Simplifying group presentations with the same generators
I am working with some finitely presented groups in Sagemath
. I want to perform simplifications without eliminating simplifications. This is a toy example:
g=FreeGroup(2)/[(1,1,-2,-1)]
# Finitely presented group with two generators and one relation ("too long")
g1=gap(g)
# The group is converted into a GAP object in order to use some GAP functions not existing in SAGEMATH
P=g1.PresentationFpGroup()
# The GAP presentation object is constructed, for which simplifications functions exist.
P.TzSearch()
# This function simplifies too much the presentation.
It eliminates the first and last element of the relation (which was the goal) but it eliminates also a generator. Presentations have a Gap
record called TzOptions
, it is accessible in Sagemath
with
P.TzOptions()
One of the options is called protected
and it is set to 0 by default. If it is set to n
, among the simplifications it avoids to eiminate the first n
generators. My problems is to modify this Gap
record in Sagemath
, I do not know how. Since it is a tool to work with finitely presented groups in Sagemath
, it would be too cumbersome to translate the problem into Gap
and come back to Sagemath
. Any help is welcome.
Thanks, Enrique.
Can you provide code for a toy example?
Really toy example g=FreeGroup(2)/[(1,1,-2,-1)] g1=gap(g) P=g1.PresentationFpGroup() P.TzSearch() I want the last order to simplify the relation without eliminating a generator
Ideally, edit your question to include the example.
Use a blank line before and after the code block, and indent it by four spaces.
Thanks for the tip!