/*
 * 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
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 * 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/mat,v 1.1 2018/09/19 05:45:08 noro Exp $
*/
/* fraction free gaussian elimination; detructive */

def deter(MAT)
{
	S = size(MAT);
	if ( car(S) != car(cdr(S)) )
		return 0;
	N = car(S);
	for ( J = 0, D = 1; J < N; J++ ) {
		for ( I = J; (I<N)&&(MAT[I][J] == 0); I++ );
		if ( I != N ) {
			for ( L = I; L < N; L++ )
				if ( MAT[L][J] && (nmono(MAT[L][J]) < nmono(MAT[I][J])) )
					I = L;
			if ( J != I )
				for ( K = 0; K < N; K++ ) {
					B = MAT[J][K]; MAT[J][K] = MAT[I][K]; MAT[I][K] = B;
				}

			for ( I = J + 1, V = MAT[J][J]; I < N; I++ )
				for ( K = J + 1, U = MAT[I][J]; K < N; K++ )
					MAT[I][K] = sdiv(MAT[I][K]*V-MAT[J][K]*U,D);
			D = V;
		} else
			return ( 0 );
	}
	return (D);
}

/* characteristic polynomial */

def cp(M)
{
	tstart;
	S = size(M);
	if ( car(S) != car(cdr(S)) )
		return 0;
	N = car(S);
	MAT = newmat(N,N);
	for ( I = 0; I < N; I++ )
		for ( J = 0; J < N; J++ )
			if ( I == J ) 
				MAT[I][J] = red(M[I][J]-x);
			else
				MAT[I][J] = red(M[I][J]);
	D = deter(MAT);
	tstop;
	return (D);
}

/* calculation of charpoly by danilevskii's method */

def da(MAT)
{
	tstart;
	S = size(MAT);
	if ( car(S) != car(cdr(S)) )
		return 0;
	N = car(S);
	M = newmat(N,N);
	for ( I = 0; I < N; I++ )
		for ( J = 0; J < N; J++ )
			M[I][J] = red(MAT[I][J]);

	for ( W = newvect(N), J = 0, K = 0, D = 1; J < N; J++ ) {
		for ( I = J + 1; (I<N) && (M[I][J] == 0); I++ );
		if ( I == N ) {
			for ( L = J, S = 1; L >= K; L-- )
				S = S*x-M[L][J];
			D *= S;
			K = J + 1;
		} else {
			B = J + 1;
			for ( L = 0; L < N; L++ ) {
				T = M[I][L]; M[I][L] = M[B][L]; M[B][L] = T;
			}
			for ( L = 0; L < N; L++ ) {
				T = M[L][B]; M[L][B] = M[L][I]; M[L][I] = T;
				W[L] = M[L][J];
			}
			for ( L = K, T = red(1/M[B][J]); L < N; L++ )
				M[B][L] *= T;
			for ( L = K; L < N; L++ )
				if ( W[L] && (L != J + 1) )
					for ( B = K, T = W[L]; B < N; B++ )
						M[L][B] -= M[J+1][B]*T;
			for ( L = K; L < N; L++ ) {
				for ( B = 0, T = 0; B < N ; B++ )
					T += M[L][B] * W[B];
				M[L][J + 1] = T;
			}
		}
	}
	tstop;
	return ( D );
}

def newvmat(N) {
	M = newmat(N,N);
	for ( I = 0; I < N; I++ )
		for ( J = 0; J < N; J++ )
			M[I][J] = strtov(rtostr(x)+rtostr(I))^J;
	return M;
}

def newssmat(N) {
	M = newmat(N,N);
	for ( I = 0; I < N; I++ )
		for ( J = 0; J < N; J++ )
			M[I][J] = strtov(rtostr(x)+rtostr(I)+"_"+rtostr(J));
	return M;
}

def newasssmat(N) {
	N *= 2;
	M = newmat(N,N);
	for ( I = 0; I < N; I++ )
		for ( J = 0; J < I; J++ )
			M[I][J] = strtov(rtostr(x)+rtostr(I)+"_"+rtostr(J));
	for ( I = 0; I < N; I++ )
		for ( J = I + 1; J < N; J++ )
			M[I][J] = -M[J][I];
	return M;
}

/* calculation of determinant by minor expansion */

def edet(M) {
	S = size(M);
	if ( S[0] == 1 )
		return M[0][0];
	else {
		N = S[0];
		L = newmat(N-1,N-1);
		for ( I = 0, R = 0; I < N; I++ ) {
			for ( J = 1; J < N; J++ ) {
				for ( K = 0; K < I; K++ )
					L[J-1][K] = M[J][K];
				for ( K = I+1; K < N; K++ )
					L[J-1][K-1] = M[J][K];
			}
			R += (-1)^I*edet(L)*M[0][I];
		}
		return R;
	}
}

/* sylvester's matrix */

def syl(V,P1,P2) {
	D1 = deg(P1,V); D2 = deg(P2,V);
	M = newmat(D1+D2,D1+D2);
	for ( J = 0; J <= D2; J++ )
		M[0][J] = coef(P2,D2-J,V);
	for ( I = 1; I < D1; I++ )
		for ( J = 0; J <= D2; J++ )
		M[I][I+J] = M[0][J];
	for ( J = 0; J <= D1; J++ )
		M[D1][J] = coef(P1,D1-J,V);
	for ( I = 1; I < D2; I++ )
		for ( J = 0; J <= D1; J++ )
		M[D1+I][I+J] = M[D1][J];
	return M;
}

/* calculation of resultant by edet() */

def res_minor(V,P1,P2)
{
	D1 = deg(P1,V); D2 = deg(P2,V);
	M = newmat(D1+D2,D1+D2);
	for ( J = 0; J <= D2; J++ )
		M[0][J] = coef(P2,D2-J,V);
	for ( I = 1; I < D1; I++ )
		for ( J = 0; J <= D2; J++ )
		M[I][I+J] = M[0][J];
	for ( J = 0; J <= D1; J++ )
		M[D1][J] = coef(P1,D1-J,V);
	for ( I = 1; I < D2; I++ )
		for ( J = 0; J <= D1; J++ )
		M[D1+I][I+J] = M[D1][J];
	return edet(M);
}
end$