# Questions tagged [computer-algebra]

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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### Runtime order of Groebner basis computations over prime field

While there seems to be few resources detailing explicit complexity bounds for computing Groebner Bases over the integers, I'm finding it even harder to search for such bounds for computations over ...
53 views

### Recommendations for distributed calculations of Groebner Bases

There are many computer algebra systems available which can compute a Groebner basis, including: Mathematica Singular Macaulay2 Magma Maple CoCoA However (please correct me if I've missed something) ...
1 vote
293 views

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### Reliability of ILP approach to number-theoretic optimization

This question is inspired by the recent answer, where @RobPratt proposed to use integer linear programming (ILP) for solving a number-theoretic optimization problem. I will consider a very similar ...
1 vote
154 views

### Find $x$ that solves $x\left(e^{\frac{a}{x}}-1\right)-y=0$

When trying to solve the equation in the title with WA, it produced the following as the solution: now, if you divide the numerator and denominator by $y$ and set $z:=-\frac{a}{y}$ the solution ...
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1 vote
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### Computer verification for hyperbolic trigonometry

I am currently writing a paper that requires some lengthy computations using basic hyperbolic trigonometry. So, several hyperbolic figures appear, and we apply the law of sines and so on in order to ...
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### Classification of multiplicative lattices

Question 1:Is there a classification of finite lattices which admit a multiplication making them into a finite multiplicative lattices? (see https://encyclopediaofmath.org/wiki/Multiplicative_lattice ...
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### Solving a large system of equations when a large subset factors

I have a large (~1000 equations) overdetermined system of degree 3 polynomials with ~140 variables. I would like to find a complete solution set for this system, however, the Gröbner basis seems to be ...
91 views

### Finite global dimension via the Cartan determinant

Let $A=T(KQ)$ be the trivial extension algebra of a path algebra of Dynkin type $KQ$. The indecomposable module of $A$ correspond to the roots of $Q$ (and not just the positive roots as for $KQ$). Let ...
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### Computational tool for checking the existence of non-trivial rational zero of a cubic form

Suppose we consider a arbitrary cubic homogeneous form $f$ in in four or five variables over the rational field. Is there any computational tool or algorithm to check whether this cubic homogeneous ...
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1 vote
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### Fitting point on a Quadric curve [closed]

I am working on research project. I am currently using CloudCompare for my project, which calculates the Gaussian curvature and mean curvature to extract the geometric features of the points. I have a ...
152 views

### Algorithm to compute automorphism group of a finite group

Is there an algorithm to compute automorphism group of a finite group? GAP has a function to do this, but while perusing their GitHub repo, I could not find an implementation. I'm struggling to find ...
224 views

### Number of rings with additive group $(\mathbb{Z}_{16})^2$. A341547(16) in OEIS

I would like to know if somewhere the number of non-isomorphic rings with additive group $(\mathbb{Z}_{16})^2$ is mentioned. If not, is someone able to calculate it? And (easier) the commutative case? ...
5k views

### How does Mathematica do symbolic integration?

I suppose there was at least once in our lifetime the point where we resorted to mathematica for help with an integral.-Unless you chose not to have the pleasure of using the continuum in your ...
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### Is it easy to certify whether a given set of solutions to a polynomial system is complete?

Given a system of complex polynomial equations, we seek the solution set. If we have more equations than variables, then we might expect a finite solution set. One may obtain the solution set by ...
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### Transforming a symmetric matrix into pentadiagonal form

Given a symmetric matrix $A$, which has complex values in the diagonal, but whose all other entries are real, I am interested in finding an orthonormal transformation $Q$ such that $Q^tAQ$ is a ...
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### Where to publish a long classification?

Suppose that the classification of some mathematical (say algebraic) notions requires (say) 70 pages. Let clarify that (say) 90% of the pages are used to write the result itself, whereas only 10% are ...
64 views

### Checking for norm-Euclidean with a computer

Let $K$ be a finite Galois extension of $\mathbb{Q}$ and $O$ the ring of integers in $K$. Question: Is there an algorithm to test whether $O$ is norm-euclidean? In case the question has a positive ...
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107 views

### String compression algorithms for simplifying an expression by introducing variables

I have a very long algebraic expression computed with Maple, and when I inspect it visually, it is clear that it consists of a set of terms that appear over and over again. For purposes of human ...
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1 vote