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 http://mathematica....

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Are there symbolic methods/computing for stochastic processes and stochastic differential equations?

Are there symbolic methods/computing for stochastic processes and stochastic differential equations? Are there some research trends along these lines? Can this be perspective and fruitful endeavour ...
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Is any matrix representation of a monomial ordering invertible?

We know that any monomial ordering has a matrix representation. Let $\prec$ be a monomial ordering and $M$ be its matrix representation. Is $M$ invertible?
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GRAPE package in GAP cannot create automorphism groups

I tried to get the automorphism group of a graph in gap, using the GRAPE package, but I got the following error: ...
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1answer
422 views

In SAGE, what function factors a polynomial whose coefficients are parameters?

In SAGE the function "factor" will factorize elementary polynomials with coefficients in $\Bbb Q$. For example: x,y = var('x,y') poly = x^3-y^2*x factor(poly) SAGE: x*(x-y)*(x+y) ...
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1answer
30 views

Print LIST of polynomials in Magma in one line instead of multiline

Suppose I have list of two polynomials and want to print it. I will get multi line output: ...
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1answer
48 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 Christoffel ...
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3answers
129 views

Does MAPLE not simplify correctly or am I goofing?

While attempting to answer this question with help of MAPLE, something very strange happened, at least according to me. We have the following function: $$ \phi(x,y) = x^2-y^2+\frac{x^2-y^2}{(x^2+y^2)^...
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Computer-supported (SINGULAR) decision making on commutative-algebra Topics: Is a given quotient ring integrally closed in a specific field/ring?

is there a way to decide in the CAS SINGULAR, whether a given quotient ring, say $\mathbb C[x,y,z]/I$, where I is an ideal of $\mathbb C[x,y,z]$, is integrally closed in a given ring, say $\mathbb C[x]...
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Print the image of a map (morphism) in Singular

I try to learn some basics in SINGULAR. I just wonder, how to get the image of a morphism printed. Here's a short example: (for those, who don't know Singular, there is a small description added) <...
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35 views

Possible uses of computer algebra systems in mathematics research?

How common is it for researchers to use computer algebra systems? I'm working in electrical engineering and moving into quite theoretical areas. For example, I'm reading right now some papers on ...
2
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2answers
46 views

Computing a double integral with applications to prime numbers

I was reading the preprint [1] which contains on p. 7 the following formula (for $4<s\le6$): $$ f_1(s)=\frac{2e^\gamma}{s}\left\{\log(s-1)+\int_4^s\int_3^t\frac{\log(u-2)}{u-1}du\,dt \right\} $$ ...
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483 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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4answers
65 views

I know that the binary and hexadecimal are useful, but what are the point of other bases, for example base 12?

I know about the uses of binary and hexadecimal, but what are the uses of other bases, for example base 12? (or duodecimal)
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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 ...
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Construction of polynomials in sagemath

This post is the mathematical part of a question I asked on Stackoverflow, which does not have $\LaTeX$. The question in here : http://stackoverflow.com/questions/37466781/constructing-polynomials-by-...
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1answer
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Questions that SAGE, MAGMA can answer?

I practice theoretical mathematics and I know (almost) nothing about SAGE, MAGMA. I would like to know (in general) what type of questions can I ask SAGE to do? For example, I know that given an ...
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24 views

GF(2^n) Multiplication using normal base

I want to implement the multiplication using normal basis in the binary field $GF(2^n)$ (where n=163, 233 for example). The multiplication with normal basis is performed by $c_0=A*M*B^T$, where $M$ is ...
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The software for finite field arithmetic

Is there any software, library,or toolkit that support arithmetic with normal basis on $GF(2n)$ field? What is the best one? Especially, which software can implement the conversion between normal ...
3
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52 views

Software for computing generators of the invariant rings of the symmetric groups

(Please skip to the last paragraph if you are interested in just the question) I wish to compute the generators of the ring of invariants for a symmetric group acting on a polynomial ring using a ...
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2answers
63 views

How do I include an integer constraint in Wolfram Alpha?

Related question: Tell Wolfram Alpha that a variable is a natural number I want to do the following in Wolfram Alpha: Minimise $$z = (y_1-x_1)+(x_2-y_2)+(1/2)(x_3)$$ s.t. $$0 \le ...
5
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3answers
621 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 ...
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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 ...
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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
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1answer
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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 ...
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1answer
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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 ...
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1answer
32 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 \...
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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 $x=1+2+3$ ...
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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
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2answers
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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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1answer
39 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 ...
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1answer
18 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 $...
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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 $$A:=k[x_1,\ldots,...
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1answer
64 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
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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: ...
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1answer
38 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 ...
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1answer
47 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
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1answer
73 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 ...
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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 ...
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10answers
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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 ...
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0answers
25 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 ...
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1answer
77 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
65 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
126 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
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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
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1answer
52 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 ...
8
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3answers
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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} = \frac{1}{\sqrt{n\...
2
votes
1answer
52 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
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1answer
59 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 ...