# Tagged Questions

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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### A field of Radical Sums

I am dealing with a computation that yields numbers that are sums of radicals of the following form: $N=\sum_{i=0}^{m}{a_i\sqrt{b_i}}$ Where $a_i,b_i \in \mathbb{Q}$ (rationals). The context is ...
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### Different Representation Matrices from same Generating Set

Motivation: This post. $K \subset S_n, \langle K \rangle =G \leq S_n$. We can create a Representation Matrix $M$ from $K$ that represnts $G$ (Furst. Hopcroft, Luks). Question: Is $M$ unique for a ...
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### Ordering of elements in the base of a group

In section 4.6.7 of HANDBOOK OF COMPUTATIONAL GROUP THEORY, the authors use an ordering $\prec$ for the elements in a coset. That ordering, $\prec$, was defined in section 4.6 as follows. Throughout ...
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### Minimize the rank of a matrix with some entries known

Let $m,n$ be two positive integers, with $m\geq n$. Suppose we have $m$ sets $A_1,\ldots, A_m\subseteq [n]$, with $|A_i|=d_i$. Let $\mathbb F$ be a finite field of size $q$. Let $D$ be the set ...
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### A rather special monoid

While implementing an embryo of computational algebra on my blog I ran into a rather special monoid and I wonder if it's studied before. After implementing a very simple concept of dynamic sets I ...
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### A GAP code for maximum and minimum cardinals of some classes of subsets of a finite group

Let $G$ be a finite group with a fixed subset $A$. Put $$S_r(A)=\{B\subseteq G : |AB|=|A||B|\; \& \; B \; \mbox{is inclusion-maximal with respect to this property}\}$$  M_r(A)=\max\{|B| : B\...
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### Proposition 4.7 of Handbook of Computational Group Theory

I have been studying Derek Holt's Handbook of Computational Group Theory. I am looking at Proposition 4.7, and I can't figure out what I'm doing wrong. Proposition 4.7(i) states that, given $K$, a ...
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