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How are free group homomorphisms implemented?

asked 2013-10-22 18:11:52 -0500

glaun gravatar image

updated 2013-10-22 18:12:27 -0500

I see from the documentation that homomorphisms are implemented for matrix groups, symmetric groups, and abelian groups. I would assume that homomorphisms would be implemented for free groups, but I get an error if I do the following:

sage: F.<a,b> = FreeGroup(2)

sage: F.hom([a,b]) # Should be unique homomorphism with a |--> a, b |--> b

TypeError Traceback (most recent call last) ...

TypeError: Unable to coerce x (=[a, b]) to a morphism in Set of Morphisms from Free Group on generators {a, b} to Free Group on generators {a, b} in Category of groups

Do I have the syntax wrong, or are these not implemented?

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answered 2013-10-22 23:51:28 -0500

Hello,

Free group are currently implemented using GAP and it seems that morphisms are not supported.

You may have a look at sage-train-track where a ad-hoc implementation of FreeGroup is provided together with its automorphisms... and much more.

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Asked: 2013-10-22 18:11:52 -0500

Seen: 89 times

Last updated: Oct 22 '13