I have the following group presentation D4=⟨r,s|r4=s2=rsrs=1⟩.
This is written in sage as
F.<r,s> = FreeGroup()
D4 = F / [r^4, s^2, r*s*r*s, 1]
r,s = D4.gens()Say I wanted to compute s^2, this should equal 1 but sage gives me just s^2.
s^2output:
s^2I am doing more involved calculations and I want to return the result in the simplified form. How do I simplify the expression in sage?
Reduction here can be performed via rewriting system - like:
R = D4.rewriting_system()
R.reduce(s^2)Thanks, this seems to work. However I got another problem when constructing my expression by using the generators of D4 in a group algebra:
F.<r,s> = FreeGroup()
D4 = F / [r^4, s^2, r*s*r*s, 1]
R = D4.rewriting_system()
A = D4.algebra(QQ)
r,s = A.gens()
e = r + s
R.reduce(e^3)I get the error "unsupported operand parent(s) for >: 'Integer Ring' and '<class 'tuple'="">'".
When using the permutation group instead of the presentation of the group it seems to give the simplified result directly without needing to use R.reduce(...), but I don't want the result in cycle notation.
Perhaps, you'd need to explicitly apply reduce to the terms of e^3 - like: sum(c*A(R.reduce(t)) for t,c in e^3)
Asked: 3 years ago
Seen: 199 times
Last updated: Dec 05 '21
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