The new aim of this ticket is to add an interface to the letterplace component of Singular, that actually goes beyond what Singular offers.

The patch provides

• A new implementation of free algebras with fast arithmetic, but restricted to weighted homogeneous elements, with positive integral degree weights.
• Degree-wise Gröbner basis computation for twosided weighted homogeneous ideals of free algebras. If a finite complete Gröbner basis exists, it can be computed.
• Normal form computation with respect to such ideals.
• 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_combined.patch and attachment: trac_7797-ref.patch

Depends on #11068 #11268 #12641 #12749

Depends on #4539
Depends on #11268
Depends on #12461
Depends on #12749
Depends on #12988
Depends on #13237

Upstream: None of the above - read trac for reasoning.

CC: @sagetrac-PolyBoRi @saliola @malb @jhpalmieri @sagetrac-sage-combinat @sagetrac-OleksandrMotsak

Component: algebra

Keywords: singular, free algebra, letterplace

Author: Simon King, Michael Brickenstein, Burcin Erocal

Reviewer: Alexander Dreyer

Merged: sage-5.5.beta2

Issue created by migration from https://trac.sagemath.org/ticket/7797