/* $OpenXM: OpenXM_contrib2/asir2000/lib/cyclic,v 1.1 1999/12/03 07:39:11 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;
}

/* 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$