ASKSAGE: Sage Q&A Forum - Latest question feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Fri, 05 Jan 2018 17:53:14 -0600coercion into/from subgroup or Tietze of generator changehttps://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 -0600https://ask.sagemath.org/question/40483/