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 -- Colorado State University, Department of Mathematics, Weber Building, 1874 Campus Delivery, Fort Collins, CO 80523-1874, USA email: hul...@math.colostate.edu, Phone: ++1-970-4914288 http://www.math.colostate.edu/~hulpke _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
