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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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 ...
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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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56 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 ...
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48 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 ...
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44 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?
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41 views

How to calculate the polynomial coefficients of a fraction of polynomials?

I have a polynomial fraction which results in a polynomial $$\frac{f(x)}{g(x)}=q(x)$$ with $f$ $g$ and $q$ being polynomials. I have formulas for the coefficients of $f(x)$ and $g(x)$ dependent on the ...
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91 views

Help with Math software (macaulay 2)

I just started working with Macaulay 2 and need some help. I need to find the number of solutions of a system of equations. I am having difficulty imputing this into the software so please be specific ...
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370 views

MuPAD - rearrange an equation

I have a huge expression, say $f(x_1,x_2,x_3) = 0,$ and I want MuPAD to try to express $x_1 $ in terms of $x_2$ and $x_3$ Is this possible?
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82 views

What are elementary field extensions?

While reading about symbolic integration I encountered some concepts of Differential Algebra. I do not know much of D.A and Fields in general also I have encountered as an extension of Rings. I ...
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294 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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301 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 $b > 1$?
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281 views

Problems Using Wolfram Alpha

I've always had some problem with the usage of wolfram alpha.It computes simple derivates, integrals and solves simple linear and quadratic equations flawlessly.It seems to me that it ignores step by ...
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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 ...
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994 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 ...
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1answer
47 views

Computing group cohomology in magma?

I don't how to construct a group module in MAGMA. Can someone show me how to compute group cohomology using MAGMA? For example, I am interested in the action of finite p-groups on abelian p-groups, ...
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64 views

Any mathematical software to verify no unique products.

Let $D^3= D \times D \times D$ where $D = D_\infty$ where we see $D$ as the group generated by $\mathbb{Z}$ and element $0^*$ of order $2$ such that $0^*n0^*=-n$ for all $n \in \mathbb{Z}$. Letting ...
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714 views

Given the graph below, use Dijkstra’s algorithm to find the shortest path (More details included)

So I've found out a few things and was wondering if someone could verify if I'm doing this correctly. So here is an example I've been given: Here is the solution to that example: Now here is the ...
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1answer
121 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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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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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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214 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 ...
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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 ...
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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 ...
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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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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 ...
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How to name the branch of the Lambert W function?

The Lambert W function has two real branches: the principal branch and the secondary real branch: the former is denoted by $W_0$ or $W$, the latter by $W_{-1}$. How do we name them ? For example, we ...
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Can SAGE or othe software compute or guess growth rates of infinite discrete groups?

I am interested in the growth rate of some finitely generated (infinite, non-abelian) discrete groups. Knowing very little about geometric group theory, I am wondering if I can plug them into sage and ...
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signature function of Weyl group element in LieArt

I am currently using LieArt Mathematica package for some calculations in Lie algebra, I am wondering if there is a way to know what is the signature of a Weyl group element, it seems the package can ...
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0answers
101 views

Understanding BlowUp Computation in Singular

Many of us might know that "Singular" is a computer algebra system for Algebraic Geometry, Commutative Algebra and Non-commutative algebra. This is a procedure in "Singular" for computing blowups. ...
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47 views

Is there any Software package to confirm correctness of your derivation steps?

Suppose I made a very complicated (not necessarily difficult) derivations in which it is very likely for anyone to make some silly mistakes, e.g., incorrect sign, overlooking a term, and so on. I ...
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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 ...
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Improvement of Buchberger's Algorithm (second part)

Suppose $S_j$ is a homogeneous syzygy of multidegree $\gamma_j$ in $S(G)$, where $G=\{g_1,\dots,g_t\}$. Show that $S_j G=\Sigma_{i=1}^{t} c_ix^{\alpha(i)}g_i$ has multidegree $< \gamma_j$. Now, I ...
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Algorithm to reduce expressions to canonical form

I'm writing a small computer algebra system that only knows rational numbers and all expressions that you can get from them by using basic arithmetic operations and powers. So the expressions are ...
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96 views

Computing intersection of vector spaces spanned by two lists

Assume that I'm given two lists of vectors $l_1$ and $l_2$, where all the vectors have equal dimension. I want to compute a basis for the intersection of their spans. What is the easiest setup for ...
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156 views

How to solve this complicated differential equation?

I need to know how to solve this complicated differential equation in $z$ either analytically or numerically : \begin{eqnarray} \frac{dx_1}{dz} &=& -ib_1x_1 - ikx_2 \\ \frac{dx_2}{dz} ...
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90 views

Are there high performance computing applications for symbolic integration?

Currently there are a number of applications for numerical integration in applied mathematics and physics. Many of these are integral transforms (often Fourier or Laplace), or solving definite ...
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Muirhead's Inequality (software?)

I just started learning about inequalities: Schur's, Karamata's, Muirhead's, etc... They are beautiful but it seems that in the case of more than two variables, some of the computations become a ...
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331 views

How does one solve equations over finite fields in SAGE?

Sage has the method solve (or function, I'm not sure what's the correct terminology) that finds solutions to 'symbolic expressions'. In particular, if one wants to find solutions for a given set of ...
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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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693 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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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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2answers
243 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 $k[x_1,\ldots,x_n]$. ...
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Free software for expresing a resolvent as function of coefficients

This relates to question "Expressing a symmetric polynomial in terms of elementary symmetric polynomials using computer?" I would like to try absolute resolvent for group $C_5$ in $S_5$. For example ...
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201 views

Introduction to Elementary Functions

I'm looking for an introductory text on algebraic treatment of elementary functions. Really short and easy-going. Video lectures are even better. I want to learn basic ideas (i.e. definitions) behind ...
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How do mathematicians handle functions of functions that may change?

E.g. let $f(x) = $ some function. Now define $h(x) = f(g(x))$. Now suppose the definition of $g(x)$ changes around in a discussion. Do we still refer to $h(x)$ as the original $h(x)$ or only when ...
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What is a good software package for ( assisted ) theorem proving and documenting?

Background: An issue in my math study is that I haven't found a good way of storing the theorems ( mostly abstract algebra ) I studied and want to (re-)use in proofs. At the moment I use a personal ...
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91 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: ...
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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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1answer
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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, ...