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!