ASKSAGE: Sage Q&A Forum - Latest question feedhttp://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 idealhttp://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 -0500http://ask.sagemath.org/question/45824/Rings, Ideals, Quotient Rings in Sagehttp://ask.sagemath.org/question/29990/rings-ideals-quotient-rings-in-sage/Hi everybody.
I am new to sage. I want to construct rings, ideals, and quotient rings.
I used Z.IntegerRing() to generate the ring of integers.
Question 1:
Then I used I = Z.ideal(2) to get the ideal generated by 2 (even numbers).
Question: How can I display the Elements. E.g. I(2) does not work in order to display the second element of the ideal.
Question 2:
To generate the quotientring Z/2Z i used S = Z.quotient_ring(I).
What if I want to generate the quotientring 2Z/6Z ? S = I.quotient_ring(J) does not work (I = Z.ideal(2), J = Z.ideal(6).
Thanks for any help
DesperateUserWed, 14 Oct 2015 02:38:47 -0500http://ask.sagemath.org/question/29990/Quotient of Polynomial rings reduction not workinghttp://ask.sagemath.org/question/27068/quotient-of-polynomial-rings-reduction-not-working/<code>
<br>R.<x>=PolynomialRing(QQ)
<br>R.ideal(x^4).reduce(x^8+1)
<br>R.<x>=PolynomialRing(ZZ)
<br>R.ideal(x^4).reduce(x^8+1)
1
x^8 + 1
</code>
Why am I not getting the result 1 in both cases?WizqTue, 09 Jun 2015 08:44:26 -0500http://ask.sagemath.org/question/27068/