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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Could we find an element on finite field? [closed]

Let $F$ be a finite field. Given an element $a^x$ in $F\setminus\{0\}$, could we find $a$?? I know that finding an integer $x$ is very hard problem (Discrete Logarithm Problem). However, I don't know ...
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Software for computing generators of the invariant rings of the symmetric groups

(Please skip to the last paragraph if you are interested in just the question) I wish to compute the generators of the ring of invariants for a symmetric group acting on a polynomial ring using 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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Algorithm for isomorphic groups?

As I understand There can't be a general algorithm to decide if two finite groups are isomorphic, Wikipedia. But are there efficient algorithms for all subgroups of $S_n$ for say $n=10$ or so? ...
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Janko Group and subgroups.

I want to work with the Janko simple group $J_2$ using the computer, and if it is possible, the Janko simple group $J_4$ too. In specific, I want to take certain subgroups of it and compute their ...
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How to find a base of a permutation group?

How to find a base of the permutation group G=âŸ¨x,yâŸ©â‰¤S4 x=(1,2,3), y=(1,2,4)? I hear that base for G is a sequence B = [$b_1, ..., b_m$] âŠ‚ â„¦ such that the only element of G which stabilizes each $b_i$ ...
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Can someone explain how the Schreier-Sims Algorithms works on a permutation group with a simple example?

Can someone explain how the Schreier-Sims Algorithms works on a permutation group with a simple example? All the books I read have a dense notation that hard to comprehend but a simple and concrete ...
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Efficient way to compute the symmetric reduction of special polynomials (specially for resolvents)

By the Fundamental Theory of Symmetric Polynomials every symmetric polynomial in $K[x_1, \dots, x_n]$ can be written uniquely in the elementary symmetric functions $s_1, \dots, s_n$. I know there are ...
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“Out of memory” in MAGMA

I'm trying to find some information about Sporadic simple groups of the large order using MMAGM and ATLAS of Brauer. While I am sure that the memory of the cpu is enough, after while, MAGMA says that ...
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Recently I have come across a book of GrÃ¶bner Bases written by Adams & Loustaunau. The book is excellent and I have become interested in GrÃ¶bner bases after reading the book. I want to read more ...
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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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Indirect Left recursion.

I'm solving (indirect Left Recursion) for these production rules . S is the starting symbol. S -> Aa / a eq1 A -> Sb / b. eq2 Now I can do this in two ...
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Group conjecture

Conjecture: Given a finite group $G$ and a subset $A\subset G$. Then $\{A,A^2,A^3,\dots\}$ is a group iff $\forall n\in \mathbb N: |A^n|=|A^{n+1}|$. Given that the composition between the ...
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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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Quasi canonical isomorphisms between finite groups and subgroups of the symmetric group?

I'm implementing finite groups in Forth for my blog and since any group is a subgroup of a permutation group it make sense to let the standard elements be permutation schemas: ...
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Most wanted reproducible results in computational algebra

I am interested in suggestions for major computational results obtained with the help of mathematical software but not easily verifiable using computers. "Most wanted" could refer, for example, to ...
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Minimizing computations for evaluating two polynomial simultaneously

I want to evaluate two polynomials $f$ and $g$ simultaneously, on the same input (in a computer program). These polynomial have only coefficients $0, 1, a , b$ and their degree is less than 700. I ...
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The equation $|A^{-1}A|=|A|^2-|A|+1$ for finite subsets of a group

Let $A$ be a finite subset of a group $G$. It is clear that $|A^{-1}A|\leq|A|^2-|A|+1$. If $A$ is singleton or $A=\{1,a\}$ with $O(a)\neq 2$ then the equality holds. Now, can somebody characterize all ...
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