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A very^3 experimental implementation of Weyl algebra.

example:

[...] ctrl("do_weyl",1);
[...] <<1,2,3,4>>*<<4,5,6,7>>;  <--- (x*y^2*Dx^3*Dy^4)*(x^4*y^5*Dx^6*Dy^7)
(1)*<<5,7,9,11>>+(20)*<<5,6,9,10>>+(12)*<<4,7,8,11>>+(120)*<<5,5,9,9>>
+(240)*<<4,6,8,10>>+(36)*<<3,7,7,11>>+(240)*<<5,4,9,8>>+(1440)*<<4,5,8,9>>
+(720)*<<3,6,7,10>>+(24)*<<2,7,6,11>>+(120)*<<5,3,9,7>>+(2880)*<<4,4,8,8>>
+(4320)*<<3,5,7,9>>+(480)*<<2,6,6,10>>+(1440)*<<4,3,8,7>>+(8640)*<<3,4,7,8>>
+(2880)*<<2,5,6,9>>+(4320)*<<3,3,7,7>>+(5760)*<<2,4,6,8>>+(2880)*<<2,3,6,7>>

etc.

/* $OpenXM: OpenXM_contrib2/asir2000/engine/dist.c,v 1.2 2000/04/05 08:32:17 noro Exp $ */
#include "ca.h"

#define NV(p) ((p)->nv)
#define C(p) ((p)->c)

#define ORD_REVGRADLEX 0
#define ORD_GRADLEX 1
#define ORD_LEX 2
#define ORD_BREVGRADLEX 3
#define ORD_BGRADLEX 4
#define ORD_BLEX 5
#define ORD_BREVREV 6
#define ORD_BGRADREV 7
#define ORD_BLEXREV 8
#define ORD_ELIM 9

int (*cmpdl)()=cmpdl_revgradlex;
int (*primitive_cmpdl[3])() = {cmpdl_revgradlex,cmpdl_gradlex,cmpdl_lex};

void comm_muld(VL,DP,DP,DP *);
void weyl_muld(VL,DP,DP,DP *);
void weyl_muldm(VL,DP,MP,DP *);
void weyl_mulmm(VL,MP,MP,int,DP *);
void mkwc(int,int,Q *);

int do_weyl;

int dp_nelim,dp_fcoeffs;
struct order_spec dp_current_spec;
int *dp_dl_work;

int has_fcoef(DP);
int has_fcoef_p(P);

int has_fcoef(f)
DP f;
{
	MP t;

	if ( !f )
		return 0;
	for ( t = BDY(f); t; t = NEXT(t) )
		if ( has_fcoef_p(t->c) )
			break;
	return t ? 1 : 0;
}

int has_fcoef_p(f)
P f;
{
	DCP dc;

	if ( !f )
		return 0;
	else if ( NUM(f) )
		return (NID((Num)f) == N_LM || NID((Num)f) == N_GF2N) ? 1 : 0;
	else {
		for ( dc = DC(f); dc; dc = NEXT(dc) )
			if ( has_fcoef_p(COEF(dc)) )
				return 1;
		return 0;
	}
}

void initd(spec)
struct order_spec *spec;
{
	switch ( spec->id ) {
		case 2:
			cmpdl = cmpdl_matrix;
			dp_dl_work = (int *)MALLOC_ATOMIC(spec->nv*sizeof(int));	
			break;
		case 1:
			cmpdl = cmpdl_order_pair;
			break;
		default:
			switch ( spec->ord.simple ) {
				case ORD_REVGRADLEX:
					cmpdl = cmpdl_revgradlex; break;
				case ORD_GRADLEX:
					cmpdl = cmpdl_gradlex; break;
				case ORD_BREVGRADLEX:
					cmpdl = cmpdl_brevgradlex; break;
				case ORD_BGRADLEX:
					cmpdl = cmpdl_bgradlex; break;
				case ORD_BLEX:
					cmpdl = cmpdl_blex; break;
				case ORD_BREVREV:
					cmpdl = cmpdl_brevrev; break;
				case ORD_BGRADREV:
					cmpdl = cmpdl_bgradrev; break;
				case ORD_BLEXREV:
					cmpdl = cmpdl_blexrev; break;
				case ORD_ELIM:
					cmpdl = cmpdl_elim; break;
				case ORD_LEX: default:
					cmpdl = cmpdl_lex; break;
			}
			break;
	}
	dp_current_spec = *spec;
}

void ptod(vl,dvl,p,pr)
VL vl,dvl;
P p;
DP *pr;
{
	int isconst = 0;
	int n,i;
	VL tvl;
	V v;
	DL d;
	MP m;
	DCP dc;
	DP r,s,t,u;
	P x,c;

	if ( !p )
		*pr = 0;
	else {
		for ( n = 0, tvl = dvl; tvl; tvl = NEXT(tvl), n++ );
		if ( NUM(p) ) {
			NEWDL(d,n);
			NEWMP(m); m->dl = d; C(m) = p; NEXT(m) = 0; MKDP(n,m,*pr); (*pr)->sugar = 0;
		} else {
			for ( i = 0, tvl = dvl, v = VR(p);
				tvl && tvl->v != v; tvl = NEXT(tvl), i++ );
			if ( !tvl ) {
				for ( dc = DC(p), s = 0, MKV(v,x); dc; dc = NEXT(dc) ) {
					ptod(vl,dvl,COEF(dc),&t); pwrp(vl,x,DEG(dc),&c);
					muldc(vl,t,c,&r); addd(vl,r,s,&t); s = t;
				}
				*pr = s;
			} else {
				for ( dc = DC(p), s = 0; dc; dc = NEXT(dc) ) {
					ptod(vl,dvl,COEF(dc),&t);
					NEWDL(d,n); d->td = QTOS(DEG(dc)); d->d[i] = d->td;
					NEWMP(m); m->dl = d; C(m) = (P)ONE; NEXT(m) = 0; MKDP(n,m,u); u->sugar = d->td;
					comm_muld(vl,t,u,&r); addd(vl,r,s,&t); s = t;
				}
				*pr = s;
			}
		}
	}
	if ( !dp_fcoeffs && has_fcoef(*pr) )
		dp_fcoeffs = 1;
}

void dtop(vl,dvl,p,pr)
VL vl,dvl;
DP p;
P *pr;
{
	int n,i;
	DL d;
	MP m;
	P r,s,t,u,w;
	Q q;
	VL tvl;

	if ( !p )
		*pr = 0;
	else {
		for ( n = p->nv, m = BDY(p), s = 0; m; m = NEXT(m) ) {
			t = C(m);
			if ( NUM(t) && NID((Num)t) == N_M ) {
				mptop(t,&u); t = u;
			}
			for ( i = 0, d = m->dl, tvl = dvl;
				i < n; tvl = NEXT(tvl), i++ ) {
				MKV(tvl->v,r); STOQ(d->d[i],q); pwrp(vl,r,q,&u);
				mulp(vl,t,u,&w); t = w;
			}
			addp(vl,s,t,&u); s = u;
		}
		*pr = s;
	}
}

void nodetod(node,dp)
NODE node;
DP *dp;
{
	NODE t;
	int len,i,td;
	Q e;
	DL d;
	MP m;
	DP u;

	for ( t = node, len = 0; t; t = NEXT(t), len++ );
	NEWDL(d,len);
	for ( t = node, i = 0, td = 0; i < len; t = NEXT(t), i++ ) {
		e = (Q)BDY(t);
		if ( !e )
			d->d[i] = 0;
		else if ( !NUM(e) || !RATN(e) || !INT(e) )
			error("nodetod : invalid input");
		else {
			d->d[i] = QTOS((Q)e); td += d->d[i];
		}
	}
	d->td = td;
	NEWMP(m); m->dl = d; C(m) = (P)ONE; NEXT(m) = 0;
	MKDP(len,m,u); u->sugar = td; *dp = u;
}

int sugard(m)
MP m;
{
	int s;

	for ( s = 0; m; m = NEXT(m) )
		s = MAX(s,m->dl->td);
	return s;
}

void addd(vl,p1,p2,pr)
VL vl;
DP p1,p2,*pr;
{
	int n;
	MP m1,m2,mr,mr0;
	P t;

	if ( !p1 )
		*pr = p2;
	else if ( !p2 )
		*pr = p1;
	else {
		for ( n = NV(p1), m1 = BDY(p1), m2 = BDY(p2), mr0 = 0; m1 && m2; )
			switch ( (*cmpdl)(n,m1->dl,m2->dl) ) {
				case 0:
					addp(vl,C(m1),C(m2),&t);
					if ( t ) {
						NEXTMP(mr0,mr); mr->dl = m1->dl; C(mr) = t;
					}
					m1 = NEXT(m1); m2 = NEXT(m2); break;
				case 1:
					NEXTMP(mr0,mr); mr->dl = m1->dl; C(mr) = C(m1);
					m1 = NEXT(m1); break;
				case -1:
					NEXTMP(mr0,mr); mr->dl = m2->dl; C(mr) = C(m2);
					m2 = NEXT(m2); break;
			}
		if ( !mr0 )
			if ( m1 )
				mr0 = m1;
			else if ( m2 )
				mr0 = m2;
			else {
				*pr = 0;
				return;
			}
		else if ( m1 )
			NEXT(mr) = m1;
		else if ( m2 )
			NEXT(mr) = m2;
		else
			NEXT(mr) = 0;
		MKDP(NV(p1),mr0,*pr);
		if ( *pr )
			(*pr)->sugar = MAX(p1->sugar,p2->sugar);
	}
}

/* for F4 symbolic reduction */

void symb_addd(p1,p2,pr)
DP p1,p2,*pr;
{
	int n;
	MP m1,m2,mr,mr0;
	P t;

	if ( !p1 )
		*pr = p2;
	else if ( !p2 )
		*pr = p1;
	else {
		for ( n = NV(p1), m1 = BDY(p1), m2 = BDY(p2), mr0 = 0; m1 && m2; ) {
			NEXTMP(mr0,mr); C(mr) = (P)ONE;
			switch ( (*cmpdl)(n,m1->dl,m2->dl) ) {
				case 0:
					mr->dl = m1->dl;
					m1 = NEXT(m1); m2 = NEXT(m2); break;
				case 1:
					mr->dl = m1->dl;
					m1 = NEXT(m1); break;
				case -1:
					mr->dl = m2->dl;
					m2 = NEXT(m2); break;
			}
		}
		if ( !mr0 )
			if ( m1 )
				mr0 = m1;
			else if ( m2 )
				mr0 = m2;
			else {
				*pr = 0;
				return;
			}
		else if ( m1 )
			NEXT(mr) = m1;
		else if ( m2 )
			NEXT(mr) = m2;
		else
			NEXT(mr) = 0;
		MKDP(NV(p1),mr0,*pr);
		if ( *pr )
			(*pr)->sugar = MAX(p1->sugar,p2->sugar);
	}
}

void subd(vl,p1,p2,pr)
VL vl;
DP p1,p2,*pr;
{
	DP t;

	if ( !p2 )
		*pr = p1;
	else {
		chsgnd(p2,&t); addd(vl,p1,t,pr);
	}
}

void chsgnd(p,pr)
DP p,*pr;
{
	MP m,mr,mr0;

	if ( !p )
		*pr = 0;
	else {
		for ( mr0 = 0, m = BDY(p); m; m = NEXT(m) ) {
			NEXTMP(mr0,mr); chsgnp(C(m),&C(mr)); mr->dl = m->dl;
		}
		NEXT(mr) = 0; MKDP(NV(p),mr0,*pr);
		if ( *pr )
			(*pr)->sugar = p->sugar;
	}
}

void muld(vl,p1,p2,pr)
VL vl;
DP p1,p2,*pr;
{
	if ( ! do_weyl )
		comm_muld(vl,p1,p2,pr);
	else
		weyl_muld(vl,p1,p2,pr);
}

void comm_muld(vl,p1,p2,pr)
VL vl;
DP p1,p2,*pr;
{
	MP m;
	DP s,t,u;

	if ( !p1 || !p2 )
		*pr = 0;
	else if ( OID(p1) <= O_P )
		muldc(vl,p2,(P)p1,pr);
	else if ( OID(p2) <= O_P )
		muldc(vl,p1,(P)p2,pr);
	else {
		for ( m = BDY(p2), s = 0; m; m = NEXT(m) ) {
			muldm(vl,p1,m,&t); addd(vl,s,t,&u); s = u;
		}
		*pr = s;
	}
}

void muldm(vl,p,m0,pr)
VL vl;
DP p;
MP m0;
DP *pr;
{
	MP m,mr,mr0;
	P c;
	DL d;
	int n;

	if ( !p )
		*pr = 0;
	else {
		for ( mr0 = 0, m = BDY(p), c = C(m0), d = m0->dl, n = NV(p); 
			m; m = NEXT(m) ) {
			NEXTMP(mr0,mr);
			if ( NUM(C(m)) && RATN(C(m)) && NUM(c) && RATN(c) )
				mulq((Q)C(m),(Q)c,(Q *)&C(mr));
			else
				mulp(vl,C(m),c,&C(mr));
			adddl(n,m->dl,d,&mr->dl);
		}
		NEXT(mr) = 0; MKDP(NV(p),mr0,*pr);
		if ( *pr )
			(*pr)->sugar = p->sugar + m0->dl->td;
	}
}

void weyl_muld(vl,p1,p2,pr)
VL vl;
DP p1,p2,*pr;
{
	MP m;
	DP s,t,u;

	if ( !p1 || !p2 )
		*pr = 0;
	else if ( OID(p1) <= O_P )
		muldc(vl,p2,(P)p1,pr);
	else if ( OID(p2) <= O_P )
		muldc(vl,p1,(P)p2,pr);
	else {
		for ( m = BDY(p2), s = 0; m; m = NEXT(m) ) {
			weyl_muldm(vl,p1,m,&t); addd(vl,s,t,&u); s = u;
		}
		*pr = s;
	}
}

void weyl_muldm(vl,p,m0,pr)
VL vl;
DP p;
MP m0;
DP *pr;
{
	DP r,t,t1;
	MP m;
	int n;

	if ( !p )
		*pr = 0;
	else {
		for ( r = 0, m = BDY(p), n = NV(p); m; m = NEXT(m) ) {
			weyl_mulmm(vl,m,m0,n,&t);
			addd(vl,r,t,&t1); r = t1;
		}
		if ( r )
			r->sugar = p->sugar + m0->dl->td;
		*pr = r;
	}
}

/* m0 = x0^d0*x1^d1*... * dx0^d(n/2)*dx1^d(n/2+1)*... */

void weyl_mulmm(vl,m0,m1,n,pr)
VL vl;
MP m0,m1;
int n;
DP *pr;
{
	MP m,mr,mr0;
	DP r,t,t1;
	P c,c0,c1,cc;
	DL d,d0,d1;
	int i,j,a,b,k,l,n2,s,min;
	Q *tab;

	if ( !m0 || !m1 )
		*pr = 0;
	else {
		c0 = C(m0); c1 = C(m1);
		mulp(vl,c0,c1,&c);
		d0 = m0->dl; d1 = m1->dl;
		n2 = n>>1;
		for ( i = 0, r = (DP)ONE; i < n2; i++ ) {
			a = d0->d[i]; b = d1->d[n2+i];
			k = d0->d[n2+i]; l = d1->d[i];
			/* compute xi^a*(Di^k*xi^l)*Di^b */
			min = MIN(k,l);
			tab = (Q *)ALLOCA((min+1)*sizeof(Q));
			mkwc(k,l,tab);
			for ( mr0 = 0, s = 0, j = 0; j <= min; j++ ) {
				NEXTMP(mr0,mr);
				NEWDL(d,n);
				d->d[i] = l-j+a; d->d[n2+i] = k-j+b;
				d->td = d->d[i]+d->d[n2+i]; /* XXX */
				s = MAX(s,d->td); /* XXX */
				mr->c = (P)tab[j];
				mr->dl = d;
			}
			if ( mr0 )
				NEXT(mr) = 0;
			MKDP(n,mr0,t);
			if ( t )
				t->sugar = s;
			comm_muld(vl,r,t,&t1); r = t1;
		}
		muldc(vl,r,c,pr);
	}
}

void muldc(vl,p,c,pr)
VL vl;
DP p;
P c;
DP *pr;
{
	MP m,mr,mr0;

	if ( !p || !c )
		*pr = 0;
	else if ( NUM(c) && UNIQ((Q)c) )
		*pr = p;
	else if ( NUM(c) && MUNIQ((Q)c) )
		chsgnd(p,pr);
	else {
		for ( mr0 = 0, m = BDY(p); m; m = NEXT(m) ) {
			NEXTMP(mr0,mr);
			if ( NUM(C(m)) && RATN(C(m)) && NUM(c) && RATN(c) )
				mulq((Q)C(m),(Q)c,(Q *)&C(mr));
			else
				mulp(vl,C(m),c,&C(mr));
			mr->dl = m->dl;
		}
		NEXT(mr) = 0; MKDP(NV(p),mr0,*pr);
		if ( *pr )
			(*pr)->sugar = p->sugar;
	}
}

void divsdc(vl,p,c,pr)
VL vl;
DP p;
P c;
DP *pr;
{
	MP m,mr,mr0;

	if ( !c )
		error("disvsdc : division by 0");
	else if ( !p )
		*pr = 0;
	else {
		for ( mr0 = 0, m = BDY(p); m; m = NEXT(m) ) {
			NEXTMP(mr0,mr); divsp(vl,C(m),c,&C(mr)); mr->dl = m->dl;
		}
		NEXT(mr) = 0; MKDP(NV(p),mr0,*pr);
		if ( *pr )
			(*pr)->sugar = p->sugar;
	}
}

void adddl(n,d1,d2,dr)
int n;
DL d1,d2;
DL *dr;
{
	DL dt;
	int i;

	if ( !d1->td )
		*dr = d2;
	else if ( !d2->td )
		*dr = d1;
	else {
		*dr = dt = (DL)MALLOC_ATOMIC((n+1)*sizeof(int));
		dt->td = d1->td + d2->td;
		for ( i = 0; i < n; i++ )
			dt->d[i] = d1->d[i]+d2->d[i];
	}
}

int compd(vl,p1,p2)
VL vl;
DP p1,p2;
{
	int n,t;
	MP m1,m2;

	if ( !p1 )
		return p2 ? -1 : 0;
	else if ( !p2 )
		return 1;
	else {
		for ( n = NV(p1), m1 = BDY(p1), m2 = BDY(p2);
			m1 && m2; m1 = NEXT(m1), m2 = NEXT(m2) )
			if ( (t = (*cmpdl)(n,m1->dl,m2->dl)) ||
				(t = compp(vl,C(m1),C(m2)) ) )
				return t;
		if ( m1 )
			return 1;
		else if ( m2 )
			return -1;
		else
			return 0;
	}
}

int cmpdl_lex(n,d1,d2)
int n;
DL d1,d2;
{
	int i;

	for ( i = 0; i < n && d1->d[i] == d2->d[i]; i++ );
	return i == n ? 0 : (d1->d[i] > d2->d[i] ? 1 : -1);
}

int cmpdl_revlex(n,d1,d2)
int n;
DL d1,d2;
{
	int i;

	for ( i = n - 1; i >= 0 && d1->d[i] == d2->d[i]; i-- );
	return i < 0 ? 0 : (d1->d[i] < d2->d[i] ? 1 : -1);
}

int cmpdl_gradlex(n,d1,d2)
int n;
DL d1,d2;
{
	if ( d1->td > d2->td )
		return 1;
	else if ( d1->td < d2->td )
		return -1;
	else
		return cmpdl_lex(n,d1,d2);
}

int cmpdl_revgradlex(n,d1,d2)
int n;
DL d1,d2;
{
	if ( d1->td > d2->td )
		return 1;
	else if ( d1->td < d2->td )
		return -1;
	else
		return cmpdl_revlex(n,d1,d2);
}

int cmpdl_blex(n,d1,d2)
int n;
DL d1,d2;
{
	int c;

	if ( c = cmpdl_lex(n-1,d1,d2) )
		return c;
	else {
		c = d1->d[n-1] - d2->d[n-1];
		return c > 0 ? 1 : c < 0 ? -1 : 0;
	}
}

int cmpdl_bgradlex(n,d1,d2)
int n;
DL d1,d2;
{
	int e1,e2,c;

	e1 = d1->td - d1->d[n-1]; e2 = d2->td - d2->d[n-1];
	if ( e1 > e2 )
		return 1;
	else if ( e1 < e2 )
		return -1;
	else {
		c = cmpdl_lex(n-1,d1,d2);
		if ( c )
			return c;
		else
			return d1->td > d2->td ? 1 : d1->td < d2->td ? -1 : 0;
	}
}

int cmpdl_brevgradlex(n,d1,d2)
int n;
DL d1,d2;
{
	int e1,e2,c;

	e1 = d1->td - d1->d[n-1]; e2 = d2->td - d2->d[n-1];
	if ( e1 > e2 )
		return 1;
	else if ( e1 < e2 )
		return -1;
	else {
		c = cmpdl_revlex(n-1,d1,d2);
		if ( c )
			return c;
		else
			return d1->td > d2->td ? 1 : d1->td < d2->td ? -1 : 0;
	}
}

int cmpdl_brevrev(n,d1,d2)
int n;
DL d1,d2;
{
	int e1,e2,f1,f2,c,i;

	for ( i = 0, e1 = 0, e2 = 0; i < dp_nelim; i++ ) {
		e1 += d1->d[i]; e2 += d2->d[i];
	}
	f1 = d1->td - e1; f2 = d2->td - e2;
	if ( e1 > e2 )
		return 1;
	else if ( e1 < e2 )
		return -1;
	else {
		c = cmpdl_revlex(dp_nelim,d1,d2);
		if ( c )
			return c;
		else if ( f1 > f2 )
			return 1;
		else if ( f1 < f2 )
			return -1;
		else {
			for ( i = n - 1; i >= dp_nelim && d1->d[i] == d2->d[i]; i-- );
			return i < dp_nelim ? 0 : (d1->d[i] < d2->d[i] ? 1 : -1);
		}
	}
}

int cmpdl_bgradrev(n,d1,d2)
int n;
DL d1,d2;
{
	int e1,e2,f1,f2,c,i;

	for ( i = 0, e1 = 0, e2 = 0; i < dp_nelim; i++ ) {
		e1 += d1->d[i]; e2 += d2->d[i];
	}
	f1 = d1->td - e1; f2 = d2->td - e2;
	if ( e1 > e2 )
		return 1;
	else if ( e1 < e2 )
		return -1;
	else {
		c = cmpdl_lex(dp_nelim,d1,d2);
		if ( c )
			return c;
		else if ( f1 > f2 )
			return 1;
		else if ( f1 < f2 )
			return -1;
		else {
			for ( i = n - 1; i >= dp_nelim && d1->d[i] == d2->d[i]; i-- );
			return i < dp_nelim ? 0 : (d1->d[i] < d2->d[i] ? 1 : -1);
		}
	}
}

int cmpdl_blexrev(n,d1,d2)
int n;
DL d1,d2;
{
	int e1,e2,f1,f2,c,i;

	for ( i = 0, e1 = 0, e2 = 0; i < dp_nelim; i++ ) {
		e1 += d1->d[i]; e2 += d2->d[i];
	}
	f1 = d1->td - e1; f2 = d2->td - e2;
	c = cmpdl_lex(dp_nelim,d1,d2);
	if ( c )
		return c;
	else if ( f1 > f2 )
		return 1;
	else if ( f1 < f2 )
		return -1;
	else {
		for ( i = n - 1; i >= dp_nelim && d1->d[i] == d2->d[i]; i-- );
		return i < dp_nelim ? 0 : (d1->d[i] < d2->d[i] ? 1 : -1);
	}
}

int cmpdl_elim(n,d1,d2)
int n;
DL d1,d2;
{
	int e1,e2,i;

	for ( i = 0, e1 = 0, e2 = 0; i < dp_nelim; i++ ) {
		e1 += d1->d[i]; e2 += d2->d[i];
	}
	if ( e1 > e2 )
		return 1;
	else if ( e1 < e2 )
		return -1;
	else 
		return cmpdl_revgradlex(n,d1,d2);
}

int cmpdl_order_pair(n,d1,d2)
int n;
DL d1,d2;
{
	int e1,e2,i,j,l;
	int *t1,*t2;
	int len;
	struct order_pair *pair;

	len = dp_current_spec.ord.block.length;
	pair = dp_current_spec.ord.block.order_pair;

	for ( i = 0, t1 = d1->d, t2 = d2->d; i < len; i++ ) {
		l = pair[i].length;
		switch ( pair[i].order ) {
			case 0:
				for ( j = 0, e1 = e2 = 0; j < l; j++ ) {
					e1 += t1[j]; e2 += t2[j];
				}
				if ( e1 > e2 )
					return 1;
				else if ( e1 < e2 )
					return -1;
				else {
					for ( j = l - 1; j >= 0 && t1[j] == t2[j]; j-- );
					if ( j >= 0 )
						return t1[j] < t2[j] ? 1 : -1;
				}
				break;
			case 1:
				for ( j = 0, e1 = e2 = 0; j < l; j++ ) {
					e1 += t1[j]; e2 += t2[j];
				}
				if ( e1 > e2 )
					return 1;
				else if ( e1 < e2 )
					return -1;
				else {
					for ( j = 0; j < l && t1[j] == t2[j]; j++ );
					if ( j < l )
						return t1[j] > t2[j] ? 1 : -1;
				}
				break;
			case 2:
				for ( j = 0; j < l && t1[j] == t2[j]; j++ );
				if ( j < l )
					return t1[j] > t2[j] ? 1 : -1;
				break;
			default:
				error("cmpdl_order_pair : invalid order"); break;
		}
		t1 += l; t2 += l;
	}
	return 0;
}

int cmpdl_matrix(n,d1,d2)
int n;
DL d1,d2;
{
	int *v,*w,*t1,*t2;
	int s,i,j,len;
	int **matrix;

	for ( i = 0, t1 = d1->d, t2 = d2->d, w = dp_dl_work; i < n; i++ )
		w[i] = t1[i]-t2[i];
	len = dp_current_spec.ord.matrix.row;
	matrix = dp_current_spec.ord.matrix.matrix;
	for ( j = 0; j < len; j++ ) {
		v = matrix[j];
		for ( i = 0, s = 0; i < n; i++ )
			s += v[i]*w[i];	
		if ( s > 0 )
			return 1;
		else if ( s < 0 )
			return -1;
	}
	return 0;
}