Unexpected result: quotient of algebra of free monoid by ideal

asked 2019-03-18 13:52:28 -0600

Dustin01 gravatar image

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

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