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Questions tagged [computer-algebra-systems]

A computer algebra system (CAS) is a program which is able to carry out various symbolic manipulations with mathematical expressions. Some well-known computer-algebra systems are Mathematica, Maple, Wolfram Alpha, GAP, SAGE. Questions on this site about computer algebra systems should be mathematical in nature, and not just about the syntax or the mechanics of the CAS. Otherwise the question would be better suited for a different Stack Exchange site.

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Computing the zeta function of curves over finite fields.

Given a nonsingular curve $X/\mathbb{F}_q$, how can one efficiently compute its zeta function $Z(X/\mathbb{F},T)$? My current strategy is to determine the genus $g$ of $X$, then count the points $N_1,...
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Get one of the solutions as Variable Value in Maxima

I want to create random variables for a way more complex program to read. Some example code is: ...
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Constructing minimal supplements with GAP

The problem is this: Suppose we are given a finite group $G$ and a normal subgroup $N$ of $G$ which is not contained in $\Phi(G)$. Call a subgroup $H$ of $G$ a minimal supplement for $N$ (in $G$) ...
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Can someone help me simplify this boolean algebra [closed]

ABCD + AB(CD)' + (AB)'CD when i used basic rule it becomes weird but boolean calculator shows something else The Question is to simplify the expression using the boolean algebra so My solution was ...
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Computing subresultants in WolframAlpha

Let $f(x)=(x-a_1)(x-a_2)\cdots(x-a_m)$ and $g(x)=(x-a_{m+1})(x-a_{m+2})\cdots(x-a_n)$, where $m,n \in \mathbb{N}$, $m < n$, $a_i \in F$, $F$ is a field of characteristic zero (for example, $k \in \{...
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Random subgroup of a group

Given a finite group $G$, Is there any known algorithm which gives a random subgroup of $G$?
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Computer program for the conjugacy problem of $GL_n(\mathbb{Z})$

In "Solution of the conjugacy problem in certain arithmetic groups" Grunewald provided an algorithm for solving the conjugacy problem of $GL_n(\mathbb{Z})$. My question is: Is there some computer ...
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Type casting in Magma

I'm doing a Magma implementation of the Camellia block chiper for an university project. I'm facing an annoying problem, I have a sequence, representing a binary value, that I need to convert to an ...
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Fast modular composition and irreducibility testing

Given a polynomials $f\in F_q[t]$ we want an algorithm that says if $f$ is irreducible or not. In the book "Modern Computer Algebra" by von zur Gathen and Jürgen Gerhard, an algorithm for that is ...
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Fast Modular Composition algorithm

Given the polynomials $f,g,h\in A[t]$ such that $\deg(h),\deg(g)<\deg(f)=n$ where $f\not=0$ is monic and $A$ is a commutative ring with unity, the problem is to compute the polynomial $g(h)\mod{f}$....
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Which algorithm is used to multiply two arbitrarily large unsigned integers in PARI/GP?

What is the underlying algorithm that PARI/GP uses to multiply two arbitrary unsigned integers (with arbitrary precision), assuming that all these integers are stored as sequences of N-bit words? I ...
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Is there a certain program with which I could make several substitutions in a very large algebraic expression?

I'm doing some fairly basic (but incredibly messy) mathematics that involves a lot of algebra. I've gotten to a point where I need to substitute certain sets of variables to make the expressions more ...
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1answer
21 views

Programming the Euclidean algorithm for arbitrary Euclidean Domains in Maple

I have to implement the Euclidean algorithm for arbitrary domains in Maple. I know how to do this for integers: ...
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Maxima — Drawing the feasable region of some inequations

I don't have much experience with Maxima but, I'd like to know how to plot the solution of a set of inequalities with two (or three) variables. It doesn't have to be Maxima, but any software I can ...
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sympy - manipulate expressions containing commutator

Let's consider this simple example: a particle in a one-dimensional parabolic potential. In the following, $p$ is the particle momentum operator, $m$ is the mass, $x$ is the position operator, and $\...
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computing polynomials whose roots are the vertices of 4-polytopes of circumradius one interpreted as quaternions

Suppose we have the vertices of 4-polytopes which have been scaled so that their are on the unit sphere. Interpret them as quaternions. If these have been computed before, I'm looking for a ...
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1answer
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Looking for computer package for doing Lie algebras

As it stated in the title I'm looking for specific software for doing computation with Lie algebras. It could be some add-on for wolfram mathematica or for else computing systems. The precise thing I ...
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How to get Maxima to collapse expressions with i^2

Example from attempting to reproduce https://en.wikipedia.org/wiki/Butterworth_filter#Example: I've got Maxima to generate: ...
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CAS that can simplify sums of integral powers?

Is there a CAS that can automatically apply the following simplification: Given $I_k = \int_a^b f_k(x) dx$, rewrite $$\sum_{k=1}^K I_k^m = \int_{[a,b]^m}\sum_{k=1}^K \prod_{i=1}^m f_k(x_i) dx_1\...
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a way to represent algebraic numbers in a computer

Say you want to represent the rational numbers in a computer. This is quite easy, you can think of them as pairs of integers. It is also easy to develop algorithms for adding, subtracting, multiplying ...
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1answer
35 views

Cantor&Zasenhaus - Polynomial factoring

I'm having problems factoring the following polynomial in $\mathbb{F}_5\left [ x \right ]$, someone could guide me please :'( $x^5+2x^4+3x^3+x^2+2x+4 \in \mathbb{F}_5\left [ x \right ]$. Here is my ...
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Is there a systematic method to simplify complicated multi-nested radicals?

I am currently working on a project in which I use symbolic computer algebra to demonstrate the Schläfli symbol of regular polyhedra. The program I wrote is correct when computing the vertex ...
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Implementing algebraic structures in code

There are quite a few computer algebra systems: MAGMA, Singular, Maple, Macaulay2 are just a few that come to mind. I've been interested in how these programs implement structures such as fields, ...
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Is the Picard group computable by a computer algebra system?

My question is, as the title suggests: Given the defining ideal of a variety $X$ (over $\mathbb C$), can we compute $Pic(X)$ with a computer algebra system? Even if the answer is no in general, are ...
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Any software for calculating Lie Group Quotients?

Are there any software packages out there that can do equations like: $$ \frac{SU(5)}{SU(3)}=SU(2)\times U(1)$$ or... $$\frac{E_8}{E_6} = SU(3)$$ or... $$ \frac{O(32)}{O(10)\times O(4)} = \text{?}...
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Calling the degree $d$ homogeneous component of a graded ring/module in Macaulay2

Suppose $R=F[x_1,\dots, x_n]/(x_1^m,\dots, x_n^m)$ with the standard grading and $F$ is any field. I want to be able to define the $i$th graded component $R_i$ in Macaulay2. Right now, I'm comfortable ...
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How can I restrict a variable to a given domain in Wolfram Alpha?

Ever since I began using Wolfram Alpha for quick online calculations I have had trouble specifying the domain of my variables. Note that I have already read the related MSO question "Tell Wolfram ...
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Algorithm for inverse of polynomial

In Modern Computer Algebra book the Algorithm 9.3 is given for calculating "the inverse of $f\,\text{mod}\,x^l$: $g_0 \leftarrow 1, r \leftarrow \lceil{\text{log} l}\rceil$ $\textbf{for}\,i=1,...,r\,\...
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Order of roots in MAGMA and/or Pari for computing Galois groups

I am trying to understand the Galois group of splitting fields (over $\mathbb Q$) of some polynomials. Especially those for which the Galois group is not the full symmetric group. For instance the ...
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How to use string operations on braid groups in MAGMA

I am currently learning to use the computer algebra program MAGMA. It might be a very basic question but I could not find anything about it. I am working with elements in braid groups and I want to ...
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Mathematical concepts motivated by computational results

What are some interesting and important pure mathematics concepts, results or theorems that have been motivated, discovered, or proven using computers/computational methods? I know little about these ...
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cusp point of a curve

I use a computer algebra to plot a function $f(x,y)$ and notice the existence of a cusp point. See figure below. Now, I want to determine the exact values $x$ and $y$ of the cusp point. I compute the ...
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Hyperdeterminant in Macaulay2

The hyperdeterminant command in Macaulay2 for a $a\times b_1\times ...\times b_n$-tensor only works for tensors whose size satisfies $$a-\sum_{i=1}^n(b_i-1)=1.$$ Is there a reason for this? Does ...
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Find integral solutions of a elliptic curve

I want to find the integral points of the following equation $$y^{2}=x^{3}-219x+1652$$ But, I don't have any computational program.
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Software to simplify linear inequalities connected by booleans

For some application, I am trying to generate a list of lattice points in a certain polytope $P$ given by linear inequalities, along with constraints $C_{ij}$ of the form $\{x_i \leq a_{ij} \text{ OR }...
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Learn mathematical thinking with open source (SageMath, GeoGebra, …)

Hi do you know a good introduction about mathematical thinking using opensource software like Sage math and/or geogebra ? I found http://abstract.ups.edu/download/aata-20170805-sage-8.0.pdf but I ...
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Investigating the subgroup structure of $SL_{3}(\mathbb{Z}/4\mathbb{Z})$ [closed]

I'm trying to investigate the subgroups of $SL_{3}(\mathbb{Z}/4\mathbb{Z})$ through the use of GAP. However, whenever I try using LatticeSubgroups or ConjugacyClassesSubgroups, I either get a message ...
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Solve the following system of equations: $[x[i-1]-(2-h^2)x[i]+x[i+1]=0, \ x[1]=1, \ x[50]-x[49]=h$, where $h=0.1$

This is my attempt at the solution using MuPAD: $x[1]:=1;\ h:=0.1; \ x[50]-x[49]=h$ eqs:= $[x[i-1]-(2-h^2)x[i]+x[i+1]=0; \ i=2,...,49]$ vars:=$[x[i]; \ i = 1,...,50]$ numeric::linsolve(eqs,vars);...
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Use MuPAD to prove $(4^{(x-1)}+2^{(2x-4)})/(2^{(2x+1)}+5\cdot(2^{(2x-3)}))=5/42$

I attempted to answer this in the following way, but got stuck on being unable to cancel out $4^x$ and $2^{2x}$. Even though they are clearly mathematically the same, I failed to find a command that ...
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Monster coefficients

For three irreducible characters $\phi,\psi,\rho$ of a finite group $G$ define the Kronecker multiplicities as: $$g(\phi,\psi,\rho) = \langle \phi,\psi\cdot\rho\rangle $$ where $$\langle \chi,\eta\...
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Changing basis of indeterminates in polynomial ring

In the polynomial ring $R={\mathbb Q}[a,b,c,d,\beta_0,\beta_1,\beta_2,\beta_3]$, consider the quotient commutative algebra $A=R/I$ where $I$ is the ideal generated by the four polynomials $$ \begin{...
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Recursion relations: Coding a procedure to compute the number of planar rooted bipartite graphs

so I'm trying to come up with a procedure for maple to compute the number of planar, rooted bipartite graphs with k undirected edges using a particular recurrence relation from two generating ...
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calculation of multiplicity of a subvariety

Suppose $I$ is a primary ideal and $J=\sqrt{I}$ , radical of it and $J$ now is a prime ideal. How can I use Macaulay2 to compute the multiplicity of $I$ along $J$. When the scheme-theoretically ...
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Declaring identifiers in MAGMA

Sorry this is probably a really stupid question for anyone who's done any computing.. Anyway I've been trying to learn MAGMA (since it seems to work better than SAGE/Maple on some aspects) and I just ...
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1answer
219 views

How do I copy an output of magma to a .txt file? [closed]

While I have created a function to compute something on magma, when am running the computations the list of things I take back is so big, that I can't see them all when I scroll up on magma, it ...
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Entry systems for math that are simpler than LaTeX

This may belong in Meta. Please don't say Software Recommendations. I have yet to receive a meaningful recommendation from that group due to a paucity of other users. I work with kids whose ...
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open-source illustrations of Riemann surfaces

I'd like to generate publication-quality images of Riemann surfaces using open source software. Is Inkscape the best tool? If so, are there libraries of vector images of Riemann surfaces one can ...
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1answer
156 views

List Conjugacy Classes in GAP?

I have a permutation group $G$, a subgroup of $S_{81}$, defined by a set of 6 specific permutations. This permutation group has order 2592, and 54 Conjugacy Classes. I can obtain a class ...
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Trouble reading files in GAP [closed]

I am trying to read a file in GAP. However, GAP believes the file does not exist. Using the IsExistingFile command, I have determined that GAP sees the parent folder, but not the .g file that I am ...
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How to handle properly big factorials in Maxima?

When I tried to solve a very basic probability problem using Maxima, I stumbled upon the following error: EXPT: floating point overflow I got it when I tried to ...