# Tagged Questions

Using computers 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.

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### How to do integrals involving two Bessel functions and another function?

I often encounter the integrals in the following form: $\int_0^\infty{\rm Bessel}(ax)\cdot{\rm Bessel}(bx)\cdot f(cx)dx$, where Bessel can be $J$, $N$, $H^{(1)}$, $H^{(2)}$, $I$, or $K$; and $f(x)$ ...
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### Using MAGMA for Group Theory

I've just started a PhD in Group Theory and need to use the computer programme MAGMA. I wonder if anyone could help me with a couple of (probably very basic things). I need to produce a Hasse ...
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### Fastest Algorithm to Compute the Sum of Primes?

Can anyone help me with references to the current fastest algorithms for counting the exact sum of primes less than some number n? I'm specifically curious about the best case running times, of ...
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### Reference for complexity of primitive polynomials

What is the fastest known way to check if a given polynomial of degree $n$ in $F_{2}[X]$ is primitive? In response to Greg Kuperberg's answer. If we known factorization of $2^{n} - 1$, then what is ...
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### Is Gauss-Seidel guaranteed to converge on *semi* positive definite matrices?

I know that the Gauss-Seidel method is guaranteed to converge given that the matrix you want to solve is positive definite. I've looked at the proofs of convergence, and it appears that one cannot ...
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### Is it possible to check two curves on birational equivalence by some computer algebra system?

I have two curves, for example hyperelliptic: \begin{align} &y^2 = x^6 + 14x^4 + 5x^3 + 14x^2 + 18, \\\\ &y^2 = x^6 + 14x^4 + 5x^3 + 14x^2 + 5x + 1 \end{align} Is it possible to check them ...
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### Computer algebra system for calculation of characteristic polynomial of sparse matrix

I have a $n \times n$ matrix, for which i need to calculate the characteristic polynomial. The matrix is over $GF(2)$, and $n \approx 10^4$. However the matrix is very sparse, with around $n$ non ...
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### Polynomial of degree N with integer coefficient for a given root.

Is it possible to construct a polynomial of degree N, with all of them as integer coefficient have a root as the given value. ...
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### Is there a free action on a given variety?

Given a variety $V$, and a prime $p$ I want to decide if there is a free action of $\mathbb{Z}/p\mathbb{Z}$ on $V$, and to find the generator of an action if it exists. Is there a known algorithm to ...
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### Computational solutions to families of systems of linear equations

Question Does there exist a computer package that will solve families of systems of linear equations over a field of prime characteristic? An Example Suppose I wanted to know when the following ...
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### Compute Lie algebra cohomology

Is there a computer algebra system that is able to compute the Lie algebra cohomology in a given representation? What if the Lie algebra is finite dimensional? In my case I would like to be able to ...
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### Quantum Group Calculations in Mathematica

I'm trying to learn how to do algebraic manipulations in Mathematica but not finding the help very helpful. I'm going to ask about a specific quantum group example related to a previous question of ...
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### Algorithm for Weierstrass Preparation Theorem for Formal Power Series

The Weierstrass preparation theorem for formal power series rings guarantees that if a given formal series $f(z) = \sum a_k z^k \in R[[z]]$ where $R$ is a complete local ring with maximal ideal $M$ ...
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### Finding generators of subalgebra of polynomial algebra $K[x_1,\cdots,x_n]$ that are invariant under the action of symmetric group

Let $I =\langle f_1,\cdots,f_m\rangle \subset K[x_1,\cdots,x_n]$be an ideal, where $f_k\in K[x_1,\cdots,x_n].$ $K[e_1,\cdots,e_n]$ the polynomial algebra generated by the elementary symmetric ...
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### Mul + div using only add/sub ? [closed]

In an algorithm book once the first example was how to compute a multiplication in a loop (only that, so I just remembered, and wanted to do it programmatically but with all operations) ...
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### Computational Question about finite local rings:

Let $(A,\mathfrak{m})$ be a local Artinian ring with finite residue field, which I'm happy to assume is $\mathbf{F}_3$. (In particular, $A$ has finitely many elements.) I would like to do some ...
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### Bounds on remainder term of power series of elementary functions

This is mainly a question about the remainder term of power series for elementary functions. I'm very interested in aspects of calculating or computing elementary operations and functions, by which I ...
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### Indexed tensor manipulation CAS

hello. I am looking for tensor manipulation software that would allow me: declare indices declare results of contraction (or simplification rules) allow algebraic simplifications and expansion ...
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### Automatic proving some expression is positive

Is there any automated (i.e., some algorithm) to prove that a certain algebraic expression is always non-negative in some range ? If so, is there any implementation you would suggest? My concrete ...
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### Mathematical software for computing in integral group rings of discrete groups?

I'm doing computations in the integral group ring of a discrete group, in particular the discrete Heisenberg group. In this case elements are integral combinations of monomials $x^k y^m z^n$, where ...
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### Complexity of high-order differentiation

Let $g(x) = \exp(f(x))$. Assuming numerical (or symbolic) values of $f(x), f'(x), f''(x), \ldots, f^{(n)}(x)$ are known, is there a way to compute $g'(x), g''(x), \ldots g^{(n)}(x)$ (or even the ...
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### Computer power in plane geometry

I often hear that modern computer programs "may prove any theorem in elementary Eucledian geometry". Of course, as stated it is false - say, they can not prove theorems about $n$-gons for arbitrary or ...
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I'm using a wavelet transform in Matlab, so I think of it as a black-box. I'll represent it here as $W(x)$. There's a reconstruction function as well, which I'll write as $W^\dagger(y)$. I can ...
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### What are you using for symbolic computation?

What are the pluses and minuses of different software packages? Anything new worth checking out? I'm especially interested in open source packages.
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### An experiment on random matrices

A bit unsure if my use/mention of proprietary software might be inappropriate or even frowned upon here. If this is the case, or if this kind of experimental question is not welcome, please let me ...
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### The unification of Mathematics via Topos Theory

When the paper The unification of Mathematics via Topos Theory by Olivia Caramello, says "one can generate a huge number of new results in any mathematical field without any creative effort." is this ...
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### Computing only the order of Galois group (not the group itself).

My question is related to this one: Computing the Galois group of a polynomial. I was wondering if there is a faster algorithm just to compute the order of the group rather than the group itself. ...
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### software for computations on flag varieties in arbitrary characteristic

Is there any software that will compute cohomology of vector bundles (or just line bundles) on flag manifolds? The only one I know of is Macaulay2, via the Schubert2 package, but it works with what ...