# Tagged Questions

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 http://mathematica....

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### Most wanted reproducible results in computational algebra

I am interested in suggestions for major computational results obtained with the help of mathematical software but not easily verifiable using computers. "Most wanted" could refer, for example, to ...
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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 Res(...
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### Can you recommend a decent online or software calculator?

I'm looking for an online or software calculator that can show me the history of items I typed in, much like an expensive Ti calculator. Can you recommend any?
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### What are some good iPhone/iPod Touch/iPad Apps for mathematicians? [closed]

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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### 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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### 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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### What free software can I use to solve a system of linear equations containing an unknown?

Question: What free software can I use to solve a system of linear equations $M\mathbf{x}=\mathbf{y}$ where the entries of $\mathbf{y}$ vary with an unknown quantity $n$? Presumably I could do this ...
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### Wisdom of using Sympy as a first CAS

I'm an undergrad. maths student and have been looking at a few different free maths programs (mainly CAS systems, I've been very impressed with Octave as a MATLAB clone.) I've been tossing up between ...
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### Computer Algebra Systems for Experimental Mathematics (especially Integer Relations with PSLQ)

I would like to use a computer algebra system to do some experimental mathematics, particularly Integer Relation problems using the PSLQ algorithm. I know that Maple has a PSLQ implementation, but I'...
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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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### 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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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 $$p(x_1,x_2,x_3,x_6)=\frac{1}{12}(x_1^6 + 3x_1^... 1answer 64 views ### What is sample variance of sample variance, and what is theoretical sampling distribution? I am trying to work some things in R and I am having trouble understanding some of the instructions. I generated 1000 samples of size 5 from the standard normal distribution, and I calculated the ... 2answers 244 views ### Simple generators with a complex Gröbner basis It's known that finding a GrÃ¶bner basis of a polynomial ideal has a worst-case space complexity of O(2^{2^{c\cdot n}}), where c is constant and n is the number of variables k[x_1,\ldots,x_n]. ... 1answer 485 views ### Computing 2d radially symmetric Fourier transforms (with Wolfram Alpha) Let's assume that I "know" \mathcal{F}\{\operatorname{circ}(r)\}(\rho)=\frac{J_1(2\pi\rho)}{\rho} \mathcal{F}\{(1-r^2)\operatorname{circ}(r)\}(\rho)=\frac{J_2(2\pi\rho)}{\pi\rho^2} because I ... 1answer 419 views ### In SAGE, what function factors a polynomial whose coefficients are parameters? In SAGE the function "factor" will factorize elementary polynomials with coefficients in \Bbb Q. For example: x,y = var('x,y') poly = x^3-y^2*x factor(poly) SAGE: x*(x-y)*(x+y) ... 2answers 102 views ### Simple algebra in a differential equation. I have the differential equation:$$\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.$$Multiplying the LHS by \dfrac{1+\sin (v)}{... 2answers 2k views ### How to define a recurrence relation in Maple? I'm new with Maple and want to define a recurrence relation. I want to 1) have Maple solve it to the explicit formula 2)have Maple output a few evaluations of it for various values of ... 1answer 248 views ### Computing univariate resultant via modified Euclidean algorithm In an answer to the question Resultant of Two Univariate Polynomials, a PDF of course slides was linked which describes a modification of Euclid's algorithm for computing univariate polynomial ... 1answer 313 views ### How to effectively compute a periodic function? I'm writing a program to compute a value of periodic function for any arbitrary large argument: f(k) = (\sum_{n=1}^{2^k} n)\mod\ (10^9 + 7), where n,k \in \mathbb{N}  I know that  f(k + P) = f(... 1answer 129 views ### Is there CAS design wisdom regarding categorizing expressions? Is there CAS design wisdom regarding categorizing expressions? For instance. A user types in the expression X^2 + X + 1. Would it be best to classify it as a member of R[X] (for some R, yet to ... 2answers 62 views ### How do I include an integer constraint in Wolfram Alpha? Related question: Tell Wolfram Alpha that a variable is a natural number I want to do the following in Wolfram Alpha: Minimise$$z = (y_1-x_1)+(x_2-y_2)+(1/2)(x_3)$$s.t.$$0 \le ...
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) = x^2-y^2+\frac{x^2-y^2}{(x^2+y^2)^...