gh-36224: Add cycle_type() and fix to_cycle() to SignedPermutation.
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We fix a "bug" in `to_cycle()` of `SignedPermutation` that does not
return the negation of a positive cycle, and add an option to hide these
cycles (the current behavior in Sage).
We add a `cycle_type()` method that returns the corresponding
`PartitionTuple` object.
We add a `conjugacy_class_reprensentative()` method.
A while-we-are-at-it thing: we fix a bug in the error output for
`Permutation.element_in_conjugacy_class()` (which a better name IMO is
`conjugacy_class_reprensentative()`).
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URL: https://github.com/sagemath/sage/pull/36224
Reported by: Travis Scrimshaw
Reviewer(s): ayyer, Martin Rubey, Travis Scrimshaw
