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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1answer
30 views

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
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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7 views

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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0answers
7 views

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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53 views

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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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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19 views

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
57 views

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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0answers
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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0answers
49 views

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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0answers
51 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
62 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 ...
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0answers
38 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
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1answer
77 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 ...
3
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0answers
34 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 $x=1+2+3$ ...
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1answer
41 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 ...
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
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2answers
62 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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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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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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0answers
22 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 $$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 ...
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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 ...
-1
votes
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 ...
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: ...
0
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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 ...
18
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2answers
482 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 ...
0
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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
74 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
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1answer
64 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, ...
4
votes
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 ...
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 ...
2
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0answers
43 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 ...
1
vote
1answer
46 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
28 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
32 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 be ...
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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

How can I find an approximation for y(1) using MATLAB without ODE solvers? (Euler's Method & Matrices)

Task: Given \begin{align*} y(t+h)&\approx \underbrace{\left(\begin{matrix}1-h & 5h & h\\3h & 1-h & 0\\0 & -th & 1+h\end{matrix}\right)}_{F(t,h)}y(t)+\underbrace{\left(\...
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
34 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 ...
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vote
0answers
92 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 ...
0
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1answer
581 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 ...
1
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1answer
133 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
140 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: ...