#10052: Improve the implementation of the Steenrod algebra
-----------------------------+----------------------------------------------
Reporter: jhpalmieri | Owner: AlexGhitza
Type: enhancement | Status: new
Priority: major | Milestone: sage-4.6.1
Component: algebra | Keywords:
Author: John Palmieri | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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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.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10052>
Sage <http://www.sagemath.org>
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