#7797: Full interface to letterplace from singular
---------------------------+------------------------------------------------
Reporter: burcin | Owner: burcin
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-4.7.1
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]
>
> [attachment:trac7797-latex_letterplace.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]
[attachment:trac7797-letterplace_coercion.patch]
Depends on #11068 #11268
--
Comment(by SimonKing):
In my application, I also need conversion from graded sub-algebras. Hence,
I implemented it in the new patch.
To be precise: If we have free graded algebras A and B in letterplace
implementation, then there is a coercion from A to B if and only if there
is a coercion from the base ring of A to the base ring of B, and the set
of generator names of A is a subset of the generator names of B, and the
degrees of equally named generators of A and B are equal.
The coercion is always name and degree preserving.
Example:
{{{
sage: F.<t,y,z> = FreeAlgebra(ZZ, implementation='letterplace',
degrees=[4,2,3])
sage: G = FreeAlgebra(GF(5), implementation='letterplace',
names=['x','y','z','t'], degrees=[1,2,3,4])
sage: t*G.0 # indirect doctest
t*x
sage: (t*G.0 + G.1*G.2)*y
y*z*y + t*x*y
}}}
Apply trac7797-full_letterplace_wrapper_rel11068.patch
trac7797-letterplace_degree_weights.patch trac7797-latex_letterplace.patch
trac7797-letterplace_coercion.patch
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/7797#comment:53>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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