===================================================================
RCS file: /home/cvs/OpenXM_contrib2/asir2000/engine/dalg.c,v
retrieving revision 1.6
retrieving revision 1.13
diff -u -p -r1.6 -r1.13
--- OpenXM_contrib2/asir2000/engine/dalg.c	2004/12/07 15:15:52	1.6
+++ OpenXM_contrib2/asir2000/engine/dalg.c	2006/01/05 00:21:20	1.13
@@ -1,5 +1,5 @@
 /*
- * $OpenXM: OpenXM_contrib2/asir2000/engine/dalg.c,v 1.5 2004/12/04 09:39:27 noro Exp $
+ * $OpenXM: OpenXM_contrib2/asir2000/engine/dalg.c,v 1.12 2005/10/12 14:43:36 noro Exp $
 */
 
 #include "ca.h"
@@ -8,7 +8,7 @@
 static NumberField current_numberfield;
 extern struct order_spec *dp_current_spec;
 void simpdalg(DAlg da,DAlg *r);
-void invdalg(DAlg a,DAlg *c);
+int invdalg(DAlg a,DAlg *c);
 void rmcontdalg(DAlg a, DAlg *c);
 void algtodalg(Alg a,DAlg *r);
 void dalgtoalg(DAlg da,Alg *r);
@@ -62,9 +62,51 @@ void setfield_dalg(NODE alist)
 	nf->dim = dim = length(mblist);
 	nf->mb = mb = (DP *)MALLOC(dim*sizeof(DP));
 	for ( i = 0, t = mblist; t; t = NEXT(t), i++ )
-		mb[i] = (DP)BDY(t);	
+		mb[dim-i-1] = (DP)BDY(t);	
 }
 
+void setfield_gb(NODE gb,VL vl,struct order_spec *spec)
+{
+	NumberField nf;
+	VL vl1,vl2;
+	int n,i,dim;
+	Alg *gen;
+	P *defpoly;
+	P p;
+	Q c,iq,two;
+	DP *ps,*mb;
+	DP one;
+	NODE t,b,b1,b2,hlist,mblist;
+	struct order_spec *current_spec;
+
+	nf = (NumberField)MALLOC(sizeof(struct oNumberField));
+	current_numberfield = nf;
+	for ( vl1 = vl, n = 0; vl1; vl1 = NEXT(vl1), n++ );
+	nf->n = n;
+	nf->psn = length(gb);
+	nf->vl = vl;
+	nf->defpoly = defpoly = (P *)MALLOC(nf->psn*sizeof(P));
+	nf->ps = ps = (DP *)MALLOC(nf->psn*sizeof(DP));
+	current_spec = dp_current_spec;
+	nf->spec = spec;
+	initd(nf->spec);	
+	for ( b = hlist = 0, i = 0, t = gb; i < nf->psn; t = NEXT(t), i++ ) {
+		ptozp((P)BDY(t),1,&c,&defpoly[i]);
+		ptod(CO,vl,defpoly[i],&ps[i]);
+		STOQ(i,iq); MKNODE(b1,(pointer)iq,b); b = b1;
+		MKNODE(b2,(pointer)ps[i],hlist); hlist = b2;
+	}
+	ptod(ALG,vl,(P)ONE,&one);
+	MKDAlg(one,ONE,nf->one);
+	nf->ind = b;
+	dp_mbase(hlist,&mblist);
+	initd(current_spec);
+	nf->dim = dim = length(mblist);
+	nf->mb = mb = (DP *)MALLOC(dim*sizeof(DP));
+	for ( i = 0, t = mblist; t; t = NEXT(t), i++ )
+		mb[dim-i-1] = (DP)BDY(t);	
+}
+
 void qtodalg(Q q,DAlg *r)
 {
 	NumberField nf;
@@ -294,7 +336,7 @@ void algtodalg(Alg a,DAlg *r)
 				NTOQ(NM(c),SGN(c),c1);
 				NTOQ(DN(c),1,d1);
 				muldc(CO,nf->one->nm,(P)c1,&dp);
-				MKDAlg(dp,c1,*r);
+				MKDAlg(dp,d1,*r);
 			}
 			break;
 		case N_A:
@@ -358,10 +400,13 @@ void simpdalg(DAlg da,DAlg *r)
 	}
 	current_spec = dp_current_spec; initd(nf->spec);
 	dp_true_nf(nf->ind,da->nm,nf->ps,1,&nm,&dn);
-	initd(current_spec);
-	mulq(da->dn,dn,&dn1);
-	MKDAlg(nm,dn1,d);
-	rmcontdalg(d,r);
+	if ( !nm ) *r = 0;
+	else {
+		initd(current_spec);
+		mulq(da->dn,dn,&dn1);
+		MKDAlg(nm,dn1,d);
+		rmcontdalg(d,r);
+	}
 }
 
 void adddalg(DAlg a,DAlg b,DAlg *c)
@@ -463,6 +508,7 @@ void muldalg(DAlg a,DAlg b,DAlg *c)
 void divdalg(DAlg a,DAlg b,DAlg *c)
 {
 	DAlg inv,t;
+	int ret;
 
 	if ( !current_numberfield )
 		error("divdalg : current_numberfield is not set");
@@ -472,7 +518,10 @@ void divdalg(DAlg a,DAlg b,DAlg *c)
 		c = 0;
 	else {
 		qtodalg((Q)a,&t); a = t; qtodalg((Q)b,&t); b = t;
-		invdalg(b,&inv);
+		ret = invdalg(b,&inv);
+		if ( !ret ) {
+			error("divdalg : the denominator is not invertible");
+		}
 		muldalg(a,inv,c);
 	}
 }
@@ -496,20 +545,22 @@ void rmcontdalg(DAlg a, DAlg *r)
 	}
 }
 
-void invdalg(DAlg a,DAlg *c)
+int invdalg(DAlg a,DAlg *c)
 {
 	NumberField nf;
-	int dim,n,i,j;
+	int dim,n,i,j,k,l;
 	DP *mb;
 	DP m,d,u;
 	N ln,gn,qn;
 	DAlg *simp;
 	DAlg t,a0,r;
-	Q dn,dnsol,mul;
+	Q dn,dnsol,mul,nmc,dn1;
 	MAT mobj,sol;
 	Q **mat,**solmat;
 	MP mp0,mp;
 	int *rinfo,*cinfo;
+	int rank,nparam;
+	NODE nd0,nd,ndt;
 	struct order_spec *current_spec;
 	struct oEGT eg0,eg1;
 	extern struct oEGT eg_le;
@@ -526,15 +577,16 @@ void invdalg(DAlg a,DAlg *c)
 	mb = nf->mb;
 	n = nf->n;
 	ln = ONEN;
-	MKDAlg(a->nm,ONE,a0);
+	dp_ptozp(a->nm,&u); divq((Q)BDY(a->nm)->c,(Q)BDY(u)->c,&nmc);
+	MKDAlg(u,ONE,a0);
 	simp = (DAlg *)ALLOCA(dim*sizeof(DAlg));
 	current_spec = dp_current_spec; initd(nf->spec);
-	for ( i = dim-1; i >= 0; i-- ) {
+	for ( i = 0; i < dim; i++ ) {
 		m = mb[i];
-		for ( j = i+1; j < dim; j++ )
+		for ( j = i-1; j >= 0; j-- )
 			if ( dp_redble(m,mb[j]) )
 				break;
-		if ( j < dim ) {
+		if ( j >= 0 ) {
 			dp_subd(m,mb[j],&d);
 			muld(CO,d,simp[j]->nm,&u);
 			MKDAlg(u,simp[j]->dn,t);
@@ -550,28 +602,156 @@ void invdalg(DAlg a,DAlg *c)
 	NTOQ(ln,1,dn);
 	MKMAT(mobj,dim,dim+1);
 	mat = (Q **)BDY(mobj);
-	mulq(dn,a->dn,&mat[dim-1][dim]);
+	mulq(dn,a->dn,&mat[0][dim]);
 	for ( j = 0; j < dim; j++ ) {
 		divq(dn,simp[j]->dn,&mul);
-		for ( i = 0, mp = BDY(simp[j]->nm); mp && i < dim; i++ )
+		for ( i = dim-1, mp = BDY(simp[j]->nm); mp && i >= 0; i-- )
 			if ( dl_equal(n,BDY(mb[i])->dl,mp->dl) ) {
 				mulq(mul,(Q)mp->c,&mat[i][j]);
 				mp = NEXT(mp);
 			}
 	}
 	get_eg(&eg0);
-	generic_gauss_elim_hensel(mobj,&sol,&dnsol,&rinfo,&cinfo);
+	rank = generic_gauss_elim_hensel(mobj,&sol,&dnsol,&rinfo,&cinfo);
 	get_eg(&eg1); add_eg(&eg_le,&eg0,&eg1);
-	solmat = (Q **)BDY(sol);
-	for ( i = 0, mp0 = 0; i < dim; i++ )
-		if ( solmat[i][0] ) {
+	if ( cinfo[0] == dim ) {
+		/* the input is invertible */
+		solmat = (Q **)BDY(sol);
+		for ( i = dim-1, mp0 = 0; i >= 0; i-- )
+			if ( solmat[i][0] ) {
+				NEXTMP(mp0,mp);
+				mp->c = (P)solmat[i][0];
+				mp->dl = BDY(mb[i])->dl;
+			}
+		NEXT(mp) = 0; MKDP(n,mp0,u);
+		mulq(dnsol,nmc,&dn1);
+		MKDAlg(u,dn1,r);
+		rmcontdalg(r,c);
+		return 1;
+	} else
+		return 0;
+}
+
+NODE inv_or_split_dalg(DAlg a,DAlg *c)
+{
+	NumberField nf;
+	int dim,n,i,j,k,l;
+	DP *mb;
+	DP m,d,u;
+	N ln,gn,qn;
+	DAlg *simp;
+	DAlg t,a0,r;
+	Q dn,dnsol,mul,nmc,dn1;
+	MAT mobj,sol;
+	Q **mat,**solmat;
+	MP mp0,mp;
+	int *rinfo,*cinfo;
+	int rank,nparam;
+	NODE nd0,nd,ndt;
+	struct order_spec *current_spec;
+	struct oEGT eg0,eg1;
+	extern struct oEGT eg_le;
+	extern int DP_Print;
+
+	if ( !(nf=current_numberfield) )
+		error("invdalg : current_numberfield is not set");
+	if ( !a )
+		error("invdalg : division by 0");
+	else if ( NID(a) == N_Q ) {
+		invq((Q)a,&dn); *c = (DAlg)dn;
+		return;
+	}
+	dim = nf->dim;
+	mb = nf->mb;
+	n = nf->n;
+	ln = ONEN;
+	dp_ptozp(a->nm,&u); divq((Q)BDY(a->nm)->c,(Q)BDY(u)->c,&nmc);
+	MKDAlg(u,ONE,a0);
+	simp = (DAlg *)ALLOCA(dim*sizeof(DAlg));
+	current_spec = dp_current_spec; initd(nf->spec);
+	for ( i = 0; i < dim; i++ ) {
+		if ( DP_Print ) { fprintf(asir_out,"."); fflush(asir_out); }
+		m = mb[i];
+		for ( j = i-1; j >= 0; j-- )
+			if ( dp_redble(m,mb[j]) )
+				break;
+		if ( j >= 0 ) {
+			dp_subd(m,mb[j],&d);
+			if ( simp[j] ) {
+				muld(CO,d,simp[j]->nm,&u);
+				MKDAlg(u,simp[j]->dn,t);
+				simpdalg(t,&simp[i]);
+			} else
+				simp[i] = 0;
+		} else {
+			MKDAlg(m,ONE,t);
+			muldalg(t,a0,&simp[i]);
+		}
+		if ( simp[i] ) {
+			gcdn(NM(simp[i]->dn),ln,&gn); divsn(ln,gn,&qn);
+			muln(NM(simp[i]->dn),qn,&ln);
+		}
+	}
+	initd(current_spec);
+	NTOQ(ln,1,dn);
+	MKMAT(mobj,dim,dim+1);
+	mat = (Q **)BDY(mobj);
+	mulq(dn,a->dn,&mat[0][dim]);
+	for ( j = 0; j < dim; j++ ) {
+		if ( simp[j] ) {
+			divq(dn,simp[j]->dn,&mul);
+			for ( i = dim-1, mp = BDY(simp[j]->nm); mp && i >= 0; i-- )
+				if ( dl_equal(n,BDY(mb[i])->dl,mp->dl) ) {
+					mulq(mul,(Q)mp->c,&mat[i][j]);
+					mp = NEXT(mp);
+				}
+		}
+	}
+	get_eg(&eg0);
+	rank = generic_gauss_elim_hensel_dalg(mobj,&sol,&dnsol,&rinfo,&cinfo);
+	get_eg(&eg1); add_eg(&eg_le,&eg0,&eg1);
+	if ( cinfo[0] == dim ) {
+		/* the input is invertible */
+		solmat = (Q **)BDY(sol);
+		for ( i = dim-1, mp0 = 0; i >= 0; i-- )
+			if ( solmat[i][0] ) {
+				NEXTMP(mp0,mp);
+				mp->c = (P)solmat[i][0];
+				mp->dl = BDY(mb[i])->dl;
+			}
+		NEXT(mp) = 0; MKDP(n,mp0,u);
+		mulq(dnsol,nmc,&dn1);
+		MKDAlg(u,dn1,r);
+		rmcontdalg(r,c);
+		return 0;
+	} else {
+		/* the input is not invertible */
+		nparam = sol->col;
+		solmat = (Q **)BDY(sol);
+		nd0 = 0;
+		for ( k = 0; k < nparam; k++ ) {
+			/* construct a new basis element */
+			m = mb[cinfo[k]];
+			mp0 = 0;
 			NEXTMP(mp0,mp);
-			mp->c = (P)solmat[i][0];
-			mp->dl = BDY(mb[i])->dl;
+			chsgnq(dnsol,&dn1); mp->c = (P)dn1;
+			mp->dl = BDY(m)->dl;
+			/* skip the last parameter */
+			for ( l = rank-2; l >= 0; l-- ) {
+				if ( solmat[l][k] ) {
+					NEXTMP(mp0,mp);
+					mp->c = (P)solmat[l][k];
+					mp->dl = BDY(mb[rinfo[l]])->dl;
+				}
+			}
+			NEXT(mp) = 0; MKDP(n,mp0,u);
+			NEXTNODE(nd0,nd);
+			BDY(nd) = (pointer)u;
+			NEXT(nd) = 0;
 		}
-	NEXT(mp) = 0; MKDP(n,mp0,u);
-	MKDAlg(u,dnsol,r);
-	rmcontdalg(r,c);
+		NEXT(nd) = 0;
+		return nd0;
+	}
 }
 
 void chsgndalg(DAlg a,DAlg *c)
@@ -595,6 +775,7 @@ void pwrdalg(DAlg a,Q e,DAlg *c)
 	Q q;
 	N en,qn;
 	int r;
+	int ret;
 
 	if ( !(nf=current_numberfield) )
 		error("pwrdalg : current_numberfield is not set");
@@ -608,7 +789,10 @@ void pwrdalg(DAlg a,Q e,DAlg *c)
 		*c = a;
 	else {
 		if ( SGN(e) < 0 ) {
-			invdalg(a,&t); a = t;
+			ret = invdalg(a,&t); 
+			if ( !ret )
+				error("pwrdalg : the denominator is not invertible");
+			a = t;
 		}
 		en = NM(e);
 		y = nf->one;
@@ -636,3 +820,48 @@ int cmpdalg(DAlg a,DAlg b)
 	else
 		return SGN((Q)BDY(c->nm)->c);
 }
+
+/* convert da to a univariate poly; return the position of variable */
+
+int dalgtoup(DAlg da,P *up,Q *dn)
+{
+	int nv,i,hi,current_d;
+	DCP dc0,dc;
+	MP h,mp0,mp,t;
+	DL hd,d;
+	DP c;
+	DAlg cc;
+	P v;
+
+	nv = da->nm->nv;
+	h = BDY(da->nm);
+	*dn = da->dn;
+	hd = h->dl;
+	for ( i = 0; i < nv; i++ )
+		if ( hd->d[i] ) break;
+	hi = i;
+	current_d = hd->d[i];
+	dc0 = 0;
+	mp0 = 0;
+	for ( t = h; t; t = NEXT(t) ) {
+		NEWDL(d,nv);
+		for ( i = 0; i <= hi; i++ ) d->d[i] = 0;
+		for ( ; i < nv; i++ ) d->d[i] = t->dl->d[i];
+		d->td = t->dl->td - t->dl->d[hi];
+		if ( t->dl->d[hi] != current_d ) {
+			NEXT(mp) = 0; MKDP(nv,mp0,c); MKDAlg(c,ONE,cc);
+			NEXTDC(dc0,dc); STOQ(current_d,DEG(dc)); COEF(dc) = (P)cc;
+			current_d = t->dl->d[hi];
+			mp0 = 0;
+		}
+		NEXTMP(mp0,mp);
+		mp->c = t->c; mp->dl = d;
+	}
+	NEXT(mp) = 0; MKDP(nv,mp0,c); MKDAlg(c,ONE,cc);
+	NEXTDC(dc0,dc); STOQ(current_d,DEG(dc)); COEF(dc) = (P)cc;
+	NEXT(dc) = 0;
+	makevar("x",&v);
+	MKP(VR(v),dc0,*up);
+	return hi;
+}
+