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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votes
14answers
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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 ...
21
votes
22answers
881 views
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?
12
votes
7answers
1k 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 ...
9
votes
3answers
305 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 ...
8
votes
5answers
781 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!
7
votes
4answers
688 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 ...
7
votes
2answers
168 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 ...
6
votes
4answers
334 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 ...
6
votes
1answer
107 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 ...
5
votes
4answers
459 views
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 ...
5
votes
2answers
296 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 ...
5
votes
3answers
120 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 ...
5
votes
1answer
81 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
158 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
votes
4answers
220 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) ...
5
votes
1answer
290 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
2answers
1k views
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
...
5
votes
0answers
109 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
1answer
101 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 ...
4
votes
5answers
166 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
votes
1answer
105 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
1answer
308 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
votes
1answer
89 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.
4
votes
1answer
126 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 ...
3
votes
2answers
269 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 ...
3
votes
2answers
101 views
Question about products of group elements using GAP
Background: In GAP I created the DihedralGroup of an octagon as a quotient of the freegroup on 2 variables and the presentation $r^8=s^2=s*r*(r^7*s)^{-1}=e \ $ as follows:
...
3
votes
2answers
182 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 ...
3
votes
2answers
55 views
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 ...
3
votes
1answer
97 views
Computer Algebra: How does the TI-89 do it?
I've always been amazed with the TI-$89$'s ability to deal with symbolic expressions so effortlessly. I've attempted to build several CASs in the past (mostly for fun, they are one of the most ...
3
votes
1answer
172 views
CAS: Computing homology of complex of non-free abelian groups
Which computer algebra system allows me to compute the homology of a complex of finitely presented abelian groups which are not necessarily free?
Sage and Magma apparently don't: see here and here.
...
3
votes
1answer
101 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 + ...
3
votes
1answer
91 views
Software for proving sum identites
Summations can really get complicated - esp. when you have convoluted n-fold summations with all kinds of different indices.
My question: Is there some software (or add-on) with which you can find ...
3
votes
1answer
62 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 ...
3
votes
2answers
176 views
How do I break MAGMA? [closed]
Is there any way I can break and get back to the prompt in MAGMA when MAGMA is spending forever doing some computation? I don't wan't to Ctrl-D, because then I will lose all sorts of stored variables, ...
3
votes
1answer
98 views
Find $k^{th}$ root of $M \in GL(n,F_2)$
Given $M \in GL(n,F_2)$ which is known to have a $k^{th}$ root.
How can I find a root algorithmically? Can I find all roots?
Other than being invertible and having a $k^{th}$ root I know nothing of ...
2
votes
1answer
62 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$ ...
2
votes
2answers
67 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 ...
2
votes
3answers
66 views
Prove that $\log f(n)$ is $O(\log n)$.
If $f(n)$ is any polynomial in n with positive coefficients, how could I prove that $\log f(n)$ is $O(\log n)$? I've been having trouble how to do this for a while now.
2
votes
2answers
171 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 ...
2
votes
1answer
304 views
Derivatives of Brownian motion or Box Options Greeks
Here's the probability (I think) that a particle in Brownian motion
(w/ standard deviation $\sqrt{t}$) will exceed $m$ between times $t_1$ and $t_2$:
$$\frac1{2\sqrt{2\pi}}\int_{-\infty }^m ...
2
votes
1answer
72 views
How can I get Macaulay2 to tell me if this ideal is prime?
I am trying to get Macaulay2 to confirm if $(y+zi,x^2 - z^2 - 1)$ is a prime ideal in $\Bbb{C}[x,y,z]$. Now as a small test, I tried to compute its radical by doing ...
2
votes
1answer
68 views
Picking out columns from a matrix using MAGMA
How do I form a new matrix from a given one by picking out some of its columns, using MAGMA?
2
votes
1answer
81 views
Maple: How to input such system so that it would be solved?
How to input such system
into maple so that it would solve it?
BTW we some part of system will be given to us,, which we do not know certently - may be some Ai's may be some Bi's as constants. we ...
2
votes
1answer
74 views
Prove $\log_bf(x)$ is big-theta $\log f(x)$
How can I prove that $\log_bf(x)$ is big-theta of $\log f(x)$ for any constant $b > 1$?
2
votes
1answer
454 views
Solving a matrix equation $AX=XB$ in a CAS
I have the following computational problem. Let $N$ be a positive integer and $A\in \mathbb{C}^{2N\times 2N}$, $X\in \mathbb{C}^{2N\times 4}$ and $B\in \mathbb{C}^{4\times 4}$. I want to solve the ...
2
votes
2answers
114 views
Simplifying expressions
I have a polynomial ring $R=k[x,y,z...]$ and a given ideal $I$ (defined by given generators) and several polynomials $f_1,f_2,...$ in the ring. I also have several other elements of $R$ given as ...
2
votes
1answer
435 views
Solving a nonlinear system using Groebner basis computations
I have discovered that Groebner basis computations may help in a problem I am working on. However, I am having some very specific problems. First, the literature I have discovered on Groebner basis ...
2
votes
1answer
58 views
Simple generators with a complex Gröbner basis
It's known that finding a Gröbner basis of a polynomial ideal has a worst-case space complexity of $O(2^{2^{c\cdot n}})$, where c is constant and n is the number of variables $k[x_1,\ldots,x_n]$.
...
2
votes
1answer
52 views
Character table in MAGMA
Below is a character table created using the MAGMA computer algebra system.
What is the meaning of the rows starting with $p=2$, $p=3$, etc.?
I've tried looking in the documentation, but couldn't ...
2
votes
2answers
140 views
How to solve generic algebraic problem using solver/library programmatically? Matlab, Mathematica, Wolfram etc?
I'm trying to build an algebra trainer for students. I want to construct a representative problem, define constraints and relationships on the parameters, and then generate a bunch of Latex formatted ...
