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D.4.27.4 eigenvalues

Procedure from library symodstd.lib (see symodstd_lib).

Usage:
eigenvalues(I,sigma); I ideal, sigma intvec

Assume:
size(sigma) = nvars(basering) =: n

Return:
list of eigenvalues of generators of I under permutation sigma

Note:
sigma is a permutation of the variables of the basering, i.e. sigma: var(i) ----> var(sigma[i]), 1 <= i <= n.

Example:
 
LIB "symodstd.lib";
ring R = 11, x(1..5), dp;
poly p1 = x(1)+x(2)+x(3)+x(4)+x(5);
poly p2 = x(1)+4*x(2)+5*x(3)-2*x(4)+3*x(5);
poly p3 = x(1)+5*x(2)+3*x(3)+4*x(4)-2*x(5);
poly p4 = x(1)-2*x(2)+4*x(3)+3*x(4)+5*x(5);
poly p5 = x(1)+3*x(2)-2*x(3)+5*x(4)+4*x(5);
ideal I = p1,p2,p3,p4,p5;
intvec tau = 2,3,4,5,1;
eigenvalues(I,tau);
==> [1]:
==>    1
==> [2]:
==>    3
==> [3]:
==>    -2
==> [4]:
==>    5
==> [5]:
==>    4