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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29 views

Division of two polynomial expressions

Is $$1/(X^n - 1), n \in N$$ a polynomial? Intuitively I would say yes, because 1 is a polynomial($ X^0$) and so is $X^n - 1$. But Sage(The CAS) appears to disagree, when I type the expression in and ...
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152 views

GAP code related to supersoluble abnormal subgroups

The property I want to check is whether there exists a finite non-supersoluble group $G$ which admits a triple factorisation $G=AB=AC=BC$, where $A, B, C$ are abnormal supersoluble subgroups of $G$. (...
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Renaming variables in FriCAS sandbox output

I'm playing with FriCAS in sandbox and the problem is, When asked to find indefinite integral (as well as in many other cases), FriCAS outputs auto-generated variables in a rather unsightly manner, ...
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Desmos - Finding zeros (and storing them)

In Desmos, I frequently label my graphs in terms of parameters in the problem. For example, if a is a slider, I could write m = f'(a) and then in a label I could write "The slope of this tangent ...
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Computer algebra systems in logic and set theory

I am a big proponent of computer algebra systems (in particular Sage) and I know that I use sage a lot in my day to day research. When I'm learning a new branch of math, I like to see what packages ...
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Symmetric group irreducible representations

Given a symmetric group, I'd like to get explicit matrices for the Young natural irreducible representations. (These are different from the generic unitary/orthogonal irreps; the natural irreps are ...
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How to use GAP/magma to list all the elements of some order in a finite group? [closed]

How to use GAP/magma to list all the elements of some order in a finite group? For example, let $G\cong \mathbb{Z}_2\times \mathbb{Z}_{24}$, how to use GAP/magma to list all the elements of order $24$?...
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How to use GAP to cumpute $S=\{s|s=h^2, h\in H\}$ for every subgroup $H$ of $G$?

Let $G$ be a finite group, then how to use GAP to cumpute $S=\{s|s=h^2, h\in H\}$ for every subgroup $H$ of $G$?
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List of equations in MAGMA

I have some integer $n$, some ambient affine space $\mathbb{A}^n$, and a list $L$ of equations $f_{ij}$ cutting out a variety $X$ in the ambient space. I have problems defining the list $L$ correctly. ...
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lower bound the distance between two varieties

$\DeclareMathOperator{\complex}{\mathbb{C}}$ Let $X,Y \subseteq \complex^n$ be homogeneous, smooth, irreducible, closed algebraic sets with $X \cap Y=\{0\}$. I would like to numerically lower bound ...
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Symbolic computation software for macroeconomic model

I am looking for software that is capable of symbolically solving a typical macroeconomic model. The rest of my question gives an example of a small model. A country maximises: $$\mathbb{E}_0\sum_{t=...
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Non-Homogeneous System Solver

By chance does any one know if there are any nonhomogenous system of Differential equations software? I have Octave, Sage, and Python however, I have explored and seemed to find none. I am just going ...
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Efficiently constructing a certain subgroup in GAP

Let $G$ be a finite group and let $N$ be a normal subgroup of $G$. Let's call $N$ $\mathcal{U}$-central in $G$ if it is true that all $G$-chief factors below $N$ are cyclic. Now put $$Z_{\mathcal{U}}(...
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Software to express a mathematical expression in terms of three other functions?

I need a software to simplify a function $\Phi(x,y)$ which is obtained analytically and is in a much complicated form. I require to rewrite $\Phi(x,y)$ in terms of three other functions $f(x,y)$, $g(x,...
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Deleting arrows of a Quiver (GAP/QPA)

Given a quiver $Q$ Q := Quiver( 1, [ [1,1,"a"], [1,1,"b"] ] ); I would like a new quiver $Q1$ deleting a arrow from quiver $Q$. My attempts (trying to ...
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Standardization of coset tables in GAP

I struggle to understand the notion of a standard coset table. In particular, I do not understand what the GAP function 'StandardizeTable' really does. My guess is that it relabels the cosets such ...
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Expression simplification in sympy — symbolic integration

I am trying to integrate $$p_1=\int_0^1\int_z^1\int_y^1\frac{6x^2}{(x+y)(x+y+z)}\,\mathrm{d}x\,\mathrm{d}y\,\mathrm{d}z$$ which arose in connection with an earlier question. When I plug it into sympy,...
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Formula equation builder from samples

Does any one know about mathematical tools used for generating equations from input and output samples provided. I have used geneticsharp https://github.com/giacomelli/GeneticSharp but formula ...
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320 views

Singular Procedure: Vanishing polynomial function (A Singular Introduction to Commutative Algebra)

I have recently started studying the computer algebra system Singular with help of the book „A Singular Introduction to Commutative Algebra“ by Gert-Martin Greuel & Gerhard Pfister. Since a few ...
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Evaluating a polynomial using the computer algebra system Singular

I recently started learning the computer algebra system Singular. Working through some early exercises of the book "A Singular introduction to Commutative Algebra" by Gert-Martin Greuel and Gerhard ...
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1answer
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Zero equivalence in computer algebra systems

Testing whether an expression (say, on the real or complex numbers), with or without variables, is known to be difficult. There is an semi-algorithm by Daniel Richardson to solve it for the exp–log ...
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1answer
21 views

Almost split sequences inside a subcategory using QPA

Let $A$ be a finite dimensional connected quiver algebra and $\Omega^n(A)$ the fullsubcategory of direct summands of $n$-th syzygy modules for some $n \geq 1$. For example in case $A$ is Gorenstein of ...
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1answer
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What is the function of lift(Q) in PARI/GP?

I would like to call PARI/GP from Python. I need to use ellisdivisible(E; P; n;{&Q}) function of PARI (see function no 3.15.35 on page 441 in this link:) ...
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Computing Constant $C_2$ of Inequality $h_x([2]P) \geq 4h_x(P) − C_2 $

Let $E/Q$ be an elliptic curve given by a Weierstrass equation $E : y^2 = x^3 + Ax + B$ with $A, B ∈ Z$ and, $h_x(P) = \log H(x(P))$, where, $x(P) = p/q, H(x(P))=\max\{|p|, |q|\}$. There is a ...
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Solving Quartic Equation with a Coefficient of $1$ MB Space

I have an equation of $4$ degree (Quartic equation)and a coefficient of this equation takes $1$ megabyte space in a text file. I want to solve this Quartic equation using computer. If the the equation ...
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1answer
76 views

Can GAP test, if two ordinary character tables are isomorphic?

I'd like to ask the following question: Is there a way to let GAP test, if two (previously with GAP computed) ordinary character tables are isomorphic? Here, two ordinary character tables shall ...
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Given a formal power series $f_1$, can we produce another formal power series $f_2$ suing computer program s.t. $f_1 \circ f_2=f_2 \circ f_1$?

When two formal power series commutes ? Algorithm: Let $f = \sum a_n x^n$ and $g = \sum b_n x^n$ be two formal series without constant term. Then $$ f \circ g = \sum a_n g(x)^n = \sum a_n \left(\sum ...
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Partial sums of the Dedekind zeta function

Is there a way to find the partial sums of the Dedekind zeta function? In particular, I would like to find the sum $$\sum_{0 \neq I \subset\mathcal{O}_K \\N(I) \le n} \frac{1}{N(I)^s}$$ for a given $n$...
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How to solve this incomplete elliptic equation in Matlab? Thank you!

I am trying to solve this formula in Matlab $$V= \frac{ 2r_{1}r_{2}^{2}k^{2}}{3}(2 \bullet R_{f} (0,1-k^{2},1) - \frac{1+k^{2}}{3} R_{d}(0,1-k^{2},1)$$ where $k = \frac{r_{1}}{r_{2}}$ I thought it ...
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How to efficiently compute the minimal polynomial of a number expressed in radicals?

Preamble: I want to calculate the minimal polynomial of a number of the form $$x=\sum_{i=1}^k \pm a_i^\frac 1{k_i}$$ Where the $a_i$ are algebraic numbers also of this form with a finite ...
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1answer
47 views

How do computer algebra systems like Sage perform operations on infinite structures

Allow me to preface this question with a little bit of background: I am not a computer scientist. I have coded some small programs in Python and Java to do very basic things like generate fractals ...
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Need help in solving complicated integral

How this integral could be solved? Mathematica and Rubi failed. $$\int _{-\infty }^{\infty }\int _{-\infty }^{\infty }\int _{-\infty }^{\infty }\int _{-\infty }^{\infty }\int _{-\infty }^{\infty }\...
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1answer
140 views

Problematic definition (property is already set the other way in GAP) [closed]

I want to define a probabilistic measure for finite groups in GAP and it seems that I'm doing something wrong but I can't figure out what the mistake is. For example: ...
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1answer
73 views

Defining a subgroup of $\mathrm{Aut}(G)$ in GAP

Let $G$ be a finite group and let $A$ be a normal subgroup of $G$. What I would like to do is construct the following subgroup of $\mathrm{Aut}(G)$ in GAP: $$ X(G,A) = \{ \phi \in \mathrm{Aut}(G): g^{...
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2answers
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Q: how to describe these results by a descendants tree in gap

I wrote an implement to find the "fullyInvariantGroups" in GAP and the results appeared as below: ...
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Macaulay Matrix Reduction in Macaulay2

I am trying to get the Groebner bases of an ideal in Macaulay 2 through the triangularization of the Macaulay matrix. Indeed, I would like to know how far I should go -how big the matrix should be- ...
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About the name of the case where an equation have some integer solutions but it is unknown if there is infinitely many integer solutions

I read this article of Wikipedia (https://en.wikipedia.org/wiki/Consistent_and_inconsistent_equations) and I am asking about the name of the case where an equation have some integer solutions but it ...
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Is there a CAS that by default handles monoid rings?

I'm aware that sage has monoid features, but not necc. monoid ring. Is there a CAS specializing in: rings, groups, modules, monoid rings, group rings? Reason, is that these structures are hard to ...
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2answers
56 views

Finding a presentation of a permutation group given the generators

I'm attempting to solve the following problem. Consider the permutation group $G=\langle\rho,\sigma\rangle\leq S_{14}$ where $\rho=(1,3,5,7,9,11,13)(2,4,6,8,10,12,14)$ and $\sigma=(1,2)(3,6)(4,5)(7,...
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Maple simplify a polynomial without using functions that uses gcd.

Currently trying to find a way to simplify a polynomial in $x,y$ without using functions that uses gcd, eg. simplify(). And failing spectacularly. $2 + 3*x + 3*x^3*y + 3*x*y - x^4*y^3 - x^3*y^4 - x^2*...
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1answer
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GAP express word as product of conjugates of relators

GAP can tell you if a word on a finite alphabet is expressible as a product of conjugates of a given list of words. In the example below, it tells us that the word $x^3yx^3y$ is expressible as a ...
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Calculating infinitely near points of a curve singularity

Let $f(x,y)$ be a polynomial in $\mathbb{Q}[x,y]$ with a singular point at the origin $(0,0)$. Currently I am writing a Maple program to compute its iterated blow-up embedded resolution as a hierarchy ...
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55 views

How can I show that this integral is zero?

I am facing the following definite integral: $$\int_{-\infty}^{\infty} d\tau_3 \int_{-\infty}^{\infty} d\tau_4 \frac{1}{x_1^2+\tau_3^2}\frac{1}{a \tau_3^2+b\tau_4^2+c\tau_3\tau_4+d} \tag{1}$$ with $...
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51 views

Library for symbolic polynomial manipulation on extension fields

What are good libraries that can be used in C/C++ for symbolic polynomial manipulation in extension fields? To the day, I use Mathematica's "FiniteFields" package or PolynomialRemainder function for ...
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1answer
38 views

Given two randomly ordered integer arrays A and B each of n integer numbers. Consider the following function:

bool Quiz (int A[0..n-1 ], int B[0..n-1 ], int n) { int k = 0; for (i = 0; i < n; i++) if (A[i] == B[i]) k++; if (k == n) return false; Sort (A , n); Sort (B , n); for (i = 0; i < n; i++) ...
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96 views

Prove this inequality via weighted Jensen inequality

The following inequality is derived from this difficult olympiad problem. Suppose $a,b,c$ are three positive real numbers such that $abc = 8$, show that $$\frac{1}{\sqrt{a + 1}} + \frac{1}{\sqrt{b + ...
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51 views

Re-substituting solution to differential equation yields a contradiction

I have found a solution to the differential equation: $$\frac{dx}{dt} = \frac{x^2 +t\sqrt{t^2 + x^2}}{tx}$$ where $t, x > 0$ to be: $$x = t\ln{t} + ct$$ I calculated this by using the fact that ...
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1answer
53 views

Number of bits for a scalar product

let's consider two vectors $v_1[i]$, $v_2[i]$, for $i = 0, 1, ... , N-1$. Suppose you want to calculate the scalar product between them: it is simply the sum of all $v_1[i] * v_2[i]$ terms $(i=0,...,...
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1answer
148 views

$\int \log(x+e^x) \mathbb{d}x$, or When every CAS fails

No computer algebra system -- at least to my knowledge -- managed to either compute the integral $\int \log(x+e^x)\space \mathbb{d}x$, in terms of any known functions, or even just prove that it is ...
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79 views

Latex code questions for curly C [closed]

What is the latex code for the curly C? (on the second line of the picture)

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