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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Relationship between the Carmichael function and Euler's totient function

Let $\lambda$ denote the Carmichael function and $\varphi$ Euler's totient function. Furthermore, let $p$ denote any prime number and $k\in\mathbb{N}$. The wikipedia article about $\lambda$ states: ...
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Simplify basic expression

Please, does anyone know which tool can simplify expressions like: $$a^4 - 4a^3b + 6a^2b^2 - 4ab^3 - a + b^4$$ into: $$(a - b)^4 - a$$ I tried SymPy, Maxima and W|A without success. PS: I'm ...
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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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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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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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Maple: How to turn a set of vectors into a matrix?

In Maple the command NullSpace turns a given matrix into a set of vectors -- a basis for its null space. This is precisely what it should in a mathematical sense. However, for computations using the ...
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How to reduce a graph via decomposition?

Is there a Java / C# library that can be used to reduce a graph via decomposition? Or could someone point me to a good tutorial where I can learn all these? E.g.
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Risch differential equation algorithm by Bronstein

I was implementing the algorithm by Manuel Bronstein for solving the Risch differential equation. My question is: What does Bronstein mean by "Order" in the algorithm poly_DE (exponential case, ...
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Changing the “Type” of an object in Magma

The computer algebra system Magma can store groups as one of many different types. For example, using AbelianGroup([2,2]) we obtain the Klein $4$-group stored as type GrpAb. However, we can also ...
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Why $face_w(New(f))=New(in_w(f))$?

Is there anyone who can help me with this problem? Any hint to the solution would be appreciated! Let $f\in \Bbb K[x_1,\ldots,x_n], w\in \Bbb R^n$ and $New(f)$ be the Newton polytope of $f$. Why ...
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Why are these CAS calculated integrals equal

I let Wolfram evaluate this integral: $$\int\frac{-2\sin(x)\cos(x)}{2\cos^2(x)+\cos(x)-1}dx$$ 1st result from WolframAlpha online was $$\frac43 \log(\cos(\frac{x}2))+\frac{1}{3\log(1-2 \cos(x))}+C$$ ...
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Graded piece of ring in Macaulay2

I apologize for the basic question, but I couldn't figure how to do this. I'm looking at the homogenous ring $R = QQ[w,x,y,z]$, I take $I = ideal(w*z-x*y)$ and $S=R/I$. Then I construct some ideal $J$ ...
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Computing univariate resultant via modified Euclidean algorithm

In an answer to the question Resultant of Two Univariate Polynomials, a PDF of course slides was linked which describes a modification of Euclid's algorithm for computing univariate polynomial ...
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How to get 2 percentages to a 100%

First of im new to this site and I've never been the sharpest at math, im a web developer by trade. My question is math related but ill just give you a quick background about my website so that you ...
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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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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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Coercing a vector into a module in MAGMA.

Given a $1\times n$ row vector $v$ over a ring $R$, and an $n$-dimensional $R$-module $M$, is there any way to coerce the vector $v$ into $M$ (the obvious $M!v$ does not work).
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Can Maple solve recurrence relations when n is only certain numbers?

If you have an equation $a(n)=a_{n-1}+2a_{n-2}$ only defined when n is powers of 2, how would convey that to Maple that n has a restriction? What if you wanted only $n \ge 2$?
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R code for triple integration

I am trying to write R code for triple integration. Here, I am just using a simple function as an example: f(x,y,z) = x^2*y+z. Here's what I have : fvec = function(x,y,z) sapply(x, function(t,y,z) ...
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Evaluating polynomials at elements of algebras in Magma

I've defined a $2$ dimensional algebra, $A$ in Magma as follows: R:=FieldOfFractions(PolynomialRing(GF(2),10)); A:=Algebra< R,2|[1,0,0,1,0,1,1,1]>; The sequence of $1$'s and $0$'s just ...
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Picking out Vector Coefficients in Magma

Suppose $K/k$ is a finite field extension, with fixed basis $e_1,\ldots,e_d$, and $f\in K[x_1,\ldots,x_n]$. Using our basis, $f$ has a unique expression as a sum of polynomials in ...
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How to use computer software for q-series calculations?

I have been reading about the dissections of cranks and there are lot of calculations with q-series identities which are very tedious by hand. What kind of computer algebra packages can we use in ...
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Computing a linear combination in $\mathbb{Z}_p[r,s,t,u,v]$

Let $F, f_1, \ldots f_5$ be polynomials in $\mathbb{Z}_p[r,s,t,u,v]$, the ring of polynomials in 5 variables over the integers modulo an odd prime $p$. By forming the ideal $J:=< f_1, \ldots ...
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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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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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176 views

A (contour?) integration (even if by using Mathematica!)

I need to be able to calculate integrals of this type where the sum over $R$ is the sum over representations of a Lie group $G$ on whom $dU$ is the Haar measure and $\chi _ R ()$ is the character of ...
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How are arrays defined with GAP? [closed]

Is it possible to define arrays in GAP ? If not what is the replacement ?
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Computing permutations

For a given permutation $\pi\in S_n$ I want to compute as many representations by products of transpositions of the form $(1, k)$ for $k\in\{2,...,n\}$ as possible. Is there any known ...
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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 ...