOFTWARE.
 * (4) In the event that you modify the SOFTWARE, you shall notify FLL by
 * e-mail at risa-admin@sec.flab.fujitsu.co.jp of the detailed specification
 * for such modification or the source code of the modified part of the
 * SOFTWARE.
 * 
 * THE SOFTWARE IS PROVIDED AS IS WITHOUT ANY WARRANTY OF ANY KIND. FLL
 * MAKES ABSOLUTELY NO WARRANTIES, EXPRESSED, IMPLIED OR STATUTORY, AND
 * EXPRESSLY DISCLAIMS ANY IMPLIED WARRANTY OF MERCHANTABILITY, FITNESS
 * FOR A PARTICULAR PURPOSE OR NONINFRINGEMENT OF THIRD PARTIES'
 * RIGHTS. NO FLL DEALER, AGENT, EMPLOYEES IS AUTHORIZED TO MAKE ANY
 * MODIFICATIONS, EXTENSIONS, OR ADDITIONS TO THIS WARRANTY.
 * UNDER NO CIRCUMSTANCES AND UNDER NO LEGAL THEORY, TORT, CONTRACT,
 * OR OTHERWISE, SHALL FLL BE LIABLE TO YOU OR ANY OTHER PERSON FOR ANY
 * DIRECT, INDIRECT, SPECIAL, INCIDENTAL, PUNITIVE OR CONSEQUENTIAL
 * DAMAGES OF ANY CHARACTER, INCLUDING, WITHOUT LIMITATION, DAMAGES
 * ARISING OUT OF OR RELATING TO THE SOFTWARE OR THIS AGREEMENT, DAMAGES
 * FOR LOSS OF GOODWILL, WORK STOPPAGE, OR LOSS OF DATA, OR FOR ANY
 * DAMAGES, EVEN IF FLL SHALL HAVE BEEN INFORMED OF THE POSSIBILITY OF
 * SUCH DAMAGES, OR FOR ANY CLAIM BY ANY OTHER PARTY. EVEN IF A PART
 * OF THE SOFTWARE HAS BEEN DEVELOPED BY A THIRD PARTY, THE THIRD PARTY
 * DEVELOPER SHALL HAVE NO LIABILITY IN CONNECTION WITH THE USE,
 * PERFORMANCE OR NON-PERFORMANCE OF THE SOFTWARE.
 *
 * $OpenXM: OpenXM_contrib2/asir2000/engine/E.c,v 1.7 2001/06/07 04:54:40 noro Exp $ 
*/
#include "ca.h"

void henmv(vl,vn,f,g0,h0,a0,b0,lg,lh,lg0,lh0,q,k,gp,hp)
VL vl;
VN vn;
P f,g0,h0,a0,b0,lg,lh,lg0,lh0;
Q q;
int k;
P *gp,*hp;
{
	P g1,h1,a1,b1;
	N qn;
	Q q2;

	divin((NM(q)),2,&qn); NTOQ(qn,1,q2);
	adjc(vl,g0,a0,lg0,q,&g1,&a1); adjc(vl,h0,b0,lh0,q,&h1,&b1);
	henmvmain(vl,vn,f,g1,h1,b1,a1,lg,lh,q,q2,k,gp,hp);
}

void henmvmain(vl,vn,f,fi0,fi1,gi0,gi1,l0,l1,mod,mod2,k,fr0,fr1)
VL vl;
VN vn;
P f,fi0,fi1,gi0,gi1,l0,l1;
Q mod,mod2;
int k;
P *fr0,*fr1;
{
	V v;
	int n,i,j;
	int *md;
	P x,m,m1,c,q,r,a,s,u,ff,f0,f1;
	P w0,w1,cf,cfi,t,q1,dvr;
	P *c0,*c1;
	P *f0h,*f1h;

	v = VR(f); n = deg(v,f); MKV(v,x);
	c0 = (P *)ALLOCA((n+1)*sizeof(P));
	c1 = (P *)ALLOCA((n+1)*sizeof(P));
	invl((Q)LC(fi1),mod,(Q *)&c); mulp(vl,fi1,c,&t); cmp(mod,t,&dvr); 
	cm2p(mod,mod2,gi0,&c0[0]); cm2p(mod,mod2,gi1,&c1[0]);
	for ( i = 1; i <= n; i++ ) {
		mulp(vl,x,c1[i-1],&m); divsrp(vl,m,dvr,&q,&r); mulp(vl,q,c,&q1);
		cm2p(mod,mod2,r,&c1[i]); 
		mulp(vl,x,c0[i-1],&m); mulp(vl,q1,fi0,&m1); addp(vl,m,m1,&a);
		cm2p(mod,mod2,a,&c0[i]); 
	}
	affine(vl,f,vn,&t); cm2p(mod,mod2,t,&ff); 
	for ( i = 0; vn[i].v; i++ );
	md = ( int *) ALLOCA((i+1)*sizeof(int));
	for ( i = 0; vn[i].v; i++ )
		md[i] = getdeg(vn[i].v,ff);
	cm2p(mod,mod2,fi0,&f0); affine(vl,l0,vn,&t);
	if ( NUM(f0) )
		cm2p(mod,mod2,t,&f0);
	else
		cm2p(mod,mod2,t,&COEF(DC(f0)));
	cm2p(mod,mod2,fi1,&f1); affine(vl,l1,vn,&t);
	if ( NUM(f1) )
		cm2p(mod,mod2,t,&f1);
	else
		cm2p(mod,mod2,t,&COEF(DC(f1)));
	W_CALLOC(k,P,f0h); W_CALLOC(k,P,f1h);
	for ( i = 0; i <= k; i++ ) {
		exthpc(vl,v,f0,i,&f0h[i]); exthpc(vl,v,f1,i,&f1h[i]);
	}
	for ( j = 1; j <= k; j++ ) {
		for ( i = 0; vn[i].v; i++ ) 
			if ( getdeg(vn[i].v,f0)+getdeg(vn[i].v,f1) > md[i] )
				goto END;
		for ( i = 0, s = 0; i <= j; i++ ) {
			mulp(vl,f0h[i],f1h[j-i],&t); addp(vl,s,t,&u); s = u;
		}
		cm2p(mod,mod2,s,&t);
		exthpc(vl,v,ff,j,&u); subm2p(vl,mod,mod2,u,t,&cf);
		for ( i = 0, w0 = 0, w1 = 0; i <= n; i++ ) {
			if ( !cf ) 
				cfi = 0;
			else if ( VR(cf) == v ) 
				coefp(cf,i,&cfi);
			else if ( i == 0 ) 
				cfi = cf;
			else 
				cfi = 0;
			if ( cfi ) {
				mulp(vl,cfi,c0[i],&m); addp(vl,w0,m,&a); w0 = a;
				mulp(vl,cfi,c1[i],&m); addp(vl,w1,m,&a); w1 = a;
			}
		}
		cm2p(mod,mod2,w0,&t); addm2p(vl,mod,mod2,f0,t,&a); 
		addm2p(vl,mod,mod2,f0h[j],t,&s); f0h[j] = s; f0 = a;
		cm2p(mod,mod2,w1,&u); addm2p(vl,mod,mod2,f1,u,&a); 
		addm2p(vl,mod,mod2,f1h[j],u,&s); f1h[j] = s; f1 = a;
		if ( !t ) {
			restore(vl,f0,vn,&s); cm2p(mod,mod2,s,&t);
			if ( divtpz(vl,f,t,&s) ) {
				*fr0 = t; *fr1 = s;	
				return;
			} 
		}
		if ( !u ) {
			restore(vl,f1,vn,&s); cm2p(mod,mod2,s,&t);
			if ( divtpz(vl,f,t,&s) ) {
				*fr0 = s; *fr1 = t;	
				return;
			} 
		}
	}
END:
	restore(vl,f0,vn,&t); cm2p(mod,mod2,t,fr0); 
	restore(vl,f1,vn,&t); cm2p(mod,mod2,t,fr1); 
}

/*
	input : f, fi0, fi1, p, k; f = fi0 * fi1 mod p; ( p, k : integer )
	output : gr1 * fr0 + gr0 * fr1 = 1 mod qr; ( qr = p^(2^(k-1)) )
*/

void henzq(f,i0,fi0,i1,fi1,p,k,fr0p,fr1p,gr0p,gr1p,qrp)
P f;
UM fi0,fi1;
int p,k;
P i0,i1;
P *fr0p,*fr1p,*gr0p,*gr1p;
Q *qrp;
{
	N qn;
	Q q,qq,q2;
	int n,i;
	UM wg0,wg1,wf0,wf1;
	P f0,f1,g0,g1,m,m1,s,c,d,q1,r1,rm,rm1,a,a1,a2;

	n = UDEG(f);
	wf0 = W_UMALLOC(n); wf1 = W_UMALLOC(n);
	wg0 = W_UMALLOC(n); wg1 = W_UMALLOC(n);
	cpyum(fi0,wf0); cpyum(fi1,wf1);
	eucum(p,wf0,wf1,wg1,wg0);
	umtop(VR(f),fi0,&f0); umtop(VR(f),fi1,&f1);
	umtop(VR(f),wg0,&g0); umtop(VR(f),wg1,&g1);

	STOQ(p,q); divin(NM(q),2,&qn); NTOQ(qn,1,q2);
	for ( i = 1; i < k; i++ ) {
#if 0
		mulp(CO,i1,g0,&m); mulp(CO,i0,g1,&m1); addp(CO,m,m1,&a);
		if ( NUM(a) ) {
			for ( STOQ(p,q), j = 1; j < k; j++ ) {
				mulq(q,q,&qq); q = qq;
			}
			f0 = i0; f1 = i1;
			invl(a,q,&qq);
			mulp(CO,g0,qq,&s); g0 = s; mulp(CO,g1,qq,&s); g1 = s;
			break;
		}
#endif
	/*	c = ((f - f0*f1)/q) mod q;
		q1 = (c*g1) / f1; 
		r1 = (c*g1) mod f1;
		f1 += (r1 mod q)*q;
		f0 += ((c*g0 + q1*f0) mod q)*q;

		d = ((1 - (f1*g0 + f0*g1))/q) mod q;
		q1 = (d*g0) / f1;
		r1 = (d*g0) mod f1;
		g1 += (r1 mod q)*q;
		g0 += ((c*g0 + q1*f0) mod q)*q;
		q = q^2;
	*/

	/* c = ((f - f0*f1)/q) mod q */
		mulp(CO,f0,f1,&m); subp(CO,f,m,&s); 
		divcp(s,q,&m); cm2p(q,q2,m,&c); 

	/* q1 = (c*g1) / f1; r1 = (c*g1) mod f1; */
		mulp(CO,c,g1,&m); cm2p(q,q2,m,&s); 
		udivpwm(q,s,f1,&q1,&r1); 

	/* f1 = f1 + (r1 mod q)*q; */
		cm2p(q,q2,r1,&rm); 
		mulpq(rm,(P)q,&rm1); addp(CO,f1,rm1,&a); 
		f1 = a;

	/* a1 = (c*g0 + q1*f0) mod q; */
		mulp(CO,c,g0,&m); mulp(CO,q1,f0,&m1); addp(CO,m,m1,&a);
		cm2p(q,q2,a,&a1); 

	/* f0 = f0 + a1*q; */
		mulpq(a1,(P)q,&a2); 
		addp(CO,f0,a2,&a); 
		f0 = a;

	/* d = ((1 - (f1*g0 + f0*g1))/q) mod q; */
		mulp(CO,f1,g0,&m); mulp(CO,f0,g1,&m1); addp(CO,m,m1,&a);
		subp(CO,(P)ONE,a,&s); 
		divcp(s,q,&m); cm2p(q,q2,m,&d); 

	/* q1 = (d*g0) / f1; r1 = (d*g0) mod f1; */
		mulp(CO,d,g1,&m); udivpwm(q,m,f1,&q1,&r1); 

	/* g1 = g1 + (r1 mod q )*q; */
		cm2p(q,q2,r1,&rm); 
		mulpq(rm,(P)q,&rm1); addp(CO,g1,rm1,&a); 
		g1 = a;

	/* g0 = g0 + (c*g0 + q1*f0 mod q)*q; */
		mulp(CO,d,g0,&m); mulp(CO,q1,f0,&m1); addp(CO,m,m1,&a);
		cm2p(q,q2,a,&a1); mulpq(a1,(P)q,&a2); 
		addp(CO,g0,a2,&a); 
		g0 = a;

	/* q = q^2; */
		mulq(q,q,&qq); 
		q = qq;
		divin(NM(q),2,&qn); NTOQ(qn,1,q2);
	} 
	*fr0p = f0; *fr1p = f1; *gr0p = g0; *gr1p = g1; *qrp = q;
}

void henzq1(g,h,bound,gcp,hcp,qp)
P g,h;
Q bound;
P *gcp,*hcp;
Q *qp;
{
	V v;
	Q f,q,q1;
	Q u,t,a,b,s;
	P c,c1;
	P tg,th,tr;
	UM wg,wh,ws,wt,wm;
	int n,m,modres,mod,index,i;
	P gc0,hc0;
	P z,zz,zzz;


	v = VR(g); n=deg(v,g); m=deg(v,h);
	norm(g,&a); norm(h,&b);
	STOQ(m,u); pwrq(a,u,&t); 
	STOQ(n,u); pwrq(b,u,&s); 
	mulq(t,s,&u); 

	factorial(n+m,&t); mulq(u,t,&s); 
	addq(s,s,&f); 

	wg = W_UMALLOC(m+n); wh = W_UMALLOC(m+n);
	wt = W_UMALLOC(m+n); ws = W_UMALLOC(m+n);
	wm = W_UMALLOC(m+n); 

	for ( q = ONE, t = 0, c = 0, index = 0; ; ) {
		mod = get_lprime(index++);
		if ( !rem(NM((Q)LC(g)),mod) || !rem(NM((Q)LC(h)),mod) ) 
			continue;
		ptomp(mod,g,&tg); ptomp(mod,h,&th);
		srchump(mod,tg,th,&tr);
		if ( !tr )
			continue;
		else
			modres = CONT((MQ)tr);

		mptoum(tg,wg); mptoum(th,wh); 
		eucum(mod,wg,wh,ws,wt); /* wg * ws + wh * wt = 1 */
		DEG(wm) = 0; COEF(wm)[0] = modres;
		mulum(mod,ws,wm,wt);
		for ( i = DEG(wt); i >= 0; i-- ) 
			if ( ( COEF(wt)[i] * 2 ) > mod ) 
				COEF(wt)[i] -= mod;
		chnrem(mod,v,c,q,wt,&c1,&q1); 
		if ( !ucmpp(c,c1) ) {
			mulp(CO,c,g,&z); divsrp(CO,z,h,&zz,&zzz);
			if ( NUM(zzz) ) {
				q = q1; c = c1;
				break;
			} 
		}
		q = q1; c = c1;

		if ( cmpq(f,q) < 0 ) 
			break;
	}
	ptozp(c,1,&s,&gc0); 
	/* gc0*g = zz*h + zzz -> c*g + (-zz)*h = zzz */
	mulp(CO,gc0,g,&z);
	divsrp(CO,z,h,&zz,&zzz);
	ptozp(zz,1,&s,(P *)&t); 
	if ( INT((Q)s) )
		chsgnp(zz,&hc0);
	else {
		NTOQ(DN((Q)s),1,q); mulq(q,(Q)zzz,&q1); zzz = (P)q1;
		mulp(CO,gc0,(P)q,&c); gc0 = c; mulp(CO,zz,(P)q,&c); chsgnp(c,&hc0);
	}
	if ( !INT((Q)zzz) ) {
		NTOQ(DN((Q)zzz),1,q); NTOQ(NM((Q)zzz),1,q1); zzz = (P)q1;
		mulp(CO,gc0,(P)q,&c); gc0 = c; mulp(CO,hc0,(P)q,&c); hc0 = c;
	}
	for ( index = 0; ; ) {
		mod = get_lprime(index++);
		if ( !rem(NM((Q)zzz),mod) ||
			!rem(NM((Q)LC(g)),mod) || 
			!rem(NM((Q)LC(h)),mod) ) 
			continue;
		for ( STOQ(mod,q); cmpq(q,bound) < 0; ) {
			mulq(q,q,&q1); q = q1;
		}
		*qp = q;
		invl((Q)zzz,q,&q1); 
		mulp(CO,gc0,(P)q1,hcp); mulp(CO,hc0,(P)q1,gcp);
		return;
	}
}

void addm2p(vl,mod,mod2,n1,n2,nr)
VL vl;
Q mod,mod2;
P n1,n2,*nr;
{
	P t;

	addp(vl,n1,n2,&t);
	if ( !t )
		*nr = 0;
	else 
		cm2p(mod,mod2,t,nr); 
}

void subm2p(vl,mod,mod2,n1,n2,nr)
VL vl;
Q mod,mod2;
P n1,n2,*nr;
{
	P t;

	subp(vl,n1,n2,&t);
	if ( !t )
		*nr = 0;
	else 
		cm2p(mod,mod2,t,nr); 
}

void mulm2p(vl,mod,mod2,n1,n2,nr)
VL vl;
Q mod,mod2;
P n1,n2,*nr;
{
	P t;

	mulp(vl,n1,n2,&t);
	if ( !t )
		*nr = 0;
	else 
		cm2p(mod,mod2,t,nr); 
}

void cmp(mod,p,pr)
Q mod;
P p,*pr;
{
	P t;
	DCP dc,dcr,dcr0;

	if ( !p ) 
		*pr = 0;
	else if ( NUM(p) )
		remq((Q)p,mod,(Q *)pr);
	else {
		for ( dc = DC(p), dcr0 = 0; dc; dc = NEXT(dc) ) {
			cmp(mod,COEF(dc),&t);
			if ( t ) {
				NEXTDC(dcr0,dcr);
				DEG(dcr) = DEG(dc);
				COEF(dcr) = t;
			}
		}
		if ( !dcr0 ) 
			*pr = 0;
		else {
			NEXT(dcr) = 0;
			MKP(VR(p),dcr0,*pr);
		}
	}
}

void cm2p(mod,m,p,pr)
Q mod,m;
P p,*pr;
{
	P t;
	DCP dc,dcr,dcr0;

	if ( !p ) 
		*pr = 0;
	else if ( NUM(p) ) 
		rem2q((Q)p,mod,m,(Q *)pr);
	else {
		for ( dc = DC(p), dcr0 = 0; dc; dc = NEXT(dc) ) {
			cm2p(mod,m,COEF(dc),&t);
			if ( t ) {
				NEXTDC(dcr0,dcr);
				DEG(dcr) = DEG(dc);
				COEF(dcr) = t;
			}
		}
		if ( !dcr0 ) 
			*pr = 0;
		else {
			NEXT(dcr) = 0;
			MKP(VR(p),dcr0,*pr);
		} 
	}
}

void addm2q(mod,mod2,n1,n2,nr)
Q mod,mod2;
Q n1,n2,*nr;
{
	Q t;

	addq(n1,n2,&t);
	if ( !t )
		*nr = 0;
	else 
		rem2q(t,mod,mod2,nr); 
}

void subm2q(mod,mod2,n1,n2,nr)
Q mod,mod2;
Q n1,n2,*nr;
{
	Q t;

	subq(n1,n2,&t);
	if ( !t )
		*nr = 0;
	else 
		rem2q(t,mod,mod2,nr); 
}

void mulm2q(mod,mod2,n1,n2,nr)
Q mod,mod2;
Q n1,n2,*nr;
{
	Q t;

	mulq(n1,n2,&t);
	if ( !t )
		*nr = 0;
	else 
		rem2q(t,mod,mod2,nr); 
}

void rem2q(n,m,m2,nr)
Q n,m,m2,*nr;
{
	N q,r,s;
	int sgn;

	divn(NM(n),NM(m),&q,&r);
	if ( !r ) 
		*nr = 0;
	else {
		sgn = cmpn(r,NM(m2));
		if ( sgn > 0 ) {
			subn(NM(m),r,&s); NTOQ(s,-1*SGN(n),*nr);
		} else 
			NTOQ(r,SGN(n),*nr);
	}
}

/* 
	extract d-homogeneous part with respect to vl - {v}
*/

void exthpc_generic(vl,p,d,v,pr)
VL vl;
P p;
int d;
V v;
P *pr;
{
	P w,x,t,t1,a,xd;
	V v0;
	DCP dc;

	if ( d < 0 || !p )
		*pr = 0;
	else if ( NUM(p) )
		if ( d == 0 )
			*pr = p;
		else
			*pr = 0;
	else if ( v == VR(p) )
		exthpc(vl,v,p,d,pr);
	else {
		v0 = VR(p);
		for ( MKV(v0,x), dc = DC(p), w = 0; dc; dc = NEXT(dc) ) {
			exthpc_generic(vl,COEF(dc),d-QTOS(DEG(dc)),v,&t);
			pwrp(vl,x,DEG(dc),&xd);
			mulp(vl,xd,t,&t1); addp(vl,w,t1,&a); w = a;
		}
		*pr = w;
	}
}

void exthp(vl,p,d,pr)
VL vl;
P p;
int d;
P *pr;
{
	P t,t1,a,w,x,xd;
	DCP dc;

	if ( d < 0 ) 
		*pr = 0;
	else if ( NUM(p) )
		if ( d == 0 ) 
			*pr = p;
		else 
			*pr = 0;
	else {
		for ( MKV(VR(p),x), dc = DC(p), w = 0; dc; dc = NEXT(dc) ) {
			exthp(vl,COEF(dc),d - QTOS(DEG(dc)),&t);
			pwrp(vl,x,DEG(dc),&xd); 
			mulp(vl,xd,t,&t1); addp(vl,w,t1,&a); w = a;
		}
		*pr = w;
	}
}

void exthpc(vl,v,p,d,pr)
VL vl;
V v;
P p;
int d;
P *pr;
{
	P t,t1,a,w,x,xd;
	DCP dc;

	if ( v != VR(p) ) 
		exthp(vl,p,d,pr);
	else if ( d < 0 ) 
		*pr = 0;
	else {
		for ( MKV(v,x), dc = DC(p), w = 0; dc; dc = NEXT(dc) ) {
			exthp(vl,COEF(dc),d,&t);
			pwrp(vl,x,DEG(dc),&xd);
			mulp(vl,xd,t,&t1); addp(vl,w,t1,&a); w = a;
		}
		*pr = w;
	}
}

void cbound(vl,p,b)
VL vl;
P p;
Q *b;
{
	Q n,e,t,m;
	int k;

	cmax(p,&n);
	addq(n,n,&m); 

	k = geldb(vl,p);
	STOQ(3,t); STOQ(k,e);

	pwrq(t,e,&n);
	mulq(m,n,b); 
}

int geldb(vl,p)
VL vl;
P p;
{
	int m;

	for ( m = 0; vl; vl = NEXT(vl) ) 
		m += getdeg(vl->v,p);
	return ( m );
}

int getdeg(v,p)
V v;
P p;
{
	int m,t;
	DCP dc;
	
	if ( !p || NUM(p) ) 
		return ( 0 );
	else if ( v == VR(p) ) 
		return ( deg(v,p) );
	else {
		for ( dc = DC(p), m = 0; dc; dc = NEXT(dc) ) {
			t = getdeg(v,COEF(dc));
			m = MAX(m,t);
		}
		return ( m );
	}
}

void cmax(p,b)
P p;
Q *b;
{
	DCP dc;
	Q m,m1;
	N tn;

	if ( NUM(p) ) {
		tn = NM((Q)p);
		NTOQ(tn,1,*b);
	} else {
		for ( dc = DC(p), m = 0; dc; dc = NEXT(dc) ) {
			cmax(COEF(dc),&m1);
			if ( cmpq(m1,m) > 0 ) 
				m = m1;
		}
		*b = m;
	}
}

int nextbin(vn,n)
VN vn;
int n;
{
	int tmp,i,carry;

	if ( n == 0 ) 
		return ( 1 );

	for ( i = n - 1, carry = 1; i >= 0; i-- ) {
		tmp =  vn[i].n + carry;
		vn[i].n = tmp % 2;
		carry = tmp / 2;
	}
	return ( carry );
}

void mulsgn(vn,vnt,n,vn1)
VN vn,vnt,vn1;
int n;
{
	int i;

	for ( i = 0; vn[i].v; i++ ) 
		vn1[i].n = vn[i].n;
	for ( i = 0; i < n; i++ ) 
		if ( vnt[i].n ) 
			vn1[(int)vnt[i].v].n *= -1;
}

void next(vn)
VN vn;
{
	int i,m,n,tmp,carry;

	for ( m = 0, i = 0; vn[i].v; i++ ) 
		m = MAX(m,ABS(vn[i].n));
	if ( m == 0 ) {
		vn[--i].n = 1;
		return;
	}
	for ( carry = 1, m++, i--; ( i >= 0 ) && carry; i-- ) {
		tmp = vn[i].n + carry;
		vn[i].n = tmp % m;
		carry = tmp / m;
	}
	if ( ( i == -1 ) && carry ) {
		for ( i = 0; vn[i].v; i++ ) 
			vn[i].n = 0;
		vn[--i].n = m;
	} else {
		for ( n = 0, i = 0; vn[i].v; i++ ) 
			n = MAX(n,ABS(vn[i].n));
		if ( n < m - 1 ) 
			vn[--i].n = m - 1;
	}
}
		
void clctv(vl,p,nvlp)
VL vl;
P p;
VL *nvlp;
{
	int i,n;
	VL tvl;
	VN tvn;

	if ( !p || NUM(p) ) {
		*nvlp = 0;
		return;
	}

	for ( n = 0, tvl = vl; tvl; tvl = NEXT(tvl), n++ );
	tvn = (VN) ALLOCA((n+1)*sizeof(struct oVN));
	for ( i = 0, tvl = vl; tvl; tvl = NEXT(tvl), i++ ) {
		tvn[i].v = tvl->v;
		tvn[i].n = 0;
	}

	markv(tvn,n,p);
	vntovl(tvn,n,nvlp);
}

void markv(vn,n,p)
VN vn;
int n;
P p;
{
	V v;
	DCP dc;
	int i;

	if ( NUM(p) ) 
		return;
	v = VR(p);
	for ( i = 0, v = VR(p); i < n; i++ ) 
		if ( v == vn[i].v ) {
			vn[i].n = 1;
			break;
		}
	for ( dc = DC(p); dc; dc = NEXT(dc) ) 
		markv(vn,n,COEF(dc));
}
			
void vntovl(vn,n,vlp)
VN vn;
int n;
VL *vlp;
{
	int i;
	VL tvl,tvl0;

	for ( i = 0, tvl0 = 0; ; ) {
		while ( ( i < n ) && ( vn[i].n == 0 ) ) i++;
		if ( i == n ) 
			break;
		else {
			if ( !tvl0 ) {
				NEWVL(tvl0);
				tvl = tvl0;
			} else {
				NEWVL(NEXT(tvl));
				tvl = NEXT(tvl);
			}
			tvl->v = vn[i++].v;	
		}
	}
	if ( tvl0 ) 
		NEXT(tvl) = 0;
	*vlp = tvl0;
}

int dbound(v,f)
V v;
P f;
{
	int m,t;
	DCP dc;

	if ( !f ) 
		return ( -1 );
	else if ( v != VR(f) ) 
		return homdeg(f);
	else {
		for ( dc = DC(f), m = 0; dc; dc = NEXT(dc) ) {
			t = homdeg(COEF(dc));
			m = MAX(m,t);
		}
		return ( m );
	}
}

int homdeg(f)
P f;
{
	int m,t;
	DCP dc;

	if ( !f ) 
		return ( -1 );
	else if ( NUM(f) ) 
		return( 0 );
	else {
		for ( dc = DC(f), m = 0; dc; dc = NEXT(dc) ) {
			t = QTOS(DEG(dc))+homdeg(COEF(dc));
			m = MAX(m,t);
		}
		return ( m );
	}
}

int minhomdeg(f)
P f;
{
	int m,t;
	DCP dc;

	if ( !f ) 
		return ( -1 );
	else if ( NUM(f) ) 
		return( 0 );
	else {
		for ( dc = DC(f), m = homdeg(f); dc; dc = NEXT(dc) ) {
			t = QTOS(DEG(dc))+minhomdeg(COEF(dc));
			m = MIN(m,t);
		}
		return ( m );
	}
}

void adjc(vl,f,a,lc0,q,fr,ar)
VL vl;
P f,a,lc0;
Q q;
P *fr,*ar;
{
	P m,m1;
	Q t;

	invl((Q)LC(f),q,&t);
	mulq((Q)lc0,t,(Q *)&m); 
	mulpq(f,m,&m1); cmp(q,m1,fr); 
	invl((Q)m,q,&t); 
	mulpq(a,(P)t,&m1); 
	cmp(q,m1,ar); 
}

#if 1
void affinemain(vl,p,v0,n,pl,pr)
VL vl;
V v0;
int n;
P *pl;
P p;
P *pr;
{
	P x,t,m,c,s,a;
	DCP dc;
	Q d;

	if ( !p ) 
		*pr = 0;
	else if ( NUM(p) )
		*pr = p;
	else if ( VR(p) != v0 ) {
		MKV(VR(p),x);
		for ( c = 0, dc = DC(p); dc; dc = NEXT(dc) ) {
			affinemain(vl,COEF(dc),v0,n,pl,&t);
			if ( DEG(dc) ) {
				pwrp(vl,x,DEG(dc),&s); mulp(vl,s,t,&m); 
				addp(vl,m,c,&a); c = a;
			} else {
				addp(vl,t,c,&a); c = a;
			}
		}
		*pr = c;
	} else {
		dc = DC(p);
		c = COEF(dc);
		for ( d = DEG(dc), dc = NEXT(dc); 
			dc; d = DEG(dc), dc = NEXT(dc) ) {
				mulp(vl,pl[QTOS(d)-QTOS(DEG(dc))],c,&m); 
				addp(vl,m,COEF(dc),&c); 
		}
		if ( d ) {
			mulp(vl,pl[QTOS(d)],c,&m); c = m;
		}
		*pr = c;
	}
}
#endif

#if 0
affine(vl,p,vn,r)
VL vl;
P p;
VN vn;
P *r;
{
	int n,d,d1,i;
	Q *q;
	Q **bc;

	if ( !p || NUM(p) )
		*r = p;
	else {
		for ( i = 0, d = 0; vn[i].v; i++ )
			d1 = getdeg(vn[i].v,p), d = MAX(d,d1);
		W_CALLOC(d+1,Q *,bc);
		for ( i = 0; i <= d; i++ )
			W_CALLOC(i+1,Q,q), mkbc(i,q), bc[i] = q;
		afmain(vl,bc,p,vn,r);
	}
}

afmain(vl,bc,p,vn,r)
VL vl;
Q **bc;
P p;
VN vn;
P *r;
{
	P t,s,u;
	P *c,*rc;
	Q *q;
	DCP dc;
	int n,i,j;
	
	if ( !p || NUM(p) || !vn[0].v )
		*r = p;
	else if ( vn[0].v != VR(p) ) {
		for ( i = 0; vn[i].v && (vn[i].v != VR(p)); i++ );
		if ( vn[i].v )
			afmain(vl,bc,p,vn+i,r);
		else {
			n = QTOS(DEG(DC(p))); W_CALLOC(n+1,P,c);
			for ( dc = DC(p); dc; dc = NEXT(dc) )
				afmain(vl,bc,COEF(dc),vn,&c[QTOS(DEG(dc))]);
			plisttop(c,VR(p),n,r);
		}
	} else {
		n = QTOS(DEG(DC(p))); W_CALLOC(n+1,P,c); 
		W_CALLOC(n+1,P,rc); W_CALLOC(n+1,Q,q);
		for ( dc = DC(p); dc; dc = NEXT(dc) )
			afmain(vl,bc,COEF(dc),vn+1,&c[QTOS(DEG(dc))]);
		if ( !vn[0].n )
			bcopy(c,rc,sizeof(P)*(n+1));
		else {	
			for ( q[0] = ONE, STOQ(vn[0].n,q[1]), i = 2; i <= n; i++ )
				mulq(q[i-1],q[1],&q[i]);
			for ( j = 0; j <= n; rc[j] = t, j++ )
				for ( i = j, t = 0; i <= n; i++ )
					if ( c[i] )
						mulq(bc[i][j],q[i-j],&s), mulp(vl,s,c[i],&u),
						addp(CO,u,t,&s), t = s;
		}
		plisttop(rc,VR(p),n,r);
	}
}
#endif

void restore(vl,f,vn,fr)
VL vl;
P f;
VN vn;
P *fr;
{
	int i;
	P vv,g,g1,t;
	Q s;

	g = f;
	for ( i = 0; vn[i].v; i++ ) {
		MKV(vn[i].v,t);
		if ( vn[i].n ) {
			STOQ(-vn[i].n,s);
			addp(vl,t,(P)s,&vv);
		} else 
			vv = t;

		substp(vl,g,vn[i].v,vv,&g1); g = g1;
	}
	*fr = g;
}

void mergev(vl,vl1,vl2,nvlp)
VL vl,vl1,vl2,*nvlp;
{
	int i,n;
	VL tvl;
	VN vn;

	if ( !vl1 ) {
		*nvlp = vl2; return;
	} else if ( !vl2 ) {
		*nvlp = vl1; return;
	}
	for ( i = 0, tvl = vl; tvl; i++, tvl = NEXT(tvl) ); 
	n = i;
	W_CALLOC(n,struct oVN,vn);
	for ( i = 0, tvl = vl; tvl; tvl = NEXT(tvl), i++ )
		vn[i].v = tvl->v;
	for ( i = 0, tvl = vl1; (i < n) && tvl; i++, tvl = NEXT(tvl)) {
		while ( ( i < n ) && ( vn[i].v != tvl->v ) ) 
			i++;
		if ( i == n ) 
			break;
		else 
			vn[i].n = 1;
	}
	for ( i = 0, tvl = vl2; (i < n) && tvl; i++, tvl = NEXT(tvl) ) {
		while ( ( i < n ) && ( vn[i].v != tvl->v ) ) 
			i++;
		if ( i == n ) 
			break;
		else 
			vn[i].n = 1;
	}
	vntovl(vn,n,nvlp);
}

#if 0
void substvp(vl,f,vn,g)
VL vl;
P f;
VN vn;
P *g;
{
	V v;
	int i;
	P h,h1;
	Q t;

	h = f;
	for ( i = 0; v = vn[i].v; i++ ) {
		STOQ(vn[i].n,t);
		substp(vl,h,v,(P)t,&h1); h = h1;
	}
	*g = h;
}

void affine(vl,f,vn,fr)
VL vl;
P f;
VN vn;
P *fr;
{
	int i,j,n;
	P vv,g,g1,t,u;
	Q s;
	int *dlist;
	P **plist;

	for ( n = 0; vn[n].v; n++);
	dlist = (int *)ALLOCA((n+1)*sizeof(int));	
	plist = (P **)ALLOCA((n+1)*sizeof(P *));	
	for ( i = 0; vn[i].v; i++ ) {
		if ( !vn[i].n )
			continue;
		dlist[i] = getdeg(vn[i].v,f); 
		plist[i] = (P *)ALLOCA((dlist[i]+1)*sizeof(P));

		MKV(vn[i].v,t);
		if ( vn[i].n ) {
			STOQ(vn[i].n,s); addp(vl,t,(P)s,&vv); 
		} else 
			vv = t;

		for ( j = 0, t = (P)ONE; j < dlist[i]; j++ ) {
			plist[i][j] = t;
			mulp(vl,t,vv,&u);
			t = u;
		}
		plist[i][j] = t;
	}

	g = f;
	for ( i = 0; vn[i].v; i++ ) {
		if ( !vn[i].n )
			continue;
		affinemain(vl,g,vn[i].v,dlist[i],plist[i],&g1); g = g1;
	}
	*fr = g;
}
#endif