[GAP Forum] how TzGo worked with us

[Alexander Hulpke]

Dear Forum,

On Jan 13, 2011, at 1/13/11 1:22, Igor Korepanov wrote:

> And still one more comment: we calculated yesterday the fundamental group of the 4-dimensional torus, which is, as everybody knows, the *abelian* group with 4 generators. That is, the Fp Group with 4 generators and 6 relation of type   a * b * a^-1 * b^-1 .
> 
> And all that was happily present in our GAP result, but besides that, there was one more redundant relation which we could derive manually from 6 others, but the TzGo algorithm apparently could not!

TzGo (the Tietze transformations command) uses a couple of heuristics, based on length criteria, to shorten a presentation, in particular if it was obtained from rewriting to a subgroup. It does not aim to do a systematic search for all redundancies. The primary aim is to get a presentation shorter with a moderate amount of effort, not to get an irredundant presentation or cover the largest possible class of decidable problems. It is clearly not optimal, but adding further attempts might cause an overall slowdown in other situations.

Thus I'm not surprised that thinking (or even other algorithms that would be willing to devote more time) can produce better results in particular situations.

Best wishes,

 Alexander Hulpke




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