# 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!