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Questions tagged [computer-algebra]

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Using computer-aid approach to solve algebraic problems. Questions with this tag should typically include at least one other tag indicating what sort of algebraic problem is involved, such as ac.commutative-algebra or rt.representation-theory or ag.algebraic-geometry.

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5votes
1answer
136views

Let $A=KQ/I$ with $Q$ a finite connected quiver and $I \subset J^2$ where $J$ is the ideal generated by the arrows of $Q$.Question 1: Is there a good theory (or even a finite test) to test whether $...
8votes
0answers
136views

For $n\in N$ an $n$ Cayley Hamilton algebra is an associative algebra $R$ over a commutative algebra $A$ with a norm $N:R\to A$ that is a multiplicative polynomial map of degree $n$ so that each $r ...
11votes
1answer
461views

Let us consider two monic polynomials $f(X), g(X) \in \dfrac{\mathbb{Z}}{p^k\mathbb{Z}}[X]$. Now, we call $h(X)$ is a divisor of $f(X)$, if there exists a $l(X) \in \dfrac{\mathbb{Z}}{p^k\mathbb{Z}}[X]...
5votes
2answers
336views

Let $K= \mathbb{C}$ and $q$ a root of unity with $q^2 \neq 1$ and of smallest order $d$ and set $e=d$ if $d$ is odd and $e=d/2$ if d is even. Let $U_q$ be the quantum enveloping algebra of $sl_2$ ...
1vote
0answers
115views

I have a multiprojective variety $X$ in a product of projective spaces given by a multigraded ideal $I$. Suppose that the multiprojective variety is embedded into a product of projective spaces the ...
3votes
0answers
233views

This is a follow-up question to this question. In that question, we learned that if, $T(y) = \mathrm{Res}_{x}(f(x), y - g(x))$ , then $T(g(z))$ is divisible by $f(z)$.Now, my question is:If $T(y) = ...
8votes
0answers
654views

The problem 1 of the 2025 IMO is the following:A line in the plane is called sunny if it is not parallel to any of the x-axis, the y-axis, and the line $x + y = 0$.Let $n ⩾ 3$ be a given integer....
4votes
2answers
439views

Let $A$ be the $K$-algebra defined as the quotient of the non-commutative polynomial ring in variables a,b,c,d,e,f,g,h,z modulo the relations...
4votes
0answers
159views

Let $A$ be a finite dimensional $K$-algebra for $K$ a field.Define the centralizer dimension of $A$ to be the smallest $n$ such that $A$ is the centralizer of $n$ matrices. Any algebra $A$ can be ...
1vote
1answer
156views

I have a problem that involves elimination of the radicals from equations involving a number of radicals of multivariate polynomials to then finally form multivariate polynomial equations (over Z). ...
5votes
0answers
159views

I am reading Swinnerton Dyer's paper on "On $\ell$-adic representations and congruences for coefficients of modular forms". It defines a prime $\ell$ to be exceptional for an eigenform $f \...
1vote
0answers
95views

I apologize for posting here, but I don't see much else on stackoverflow where people who know MAGMA might be able to answer. The MAGMA documentation athttps://magma.maths.usyd.edu.au/magma/...
Robert Bruner's user avatar
2votes
1answer
177views

Let $\vec{X}$ be a finite set of indeterminates, and $\sqsubseteq$ be a monomial ordering.A Gröbner Basis $B$ of an ideal $I$ of polynomials can be characterized as a finite set of polynomials ...
1vote
1answer
135views

I am working on a computational project for a supervisor working in classical and modern deformation theory; my base framework is the SageMath project. This question is inspired by a serious ...
12votes
2answers
419views

I've had a python package out for multiplying Schubert polynomials, double Schubert polynomial, quantum Schubert polynomials, and double quantum Schubert polynomials for a little over a year. Recently ...

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