Discrete helpers/sig perm/parity

Like for normal permutations, the parity corresponds to the determinant of the matrix.
It is the XOR of the weight parity of the negator pattern and parity of the permutation. (See Full octahedral group#8×6 matrix.)

The class inherits the metribute parity from Perm. But that result is currently wrong. (2024-05)

inherited parity is wrong

This part of discrete helpers seems weird. It will be checked and clarified.

import numpy as np

from discretehelpers.sig_perm import SigPerm


mat = np.zeros([8, 6], dtype=int)

for m in range(8):
    for n in range(6):
        sp = SigPerm(pair=(m, n))
        mat[m, n] = sp.parity

[[0, 1, 1, 0, 0, 1],
 [0, 1, 1, 0, 0, 1],
 [1, 0, 0, 1, 1, 0],
 [1, 0, 0, 1, 1, 0],
 [0, 1, 1, 0, 0, 1],
 [0, 1, 1, 0, 0, 1],
 [1, 0, 0, 1, 1, 0],
 [1, 0, 0, 1, 1, 0]]

While this is not the parity, it is something, and deserves a name.
In the following images this property is shown as the shade of the background color.
It changes with every arrow. So this is the parity of the rank in the Hasse diagram.