#9559: *generalized* canonical generation in Cython
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Reporter: rlm | Owner: rlm
Type: enhancement | Status: new
Priority: major | Milestone: sage-5.0
Component: group theory | Keywords:
Author: Robert Miller | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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Description changed by rlm:
Old description:
> Right now this ticket is for organization, so I'm leaving it as "new".
>
> Depends on #10804
New description:
Depends on #10804
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.
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/9559#comment:3>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
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