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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Implement some actions in Gap

I would like to calculate, in GAP, certain permutation actions on matrices. Namely: Let $G=S_n$ be the symmetric group of degree $n$ and $\Omega=GL_n(q)$ (or a suitable subset). $G$ acts by ...
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Coercing elements into a set in MAGMA

Suppose I had a permutation group $G$ for example, that corresponded to the intersection of some elements of a list $H$ where the elements are groups. Then, if I wanted to create a set or some ...
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71 views

Discrete Fourier Transform using WolframAlpha

I tried to verify a calculation with WolframAlpha. I want to compute the DFT of $[2,3,-3,1]$. So in particular one entry of the result vector should be $2+3-3+1=3$. I don't understand why I get ...
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51 views

Get the closed form of Taylor series with Maple

Is it possible to get the closed form of Taylor series with Maple? The series command can give any given number of terms, but the question is about the closed form ...
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277 views

Solve nolinear system of equaion with c/c++ [closed]

My system of equation is like this: (x-a1)^2 + (y-b1)^2 = c1 (x-a2)^2 + (y-b2)^2 = c2 I know it is simple using matlab: ...
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Any algorithm or theorem to decide whether two functions are equivalent? [duplicate]

Any algorithm or theorem to decide whether two functions that are polynomials,rationals and analytic over $\mathbb{N}$ or $\mathbb{Q}$ or $\mathbb{R}$ or $\mathbb{C}$ are equivalent ?
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Decomposition of a polynomial over generators of an ideal

Let $f$ be a polynomial in six variables, say, over complex numbers, and $l_1$, $l_2$ are some linear forms in the same variables. If I know that polynomial $f$ belong to the ideal generated by $l_1$ ...
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47 views

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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70 views

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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88 views

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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35 views

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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324 views

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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554 views

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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factor out of an expression, a couple principal ideals, software?

I have an expression, $f$, consisting of a few rational fractions of large multivariate numerators, $n1,\,n2,\ldots \in \mathbb{Q}[a1,a2,b1,b2;Q]$ and large multivariate denominators, $d1,\,d2,\ldots ...
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48 views

How does the factor command on the TI-89 works?

So to put my question in context, I am working on the following problem. Let $N=1291233941$. Eve's magic box tells her the following three encryption/decryption pairs for $N$: $$(1103927639, ...
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34 views

Maple — Lattice Algorithms

Is there any place online where I can find the code for an algorithm which computes the shortest vector in a lattice? The library only includes the algorithm for LLL.
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29 views

How to find a $k$-basis for a quotient space of a polynomial ring by a subspace?

My question is "How to find a $k$-basis for a quotient space of a polynomial ring $R$ over $k$ by a subspace $V$?" Here the point is quotient by a subspace, not by an ideal. In Singular, there is a ...
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Derivative with respect to matrix X of Tr(A Exp(-iX)) where A in another matrix

How could I numerically evaluate $\nabla_\mathbf{X} \textrm{Tr}\left(\mathbf{A} \exp(-i \mathbf{X})\right)$? Is there a simple expression for it?
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3rd order non linear differential equation

$2f'''+f.f''=0$ The boundary conditions are given as $f(0)=r, f'(0)=0, f'(∞)=1$ , where $r$ is a constant . How can I solve this differential equation using Matlab or Mathematica ??
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What is the “cost” of computation of two special CAS algorithms

Suppose I have an integer $n$ with e.g. a large number of say decimal digits. I would like to get some information about the runtime "cost" of standard CAS algorithm which factors $n$ into primes ...
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36 views

Interpolating transformation matrices

I read not to interpolate transformation matrices by linearly interpolating. Can someone explain to me why interpolating transformation matrices by linearly interpolating the matrix components is a ...
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defining an upper bound for n-tuple

Let we have $n-tuple ~~like ~ a=(a_1,...a_n) \in N_0^n ~and ~every ~a_j < (2^{m_j} -1). $ and let suppose we have another n-tuple like $b:=(b_1,...,b_n)$ such that $ b_i \leq (2^{m_j} -1)$. I ...
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Improvement of Buchberger's Algorithm

1) Let $S(F)$ be the subset of $(k[x_1,\dots,x_n])^s$ consisting of all syzygies on the leading terms of $F=\{f_1,\dots,f_s\}$. Then every element of $S(F)$ can be written uniquely as a sum of ...
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Question about multiple solutions to a polynomial

Assume that $f(X,Y,Z,V,W)\in \mathbb{Z}[X,Y,Z,V,W]$ is some polynomial and assume that $f(x,y,z,v,w)=0$. I would like to know if there is some way to figure out if there are non-trivial constants in ...
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Gram-Schmidt-procedure with PARI/GP

Can the Gram-Schmidt-procedure to find an orthogonal basis of a vector space spanned by given linear independent vectors be easily done in PARI /GP or do I have to program the procedure ?
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66 views

Can a Computer Algebra System 'experiment' with expressions?

I have recently been reading about software for symbolic manipulation, and I can see its use as a tool for performing large calculations that would be unfeasible otherwise. Given that these systems ...
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171 views

Marking the roots of a quadratic function in Scilab

I have 2D plotted a simple quadratic function in Scilab and now have to mark the roots with an X. Is there any simple way of doing that? I have written a function that calculates the roots and ...
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42 views

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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66 views

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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60 views

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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33 views

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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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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62 views

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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135 views

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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113 views

How to solve an equation in three variables fixing two of the variables?

Also, I have the following equation, I want to solve it for $b$ keeping $a$ and $c$ fixed. $5b^5+(60-5a)b^4+(125+50c-80a)b^3+(594c-445a-775)b^2+(2324c-1005a-3270)b+3000c-750a-3000=0.$ Also how to ...
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how to solve two's complement question?

i tried 9 D + (-10 D) 9= 0000 1001 10= 0000 1010 Reverse 10 = 1111 0101 and add 1 become 1111 0110 after that add up 9 D + (-10 D) == 0000 1001 + 1111 0110 but the answer is equal to 1111 1111 ...
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266 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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Verification of $F(m)^{d} \pmod n \equiv m$ with very large inputs, where $F(m)=m^e$

Does anyone have the computational power to check whether or not $F(m)^{d} \pmod n \equiv m$, where the values of the variables are found below. According to Wolfram Alpha, I found the result of the ...