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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What is a good software package for ( assisted ) theorem proving and documenting?

Background: An issue in my math study is that I haven't found a good way of storing the theorems ( mostly abstract algebra ) I studied and want to (re-)use in proofs. At the moment I use a personal ...
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Compute Automorphism Group using Computer Software

Is there a computer software that can compute Automorphism Groups. For instance $Aut(\mathbb{Z}_4\times\mathbb{Z}_2)$. I tried Sage, but could not get it to work. Output: ...
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In maple how do you evaluate combinations?

In Maple how do you have it evaluate combinatorics such as $\binom{5}{2}$ and give you the answer 10? (What is the name of what I want to do anyways, is it evaluate?) Thanks. Seems so easy now that I ...
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How do I determine if two of my software's representation of algebraic numbers are equal?

I have software which stores information about algebraic numbers with absolute precision. If you build it up by creating instances of a Python representation of an integer, float, Decimal, or string, ...
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Wolfram Alpha: How to define constants in a system of equations?

I'd like to use WA to solve a small system of nonlinear equations, that involve both constants and the variables of interest. How do I "tell" WA which variables are the constants, and which are the ...
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Coset Enumeration with GAP

I have downloaded GAP version 4.7.8. for windows, and installed everything (all packages, including"ACE") with the installer. Now I want to do a simple task, enumerating the cosets. To create a group ...
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Real valued eigenvalues in GAP?

I have a matrix in GAP, and I want its real valued eigenvalues. (Or rational approximations of them, of course.) As far as I can tell Eigenvalues(Rationals,A) only gives me the rational eigenvalues. ...
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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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An integral evaluation

I tried my luck with Wolfram Alpha, with $p \in \mathbb{R}$ $$\int_{-\infty}^{\infty} \frac{x^p}{1+x^2} dx = \frac{1}{2} \pi ((-1)^p+1) \sec(\frac{\pi p}{2})$$ for $-1<p<1$, and doesn't exist ...
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How would you represent an abstract set on a computer?

I'm trying to come up with a simple language for specifying mathematics. We can't simply define a set as a collection of objects because that's meant for human understanding and that would also lead ...
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How can I plot $y^x$?

How can I plot $y^x$? To keep things simple and to not have another $z$ variable on the other end of the equation, let's assume $y^x=10$. As long as that value is not $0$, the curve we get should look ...
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How to expand quadratic equations in Octave/Matlab?

I have some column vectors, and I put them in a row, so I have $[a \, b \, c]$. Now I want to get a matrix of the form $[a^2 \, b^2 \, c^2 \, ab \, ac \, bc]$. It is like expanding $(a+b+c)^2$, but ...
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Let $$\text{F}_{91}:=\left\{\overline{a}\in\left(\mathbb{Z}/n\mathbb{Z}\right)^\times:91\text { passes the Fermat primality test to base }a\right\}$$ and $$\text{MF}_{91}:=\left\{\overline{a}\in\left(\... 1answer 308 views Knuth-Bendix completion algorithm: word problem Can someone explain me how to set up an algorithm to find the 12 normal forms of the group A_4 by making use of the Knuth-Bendix completion algorithm? So we have that RRR=1, SSS=1 and RSRS=1. ... 1answer 43 views Specifying if a function has an elementary integral In Algorithms for Computer Algebra in the last chapter about Risch algorithm, the Rothstein-Trager method is applied to see if an elementary function has an elementary integral. For this, the ... 2answers 206 views wolfram mathematica, numerical integration, precision of a function/expression I want to obtain the best numerical approximation (up to 10 decimal place would be ok for me) to an integral:$$ \int^{\infty}_{0} f(r)r^2dr $$I am using the function f(r), which is related to ... 1answer 1k views Existence of non-trivial solution of Sylvester equation. I'm trying to solve a special case of Sylvester equation in my case it looks like$$A*X=X*B$$so it can be written in form$$A*X+X*(-B)=C$$where C consist of all 0 items. I tried to solve it in ... 1answer 1k views Algorithm for finding limits of compositions of simple functions? There are two questions: Define the set S. Compute the limit of functions f/g for functions f,g\in S, where S is defined in the following way. All constant function are in S, f(n) = n\... 1answer 41 views How to print long strings in MAGMA? I'm trying to print a very long list to a file using magma to make it "callable". The list is called F2, and the code I'm using to print this list to a file is the following ... 1answer 18 views Algorithm for computing the inverse limit of a finite inverse system Let k be a field (finite if you'd like), let (I,\le) be a finite directed poset with |I|=n, and let (A_i,f_{ij})_{i\le j\in I} be an inverse system of finitely generated, graded, commutative ... 1answer 38 views Ideal intersection in Boolean polynomial ring I'm trying to calculate  \langle x,y,z\rangle \cap \langle x+1,y+1,z+1\rangle  in the ring of Boolean polynomials. In CoCoA initially I set the ring as ... 1answer 32 views Computing Extensions of an Ideal in Singular or Macaulay2 Does Macaulay2 or Singular compute extensions of ideals under ring homomorphisms? Specifically, if \phi:R\rightarrow S is a ring homomorphism (say polynomial rings over \mathbb{Q} which can be ... 1answer 54 views Higher Level Group Actions beyond OnSets Is there a way to produce an orbit of a chain in a poset (whose elements are sets of sets) (that is, the group action is a group acting on the order complex of a poset)? I really want something that ... 1answer 74 views Math software to calculate in different rings. I was doing computational experiment by using rings of polynomial like this let f(x)=x^6+x\in\mathbb{Z_n[x]} for any given n. Is there any software which help me to calculate f(a) where a\... 1answer 50 views Variance of discrete probability distribution I was wondering how I should calculate the variance of the following discrete probability distribution:$$P(y = 0|X) = w + (1-w)e^{-\mu}P(y = j|X) = (1-w)e^{-\mu}\mu^{y}/y! \qquad j=1,2...$$... 1answer 44 views Number conversion in decimal fraction 980.85D convert to hexadecimal number = 3D4 . ?? how to solve the answer after the decimal point? Thank you in advanced. 1answer 56 views If A\ne 0 is a square matrix over a commutative ring with \det A=0, then its null space contains an element whose components are minors of A Let R denote a commutative ring and A\ne 0 a n\times n matrix over R with \det A=0. Then there exists a x\in\ker A\setminus\left\{0\right\} such that all components of x are minors of A... 1answer 102 views Number of monic irreducible polynomials over a finite field Let \mathbb{K}=\mathbb{F}_q and \nu_n denote the number of monic irreducible polynomials over \mathbb{K}. It holds$$\nu_n=\frac{1}{n}\sum_{d\mid n}\mu\left(\frac{n}{d}\right)q^d What I need ...
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Two matrices A and B are similar, if and only if there exists an invertible matrix C with $A=C^{-1}BC$. A necessary condition for the similarity is, that the characteristic polynomials coincide. I ...
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Prevent Maple to evaluate before simplify a function

I have been trying to find a domain of $f(x)=\frac{x}{\frac{(x+2)}{(x-3)}}$ using different kind of software ( its clear the domain of this function is $\mathbb{R}\backslash \{-2,3\}$ ). When I tried ...
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Computational complexity of expanding a MacLaurin/Taylor Series

What methods exist to computationally determine the first $k$ coefficients of a function (possibly polynomial or rational polynomial function)? How do Mathematica/MatLab/Maple/etc. solve this ...
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Checking if a polynomial expression is constant in SAGE

I have a huge fractional-polynomial expression in SAGE that I have good reasons to believe is the constant function. Is there a command in SAGE like "== constant function" that I could use to check ...
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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 calculate resultant of two polynomials without knowing the roots.

So in Rothstein - Trager's Method of evaluating logarithmic part they need resultant of two polynomial as shown in the image. My question is that how do they calculate the resultant without knowing ...
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Help in understanding risch algorithm

This is an excerpt from the paper that explains risch algorithm for symbolic integration. I do not understand how do we get to the residue directly and also how does it help us in the integration. ...
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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(...
I have the following problem. Let $\alpha:=\alpha(v)$ and $\beta:=\beta(v)$, where $v\in\mathbb{R}$. Using MAPLE, I would like to plot $\alpha$ and $\beta$ in the $(\alpha,\beta)$ space as $v$ varies ...