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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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 ...
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594 views

Galois group command for Magma online calculator?

I need to test if a family of 7th deg and 13 deg equations are solvable. I'm new to Magma, so my apologies, but what would I type in, http://magma.maths.usyd.edu.au/calc/ to determine the Galois ...
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84 views

Computing the decomposition of a representation of $S_n$

I have an explicitly defined representation of the symmetric group that I would like to decompose into irreducibles. How to do this most easily? The best approach I have so far is as follows: Find a ...
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33 views

Canonical Separation of variables

Do the functions of the form $\psi(x)\phi(y)$ span $L^2(\mathbf{R}^6)$? Insert proper grammar here.
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191 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 ...
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In maple how do you evaluate combinations?

In Maple how do you have it evaluate combinatorics such as $\binom{5}{2}$ and give you the answer 10? (What is the name of what I want to do anyways, is it evaluate?) Thanks. Seems so easy now that I ...
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233 views

CAS for algebraic geometry, which one?

I use Maple to compute Groebner bases and find it very efficient/fast for my current needs. However, several introductory textbooks on algebraic geometry refer to Singular, which I never used before. ...
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2k views

How to define a recurrence relation in Maple?

I'm new with Maple and want to define a recurrence relation. I want to 1) have Maple solve it to the explicit formula 2)have Maple output a few evaluations of it for various values of ...
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321 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 ...
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179 views

Resultant of Two Univariate Polynomials

I am trying to implement an algorithm for computing Res(f(x),g(x),x) where f(x) and g(x) uni variate polynomials with integer coefficients. Could any one list the various algorithms for computing ...
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51 views

Is there a known algorithm for approximating all the real and imaginary zeros of any well behaved equation of a single variable?

Does there currently exist a general algorithm (or set of algorithms used together) that will approximate all the zeros of any well behaved non-differential equation of a single variable which has a ...
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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} = ...
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Revealing output slowly in Magma

When working in Magma, is there a command to gradually reveal the output. For example, if you have a finite group $G$ and you want to calculate SubgroupLattice(G), then the output may be thousands of ...
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3k views

Using Wolfram Alpha to solve a system of linear equations

How do I input the below system of equations in Wolfram Alpha in order to solve for the unknowns? I'm wondering if there's some kind of code that can be written in order to make wolfram alpha ...
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1answer
125 views

Producing a set of matrices in MAGMA

As part of my work I need to define the set of all $n\times n$ matrices with entries in $\{0,1,\ldots,n\}$ (considered as a subset of $\mathbb{Z}$), such that each row and column of the matrix sums to ...
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124 views

How to extract the indeterminates from a set of polynomial?

I am a biologist and I am facing a huge problem. I would like to extract the indeterminates of a set of polynomials, for example, I have: $f_{1} = \{\\x_{3}^{2} + x_{1}*x_{2} + x_{1} + x_{1}*x_{3},\\ ...
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1answer
49 views

software with a routine for the vanishing ideal of a finite set of points

I am looking for an algebraic software package that provides a routine that computes the vanishing ideal of a finite set of points. So far i am working with Macaulay2 but i have not been able to find ...
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1answer
135 views

Using Janet Basis to solve a nonlinear polynomial system

I am trying to solve a nonlinear polynomial equation system using Janet basis, when they have finite many solutions. For example the solution of the system: $$xy^2-y^3-3x^2=0,x^2+y^2+xy=0.$$ There ...
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701 views

Solving large, sparse system of linear equations

I have a system of linear equations as follows: $$(A+I)x=B$$ where $I$ is the $n\times n$ identity matrix, $A$ is a $n\times n$ matrix such that the first and last rows are blank, and, for every ...
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1answer
68 views

Maple command for algebraic combinaiton of polynomial in $\mathbb{Z}_p[x]$

Let $F(x) , f_1(x),\ldots, f_r(x)$ be polynomials with coefficients in $\mathbb{Z}_p$ ($p$ is odd prime) Is there a Maple command to determine if$$ F(x) = a_1(x)f_1(x)+\dots+ a_r(x)f_r(x) \pmod{p} ...
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147 views

Vectorfields on Surfaces with MuPAD

i am working with MuPAD. I can make vectorfields in 3D and also Surfaces in 3D via plot::VectorField3D and plot::Surface. But now i want to draw a vectorfield ON a surface. If $X$ is a vectorfield ...
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1answer
187 views

Is there a computer programm or CAS (maybe GAP?) that can calculate with projective (indecomposable) A-modules (A is a finite dimensional k-algebra)?

I have the following question(s): I have an "Algebra-With-One" $R$ as a subalgebra of a full matrix algebra in GAP. Furthermore, I have 5 primitive orthogonal idempotents $e_1,...,e_5$, which sum up ...
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93 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 ...
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478 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 ...
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301 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 ...
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878 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: ...
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63 views

Minimal set of algebraically independent numbers

Suppose we have a set of polynomials $f_1, f_2, \ldots, f_n \in \mathbb{Q}[x]$. Consider the set $$S := \{\alpha \in \mathbb{C} \; | \; f_i(\alpha) = 0 \text{ for some } i \}$$ of complex roots of ...
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202 views

Computer algebra system for category theory

There are many different computer algebra systems which allows to perform computer aided computation in symbolic object like polynomials and function and also ordinals. Now being a category theory ...
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1answer
89 views

Postfix notation in MAPLE

I usually use MATHEMATICA as a computer algebra system and there I heavily employ the postfix notation (achieved by "//" at the end of some command), e.g. ...
2
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1answer
186 views

Some questions about SAGE

I search a programmable calculator like PARI/GP. In the net, I came across SAGE. I have some questions about the download of SAGE Is it really absolutely free ? Is it faster than PARI/PG ? Has it ...
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Tools for optimizing asymptotic bounds.

Is there any tool for this task ? Given the asymptotic bound in term of $n$ and other paramaters $t_1,\dots,t_r$, then return the value for each $t_i$ which optimizes the expression in term of $n$, ...
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717 views

Plotting parametric equations in Maple

I have the following problem. Let $\alpha:=\alpha(v)$ and $\beta:=\beta(v)$, where $v\in\mathbb{R}$. Using MAPLE, I would like to plot $\alpha$ and $\beta$ in the $(\alpha,\beta)$ space as $v$ varies ...
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1answer
149 views

Computing Resultant

The resultant of two polynomials is defined as the determinant of the Sylvester matrix. If the polynomials are of degree $n$ and $m$, than the Sylvester matrix will be of dimension $(m+n)\times ...
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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 ...
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1answer
303 views

Computing Invariant Subspaces of Matrix Groups

Does anyone have a program written in Mathematica (or SAGE or GAP) that computes the invariant subspace lattice of a matrix group?
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128 views

How to solve an equation in three variables fixing two of the variables?

Also, I have the following equation, I want to solve it for $b$ keeping $a$ and $c$ fixed. $5b^5+(60-5a)b^4+(125+50c-80a)b^3+(594c-445a-775)b^2+(2324c-1005a-3270)b+3000c-750a-3000=0.$ Also how to ...
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245 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 ...
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1answer
81 views

Comparing expressions exactly

Suppose I have two expressions; call them $A$ and $B$. The following values of $A$ and $B$ are good examples for my question... $$ A = \pi e^2\\ B = \pi^2 e $$ Is there a method to determine the ...
5
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390 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 ...
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1answer
370 views

Solving a nonlinear equation for one of variables with the help of a computer algebra system

Are there any solutions out there that can take a wide variety of equations with variables, like the one below, and transpose or isolate variables to other sides of the equation automatically? For ...
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1answer
106 views

How do I determine if two of my software's representation of algebraic numbers are equal?

I have software which stores information about algebraic numbers with absolute precision. If you build it up by creating instances of a Python representation of an integer, float, Decimal, or string, ...
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1answer
60 views

What are the explicit expression for this interpolation problem

We want to fit $f(x) = a_0 + a_1 *x + a_2 * x^2 + ... + a_n * x^n$ to the data $(x_i,f(x_i))$ for $i = 0 ... n.$ It will give rise to the following system $ A a = b $ Here $ a = [ a_1 a_2 a_3 ...
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1answer
43 views

Specifying if a function has an elementary integral

In Algorithms for Computer Algebra in the last chapter about Risch algorithm, the Rothstein-Trager method is applied to see if an elementary function has an elementary integral. For this, the ...
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104 views

Flatten kronecker product in CAS?

I am a new user of Maxima, and I need to trace the elements of a big messy kronecker product of symbolic matrices. I tried the following to get my feet wet, but I don't get a simple, flat matrix -- ...
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1answer
864 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 ...
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1answer
246 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 $f$ ...
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317 views

Best graphing program for Mac or PC?

I just bought the highest end iMac, with a student discount, of course, and was wondering what is the best graphing program out there. A program that can graph any equation that I throw at it AND one ...
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1answer
257 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 ...
5
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1answer
288 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 ...