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.Mon, 18 Mar 2019 13:52:28 -0500Unexpected result: quotient of algebra of free monoid by idealhttps://ask.sagemath.org/question/45824/unexpected-result-quotient-of-algebra-of-free-monoid-by-ideal/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
Dustin01Mon, 18 Mar 2019 13:52:28 -0500https://ask.sagemath.org/question/45824/Partially commutative monoid of a graphhttps://ask.sagemath.org/question/41756/partially-commutative-monoid-of-a-graph/I am interested in the free partially commutative monoid associated to a graph whose definition can be seen here www.sciencedirect.com/science/article/pii/0304397591903556 and here https://en.m.wikipedia.org/wiki/Trace_monoid.
Basically I need a free monoid in which some variables commutes.
My questions are
1. whether this notion is already implemented in Sage?
2. If not how to implement this in Sage?GA316Sun, 25 Mar 2018 10:54:57 -0500https://ask.sagemath.org/question/41756/