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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 ...

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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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25 views

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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30 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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54 views

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 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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159 views

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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170 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
116 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 ...
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Let Wolfram Alpha evaluate function for natural numbers only [duplicate]

How can I tell Wolfram Alpha that I only want it to evaluate my function for natural numbers? For example $ 2n $, assuming n integer used to work, but not anymore. Is there a new syntax I can use? ...
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1answer
73 views

Combinations with repeated elements in Maple

How does one output the combinations (with repeated elements) in Maple? I tried: with(combinat): choose([a, b, c], 2) $$[[a, b], [a, c], [b, c]]$$ These are all combinations without ...
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1answer
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Cases of additive groups in which addition is “rightward elongation” and subtraction is “leftward elongation” of a left-to-right ordered string

Are there any known real-world instantiations of additive groups/rings in which addition is rightward elongation of a left-to-right ordered string and subtraction is leftward elongation of a left-to-...
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the relationship between PCA (Eigenface) & LDA (Fisherface) on the set $S_{x} \bigcup S_{y}$

I have a question about the relationship between the result of Eigenface and Fisherface on face recognition. (Eigenface and Fisherface is the topic of Computer Vision. Those are related with PCA and ...
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1answer
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A complete, terminating set of rules for term rewriting on linear equations

Recently I have done some research on term rewriting. I feel not very experienced yet and hence there might be an easy answer to this questions, but I was curious if there is a ruleset for a term ...
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How can I run the “black box algorithms” in “computer readable format” found in the Atlas of Finite Group Representations?

The Atlas of Finite Group Representations has, among other things, generators in matrix form (over fields of positive characteristic, I think) for some groups. (Example in MeatAxe text format. ...
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Finding complementary of a collection in Macaulay2

Having a collection A of sets of the same cardinality t, I am trying to find all elements in 2^[n]\A of cardinality t. Is it possible to do so in Macaulay2? If so, which packages are required? How ...
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348 views

Boundary-value problems using sympy

I'm trying to solve a boundary-value problem using sympy. I was able to solve the ODE but the dsolve function doesn't return the values of the constants $C_1$ and $C_2$. Boundary-value problem: $u''...
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1answer
67 views

Conjectures that are false for very large numbers [duplicate]

Hi I would like to teach my students about false conjectures and computer approaches to them. I need references and/or direct examples of statements of the form $(\forall n \geq n_0)P (n)$ where $P$ ...
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1answer
55 views

Distinguish between conjugacy class 4A and 4B (ATLAS).

Is any one aware of how to distinguish between the conjugacy classes 4A and 4B in the group M$_{12}$ in GAP. Both centralizers have an order of 32 and I can't seem to find there being any difference ...
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43 views

Checking types in MAGMA

In using MAGMA, I always get type errors. How do you find out what the type of something is? For example, I have made an empty set $e := []$, how would I make MAGMA print out the type of $e$? Also, ...
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243 views

Wanted: Low-dimensional SOS certificate for the AM-GM inequality

Consider the AM-GM inequality in five variables $$a^5+b^5+c^5+d^5+e^5-5abcde\;\ge 0\qquad\forall\,a,b,c,d,e\ge 0\,.$$ Can one write the LHS as a concrete (finite) sum $\,\sum_i h_i\,s_i\,$ with ...