#7797: Full interface to letterplace from singular
---------------------------+------------------------------------------------
Reporter: burcin | Owner: burcin
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-4.7
Component: algebra | Keywords: singular
Work_issues: | Upstream: N/A
Reviewer: | Author: Simon King, Michael Brickenstein,
Burcin Erocal
Merged: | Dependencies:
---------------------------+------------------------------------------------
Changes (by SimonKing):
* status: needs_work => needs_review
* work_issues: Unigenerated free algebra vs. univariate polynomial ring;
refactoring of nc-ideals =>
Comment:
I updated the patch.
Apply trac7797-full_letterplace_wrapper_rel11068.patch
Depends on #11068
Actually I am not sure about all dependencies. #11068 should be enough on
top of sage-4.7.alpha5. However, here is a full account of the patches
that I had applied to sage-4.7.alpha5 before creating the patch here:
#10296, #9944, #9138, #9976, #11115, #11068.
In particular, I think the refactoring of rings, quotient rings and non-
commutative ideals is successfully solved in #9138 and #11068. Concerning
unigenerated free algebras, it seems better to stay in the world of free
algebras, rather than returning a polynomial ring. So, we have
{{{
sage: F.<x> = FreeAlgebra(QQ)
sage: F
Free Algebra on 1 generators (x,) over Rational Field
sage: F.is_commutative()
True
sage: F.<x> = FreeAlgebra(QQ, implementation='letterplace')
sage: F
Free Associative Unital Algebra on 1 generators (x,) over Rational Field
sage: F.is_commutative()
True
}}}
In principle, it could be reviewed now. But the patch chain in front of it
is rather large, and not everything has a positive review, yet.
My next plan: Allow positive integer degree weights on the generators,
extending the scope of the letterplace wrapper from homogeneous to
weighted homogeneous elements, and allow degree-wise computation of
weighted homogeneous Gröbner bases. Note that this goes beyond what is
currently implemented in Singular, but it should work using a little hack
(slack variables).
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/7797#comment:42>
Sage <http://www.sagemath.org>
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