Martin-Br's profile - activity

Thank you. This may be the reason. I use Sage version 9.5. The Sage Cell Server probably uses a different version, and t

Working with group algebras I want to work with group algebras in SageMath. But they do not behave as they should. Is th

Working with group algebras I want to work with group algebras in SageMath. But they do not behave as they should. Is th

Working with group algebras I want to work with group algebras in SageMath. But they do not behave as they should. Is th

Working with group algebras I want to work with group algebras in SageMath. But they do not behave as they should. Is th

Working with group algebras I want to work with group algebras in SageMath. But they do not behave as they should. Is th

Working with group algebras I want to work with group algebras in SageMath. But they do not behave as they should. Is th

Simple example of a finitely presented algebra How can I work with the finitely presented $\mathbb{F}_2$-algebra $\mat

I am trying to work with finitely presented algebras in SageMath. But apparently, I am doing something wrong.

For a simple example, I want to construct A = Q[x]/<x^2>. The image a of x in that algebra should satisfy a^2 = 0. But SageMath tells me that this is not the case. (EDIT: the code has been updated below.)

sage: F.<x> = FreeAlgebra(QQ,1)
sage: F
Free Algebra on 1 generators (x,) over Rational Field
sage: x in F
True
sage: I = F.ideal([x^2])
sage: A = F.quotient(I)
sage: A
Quotient of Free Algebra on 1 generators (x,) over Rational Field by the ideal (x^2)
sage: a = A.gen()
sage: a^2 == 0
False
sage: a^2 == A.zero()
False

What am I doing wrong here?

When the ideal is <1>, the quotient should be trivial. But again, SageMath does not believe this.

It seems that this bug has been reported here before:

• https://ask.sagemath.org/question/412...
• https://ask.sagemath.org/question/321...

Thanks! I will try to work with the homogenization then.

Apparently, it works when F is defined as a polynomial ring. The free algebra on one generator should equal the polynomi

Working with finitely presented algebras I am trying to work with finitely presented algebras in SageMath. But apparentl

sage: F.<x> = FreeAlgebra(QQ,implementation="letterplace") sage: F.quotient(Ideal(F,[x+1])) throws this error:

sage: F.<x> = FreeAlgebra(QQ,implementation="letterplace") sage: F.quotient(Ideal(F,[x+1])) throws this error: Ari

Working with finitely presented algebras I am trying to work with finitely presented algebras in SageMath. But apparentl

Thanks a lot for your answer. Actually, I encountered the same problem with F.<x>, but apparently I wrote it wrong

Thanks a lot for your answer. Actually, I encountered the same problem with F.<x>, but apparently I wrote it wrong

Working with finitely presented algebras I am trying to work with finitely presented algebras in SageMath. But apparentl

Working with finitely presented algebras I am trying to work with finitely presented algebras in SageMath. But apparentl

SageMath has a built-in method for performing the extended Euclidean algorithm for two numbers (or polynomials), called xgcd. The algorithm also works for several arguments, by recursion. One can implement this easily with a SageMath helper function, but I was wondering: does SageMath have a built-in extension of xgcd to several arguments?

xgcd for several arguments SageMath has a built-in method for performing the extended Euclidean algorithm for two number