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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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 ...
2
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2answers
331 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 ...
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2answers
135 views

Coercion in MAGMA

In MAGMA, if you are dealing with an element $x\in H$ for some group $H$, and you know that $H<G$ for some group $G$, is there an easy way to coerce $x$ into $G$ (e.g. if $H=\text{Alt}(n)$ and ...
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1answer
173 views

How to iterate over power set in MAGMA?

I want do something for all subsets J of a certain cardinality of {1,2,...,n}, for a (previously declared) number n. It seems magma is not happy with: for J in PowerSet([1..n]) do To which MAGMA ...
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1answer
291 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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3answers
138 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.
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1answer
98 views

How to test a formula online?

I have an equation I have devised, it is: $$\frac{H+O}{25}+\frac{D}{12970}+\frac{E}{363}+110 = X$$ The equation doesn't matter, I just posted it as an example. I need to be able to plug in values ...
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0answers
89 views

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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135 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?
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73 views

solving a matrix equation $X-I=a \cdot (X\cdot U^T + U \cdot X)$

I am trying to solve the $n \times n$ diagonal matrix $X$ in the following equation: $$X-I=a \cdot (X\cdot U^T + U \cdot X)$$ where $0<a<1$ is a given scalar, $U$ is a $n \times n$ given ...
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43 views

CAS for counting points of varieties over finite fields

I am looking for a computer algebra system, which is able to some of the following (in theory equivalent) things for a smooth projective variety defined over a finite field: -Count the number of ...
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803 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 ...
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2answers
373 views

Converting GAP groups into SAGE permutation groups.

I have been working with SAGE online, and have made some programs to test some hypothesis about finite groups. However, the pre-defined "named" groups in SAGE are quite limited (basically, the ...
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2answers
175 views

Any software package with Mordell equations implemented?

I admit I have no idea how to tag this post, but I'm looking for a CAS/number theory software package that would implement a decent algorithm for computing the integral solutions to $x^2 = y^3 - k$, ...
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1answer
1k views

Existence of non-trivial solution of Sylvester equation.

I'm trying to solve a special case of Sylvester equation in my case it looks like $$A*X=X*B$$ so it can be written in form $$A*X+X*(-B)=C$$ where C consist of all 0 items. I tried to solve it in ...
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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 ...
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3answers
372 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 ...
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0answers
917 views

Simple example application of Karush-Kuhn-Tucker conditions to minimization problem

I am wondering if there is a simple example application of the Karush-Kuhn-Tucker conditions to show that a minimum exists for a multivariate minimization/optimization problem. Could anyone suggest a ...
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1answer
498 views

Complex equation in maxima

I rested on this tutorial. After issuing the command with "solve" function: %i2 solve((a-b-sqrt(-c^2+2*c*y-y^2+r^2))^2+(d-y)^2=2*r^2*(1-cos(e)),y); The output ...
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1answer
48 views

Interpreting a chain of m's and o's from Macaulay2

This has been crossed referenced here as well in case a software developer understands this language. I am using Macaulay2 and does anyone know how to read the following? Example 1: -- ...
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1answer
171 views

The mathematics underlying this baroque expression of the double-factorial

On the OEIS page for the double factorial, there are three ways of getting the sequence in PARI. One of them is this curious bit of PARI code: ...
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1answer
212 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 ...
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1answer
308 views

How to effectively compute a periodic function?

I'm writing a program to compute a value of periodic function for any arbitrary large argument: $f(k) = (\sum_{n=1}^{2^k} n)\mod\ (10^9 + 7)$, where $n,k \in \mathbb{N} $ I know that $ f(k + P) = ...
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2answers
126 views

Representing Elementary Functions in a CAS

I've looked through several books about computer algebra. They are surprisingly scarce about how to actually represent elementary functions. Basically, as far as I understood elementary functions are ...
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1answer
199 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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731 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 $\left(\mathbb{Z}_p\times\mathbb{Z}_p\right)\rtimes_\varphi S_3$. ...
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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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1answer
126 views

Is there CAS design wisdom regarding categorizing expressions?

Is there CAS design wisdom regarding categorizing expressions? For instance. A user types in the expression $X^2 + X + 1$. Would it be best to classify it as a member of $R[X]$ (for some R, yet to ...
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1answer
162 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 + ...
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2answers
387 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 ...
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1answer
117 views

An integral evaluation

I tried my luck with Wolfram Alpha, with $p \in \mathbb{R}$ $$\int_{-\infty}^{\infty} \frac{x^p}{1+x^2} dx = \frac{1}{2} \pi ((-1)^p+1) \sec(\frac{\pi p}{2})$$ for $-1<p<1$, and doesn't exist ...
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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 ...
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0answers
200 views

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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2answers
176 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: ...
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votes
1answer
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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 ...
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1answer
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Plot Y-Range on Mathematica

I have a plot that I would like to slightly manipulate in Mathematica. Here is the code I am entering: Plot[{x, 2^x, log_2(x)}, {x, -1, 3}] As you can see $x$, $2^x$, and $log_2(x)$ are all ...
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votes
3answers
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software for algebraic simplifying expressions

I have many huge algebraic expressions such as: $$\frac{8Y}{1+x}-\frac{(1-Y)}{x}+\frac{Kx(1+5x)^{3/5}}{2}$$ where $\ ...
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2answers
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Using Wolfram Alpha For Solving A System Of Equations

How do i input the below system of equations in wolfram alpha in order to solve for the unknowns and plot them? If i just say "solve" and input these equations one after the other with a simicolen ...
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1answer
195 views

Why is $\operatorname{res}(fg,h)=\operatorname{res}(f,h)\cdot\operatorname{res}(g,h)$, where $\operatorname{res}$ stands 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
1answer
167 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 ...
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votes
2answers
301 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 ?
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1answer
318 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 ...
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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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votes
2answers
450 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 ...
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Algorithm for finding limits of compositions of simple functions?

There are two questions: Define the set $S$. Compute the limit of functions $f/g$ for functions $f,g\in S$, where $S$ is defined in the following way. All constant function are in $S$, $f(n) = ...
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271 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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1answer
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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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999 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 ...
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Computing relations on the columns of a matrix

Given an $m\times n$ (with $n>m)$ matrix $M$ over a polynomial ring $R=k[x_1,...,x_n]$, suppose that every column of $M$ is an $R$-linear combination of $m$ specified columns. I would like to ...
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votes
3answers
179 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 ...