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I am working with some finitely presented groups in Sage. I want to perform simplifications without eliminating simplifications. In Gap I think it can be done passing an option eliminateLImit=0 to TzOptions for a presentation. I can use gap presentations in Sage but I do not know how to pass this options. Thanks, Enrique.

I am working with some finitely presented groups in Sage. Sagemath. I want to perform simplifications without eliminating simplifications. In Gap I think it can be done passing an option eliminateLImit=0 to TzOptions 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 a presentation. I can use gap presentations in Sage 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 to pass this options. 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.