Fix cycle_index for permutation groups on an arbitrary domain + cleanup

[nthiery]

The code for cycle_index predates permutation groups with arbitrary domain, as well as their cycle_type methods. Instead it goes through plain Permutation's, which only works if the domain is 1,...n:

sage: G = PermutationGroup([['b','c','a']], domain=['a','b','c'])
sage: G.cycle_index()
ValueError                                Traceback (most recent call last)
/opt/sage-git2/local/lib/python2.7/site-packages/sage/combinat/permutation.pyc in __init__(self, parent, l, check_input)
    519             for i in lst:
    520                 try:
--> 521                     i = int(i)
    522                 except TypeError:
    523                     raise ValueError("the elements must be integer variables")

ValueError: invalid literal for int() with base 10: 'a'

This ticket fixes that, and uses the occasion to clean a bit the code, using in particular the conjugacy_classes method to avoid a direct access to GAP, and the docstring.

This bug was discovered while updating the book "Calcul Mathématique avec Sage".

[nthiery]

New commits:

​c1cdcb1

#22765: fix cycle_index for permutation groups over an arbitrary domain + cleanup

[chapoton]

wrong syntax here:

+            (see trac:`22765`)::

should be :trac:`22765`

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​6d66f65

22765: fixed reST typo

[nthiery]

Replying to chapoton:

wrong syntax here:

+            (see trac:`22765`)::

should be :trac:`22765`

Fixed. Merci Frédéric!

May I assume that you proofread the rest and the syntax is correct?

[chapoton]

no, sorry. I was in mode "break at first failure"

[nthiery]

Fair enough :-) Thanks though!

[chapoton]

same here:

(:wikipedia`Cycle_index`)

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​bbeb9db

22765: fixed another reST typo

[nthiery]

Thanks :-)

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​16eb5ec

22765: use sum_of_terms for conciseness and efficiency

[nthiery]

Oops, while updating the write up of the book, I just noticed I had not use sum_of_terms. Fixed!

[nthiery]

For the record, the patchbot is green up to:

sage -t --long src/sage/doctest/test.py  # Timed out after testing finished
sage -t --long src/sage/calculus/calculus.py  # 1 doctest failed

which I don't see how they could not be independent.

[tscrim]

Yes, they are independent. Frederic (or Dima), are you going to be doing a full review, if not, I can do it.

[chapoton]

This is slightly ambiguous, and better with more parentheses:

+            elif not hasattr(parent, "term") and hasattr(parent, "sum"):

I am satisfied with the changes. I will not look further.

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​e7add6d

22765: improved type checking

[nthiery]

Oops, the test was indeed logically broken. Fixed. I used the occasion to switch to a cleaner type checking. Thanks!

[chapoton]

ok, then let it be