# Questions tagged [computational-algebra]

Computational algebra is an area of algebra that seeks efficient algorithms to answer fundamental problems concerning basic algebraic objects (groups, rings, fields, etc.). For questions about generic computer algebra systems, use [tag:computer-algebra-systems].

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### Requesting Polynomial Systems of Equations

I am teaching a course in commutative algebra, and it includes a project where the students research on a particular topic, solve a small problem and present it to the class. I usually give my ...
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### The normalized unit group using GAP.

I want the structure of The normalized unit group using GAP for the group algebra $FD_{30}$, where $F$ is a finite field with characteristic $3$ and $D_{30}$ is the dihedral group of order $30.$ I ...
1 vote
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### Unit group structure GAP code. [duplicate]

I want the structure of the unit group of the group algebra $F_{3^k}D_{30}$ using GAP, where $F_{3^k}$ is any finite field of characteristic $3$ and $D_{30}$ is the dihedral group of order $30.$ I ...
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### Algorithm for the maximal isotropic subspace

Does anyone know of any algorithms that exist which can explicitly compute a maximal isotropic subspace of a diagonal quadratic form over the rationals? I have been searching through the literature, ...
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### Calculating the Galois Group for large degree $f(x)$

Let $f(x)\in \mathbb{Q}[x]$ with Galois group $G$ over $\mathbb{Q}$. Are we always able to calculate $G$ although it might be computationally expensive? I know if $f(x)$ has a special form we can ...
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### How to Compute a nonzero point $v= \langle v_x, v_y \rangle$ of Nodal Curve

This is not homework question. I am writing a research paper and studying the behaviors of complete algebraic curves and I came across this questions and I am interested in it. A nodal function is ...
236 views

### Orbit-Stabilizer problem for $GL(\mathbb Q,n)$ (Algorithmic approach)

The paper [1, section 1] mentions that the Orbit-Stabilizer problem is undecidable for general matrix groups. So my question is if the statement means the problem is undecidable for $G=GL(\mathbb Q,n)$...
1 vote