# 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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### Optimizing computations with nilpotents in a group algebra

Of course, I have a very concrete problem at hand, which has been vexing me for about a year now. But let me start with a question that has a better chance of having been answered. Let $G$ be a ...
327 views

### Checking for a normal p-complement with a computer

Let $G$ be a finite group. Question 1: What are the fastest available programs to test whether $G$ has a normal $p$-complement (see https://en.wikipedia.org/wiki/Normal_p-complement for a definition)?...
179 views

### Is it possible to compute Lie bialgebra structures with SageMath?

Is it possible to use SageMath (or some Linux open source program) to compute the bialgebra structures on a given finite dimensional Lie algebra? I wonder if such program can compute all the ...
427 views

### Finite subgroups of $\mathrm{SO}(n)$ and $\mathrm{O}(n)$

Question 1:Is there a reference that lists all possible finite subgroups and their orders of $\mathrm{SO}(n)$ and $\mathrm{O}(n)$ for $n=4$ or even higher $n$ over the real numbers? I can only find ...
172 views

### Degree 8 multilinear operations on Jordan algebras

I am interested in the dimension, or, even better, in the $S_8$-module structure of the space of degree 8 multilinear operations on Jordan algebras. Recall that a Jordan algebra is a commutative but ...
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### Compute the principal polarization on $J_0(N)$ in terms of modular symbols

If we consider the modular curve $X = X_0(N)$ as a curve over $\mathbb C$ then one can describe the jacobian $J(X)$ as $H^0(X,\Omega^1_X)^\vee/H_1(X,\mathbb Z)$ as one can do for any curve $X$. ...
328 views

### Tarski-Seidenberg for strict inequalities and bounded quantification

This theorem says that quantifiers over real variables can be eliminated from classical first order formulae built from equations and inequalities between polynomials with rational coefficients, ie in ...
1 vote
214 views

### Method to solve system of exponential sums of the form $a^x+b^x=c$ given more equations than variables [closed]

Cross post with mse For example, let's say I have the following equations. \begin{gather*} a^{x-1}+b^{x-1}=337 \\ a^{x}+b^{x}=1267 \\ a^{x+1}+b^{x+1}=4825 \\ a^{x+2}+b^{x+2}=18751. \end{gather*} What ...
80 views

### Checking the generic rank of a matrix

Suppose that $A,B\in M_{p,q}(\mathbb{Z})$ are two rectangular integer matrices of the same size. Suppose that one has a conjecture stating that the rank of the matrix $A+tB$ for Zariski generic values ...
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### About the complexity of some operation involving integers

There are two integers: $A, B$. Given the below four allowed operations (and only them): $A+1$, $A-1$, $\sqrt{A}$, $A^2$ Also, it is only allowed to take the square root of $A$ when this square root ...
1 vote
89 views

### Computer algebra tools for finding real dimension of an algebraic variety

I have a system of polynomial equations with the unknowns being real numbers. The set of solutions is infinite. What software can I use to compute the real dimension of the solution set? The CAD-based ...
105 views

### Software to compute generators of a module over polynomial ring

Let $A=\mathbb{R}[x_1,\dots,x_n]$ be the algebra of real polynomials in $n$ variables. Fix polynomials $p_1,\dots,p_k\in A$. Consider the subset M:=\{(q_1,\dots,q_k)\in A^k|\, p_1q_1+\dots+p_kq_k=0\}...
121 views

### 7D simple Lie algebras over $\mathbb{F}_3$

Up to isomorphism, what are all the seven-dimensional simple Lie algebras over the field with three elements?
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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 ...
85 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) ...
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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
158 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 ...
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 ...
204 views

### 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 ...
99 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 ...
85 views

### 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 ...
175 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 ...
### 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? ...