*generalized* canonical generation in Cython

[rlmill]

The basic idea is that one has objects which satisfy the criteria set out in sage/groups/perm_gps/partn_ref. In particular, one has implemented a refinement function, a comparison function, and an equivalent-children function. Then one defines the following four functions, and the code which will appear here will do the rest.

1. Given an input object X, this function will return a number k. This is the number of augmentations from X to perform, thought of abstractly as the list [0, 1, ..., k-1]. The user will keep the data of what augmentations these actually are.

2. Given a permutation of X (acting on [0, 1, ..., n-1]), and a number a in [0, 1, ..., k-1], outputs a number b in the same range, such that the augmentation represented by a maps to the one represented by b under the permutation.

3. Given a number in [0, 1, ..., k-1], outputs an object C which realizes the augmentation.

4. Given a permutation g, and an object C, applies g to C, constructs an arbitrary parent object P of C, and returns g^(-1)(P).

Function (2) will be optional. If not provided, then the list of augmentations given in (1) will have to be a set of orbit representatives.

NOTE: ticket #11369 should be set to needs_review once this one is ready

CC: @boothby @nathanncohen @kini @dimpase

Component: group theory

Author: Robert Miller

Reviewer: Tom Boothby

Merged: sage-5.7.beta0

Issue created by migration from https://trac.sagemath.org/ticket/9559

[rlmill]

Dependencies: #10549, #10804

[rlmill]

Reviewer: Tom Boothby

[boothby]

comment:9

477c477,478
< groups/perm_gps/partn_ref/refinement_graphs.pyx: 100% (8 of 8)
---
> groups/perm_gps/partn_ref/refinement_graphs.pyx: 100% (10 of 10)
> groups/perm_gps/partn_ref/refinement_sets.pyx: 100% (3 of 3)
1299,1300c1300,1301
< Total number of functions:  28567
< We need 1110 more function to get to 90% coverage.
---
> Total number of functions:  28572
> We need 1109 more function to get to 90% coverage.

[jdemeyer]

Work Issues: formatting

[jdemeyer]

comment:10

The commit message needs to be fixed, it certainly should not contain "[mq]".

Newly added files should conform to the template at http://sagemath.org/doc/developer/conventions.html#headings-of-sage-library-code-files.

New documentation strings should conform to http://sagemath.org/doc/developer/conventions.html#documentation-strings.

[rlmill]

Changed dependencies from #10549, #10804 to none

[rlmill]

Attachment: trac_9559.patch.gz

[boothby]

comment:15

Tests pass, formatting updated as requested by jdemeyer.

[jdemeyer]

Changed work issues from formatting to none

[jdemeyer]

Merged: sage-5.7.beta0