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: Mathematica, Maple, Wolfram Alpha, GAP, SAGE. For questions about Mathematica please see the ...

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3answers
559 views

The J programming language: is it useful for mathematics?

I just stumbled upon the J programming language, which has the description: J is particularly strong in the mathematical, statistical, and logical analysis of data. It is a powerful tool in ...
-1
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0answers
33 views

Primitive element in multivariate Galois field [closed]

On Singular CAS I can define a Galois field $(2^3)$ with $(x,y,z)$ variables. But I am not able to understand how $a^3+a+1$ is still its primitive element. General example taken in books is always ...
10
votes
5answers
1k views

Computer Programs for Pure Mathematicians

Question: Which computer programs are useful for a pure mathematician to familiarize themselves with? Less Briefly: I was once told that, now-a-days, any new mathematician worth his beans knows how ...
1
vote
0answers
24 views

Singular CAS vs Macaulay2 for finite fields

I intend to work on error correcting codes using finite fields. Finite fields are supported by both Singular and Macaulay2 CAS, now I am confused about which one I should start with to learn. Any ...
3
votes
1answer
62 views

Given the generators, find the entire group

my question is quite simple. If you are given the generators of a group, is there any systematic way to generate all of the elements of the group? For example, suppose that you have the Hadamard ...
1
vote
1answer
33 views

How to print long strings in MAGMA?

I'm trying to print a very long list to a file using magma to make it "callable". The list is called F2, and the code I'm using to print this list to a file is the following ...
0
votes
1answer
31 views

factor out of an expression, a couple principal ideals, software?

I have an expression, $f$, consisting of a few rational fractions of large multivariate numerators, $n1,\,n2,\ldots \in \mathbb{Q}[a1,a2,b1,b2;Q]$ and large multivariate denominators, $d1,\,d2,\ldots ...
0
votes
1answer
27 views

Compute Christoffel symbols & Riemann tesors in Maple 17

I invented a metric tensor g and now I'm trying to compute my first Christoffel symbol but an error message is popping up "Error, bad index into matrix" Is there a way for maple to compute ...
3
votes
0answers
33 views

Is math recursive or iterative?

Is the process of solving a mathematical problem (algebraic equations, limits, derivatives, integrals, EDOs, trigonometric identities proof) recursive or iterative? For example, for solving $x=1+2+3$ ...
5
votes
4answers
148 views

Rational Exponents on Calculator

I'm confused as to why my calculator is saying that $$x^\frac{n}{n}=x$$ when $n$ is an even integer. I was under the impression that $$x^\frac{n}{n}=\sqrt[n]x^n=|x|$$ when $n$ is an even integer. ...
2
votes
2answers
54 views

Janko Group and subgroups.

I want to work with the Janko simple group $J_2$ using the computer, and if it is possible, the Janko simple group $J_4$ too. In specific, I want to take certain subgroups of it and compute their ...
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votes
1answer
34 views

How to automatically assign the output from the solve function in Maple 17 to variable names [closed]

Years ago while using Maple 11 mathematical software, I accidentally came across a way to automatically assign the output from the solve function into pre-designated variable names. So that if for ...
1
vote
1answer
16 views

Algorithm for computing the inverse limit of a finite inverse system

Let $k$ be a field (finite if you'd like), let $(I,\le)$ be a finite directed poset with $|I|=n$, and let $(A_i,f_{ij})_{i\le j\in I}$ be an inverse system of finitely generated, graded, commutative ...
1
vote
0answers
18 views

Algorithm for computing an inverse image

Let $k$ be a field (finite if you'd like), and let $f:A\to B$ be a map of graded, commutative $k$-algebras. Suppose further that $A$ is finitely generated and choose a presentation ...
4
votes
1answer
56 views

What is sample variance of sample variance, and what is theoretical sampling distribution?

I am trying to work some things in R and I am having trouble understanding some of the instructions. I generated $1000$ samples of size $5$ from the standard normal distribution, and I calculated the ...
2
votes
1answer
38 views

Quasi canonical isomorphisms between finite groups and subgroups of the symmetric group?

I'm implementing finite groups in Forth for my blog and since any group is a subgroup of a permutation group it make sense to let the standard elements be permutation schemas: ...
1
vote
1answer
30 views

Ideal intersection in Boolean polynomial ring

I'm trying to calculate $ \langle x,y,z\rangle \cap \langle x+1,y+1,z+1\rangle $ in the ring of Boolean polynomials. In CoCoA initially I set the ring as ...
14
votes
1answer
370 views

Most wanted reproducible results in computational algebra

I am interested in suggestions for major computational results obtained with the help of mathematical software but not easily verifiable using computers. "Most wanted" could refer, for example, to ...
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votes
1answer
38 views

Line representation - implicit form

I am going through one of the the scan conversion techniques and it mentions the implicit equation of line as follows: $$F(x,y) = ax + by + c = 0 .$$ The text also mentions that $F(x,y)=0$ if the ...
4
votes
1answer
61 views

GAP Most efficient way to check multiple properties of a group in the small group library

In GAP I would like to search the small groups library looking for groups with specific properties (I suppose this is the most common usage). If I have a list of properties I want to test, what is ...
0
votes
0answers
25 views

Significance of various lex sort on polynomials

I have just finished writing a monomial order sort package for Maxima CAS which supports variety of lexicographic orders. But I want to know what are the uses of these sorts on polynomials. One that ...
14
votes
10answers
7k views

What are some good iPhone/iPod Touch/iPad Apps for mathematicians? [closed]

There are lots of good apps for teaching mathematics to children but I would like to learn about apps for undergraduate/graduate/research levels. Helper questions Any algebra system (like ...
0
votes
0answers
24 views

Can Any System Of Equations Be Solved By Any Variable First?

Suppose we have a system of equations with an arbitrary number of variables, but assume it is solvable for each variable (e.g. the system will have as many equations as variables and will have at ...
1
vote
1answer
37 views

How to create a matrix in pari/gp [closed]

How does one create a matrix in $\texttt{pari}$? I currently understand how to create a vector: ? vector(6,n,n^2) %1 = [1, 4, 9, 16, 25, 36] I also know how ...
2
votes
1answer
56 views

Looking Portable Mathematical Notation(s) [LaTeX, Mathematica, Maple, Macsyma] that are open

I'm looking for a portable Mathematical notation. What I mean by that is: I want to create a collection of (open-source) math problems that can be: Rendered for the Web or say in ePS format for ...
4
votes
1answer
122 views

Finding integer solutions to $y^2=x^3+7x+9$ using WolframAlpha

I am an unconditional admirer of WolframAlpha and for this reason I want to let the people of this error (or is it really the fault of mine?). If I'm not mistaken, I would be very happy to contribute, ...
14
votes
7answers
6k views

symbolic computation program/software

What is your recommended symbolic computation program/software for free and commercial respectively? What are its strength and weakness? For example, efficiency, comprehensiveness, etc Thanks!
2
votes
1answer
50 views

Is there some database or software to look for patterns in polynomials?

Like if I am looking at these polynomials, $$x^8-8x^6+20x^4-16x^2+3$$ $$x^{10}-12x^8+48x^6-72x^4+33x^2$$ $$x^{12}-16x^{10}+88x^8-192x^6+138x^4$$ And I want to know if they are members of some ...
7
votes
3answers
10k views

Tell Wolfram Alpha that a variable is a natural number

How can I tell Wolfram Alpha that some variables are natural numbers, when I want to solve a equation? An example of what I want to do: $\binom{n}{k}\cdot p^k \cdot (1-p)^{n-k} = ...
2
votes
1answer
48 views

(online) Tool to calculate $E(\mathbb{Q})/2E(\mathbb{Q})$ for $E: y^2 = x(x^2 + 3x + 5)$

For some exercise I need to compute the generators of $E(\mathbb{Q})/2E(\mathbb{Q})$, where $E: y^2 = x(x^2 + 3x + 5)$ I did this by the approach from Cassels book 'Lectures on Elliptic Curves' and ...
3
votes
1answer
58 views

Tool for construction of graph with specified properties

Is there a tool (class of algorithms for graph generation) that can construct graph with specified properties. E.g. construct graph who is homeomorphic with both to K5 and K3,3. Construct planar graph ...
2
votes
0answers
42 views

Numerical intergration of a complex, oscillatory function (Bessel function, Singularities)

I am working on a university project at the moment and at some point I needed to calculate the intergral of the following function (Please refer to "Bakthiari et al. - Analysis of radiation from an ...
2
votes
1answer
44 views

UFD test - software? [closed]

I have a quotient of a polynomial ring. I would like to check if it is a UFD. Is there software that will allow me to do that?
1
vote
1answer
27 views

Simplify fog type function chain using sympy

I need to simplify some lengthy $fog(x)$ where both $f(x)$ and $g(x)$ are known rational polynomial in one variable. For e.g. $f(x) = (7x-9)/12$ and $g(x) = (2x-5)/7$. Then I would like to get a ...
1
vote
1answer
28 views

Computing Extensions of an Ideal in Singular or Macaulay2

Does Macaulay2 or Singular compute extensions of ideals under ring homomorphisms? Specifically, if $\phi:R\rightarrow S$ is a ring homomorphism (say polynomial rings over $\mathbb{Q}$ which can ...
0
votes
1answer
123 views

Implement some actions in Gap

I would like to calculate, in GAP, certain permutation actions on matrices. Namely: Let $G=S_n$ be the symmetric group of degree $n$ and $\Omega=GL_n(q)$ (or a suitable subset). $G$ acts by ...
7
votes
1answer
204 views

Why is $\operatorname{res}(fg,h)=\operatorname{res}(f,h)\cdot\operatorname{res}(g,h)$, where $\operatorname{res}$ stands for resultant?

I'm learning Computer Algebra and met an exercise asking me to prove that $$ \operatorname{res}(fg,h)=\operatorname{res}(f,h)\cdot\operatorname{res}(g,h) $$ where $f(x)$, $g(x)$ and $h(x)$ are ...
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votes
2answers
38 views

Nullified terms of this polynomial?

This the polynomial: $6 + 3x - 5y + 7xy -8x^2 + 3y^2 + 4x^2y - 7xy^2 + 9x^3 - 5x^4 + 8y^4x$ I would like to know which terms are there (so that I will form the complete polynomial, with zero as a ...
0
votes
1answer
23 views
0
votes
2answers
142 views

Printing long lines in MAGMA without line break

In MAGMA, how do I print a long list of items to a file without automatic line breaks? It seems to me that there is an internal length limit and anything longer than it will result in a automatic ...
0
votes
1answer
54 views

About calculating limits of integrals (Part 2)

The function $tanh(\pi z)$ has its poles at the points $i(n+\frac{1}{2})$ for $n \in \mathbb{Z}$. Now I want to take an $\epsilon$ circle around such a pole and contour integrate the function $z\text{ ...
2
votes
0answers
22 views

terms of taylor expansions of multiple variables at the origin

By the fundamental theorem of symmetric polynomials, $X_1,X_2,\cdots,X_n$ are polynomials of $ e_1,\cdots,e_n$ and $$ \mathbb{Z}[ e_1,\cdots,e_n]=\mathbb{Z}[X_1,X_2,\cdots,X_n]. $$ We define a ...
0
votes
1answer
344 views

Can I get multivariable taylor series expansion on wolfram alpha or matlab?

I need something like this : say $a, x, y$ and $t$ are three non-negative real numbers. Now define the complex number, $z = -y + i(a+x-t)$ and consider the function $f(x,y) = z\text{ }tanh (\pi z) log ...
2
votes
0answers
73 views

What is the easiest to use software to draw Latex embeddable contour diagrams? [closed]

I need to draw a few diagrams of integration contours for complex integrals. What is the easiest to use software on which I can achieve this? Particular things I need, draw a zig-zag line to denote ...
1
vote
1answer
114 views

Coset Enumeration with GAP

I have downloaded GAP version 4.7.8. for windows, and installed everything (all packages, including"ACE") with the installer. Now I want to do a simple task, enumerating the cosets. To create a group ...
1
vote
2answers
91 views

Compute Automorphism Group using Computer Software

Is there a computer software that can compute Automorphism Groups. For instance $Aut(\mathbb{Z}_4\times\mathbb{Z}_2)$. I tried Sage, but could not get it to work. Output: ...
1
vote
4answers
79 views

How would you represent an abstract set on a computer?

I'm trying to come up with a simple language for specifying mathematics. We can't simply define a set as a collection of objects because that's meant for human understanding and that would also lead ...
2
votes
0answers
29 views

How to name the branch of the Lambert W function?

The Lambert W function has two real branches: the principal branch and the secondary real branch: the former is denoted by $W_0$ or $W$, the latter by $W_{-1}$. How do we name them ? For example, we ...
4
votes
0answers
62 views

Systems of linear modular equations with unknowns in the moduli

I am interested in systems of linear modular equations, where the unknowns also appear in the moduli. The general form would be: $A \vec{x}= \vec{b} \;\textrm{mod} \; (C \vec{x}+\vec{d})$ where A ...