/*
 * 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.
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 * 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/cyclic,v 1.1 2018/09/19 05:45:08 noro Exp $
*/
def mkc(L,N)
{
	if (L >= N) L -= N;
	if (L >= 0)
		return strtov("c"+rtostr(L));
	return 0;
}

/* generate cyclic N-th roots systems */

def cyclic(N)
{
	R = [];
	for (L = 1; L <= N; L++) {
		for (A = 0, I = 0; I <= N-1; I++) {
			for (B = 1,J = I; J < L+I; J++) {
				B *= mkc(J,N);
			}
			A += B;
		}
		A = ptozp(A);
		if (L == N)
			A += -1;
		R = cons(A,R);
	}
	return R;
}

def rcyclic(N)
{
	R = [];
	for (L = 1; L <= N; L++) {
		for (A = 0, I = 0; I < 3; I++) {
			for (B = 1,J = I; J < L+I; J++) {
				B *= mkc(J,N);
			}
			A += B;
		}
		A = ptozp(A);
		if (L == N)
			A += -1;
		R = cons(A,R);
	}
	return R;
}

/* generate homogenized cyclic N-th roots systems */

def hcyclic(N)
{
	R = [];
	for (L = 1; L <= N; L++) {
		for (A = 0, I = 0; I <= N-1; I++) {
			for (B = 1,J = I; J < L+I; J++) {
				B *= mkc(J,N);
			}
			A += B;
		}
		A = ptozp(A);
		if (L == N)
			A += -c^N;
		R = cons(A,R);
	}
	return R;
}

def homo(X)
{
	X=nm(red(subst(X,a,a/t,b,b/t,c,c/t)));
}

BJ6 = [a^2*b*c+a*b^2*c+a*b*c^2+a*b+b*c+c*a,a^2*b^2*c+a*b^2*c^2+b*c^2+c+a+a^2*b,
a^2*b^2*c^2+b^2*c^2+c^2+1+a^2+a^2*b^2]$
HBJ6 = [homo(BJ6[0]),homo(BJ6[1]),homo(BJ6[2])]$
BJ7 = [nm(red(a+b+c+1+1/c+1/b+1/a)),nm(red(a*b+b*c+c+1/c+1/(b*c)+1/(a*b)+1)),
nm(red(a*b*c+b*c+1+1/(b*c)+1/(a*b*c)+1/b+b))]$
HBJ7 = [homo(BJ7[0]),homo(BJ7[1]),homo(BJ7[2])]$
end$