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Finitely presented group simplification

Hi! I have a bunch of finitely presented groups, with many generators and relations. I know that all of these are in fact cyclic groups, but many times using the "simplified()" function, I get a simpler presentation with 2 generators, rather than only one. The following is one example:

 G.<x0,x5> = FreeGroup()
H  =G/[(x5^-1*x0)^2*x5^-3, (x0^-1*x5^-1)^2*x0^-2*x5*x0^-1]


H is in fact just Z/27Z. Is there another way to simplify these presentations, in order to get a minimal one? The problem here is that I do not only need to identify the specific group, but also to recover the image of the previous generators in the simplified one (as done by the simplification_isomorphism() function).

 2 retagged FrédéricC 5141 ●3 ●43 ●112

Finitely presented group simplification

Hi! I have a bunch of finitely presented groups, with many generators and relations. I know that all of these are in fact cyclic groups, but many times using the "simplified()" function, I get a simpler presentation with 2 generators, rather than only one. The following is one example:

 G.<x0,x5> = FreeGroup()
H  =G/[(x5^-1*x0)^2*x5^-3, (x0^-1*x5^-1)^2*x0^-2*x5*x0^-1]


H is in fact just Z/27Z. Is there another way to simplify these presentations, in order to get a minimal one? The problem here is that I do not only need to identify the specific group, but also to recover the image of the previous generators in the simplified one (as done by the simplification_isomorphism() function).