toqito.perms.perm_sign

Calculates the permutation sign.

Module Contents

toqito.perms.perm_sign.perm_sign(perm)

Compute the “sign” of a permutation [@WikiParPerm].

The sign (either -1 or 1) of the permutation perm is -1**inv, where inv is the number of inversions contained in perm.

Examples

For the following vector

[

[1, 2, 3, 4]

]

the permutation sign is positive as the number of elements in the vector are even. This can be performed in |toqito⟩ as follows.

```python exec=”1” source=”above” from toqito.perms import perm_sign

print(perm_sign([1, 2, 3, 4])) ```

For the following vector

[

[1, 2, 3, 4, 5]

]

the permutation sign is negative as the number of elements in the vector are odd. This can be performed in |toqito⟩ as follows.

```python exec=”1” source=”above” from toqito.perms import perm_sign

print(perm_sign([1, 2, 4, 3, 5])) ```

Parameters:

perm (numpy.ndarray | list[int]) – The permutation vector to be checked.

Returns:

The value 1 if the permutation is of even length and the value of -1 if the permutation is of odd length.

Return type:

float