ASKSAGE: Sage Q&A Forum - Latest question feedhttp://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Tue, 08 Jan 2019 18:03:52 -0600Identity in a quotient Grouphttp://ask.sagemath.org/question/44965/identity-in-a-quotient-group/ Hello everyone, I have the following groups
F3.<a1,b1,a2,b2,a3,b3> = FreeGroup()
H3 = F3.quotient([a1*b1/a1/b1*a2*b2/a2/b2*a3*b3/a3/b3])
Then I inject the variables to $H3$
H3.inject_variables()
Now when every element that I write have parent $H3$, but when I write the word `a1*b1/a1/b1*a2*b2/a2/b2*a3*b3/a3/b3`
this does not return the identity of $H3$, although if I put
a1*b1/a1/b1*a2*b2/a2/b2*a3*b3/a3/b3 == H3.one()
this is true. Does anyone know why this happen and how can I get sage to reduce this word to identity of $H3$?
MarioMTue, 08 Jan 2019 18:03:52 -0600http://ask.sagemath.org/question/44965/coercion into/from subgroup or Tietze of generator changehttp://ask.sagemath.org/question/40483/coercion-intofrom-subgroup-or-tietze-of-generator-change/Hi there,
do you know of a function, which solves the Tietze for subgroups or converts elements from parentgroup to elements of subgroup and the other way round (if possible)?
Neither of the commented codes work (but I hope it is clear what I want):
F.<a,b,c> = FreeGroup()
x=a*b/c
H=F.subgroup([a*b,b,b*c])
y=H.gens()[1]*H.gens()[0]
x in H
y in F
#F(y)
#F.coerce(y)
#H.coerce(x).Tietze()
#H(x)
I am using cocalc, if this is a version thing.
I know something like that exists for quotient groups (s. http://doc.sagemath.org/html/en/reference/groups/sage/groups/finitely_presented.html )
In my use-case I have a free group $F$ and an element $x \in F$ in it.
Now I want for a given list of generators (e.g. in above [ a*b, b, b*c ]) the $x$ as a word of these generators,
hence I would like to see $x$ as an element in $H$ and use x.Tietze().
Another solution to my problem would be to swap the generators, but I can't see a way to do that either?ctstFri, 05 Jan 2018 17:53:14 -0600http://ask.sagemath.org/question/40483/How are free group homomorphisms implemented?http://ask.sagemath.org/question/10647/how-are-free-group-homomorphisms-implemented/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:
<blockquote>
<code><p>
sage: F.<a,b> = FreeGroup(2)<p>
sage: F.hom([a,b]) # Should be unique homomorphism with a |--> a, b |--> b <p>
TypeError Traceback (most recent call last)
...<p>
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
</code>
</blockquote>
Do I have the syntax wrong, or are these not implemented?glaunTue, 22 Oct 2013 18:11:52 -0500http://ask.sagemath.org/question/10647/