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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CAS: Computing homology of complex of non-free abelian groups

Which computer algebra system allows me to compute the homology of a complex of finitely presented abelian groups which are not necessarily free? Sage and Magma apparently don't: see here and here. ...
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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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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, ...
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Systems of linear modular equations with unknowns in the moduli

I am interested in systems of linear modular equations, where the unknowns also appear in the moduli. The general form would be: $A \vec{x}= \vec{b} \;\textrm{mod} \; (C \vec{x}+\vec{d})$ where A ...
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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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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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320 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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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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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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”lesser known” rules to calculate the derivative

I was reading through the online help of WolframAlpha (link) and found this statement: Wolfram|Alpha calls Mathematica's $D$ function, which uses a table of identities much larger than one would ...
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Proving $n^{97}\equiv n\text{ mod }4501770$

How do we show $$n^{97}\equiv n\text{ mod }4501770$$ for all integer $n$? First of all, I thought I could use Fermat's little theorem or Euler's theorem, but I'm not sure if they are applicable here.
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Elementary “bugs” in computer algebra systems?

There's a discussion of bugs in CAS's here, but these are technical errors of interest mainly to the professional mathematician. I am more interested in simple errors which might arise in the use of ...
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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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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 ...
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135 views

Practical applications of computer algebra systems

(Sorry if this is not the correct place for the question) Are there practical applications of symbolic computation systems like Mathematica, Sage, Maxima and the like in software development? To ...
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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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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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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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Maple: How to input such system so that it would be solved?

How to input such system into maple so that it would solve it? BTW we some part of system will be given to us, which we do not know certainly - may be some $A_i$'s may be some $B_i$'s as ...
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Square-free factorization of polynomials over finite fields

For any $f\in\mathbb{F}_q[X]$, I want to derive an algorithm which computes a factorization $$f=\prod_{i=1}^kf_i^i\tag{1}$$ with square-free polynomials $f_i$. My Ideas: If $f'=0$, we're done ...
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Division by factorized polynomials in Macaulay2

I have this problem dividing by factorized polynomials, for example (x_1^4-x_2^4)//(factor(x_1^2-x_2^2)) does not work because the numerator is of "class R" (R is the ring kk[x_1..x_n]) and the ...
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Software for proving sum identites

Summations can really get complicated - esp. when you have convoluted n-fold summations with all kinds of different indices. My question: Is there some software (or add-on) with which you can find ...
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187 views

What is the difference between Set, and Class in object oriented languages?

What is the difference between Set in set theory, and Class in object oriented languages?
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Tool for construction of graph with specified properties

Is there a tool (class of algorithms for graph generation) that can construct graph with specified properties. E.g. construct graph who is homeomorphic with both to K5 and K3,3. Construct planar graph ...
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279 views

MuPAD - complicated solve() solutions

I am trying to solve an equation for one variable as shown in the picture: Judging from the output of the second command, I should be able to get an expression for $\ddot{\theta}$. I tried ...
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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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Find $k^{th}$ root of $M \in GL(n,F_2)$

Given $M \in GL(n,F_2)$ which is known to have a $k^{th}$ root. How can I find a root algorithmically? Can I find all roots? Other than being invertible and having a $k^{th}$ root I know nothing of ...
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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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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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Adjoint action of a Lie algebra in MAGMA

Let's say I have a Lie algebra $L$ and an element $x$ in $L$. I need to compute $(\mathrm{ad} \ x)^n(y)$ for several values of $y$ and a particular value of $n$. I thought the best way to do this ...
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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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What is the closed form of $\sum _{n=1}^{\infty }{\frac { {{\rm J_{0}}\left(2\,n\right)} ^{2}}{{n}^{2}}}$?

Using Maple I am obtaining $$\sum _{n=1}^{\infty }{\frac { {{\rm J_0}\left(2\,n\right)} ^{2}}{{n}^{2}}} = 0.09845497463 $$ Please check it. Many thanks.
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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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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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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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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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Indefinite integral that Wolfram Alpha can't solve

Does anybody know the indefinite integral problems that Wolfram Alpha can not solve but human can solve by using elementary functions? (The meaning of "solve" here is to represent primitive function ...
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Simple algebra in a differential equation.

I have the differential equation: $$\frac{dy}{dx}=\sin (x-y).$$ Substituting $v=x-y$ and $dy=dx-dv$, I got down to the equation:$$\frac{dv}{1-\sin(v)}=dx.$$ Multiplying the LHS by $\dfrac{1+\sin ...
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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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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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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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do we have any special algorithms or software to find all 2-sylow subgroups of a group?

I am working on a project that involves 2-sylow subgroups of groups,one thing that I need to do is to find all 2-sylow subgroups of a group and check that it is cyclic or not, now my question is that ...
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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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528 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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Derivatives of Brownian motion or Box Options Greeks

Here's the probability (I think) that a particle in Brownian motion (w/ standard deviation $\sqrt{t}$) will exceed $m$ between times $t_1$ and $t_2$: $$\frac1{2\sqrt{2\pi}}\int_{-\infty }^m ...
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Algorithms for generating $A_n$ and $S_n$ from specific generators

Is there a simple algorithm to generate the elements of the alternating group $A_n$ in terms of some small set of generators? For example, when $n = 4$, I'm looking for an algorithm whose output is a ...
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Nspire cx CAS - Laplace inverse fails

I'm trying to calculate that easy integral but I get undef. When I replaced $\infty$ with $1000$, I got the right answer. ($e^{-1000}$ is zero roughly). Although this calculator knows that ...
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Computing 2d radially symmetric Fourier transforms (with Wolfram Alpha)

Let's assume that I "know" $\mathcal{F}\{\operatorname{circ}(r)\}(\rho)=\frac{J_1(2\pi\rho)}{\rho}$ $\mathcal{F}\{(1-r^2)\operatorname{circ}(r)\}(\rho)=\frac{J_2(2\pi\rho)}{\pi\rho^2}$ because I ...
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Symbolic computations in finite fields of unspecified order

The general setting is that I want to multiply some matrices (to many to do it by hands) over a finite field. The problem is that these matrices depend on certain parameters taken from the field and ...