Changes between Version 1 and Version 15 of Ticket #16926

Timestamp:

02/07/15 23:18:17 (7 years ago)

Author:

tscrim

Comment:

Okay, done. So some notes for the reviewer:

• Currently descents behavior differs from that given by the category, so as to avoid backwards incompatible change, we leave warning messages and leave the behavior alone.

• reduced_word() does not respect the order of multiplication and needs to be fixed so that TestSuite passes.

• I've added as much common functionality between SymmetricGroup and Permutations since the former is a gap version of the latter. I'm leaving WeylGroup alone because it is a matrix group, but if someone wants to add better support for conjugacy classes, then go ahead.

• I made a bunch of other optimizations for iterating over elements and micro-optimizations.

• I abstracted StandardPermutations_n to better reflect the mathematics.

• Better and more careful handling of parents during multiplication.

• The from_* now can take a parent as input to better control their output (this was needed).

Some todo's for later:

1. Improve the speed of multiplying Sage permutations:

   sage: S = SymmetricGroup(5)
   sage: R = S.simple_reflections()
   sage: %timeit prod(R)
   10000 loops, best of 3: 36.6 µs per loop
   sage: P = Permutations(5)
   sage: R = P.simple_reflections()
   sage: %timeit prod(R)
   1000 loops, best of 3: 413 µs per loop
   

2. Refactor the Permutation class to better be an element class, especially parsing of input (hard and tedious).

3. Fix the issues noted above (also hard).

However, IMO the current version should be reviewed and included into Sage (as it is needed for #11111).

This is the other option, which I am keeping here for the official record:

• Create a category SymmetricGroups. Put the relevant groups in this category.
• Generalize the features (Yucis-Murphy elements, ...) from SymmetricGroupAlgebra to the category SymmetricGroups.Algebras.
• Put SymmetricGroupAlgebra in this category, and strip away all the code that is not needed anymore.
• Cross ref the different implementations in the documentation.

---

New commits:

​8144d47	Added optional argument for indexing set of SGA.
​a2d9dcd	Initial setting of StandardPermutations_n to be in FiniteWeylGroups.
​765cbdb	Fixes and tweaks and speedups.
​a63dfd3	Added support for conjugacy classes for permutation groups.
​f15f40c	Some additional fixes and cleanup.