#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, free algebra,
letterplace
Work_issues: | Upstream: N/A
Reviewer: | Author: Simon King, Michael Brickenstein,
Burcin Erocal
Merged: | Dependencies: #11068, #11268
---------------------------+------------------------------------------------
Old description:
> The new aim of this ticket is to add an interface to the
> [http://www.singular.uni-kl.de/Manual/latest/sing_427.htm#SEC480
> letterplace] component of Singular, namely providing
>
> * A new implementation of free algebras with fast arithmetic.
> * Degree-wise Gröbner basis computation for twosided homogeneous ideals
> of free algebras.
> * Normal form computation with respect to such ideals.
>
> and in addition
>
> * One- and twosided ideals of noncommutative rings.
> * Quotient rings of such ideals
>
> (Note that the original purpose was merely to compute Groebner bases up
> to a degree bound of two-sided ideals of free algebras, but without
> normal form computation etc.)
>
> Examples are below, in the comments.
>
> Apply
>
> [attachment:trac7797-full_letterplace_wrapper_rel11068.patch]
>
> [attachment:trac7797-letterplace_degree_weights.patch]
>
> Depends on #11068 #11268
New description:
The new aim of this ticket is to add an interface to the
[http://www.singular.uni-kl.de/Manual/latest/sing_427.htm#SEC480
letterplace] component of Singular, namely providing
* A new implementation of free algebras with fast arithmetic.
* Degree-wise Gröbner basis computation for twosided homogeneous ideals
of free algebras.
* Normal form computation with respect to such ideals.
and in addition
* One- and twosided ideals of noncommutative rings.
* Quotient rings of such ideals
(Note that the original purpose was merely to compute Groebner bases up to
a degree bound of two-sided ideals of free algebras, but without normal
form computation etc.)
Examples are below, in the comments.
Apply
[attachment:trac7797-full_letterplace_wrapper_rel11068.patch]
[attachment:trac7797-letterplace_degree_weights.patch]
[attachment:trac7797-latex_letterplace.patch]
Depends on #11068 #11268
--
Comment(by SimonKing):
I noticed that I forgot one detail: Latex!
With the latest patch, we also get
{{{
sage: K.<z> = GF(25)
sage: F.<a,b,c> = FreeAlgebra(K, implementation='letterplace',
degrees=[1,2,3])
sage: -(a*b*(z+1)-c)^2
(2*z + 1)*a*b*a*b + (z + 1)*a*b*c + (z + 1)*c*a*b - c*c
sage: latex(-(a*b*(z+1)-c)^2)
\left(2 z + 1\right) a b a b + \left(z + 1\right) a b c + \left(z +
1\right) c a b - c c
}}}
Apply trac7797-full_letterplace_wrapper_rel11068.patch
trac7797-letterplace_degree_weights.patch trac7797-latex_letterplace.patch
Depends on #11068, #11268
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/7797#comment:48>
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.
