#10052: Improve the implementation of the Steenrod algebra
-----------------------------+----------------------------------------------
Reporter: jhpalmieri | Owner: AlexGhitza
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-4.6.1
Component: algebra | Keywords: steenrod, notebook
Author: John Palmieri | Upstream: N/A
Reviewer: Niles Johnson | Merged:
Work_issues: |
-----------------------------+----------------------------------------------
Old description:
> The attached patch does several things:
>
> - it moves the Steenrod algebra code to a subdirectory of algebras. For
> one thing, there are already 4 files, and for another, I hope that more
> will be added: several people are working on related projects.
>
> - it reimplements the Steenrod algebra using `CombinatorialFreeModule`,
> which provides a number of conveniences: scalar multiplication is already
> defined, as are tensor products, etc. Then for example the antipode or
> the coproduct can be defined just on basis elements, and the linear
> extension to all elements is handled automatically.
>
> - it implements another way of computing products, using admissible
> sequences and the Adem relations. This provides a good way of checking
> for bugs: with two completely different algorithms for computing
> products, one can compute the same product two ways and compare answers.
>
> - it implements sub-Hopf algebras of the Steenrod algebra. These were
> classified 35 years ago, and for some applications people want to use
> sub-Hopf algebras rather than the whole thing.
>
> - the `TestSuite` has been improved: all components now pass, whereas
> before, we had some failures. From the ''old'' steenrod_algebra.py:
> {{{
> sage: TestSuite(A).run() # todo: fix category inheritance for
> elements of A
> Failure in _test_category:
> ...
> ------------------------------------------------------------
> The following tests failed: _test_category
> Failure in _test_elements
> The following tests failed: _test_elements
> }}}
> From the new one:
> {{{
> sage: TestSuite(SteenrodAlgebra()).run()
> sage: TestSuite(SteenrodAlgebra(profile=[4,3,2,2,1])).run()
> sage: TestSuite(SteenrodAlgebra(basis='adem')).run()
> sage: TestSuite(SteenrodAlgebra(basis='wall')).run()
> sage: TestSuite(SteenrodAlgebra(basis='arnonc')).run() # long
> time
> sage: TestSuite(SteenrodAlgebra(basis='woody')).run() # long
> time
> sage: A3 = SteenrodAlgebra(3)
> sage: A3.category()
> Category of graded hopf algebras with basis over Finite Field
> of size 3
> sage: TestSuite(A3).run()
> sage: TestSuite(SteenrodAlgebra(basis='adem', p=3)).run()
> sage: TestSuite(SteenrodAlgebra(basis='pst_llex', p=7)).run()
> # long time
> sage: TestSuite(SteenrodAlgebra(basis='comm_deg', p=5)).run()
> # long time
> }}}
> Not only are there no failures, but there are many more executions of
> the suite. This yields some repetition, but the method {{{an_element}}}
> varies depending on the values of {{{basis}}} and {{{p}}}, so there are
> also new tests run with each execution.
>
> Unfortunately, since the patch moves files around, it is large. It also
> trivially affects a few doctests in sageinspect, which means that it
> requires a patch to sagenb.
>
> == Apply ==
>
> 1. Patch from #9370.
> 1. [attachment:trac_10052-steenrod.v3.patch].
New description:
The attached patch does several things:
- it moves the Steenrod algebra code to a subdirectory of algebras. For
one thing, there are already 4 files, and for another, I hope that more
will be added: several people are working on related projects.
- it reimplements the Steenrod algebra using `CombinatorialFreeModule`,
which provides a number of conveniences: scalar multiplication is already
defined, as are tensor products, etc. Then for example the antipode or
the coproduct can be defined just on basis elements, and the linear
extension to all elements is handled automatically.
- it implements another way of computing products, using admissible
sequences and the Adem relations. This provides a good way of checking
for bugs: with two completely different algorithms for computing products,
one can compute the same product two ways and compare answers.
- it implements sub-Hopf algebras of the Steenrod algebra. These were
classified 35 years ago, and for some applications people want to use sub-
Hopf algebras rather than the whole thing.
- the `TestSuite` has been improved: all components now pass, whereas
before, we had some failures. From the ''old'' steenrod_algebra.py:
{{{
sage: TestSuite(A).run() # todo: fix category inheritance for
elements of A
Failure in _test_category:
...
------------------------------------------------------------
The following tests failed: _test_category
Failure in _test_elements
The following tests failed: _test_elements
}}}
From the new one:
{{{
sage: TestSuite(SteenrodAlgebra()).run()
sage: TestSuite(SteenrodAlgebra(profile=[4,3,2,2,1])).run()
sage: TestSuite(SteenrodAlgebra(basis='adem')).run()
sage: TestSuite(SteenrodAlgebra(basis='wall')).run()
sage: TestSuite(SteenrodAlgebra(basis='arnonc')).run() # long
time
sage: TestSuite(SteenrodAlgebra(basis='woody')).run() # long
time
sage: A3 = SteenrodAlgebra(3)
sage: A3.category()
Category of graded hopf algebras with basis over Finite Field
of size 3
sage: TestSuite(A3).run()
sage: TestSuite(SteenrodAlgebra(basis='adem', p=3)).run()
sage: TestSuite(SteenrodAlgebra(basis='pst_llex', p=7)).run()
# long time
sage: TestSuite(SteenrodAlgebra(basis='comm_deg', p=5)).run()
# long time
}}}
Not only are there no failures, but there are many more executions of the
suite. This yields some repetition, but the method {{{an_element}}}
varies depending on the values of {{{basis}}} and {{{p}}}, so there are
also new tests run with each execution.
Unfortunately, since the patch moves files around, it is large. It also
trivially affects a few doctests in sageinspect, which means that it
requires a patch to sagenb.
== Apply ==
1. Patch from #9370.
1. Patch from #8589 (merged into 4.6.1.alpha0)
1. [attachment:trac_10052-steenrod.v3.patch]
1. [attachment:trac_10052-sagenb.patch]
--
Comment(by niles):
For the buildbot:
Depends on #9370, #8589.
Apply [attachment:trac_10052-steenrod.v3.patch],
[attachment:trac_10052-sagenb.patch]
(p.s. I haven't forgotten about this :)
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10052#comment:20>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
--
You received this message because you are subscribed to the Google Groups
"sage-trac" group.
To post to this group, send email to [email protected].
To unsubscribe from this group, send email to
[email protected].
For more options, visit this group at
http://groups.google.com/group/sage-trac?hl=en.
