#15528: Rweriting systems for finitely presented groups.
----------------------------+---------------------------------------------
Reporter: mmarco | Owner:
Type: enhancement | Status: new
Priority: minor | Milestone: sage-6.1
Component: group theory | Keywords: finitely presented groups
Merged in: | Authors: mmarco
Reviewers: | Report Upstream: N/A
Work issues: | Branch:
Commit: | Dependencies:
Stopgaps: |
----------------------------+---------------------------------------------
This patch adds a class for rewriting systems for finitely presented
groups. Rewriting systems can be used (when the Knuth-Bendix algorithms
finishes in finite time) to get reduced forms of the elements of the
group, the same way that groebner basis can be used to get normal forms of
elements of polynomial rings modulo ideals.
This class is just a wrapper of corresponding GAP functions.
Examples:
{{{
sage: F.<a,b> = FreeGroup()
sage: G=F / [a*b/a/b]
sage: k = G.rewriting_system()
sage: k
Knuth Bendix Rewriting System for Monoid( [ a, A, b, B ], ... ) with
rules
[ [ a*A, <identity ...> ], [ A*a, <identity ...> ], [ b*B,
<identity ...> ], [ B*b, <identity ...> ], [ a*b*A*B,
<identity ...> ] ]
sage: k.reduce(a*b*a*b)
(a*b)^2
sage: k.make_confluent()
sage: k
Knuth Bendix Rewriting System for Monoid( [ a, A, b, B ], ... ) with
rules
[ [ a*A, <identity ...> ], [ A*a, <identity ...> ], [ b*B,
<identity ...> ], [ B*b, <identity ...> ], [ B*A, A*B ], [
b*A, A*b ], [ B*a, a*B ], [ b*a, a*b ] ]
sage: k.reduce(a*b*a*b)
a^2*b^2
}}}
--
Ticket URL: <http://trac.sagemath.org/ticket/15528>
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 unsubscribe from this group and stop receiving emails from it, send an email
to [email protected].
To post to this group, send email to [email protected].
Visit this group at http://groups.google.com/group/sage-trac.
For more options, visit https://groups.google.com/groups/opt_out.
