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. For questions about Mathematica please see the ...

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'Linux' math program with interactive terminal?

Are there any open source math programs out there that have an interactive terminal and that work on linux? So for example you could enter two matrices and specify an operation such as multiply and ...
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23answers
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Can you recommend a decent online or software calculator?

I'm looking for an online or software calculator that can show me the history of items I typed in, much like an expensive Ti calculator. Can you recommend any?
14
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9answers
6k views

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

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 ...
11
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6answers
4k 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!
10
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3answers
449 views

Erroneous numerical approximations of $\zeta\left(\frac{1}{2}\right)$?

By definition of the Riemann Zeta Function, $$\zeta\left(\frac{1}{2}\right) = \sum_{n=1}^\infty \frac{1}{\sqrt{n}}.$$ Since $\forall n \geq 1 : \frac{1}{\sqrt{n}} \geq \frac{1}{n}$, we have that for ...
10
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2answers
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Traditional axes in 3d Mathematica plots?

Is there any way to tell Mathematica 7 to use "traditional" axes rather than boxing a three-dimensional graph? That is, rather than the default view produced by ...
9
votes
4answers
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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 ...
9
votes
5answers
3k views

Computer Algebra: Algorithms for solving equations symbolically

As a hobby, I have written a basic computer algebra system. My CAS handles expressions as trees. I have advanced it to the point where it can simplify expressions symbolically (i.e., sin(pi/2) ...
9
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1answer
240 views

Modular subgroup lattice in GAP

I want to know if one can ask GAP to decide whether the subgroup lattice of a specific finite group $G$ is modular, via a simple command. Many thanks. Update: relevant questions have been addressed ...
8
votes
2answers
252 views

What is the closed form of $\sum _{n=1}^{\infty }{\frac { {{\it J}_{0}\left(n\right)} ^2}{{n}^4}}$?

Using Maple I am obtaining the numerical approximation $$0.5902373619$$ Please, let me know what is the closed form. Many thanks.
8
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2answers
875 views

Common Lisp for mathematicians?

I am interested in learning Common Lisp. There seems to be a lot of material either for (experienced) programmers, or for people with no background, in programming or in mathematics. I was wondering ...
8
votes
5answers
458 views

CAS with a standard language

I hope this question is suitable for the site. I recently had to work with Mathematica, and the experience was, to put it kindly, unpleasing. I do not have much experience with similar programs, but ...
7
votes
4answers
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Expressing a symmetric polynomial in terms of elementary symmetric polynomials using computer?

Are there any computer algebra systems with the functionality to allow me to enter in an explicit symmetric polynomial and have it return that polynomial in terms of the elementary symmetric ...
7
votes
1answer
180 views

Why is $\operatorname{res}(fg,h)=\operatorname{res}(f,h)\cdot\operatorname{res}(g,h)$, where $\operatorname{res}$ stand 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 ...
6
votes
2answers
894 views

Wisdom of using Sympy as a first CAS

I'm an undergrad. maths student and have been looking at a few different free maths programs (mainly CAS systems, I've been very impressed with Octave as a MATLAB clone.) I've been tossing up between ...
6
votes
6answers
401 views

How to efficiently represent and manipulate polynomials in software?

I've started to work on a package (written in matlab for now) that among other things must be able to represent and manipulate (compare, add, multiply, differentiate, etc) polynomials in several ...
6
votes
3answers
330 views

Computer Algebra Systems which implement Cylindrical Algebraic Decomposition

My understanding is that Mathematica's Reduce function is based on Cylindrical Algebraic Decomposition (CAD). The only other system I've seen which implements CAD ...
6
votes
2answers
339 views

What are well-known weaknesses of CAS/math software?

I'm starting to become more functional in Mathcad, so I wanted to take the opportunity to look into known drawbacks, mathematically speaking, of CAS/computer math systems. For instance, one of the ...
6
votes
2answers
148 views

Computing a nasty integral (probably with computer algebra system)

I'm trying to do this integral, not sure if it is possible: $$ \int_{1}^{\infty}\int_{0}^{\infty} \exp\left(\, -\,{x^{2} \over y^{2}}\,\right) \exp\left(\,-\,{y^{2} \over z^{2}}\,\right) \exp\left(\, ...
6
votes
1answer
685 views

Semidirect Products with GAP

I'm wondering how to specify to GAP which homomorphism to use when constructing a semidirect product. I'm trying to have it construct $\left(\mathbb{Z}_p\times\mathbb{Z}_p\right)\rtimes_\varphi S_3$. ...
5
votes
1answer
161 views

What's the best way to detect an algebraic number?

Suppose you calculate the first few (dozen, hundred) digits of a number which you believe to be a rational number. You can calculate the continued fraction for the number and truncate after a large ...
5
votes
2answers
710 views

Computing Subgroup Lattices

Let $G$ be a finite group, and let $L(G)$ be the lattice of subgroups, partially ordered by inclusion. For example, below is $L(D_8)$. $\quad\qquad\quad\qquad\quad\quad\qquad$ I have two questions: ...
5
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3answers
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What free software can I use to solve a system of linear equations containing an unknown?

Question: What free software can I use to solve a system of linear equations $M\mathbf{x}=\mathbf{y}$ where the entries of $\mathbf{y}$ vary with an unknown quantity $n$? Presumably I could do ...
5
votes
1answer
209 views

Finding irreducible representations of the following group using GAP

Given the following group of order 24, $$ G = \langle a,b \mid a^2=b^3=(abab^2)^2=1\rangle$$ how can one find (all) the irreducible representations using GAP? Since I have not installed GAP yet, I ...
5
votes
2answers
22k views

Using Wolfram Alpha For Solving A System Of Equations

How do i input the below system of equations in wolfram alpha in order to solve for the unknowns and plot them? If i just say "solve" and input these equations one after the other with a simicolen ...
5
votes
2answers
287 views

where can I find a library of finite groups with their multiplication tables?

Is there a library of finite groups given by their multiplication tables? can I get this result using the GAP SYSTEM ?
5
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2answers
44 views

Extracting Information from Lists in GAP

If I have a list $L$ in GAP, and a certain list of properties $a,b,c$, how can I count the the number of elements in my list that have all three properties? I've searched the manual (chapter on ...
5
votes
2answers
123 views

There is a closed form for $\sum _{n=1}^{\infty }{\frac {{{\it J}_{0}\left(\,\alpha\,n\right)} {{\it J}_{0}\left(\,\beta\,n\right)}}{{n}^{2}}}$?

Using the method showed here proposed by Olivier Oloa with simplifications proposed by Anastasiya-Romanova, it is possible to prove that $$\sum _{n=1}^{\infty }{\frac {{{\it ...
5
votes
2answers
84 views

Analogue of Fermat's primality test for polynomials and irreducibility

We've got Fermat's primality test to test if a number is probable prime. Is there an analogous test for polynomials in $\mathbb{F}_{p^n}[X]$ and irreducibility?
5
votes
2answers
252 views

How do you compute group cohomology in practice?

If you have a finite group $G$ and a finite $G$-module $K$, and you need to know $H^1(G,K)$ or $H^2(G,K)$, how do you do it? Do you use a computer algebra system? (If so, which one?) Do you use a ...
5
votes
1answer
199 views

Algorithms for symbolic definite integration?

What are the algorithms for symbolic definite integration? Apart from computing the antiderivative first. What are the basic ideas behind such algorithms? As far as I got it, the main idea behind ...
5
votes
1answer
163 views

Formula or code to compute number of subgroups of a certain order of an abelian $p$-group

Given a finite abelian $p$-group and its factorization into groups of the form $\mathbb{Z}/p^k\mathbb{Z}$, does anyone know of a formula that gives the number of subgroups of a certain index/order? As ...
4
votes
2answers
190 views

How can I find the sum of the digits of a positive integer in GAP?

(I eventually found the answer to this question after writing it. But just in case anyone finds this useful, or has an alternative or better answer, I'll ask and answer my own question.) After ...
4
votes
1answer
196 views

How do I substitute a value into a polynomial in GAP?

Question: How do I substitute a value into a polynomial in GAP? So, if I start off with the following: x:=Indeterminate(Integers,"x"); f:=x^2+3; I have $f$ ...
4
votes
2answers
76 views

”lesser known” rules to calculate the derivative

I was reading through the online help of WolframAlpha (link) and found this statement: Wolfram|Alpha calls Mathematica's $D$ function, which uses a table of identities much larger than one would ...
4
votes
2answers
666 views

Software for differential geometry

What is the software for computations with tensor fields? I'm interested in computations with vector-valued differential forms on Riemannien manifolds. Wedge product, exterior derivative, likely Hodge ...
4
votes
2answers
391 views

Learning to use MAGMA

I'm trying to learn to use MAGMA for research in group theory, but it's been slow going. I've been using the MAGMA handbook provided online, but it's rather hard to learn with. I feel like it's hard ...
4
votes
1answer
291 views

Computing Conjugacy Classes of Subgroups in GAP

GAP has the command ConjugacyClassesSubgroups which gives a list of the conjugacy classes of a finite group $G$. Is there a way I can specify further what types of subgroups GAP reports? For ...
4
votes
5answers
202 views

Are CASs useful in mathematics?

I understand that computer-algebra systems are useful for physists, engineers, or other users of mathematics. But are they useful in mathematics itself? Specifically, Are they usually taught in ...
4
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2answers
384 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 ...
4
votes
1answer
317 views

MAGMA question: SemidirectProduct using a homomorphism $f:G \rightarrow GL_n(\mathbb{F}_p)$.

Suppose I have a homomorphism $f:G\rightarrow GL_n(\mathbb{F}_p)$ and I wish to form the semidirect product $E\rtimes_f G$ with $E$ being the elementary abelian group of order $p^n$. The Semidirect ...
4
votes
2answers
128 views

Advantages to learning Sage?

I'm wondering if anyone can let me know advantages to installing/setting up Sage on my computer for doing computational math (work in groups, finite fields, and combinatorics, along with some search ...
4
votes
1answer
197 views

Computer Algebra Systems for Experimental Mathematics (especially Integer Relations with PSLQ)

I would like to use a computer algebra system to do some experimental mathematics, particularly Integer Relation problems using the PSLQ algorithm. I know that Maple has a PSLQ implementation, but ...
4
votes
1answer
147 views

How does the function CycleIndex work in GAP? ( undocumented in GAP )

Background: When I divide a hexagon in six triangles the group $D_6$ works on the triangles. The cycle index of the group action would be in this case $$p(x_1,x_2,x_3,x_6)=\frac{1}{12}(x_1^6 + ...
4
votes
1answer
316 views

Computing with ideals: over $K$ or over $\mathbb{Q}\subseteq K$? does it matter?

I'm beginning to learn to use SINGULAR, the computer algebra system (CAS) for commutative algebra. NOTATION: If $K$ is a field of characteristic $0$, then $\mathbb{Q}\subseteq K$; otherwise ...
4
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2answers
297 views

What is the fastest computational graph theory package?

What is the fastest computational graph theory package with respect to executing algorithms and computing graph theoretic data? I am aware of this related question, which requests graph theory ...
4
votes
0answers
176 views

How to integrate $\left(1+\ln(x)\right)\sqrt{1+(x\ln(x))^2}$ with Risch algorithm?

How would you integrate $\left(1 + \ln\left(x\right)\right)\, \sqrt{1 + \left(x\ln\left(x\right)\right)^{2}\,}$ using the Risch algorithm? I want to know this because Mathematica is using the Risch ...
4
votes
0answers
245 views

Test for equivalence of algebraic expressions

We are looking for the most efficient (most recent, or best) techniques to check if two algebraic expressions (elementary, Calculus-type functions) are equivalent (or if an expression is equivalent to ...
3
votes
3answers
295 views

Cornacchia's Algorithm

Can any one give the representation for a prime number 9444732965601851473921 as $x^2+15y^2$. I tried cubic cornacchia algorithm in nzmath implemented through python, but in vain. I also tried ...