/*
 * 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
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 *
 * $OpenXM: OpenXM_contrib2/asir2000/lib/bfct,v 1.9 2000/12/14 09:36:17 noro Exp $ 
*/
/* requires 'primdec' */

/* annihilating ideal of F^s */

def ann(F)
{
	V = vars(F);
	N = length(V);
	D = newvect(N);

	for ( I = 0; I < N; I++ )
		D[I] = [deg(F,V[I]),V[I]];
	qsort(D,compare_first);
	for ( V = [], I = N-1; I >= 0; I-- )
		V = cons(D[I][1],V);

	for ( I = N-1, DV = []; I >= 0; I-- )
		DV = cons(strtov("d"+rtostr(V[I])),DV);

	W = append([y1,y2,t],V);
	DW = append([dy1,dy2,dt],DV);

	B = [1-y1*y2,t-y1*F];
	for ( I = 0; I < N; I++ ) {
		B = cons(DV[I]+y1*diff(F,V[I])*dt,B);
	}
	dp_nelim(2);
	G0 = dp_weyl_gr_main(B,append(W,DW),0,0,6);
	G1 = [];
	for ( T = G0; T != []; T = cdr(T) ) {
		E = car(T); VL = vars(E);
		if ( !member(y1,VL) && !member(y2,VL) )
			G1 = cons(E,G1);
	}
	G2 = map(subst,G1,dt,1);
	G3 = map(b_subst,G2,t);
	G4 = map(subst,G3,t,-1-s);
	return G4;
}

def indicial1(F,V)
{
	W = append([y1,t],V);
	N = length(V);
	B = [t-y1*F];
	for ( I = N-1, DV = []; I >= 0; I-- )
		DV = cons(strtov("d"+rtostr(V[I])),DV);
	DW = append([dy1,dt],DV);
	for ( I = 0; I < N; I++ ) {
		B = cons(DV[I]+y1*diff(F,V[I])*dt,B);
	}
	dp_nelim(1);
	/* we use homogenization (heuristically determined) */
	G0 = dp_weyl_gr_main(B,append(W,DW),1,0,6);
	G1 = map(subst,G0,y1,1);
	Mat = newmat(2,2,[[-1,1],[0,1]]);
	G2 = map(psi,G1,t,dt);
	G3 = map(subst,G2,t,-s-1);
	return G3;
}

def psi(F,T,DT)
{
	D = dp_ptod(F,[T,DT]);
	Wmax = weight(D);
	D1 = dp_rest(D);
	for ( ; D1; D1 = dp_rest(D1) )
		if ( weight(D1) > Wmax )
			Wmax = weight(D1);
	for ( D1 = D, Dmax = 0; D1; D1 = dp_rest(D1) )
		if ( weight(D1) == Wmax )
			Dmax += dp_hm(D1);
	if ( Wmax >= 0 )
		Dmax = dp_weyl_mul(<<Wmax,0>>,Dmax);
	else
		Dmax = dp_weyl_mul(<<0,-Wmax>>,Dmax);
	Rmax = dp_dtop(Dmax,[T,DT]);
	R = b_subst(subst(Rmax,DT,1),T);
	return R;
}

def weight(D)
{
	V = dp_etov(D);
	return V[1]-V[0];
}

def compare_first(A,B)
{
	A0 = car(A);
	B0 = car(B);
	if ( A0 > B0 )
		return 1;
	else if ( A0 < B0 )
		return -1;
	else
		return 0;
}

/* b-function of F ? */

def bfct(F)
{
	V = vars(F);
	N = length(V);
	D = newvect(N);

	for ( I = 0; I < N; I++ )
		D[I] = [deg(F,V[I]),V[I]];
	qsort(D,compare_first);
	for ( V = [], I = 0; I < N; I++ )
		V = cons(D[I][1],V);
	for ( I = N-1, DV = []; I >= 0; I-- )
		DV = cons(strtov("d"+rtostr(V[I])),DV);
	V1 = cons(s,V); DV1 = cons(ds,DV);

	G0 = indicial1(F,reverse(V));
	G1 = dp_weyl_gr_main(G0,append(V1,DV1),0,1,0);
	Minipoly = weyl_minipoly(G1,append(V1,DV1),0,s);
	return Minipoly;
}

def weyl_minipolym(G,V,O,M,V0)
{
	N = length(V);
	Len = length(G);
	dp_ord(O);
	setmod(M);
	PS = newvect(Len);
	PS0 = newvect(Len);

	for ( I = 0, T = G; T != []; T = cdr(T), I++ )
		PS0[I] = dp_ptod(car(T),V);
	for ( I = 0, T = G; T != []; T = cdr(T), I++ )
		PS[I] = dp_mod(dp_ptod(car(T),V),M,[]);

	for ( I = Len - 1, GI = []; I >= 0; I-- )
		GI = cons(I,GI);

	U = dp_mod(dp_ptod(V0,V),M,[]);

	T = dp_mod(<<0>>,M,[]);
	TT = dp_mod(dp_ptod(1,V),M,[]);
	G = H = [[TT,T]];

	for ( I = 1; ; I++ ) {
		T = dp_mod(<<I>>,M,[]);

		TT = dp_weyl_nf_mod(GI,dp_weyl_mul_mod(TT,U,M),PS,1,M);
		H = cons([TT,T],H);
		L = dp_lnf_mod([TT,T],G,M);
		if ( !L[0] )
			return dp_dtop(L[1],[V0]);
		else
			G = insert(G,L);
	}
}

def weyl_minipoly(G0,V0,O0,V)
{
	for ( I = 0; ; I++ ) {
		Prime = lprime(I);
		MP = weyl_minipolym(G0,V0,O0,Prime,V);
		for ( D = deg(MP,V), TL = [], J = 0; J <= D; J++ )
			TL = cons(V^J,TL);
		dp_ord(O0);
		NF = weyl_gennf(G0,TL,V0,O0)[0];

		LHS = weyl_nf_tab(-car(TL),NF,V0);
		B = weyl_hen_ttob(cdr(TL),NF,LHS,V0,Prime);
		if ( B ) {
			R = ptozp(B[1]*car(TL)+B[0]);
			return R;
		}
	}
}

def weyl_gennf(G,TL,V,O)
{
	N = length(V); Len = length(G); dp_ord(O); PS = newvect(Len);
	for ( I = 0, T = G, HL = []; T != []; T = cdr(T), I++ ) {
		PS[I] = dp_ptod(car(T),V); HL = cons(dp_ht(PS[I]),HL);
	}
	for ( I = 0, DTL = []; TL != []; TL = cdr(TL) )
		DTL = cons(dp_ptod(car(TL),V),DTL);
	for ( I = Len - 1, GI = []; I >= 0; I-- )
		GI = cons(I,GI);
	T = car(DTL); DTL = cdr(DTL);
	H = [weyl_nf(GI,T,T,PS)];

	T0 = time()[0];
	while ( DTL != [] ) {
		T = car(DTL); DTL = cdr(DTL);
		if ( dp_gr_print() )
			print(".",2);
		if ( L = search_redble(T,H) ) {
			DD = dp_subd(T,L[1]);
			NF = weyl_nf(GI,dp_weyl_mul(L[0],dp_subd(T,L[1])),dp_hc(L[1])*T,PS);
		} else
			NF = weyl_nf(GI,T,T,PS);
		NF = remove_cont(NF);
		H = cons(NF,H);
	}
	if ( dp_gr_print() ) print("");
	TNF = time()[0]-T0;
	if ( dp_gr_print() )
		print("gennf(TAB="+rtostr(TTAB)+" NF="+rtostr(TNF)+")");
	return [H,PS,GI];
}

def weyl_nf(B,G,M,PS)
{
	for ( D = 0; G; ) {
		for ( U = 0, L = B; L != []; L = cdr(L) ) {
			if ( dp_redble(G,R=PS[car(L)]) > 0 ) {
				GCD = igcd(dp_hc(G),dp_hc(R));
				CG = idiv(dp_hc(R),GCD); CR = idiv(dp_hc(G),GCD);
				U = CG*G-dp_weyl_mul(CR*dp_subd(G,R),R);
				if ( !U )
					return [D,M];
				D *= CG; M *= CG;
				break;
			}
		}
		if ( U )
			G = U;
		else {
			D += dp_hm(G); G = dp_rest(G);
		}
	}
	return [D,M];
}

def weyl_nf_mod(B,G,PS,Mod)
{
	for ( D = 0; G; ) {
		for ( U = 0, L = B; L != []; L = cdr(L) ) {
			if ( dp_redble(G,R=PS[car(L)]) > 0 ) {
				CR = dp_hc(G)/dp_hc(R);
				U = G-dp_weyl_mul_mod(CR*dp_mod(dp_subd(G,R),Mod,[]),R,Mod);
				if ( !U )
					return D;
				break;
			}
		}
		if ( U )
			G = U;
		else {
			D += dp_hm(G); G = dp_rest(G);
		}
	}
	return D;
}

def weyl_hen_ttob(T,NF,LHS,V,MOD)
{
	T0 = time()[0]; M = etom(weyl_leq_nf(T,NF,LHS,V)); TE = time()[0] - T0;
	T0 = time()[0]; U = henleq(M,MOD); TH = time()[0] - T0;
	if ( dp_gr_print() ) {
		print("(etom="+rtostr(TE)+" hen="+rtostr(TH)+")");
	}
	return U ? vtop(T,U,LHS) : 0;
}

def weyl_leq_nf(TL,NF,LHS,V)
{
	TLen = length(NF);
	T = newvect(TLen); M = newvect(TLen);
	for ( I = 0; I < TLen; I++ ) {
		T[I] = dp_ht(NF[I][1]);
		M[I] = dp_hc(NF[I][1]);
	}
	Len = length(TL); INDEX = newvect(Len); COEF = newvect(Len);
	for ( L = TL, J = 0; L != []; L = cdr(L), J++ ) {
		D = dp_ptod(car(L),V);
		for ( I = 0; I < TLen; I++ )
			if ( D == T[I] )
				break;
		INDEX[J] = I; COEF[J] = strtov("u"+rtostr(J));
	}
	if ( !LHS ) {
		COEF[0] = 1; NM = 0; DN = 1;
	} else {
		NM = LHS[0]; DN = LHS[1];
	}
	for ( J = 0, S = -NM; J < Len; J++ ) {
		DNJ = M[INDEX[J]];
		GCD = igcd(DN,DNJ); CS = DNJ/GCD; CJ = DN/GCD;
		S = CS*S + CJ*NF[INDEX[J]][0]*COEF[J];
		DN *= CS;
	}
	for ( D = S, E = []; D; D = dp_rest(D) )
		E = cons(dp_hc(D),E);
	BOUND = LHS ? 0 : 1;
	for ( I = Len - 1, W = []; I >= BOUND; I-- )	
			W = cons(COEF[I],W);
	return [E,W];	
}

def weyl_nf_tab(A,NF,V)
{
	TLen = length(NF);
	T = newvect(TLen); M = newvect(TLen);
	for ( I = 0; I < TLen; I++ ) {
		T[I] = dp_ht(NF[I][1]);
		M[I] = dp_hc(NF[I][1]);
	}
	A = dp_ptod(A,V);
	for ( Z = A, Len = 0; Z; Z = dp_rest(Z), Len++ );
	INDEX = newvect(Len); COEF = newvect(Len);
	for ( Z = A, J = 0; Z; Z = dp_rest(Z), J++ ) {
		D = dp_ht(Z);
		for ( I = 0; I < TLen; I++ )
			if ( D == T[I] )
				break;
		INDEX[J] = I; COEF[J] = dp_hc(Z);
	}
	for ( J = 0, S = 0, DN = 1; J < Len; J++ ) {
		DNJ = M[INDEX[J]];
		GCD = igcd(DN,DNJ); CS = DNJ/GCD; CJ = DN/GCD;
		S = CS*S + CJ*NF[INDEX[J]][0]*COEF[J];
		DN *= CS;
	}
	return [S,DN];	
}

def remove_zero(L)
{
	for ( R = []; L != []; L = cdr(L) )
		if ( car(L) )
			R = cons(car(L),R);
	return R;
}

def z_subst(F,V)
{
	for ( ; V != []; V = cdr(V) )
		F = subst(F,car(V),0);
	return F;
}

def flatmf(L) {  
    for ( S = []; L != []; L = cdr(L) )
		if ( type(F=car(car(L))) != NUM )
			S = append(S,[F]);
	return S;
}

def member(A,L) {
    for ( ; L != []; L = cdr(L) )
		if ( A == car(L) )
			return 1;
	return 0;
}   

def intersection(A,B)
{
	for ( L = []; A != []; A = cdr(A) )
	if ( member(car(A),B) )
		L = cons(car(A),L);
	return L;
}

def b_subst(F,V)
{
	D = deg(F,V);
	C = newvect(D+1);
	for ( I = D; I >= 0; I-- )
		C[I] = coef(F,I,V);
	for ( I = 0, R = 0; I <= D; I++ )
		if ( C[I] )
			R += C[I]*v_factorial(V,I);
	return R;
}

def v_factorial(V,N)
{
	for ( J = N-1, R = 1; J >= 0; J-- )
		R *= V-J;
	return R;
}
end$