/*
 * 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/asir2018/lib/solve,v 1.1 2018/09/19 05:45:08 noro Exp $
*/
def kenzan(El,Sl)
{
	for ( Tl = El; Tl != []; Tl = cdr(Tl) ) {
		if ( substv(car(Tl),Sl) ) {
			print("kenzan : error");
			return 0;
		}
	}
	print("kenzan : ok");
	return 1;
}

def substv(P,Sl)
{
	for ( A = P; Sl != []; Sl = cdr(Sl) ) 
		A = subst(A,car(car(Sl)),car(cdr(car(Sl))));
	return A;
}
			
def co(X,V,D)
{
	for ( I = 0; I < D; I++ )
		X = diff(X,V);
	return sdiv(subst(X,V,0),fac(D));
}

def solve(El,Vl)
/*
 * El : list of linear forms
 * Vl : list of variable
 */
{
	N = length(El); M = length(Vl);
	Mat = newmat(N,M+1); 
	W = newvect(M+1); Index = newvect(N); Vs = newvect(M);
	for ( I = 0, Tl = Vl; I < M; Tl = cdr(Tl), I++ )
		Vs[I] = car(Tl);
	for ( I = 0, Tl = El; I < N; Tl = cdr(Tl), I++ ) {
		solve_ltov(car(Tl),Vl,W);
		for ( J = 0; J <= M; J++ )
			Mat[I][J] = W[J];
	}
	Tl = solvemain(Mat,Index,N,M); L = car(Tl); D = car(cdr(Tl));
	if ( L < 0 )
		return [];
	for ( I = L - 1, S = []; I >= 0; I-- ) {
		for ( J = Index[I]+1, A = 0; J < M; J++ ) {
			A += Mat[I][J]*Vs[J];
		}
		S = cons([Vs[Index[I]],-red((A+Mat[I][M])/D)],S);
	}
	if ( kenzan(El,S) )
		return S;
	else
		return [];
	return S;
}

def solvemain(Mat,Index,N,M) 
/* 
 *	Mat : matrix of size Nx(M+1)
 *	Index : vector of length N
 */
{
	for ( J = 0, L = 0, D = 1; J < M; J++ ) {
		for ( I = L; I < N && !Mat[I][J]; I++ );
		if ( I == N )
			continue;
		Index[L] = J;
		for ( K = 0; K <= M; K++ ) {
			T = Mat[I][K]; Mat[I][K] = Mat[L][K]; Mat[L][K] = T;
		}
		for ( I = L + 1, V = Mat[L][J]; I < N; I++ )
			for ( K = J, U = Mat[I][J]; K <= M; K++ )
				Mat[I][K] = sdiv(Mat[I][K]*V-Mat[L][K]*U,D);
		D = V; L++;
	}
	for ( I = L; I < N; I++ )
		for ( J = 0; J <= M; J++ )
			if ( Mat[I][J] )
				return -1;
	for ( I = L - 2, W = newvect(M+1); I >= 0; I-- ) {
		for ( J = 0; J <= M; J++ )
			W[J] = 0;
		for ( G = I + 1; G < L; G++ )
			for ( H = Index[G], U = Mat[I][H]; H <= M; H++ )
				W[H] += Mat[G][H]*U;
		for ( J = Index[I], U = Mat[I][J]; J <= M; J++ )
			Mat[I][J] = sdiv(Mat[I][J]*D-W[J],U);
	}
	return [L,D];
}

def solve_ltov(P,VL,W)
{
	for ( I = 0, L = VL; L != []; L = cdr(L), I++ ) {
		W[I] = co(P,car(L),1); P -= W[I]*car(L);
	}
	W[I] = P;
}
end$