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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symbolic computation program/software

What is your recommended symbolic computation program/software for free and commercial respectively? What are its strength and weakness? For example, efficiency, comprehensiveness, etc Thanks!
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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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Resultant of Two Univariate Polynomials

I am trying to implement an algorithm for computing Res(f(x),g(x),x) where f(x) and g(x) uni variate polynomials with integer coefficients. Could any one list the various algorithms for computing ...
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What are some good iPhone/iPod Touch/iPad Apps for mathematicians?

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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What is the closed form of $\sum _{n=1}^{\infty }{\frac { {{\it J}_{0}\left(n\right)} ^2}{{n}^4}}$?

Using Maple I am obtaining the numerical approximation $$0.5902373619$$ Please, let me know what is the closed form. Many thanks.
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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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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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Erroneous numerical approximations of $\zeta\left(\frac{1}{2}\right)$?

By definition of the Riemann Zeta Function, $$\zeta\left(\frac{1}{2}\right) = \sum_{n=1}^\infty \frac{1}{\sqrt{n}}.$$ Since $\forall n \geq 1 : \frac{1}{\sqrt{n}} \geq \frac{1}{n}$, we have that for ...
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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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2answers
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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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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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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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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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2answers
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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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How to define a recurrence relation in Maple?

I'm new with Maple and want to define a recurrence relation. I want to 1) have Maple solve it to the explicit formula 2)have Maple output a few evaluations of it for various values of ...
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2answers
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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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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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In SAGE, what function factors a polynomial whose coefficients are parameters?

In SAGE the function "factor" will factorize elementary polynomials with coefficients in $\Bbb Q$. For example: x,y = var('x,y') poly = x^3-y^2*x factor(poly) SAGE: x*(x-y)*(x+y) ...
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1answer
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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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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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Does MAPLE not simplify correctly or am I goofing?

While attempting to answer this question with help of MAPLE, something very strange happened, at least according to me. We have the following function: $$ \phi(x,y) = ...