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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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Polynomial ring a module over ring of invariants

Let $\mathbf{k}$ be a field of characteristic 0 and $S=\mathbf{k}[X_1,\cdots,X_n]$ be a polynomial algebra over $\mathbf{k}$. Let $G\subset GL_n(\mathbf{k})$ act linearly on $S$ and $R = S^G$ be the ...
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Use Macaulay2 to compute minimal primes of complicated ideal

I tried computing the minimal primes of a fairly complex ideal using the online Macauley2 interface. I start by letting R=QQ[z] and ...
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Workaround for Windows Magma Memory Limit [duplicate]

I found this question which said that Magma for Windows has a strict memory limit of 1.3 GB as a consequence of something weird with long ints. Is there any known workaround for this? Would running ...
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Uncountable many monomial orders for monomials with 2 variables

Why do we have for monomials with two variables x1, x2 uncountable many monomial orders? I could prove that the order defined by $x_1^ax_2^b ≤ x_1^cx_2^d$ is a monomial order if and only if $a + b\...
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Subgroups of $\operatorname{GL}_2(\mathbb Z/8\mathbb Z)$

Is there some program or a location which would allow me to work and calculate with the subgroups of the group $\operatorname{GL}_2(\mathbb Z/8\mathbb Z)$?
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1answer
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Identifying the group in GAP

I am defining a matrix group in GAP. I know that its a finite group, and can compute its order. Using sonata package and commands like ...
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Solve Ax=b using Cholesky decomposition

I was reading the following article about the direct stiffness method. When it comes to solving the system of equations: The site states: [...]There are several different methods available for ...
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Find all integer solution of the equations

I have an equation $$xy^2 + (x^2 + 1)y + x^4 + 1 = 0$$ and I need to find a set of solutions for it in integers. I tried to solve it using Maple with the isolve () ...
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How to compute a unitary representation of finite group isomorphic to a given rep?

Suppose I am given some representation of a finite group: $\rho : G \to \text{GL}(n, \mathbb{C})$. I want to compute a unitary representation $\tau$ which is isomorphic to $\rho$. I know about Weyl's ...
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Construction of a field with roots of unity in MAGMA

I would like to construct a field (NumberField) that contains a (primitive) $n$-th root of unity and $i = \sqrt{-1}$ using a computer algebra system MAGMA, i.e. $\mathbb{Q}(\zeta_n, i)$. I tried ...
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How does a CAS find closed form solutions to an integration problem?

Programs like Mathematica, Maple, Maxima and many others can compute integrals, differentiate mathematical expressions or do all other sorts of cool stuff. My question is what kind of mathematics do ...
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What computer algebra system or package for abstract algebra best suits me?

I am a mathematics student who wants a tool on the side, either specifically aimed at, or well suited for abstract algebra (ring/ideal theory, module theory, but perhaps graphs and combinatorics as ...
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How to print out a function in Maxima

I want to take two functions, substitute one into the other in several places, and then simplify and print out the result. I assume this is in the Maxima manual somewhere, but I can't find it. For ...
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Maxima / xwMaxima - How to solve for undetermined coefficients

I have something that looks a bit like: $0=-y(n)+y(n-1)+0.5\cdot x(n)$ $x(n)=\cos(\frac{\pi\cdot n}3)$ I have $y(n)$ with undetermined coefficients $C$ and $D$: $y(n)=C\cdot \cos(\frac{\pi\cdot n}...
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How can I find an isomorphism between two representations?

Suppose I have two representations (over $\mathbb{C}$) of a finite group $G$, $\rho : G \to GL(V)$ and $\tau : G \to GL(W)$. If I am given that these representations are isomorphic, i.e. there exists ...
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Redefine Variable if not defined already (CAS maxima)

I am using Maxima in a web application for user generated mathematial content. We usually generate random input variables and calculate the output, but now want to enable the user to define their own ...
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Homology of a chain complex with unknow boundary map

Question. Let $(C_\bullet,\partial)$ be a $\mathbb{Z}/2\mathbb{Z}$-chain complex generated by $a$, $b_1,b_2,b_3$, $c_1,c_2$ with gradings: $$|a|=2,|b_1|=|b_2|=|b_3|=1,|c_1|=|c_2|=0.$$ Which ...
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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
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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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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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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 ...