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. For questions about Mathematica please see the ...

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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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179 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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255 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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232 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 ...
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198 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 ...
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426 views

How can I get Macaulay2 to tell me if this ideal is prime?

I am trying to get Macaulay2 to confirm if $(y+zi,x^2 - z^2 - 1)$ is a prime ideal in $\Bbb{C}[x,y,z]$. Now as a small test, I tried to compute its radical by doing ...
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Looking for a binomial system solver

I am interested in solving binomial systems of the form $$ \begin{cases} a_1 x_1^{d_{11}} x_2^{d_{12}} \cdots x_n^{d_{1n}} + b_1 x_1^{d_{11}} x_2^{d_{12}} \cdots x_n^{d_{1n}} &= 0 \\ ...
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5answers
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Computer Algebra: Algorithms for solving equations symbolically

As a hobby, I have written a basic computer algebra system. My CAS handles expressions as trees. I have advanced it to the point where it can simplify expressions symbolically (i.e., sin(pi/2) ...
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98 views

Semi directProduct and Maximal subgroup in gap [closed]

Let $P$ be a quaternion of order 8 and $Q$ a cyclic group of order 9 and $G=[p]Q$, a semidirect product ($P$ is normal in $G$). Let $M$ be a maximal subgroup of $G$ such that $Q<M$. I want to ...
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2answers
801 views

Common Lisp for mathematicians?

I am interested in learning Common Lisp. There seems to be a lot of material either for (experienced) programmers, or for people with no background, in programming or in mathematics. I was wondering ...
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11k views

Wolfram Alpha: How to define constants in a system of equations?

I'd like to use WA to solve a small system of nonlinear equations, that involve both constants and the variables of interest. How do I "tell" WA which variables are the constants, and which are the ...
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182 views

wolfram mathematica, numerical integration, precision of a function/expression

I want to obtain the best numerical approximation (up to 10 decimal place would be ok for me) to an integral: $$ \int^{\infty}_{0} f(r)r^2dr $$ I am using the function $f(r)$, which is related to ...
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1answer
103 views

Symbolic manipulations of integral equations

I was trying to learn about solving integral equations using symbolic algorithms. After a quick web search, I mostly found items like this Mathematica journal article that mostly focuses on how to use ...
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2answers
233 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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200 views

Are CASs useful in mathematics?

I understand that computer-algebra systems are useful for physists, engineers, or other users of mathematics. But are they useful in mathematics itself? Specifically, Are they usually taught in ...
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168 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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292 views

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 ...
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2answers
270 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
110 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
136 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
234 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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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
86 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
81 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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112 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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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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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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607 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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296 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
169 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
947 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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'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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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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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
404 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
44 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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159 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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194 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
281 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
122 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
192 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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660 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
122 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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145 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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334 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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115 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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4answers
2k views

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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172 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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158 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: ...