I'm hoping to use SAGE to calculate some asymptotic results in a larger problem. Along the way, I ran into some unexpected behavior. In the minimal example below, I am trying to create a simple FreeMonoid and expand it to an Algebra where the following constraint holds: a^2 - 1 == 0.
# Create monoid + corresponding algebra
M.<a,b> = FreeMonoid(2)
F = M.algebra(QQ)
# Create two sided ideal and quotient
I = F*[F(a)^2-F(1)]*F
A = F.quotient(I)
# Returns false
A(a^2) == A(1)
This returns False, and looks like it may be related to an older bug (trac ticket 24808; can't post link b/c new user with low karma). I'm using SageMath version 8.5.
It's quite possible I'm doing something bone-headed; I haven't thought about abstract algebra in over a decade. Any suggestions would be helpful!
Thanks, Dustin
