#15174: Permutations and symmetric group algebra: Stopgap for #14885 and
noninversions
-------------------------------------------------+-------------------------
Reporter: darij | Owner:
Type: defect | Status:
Priority: major | needs_review
Component: combinatorics | Milestone: sage-5.12
Keywords: permutation, permutation | Resolution:
group, symmetric group, sage-combinat, groups | Merged in:
Authors: Darij Grinberg | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: #15170 | Stopgaps:
-------------------------------------------------+-------------------------
Changes (by darij):
* status: new => needs_review
Old description:
> This patch does the following:
>
> * Open up a way to circumvent the (in the opinion of several people)
> broken multiplication of permutations (see #14885 and
> https://groups.google.com/forum/#!searchin/sage-devel/permutations/sage-
> devel/tAAb42Edh9o/T-htA50IOZEJ ). To remind, the issue is twofold: first,
> the default order in which Sage multiplies permutation is rather unusual
> to anyone not from the English school of notation; second, the order
> depends on a global variable which can be changed at runtime, which makes
> it unpredictable and a pain to rely on. I don't address the first of
> these issues in my patch, but I ameliorate the second one: There are now
> global-independent methods {{{left_action_product}}} and
> {{{right_action_product}}} on permutations (these are just aliases for
> the already existing methods {{{_left_to_right_multiply_on_left}}} and
> {{{_left_to_right_multiply_on_right}}}, but are now documented and non-
> underscored; besides I hope that my names are clearer), and more
> importantly on symmetric group algebras (these are not just aliases
> anymore; the only multiplication method which we used to have on
> symmetric group algebras dependent on the global). These can be used
> instead of the badly predictable {{{*}}} operator (they're even a bit
> faster by virtue of not branching on the global variable).
>
> * Improve doc at a few places in {{{combinat/permutation.py}}} and
> {{{combinat/symmetric_group_algebra.py}}}. These are minor, but
> constitude most of the size of the patch.
>
> * Add methods related to the Reiner-Saliola-Welker conjectures: The
> number of noninversions of a permutation; the antipode of the symmetric
> group algebra; the Reiner-Saliola-Welker shuffling operators (as elements
> of symmetric group algebras); and some elements which can be used to
> factor the latter.
New description:
This patch does the following:
* Open up a way to circumvent the (in the opinion of several people)
broken multiplication of permutations (see #14885 and
https://groups.google.com/forum/#!searchin/sage-devel/permutations/sage-
devel/tAAb42Edh9o/T-htA50IOZEJ ). To remind, the issue is twofold: first,
the default order in which Sage multiplies permutations is rather unusual
to anyone not from the English school of notation; second, the order
depends on a global variable which can be changed at runtime, which makes
it unpredictable and a pain to rely on. I don't address the first of these
issues in my patch, but I ameliorate the second one: There are now global-
independent methods {{{left_action_product}}} and
{{{right_action_product}}} on permutations (these are just aliases for the
already existing methods {{{_left_to_right_multiply_on_left}}} and
{{{_left_to_right_multiply_on_right}}}, but are now documented and non-
underscored; besides I hope that my names are clearer), and more
importantly on symmetric group algebras (these are not just aliases
anymore; the only multiplication method which we used to have on symmetric
group algebras depended on the global). These can be used instead of the
badly predictable {{{*}}} operator (they're even a bit faster by virtue of
not branching on the global variable).
* Improve documentation at a few places in {{{combinat/permutation.py}}}
and {{{combinat/symmetric_group_algebra.py}}}. These are minor fixes, but
constitute most of the size of the patch.
* Add methods related to the Reiner-Saliola-Welker conjectures: The number
of noninversions of a permutation; the antipode of the symmetric group
algebra; the Reiner-Saliola-Welker shuffling operators (as elements of
symmetric group algebras); and some elements which can be used to factor
the latter.
--
--
Ticket URL: <http://trac.sagemath.org/ticket/15174#comment:1>
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