# 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 ...

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### 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 ...
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### Algorithm for computing an inverse image

Let $k$ be a field (finite if you'd like), and let $f:A\to B$ be a map of graded, commutative $k$-algebras. Suppose further that $A$ is finitely generated and choose a presentation ...
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### Cannot open Singular in a running emacs [closed]

I am a newbies in Singular. I just downloaded Singular4-0-2_64.dmg, mounted the image, right-ckick, show the package contents, then moved the contents folder to the Applications directory. ...
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### 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 ...
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### 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 ...
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### Line representation - implicit form

I am going through one of the the scan conversion techniques and it mentions the implicit equation of line as follows: $$F(x,y) = ax + by + c = 0 .$$ The text also mentions that $F(x,y)=0$ if the ...
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### Quasi canonical isomorphisms between finite groups and subgroups of the symmetric group?

I'm implementing finite groups in Forth for my blog and since any group is a subgroup of a permutation group it make sense to let the standard elements be permutation schemas: ...
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### Significance of various lex sort on polynomials

I have just finished writing a monomial order sort package for Maxima CAS which supports variety of lexicographic orders. But I want to know what are the uses of these sorts on polynomials. One that ...
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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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### Can Any System Of Equations Be Solved By Any Variable First?

Suppose we have a system of equations with an arbitrary number of variables, but assume it is solvable for each variable (e.g. the system will have as many equations as variables and will have at ...
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### How to create a matrix in pari/gp [closed]

How does one create a matrix in $\texttt{pari}$? I currently understand how to create a vector: ? vector(6,n,n^2) %1 = [1, 4, 9, 16, 25, 36] I also know how ...
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### Looking Portable Mathematical Notation(s) [LaTeX, Mathematica, Maple, Macsyma] that are open

I'm looking for a portable Mathematical notation. What I mean by that is: I want to create a collection of (open-source) math problems that can be: Rendered for the Web or say in ePS format for ...
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### Finding integer solutions to $y^2=x^3+7x+9$ using WolframAlpha

I am an unconditional admirer of WolframAlpha and for this reason I want to let the people of this error (or is it really the fault of mine?). If I'm not mistaken, I would be very happy to contribute, ...
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### GAP Most efficient way to check multiple properties of a group in the small group library

In GAP I would like to search the small groups library looking for groups with specific properties (I suppose this is the most common usage). If I have a list of properties I want to test, what is ...
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### (online) Tool to calculate $E(\mathbb{Q})/2E(\mathbb{Q})$ for $E: y^2 = x(x^2 + 3x + 5)$

For some exercise I need to compute the generators of $E(\mathbb{Q})/2E(\mathbb{Q})$, where $E: y^2 = x(x^2 + 3x + 5)$ I did this by the approach from Cassels book 'Lectures on Elliptic Curves' and ...
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### Numerical intergration of a complex, oscillatory function (Bessel function, Singularities)

I am working on a university project at the moment and at some point I needed to calculate the intergral of the following function (Please refer to "Bakthiari et al. - Analysis of radiation from an ...
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### UFD test - software? [closed]

I have a quotient of a polynomial ring. I would like to check if it is a UFD. Is there software that will allow me to do that?
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### Simplify fog type function chain using sympy

I need to simplify some lengthy $fog(x)$ where both $f(x)$ and $g(x)$ are known rational polynomial in one variable. For e.g. $f(x) = (7x-9)/12$ and $g(x) = (2x-5)/7$. Then I would like to get a ...
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### 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 ...
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### Nullified terms of this polynomial?

This the polynomial: $6 + 3x - 5y + 7xy -8x^2 + 3y^2 + 4x^2y - 7xy^2 + 9x^3 - 5x^4 + 8y^4x$ I would like to know which terms are there (so that I will form the complete polynomial, with zero as a ...
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### How can I find an approximation for y(1) using MATLAB without ODE solvers? (Euler's Method & Matrices)

Task: Given \begin{align*} y(t+h)&\approx \underbrace{\left(\begin{matrix}1-h & 5h & h\\3h & 1-h & 0\\0 & -th & ...
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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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### 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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### 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 to name the branch of the Lambert W function?

The Lambert W function has two real branches: the principal branch and the secondary real branch: the former is denoted by $W_0$ or $W$, the latter by $W_{-1}$. How do we name them ? For example, we ...
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### Indefinite integral that Wolfram Alpha can't solve

Does anybody know the indefinite integral problems that Wolfram Alpha can not solve but human can solve by using elementary functions? (The meaning of "solve" here is to represent　primitive function ...
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### Systems of linear modular equations with unknowns in the moduli

I am interested in systems of linear modular equations, where the unknowns also appear in the moduli. The general form would be: $A \vec{x}= \vec{b} \;\textrm{mod} \; (C \vec{x}+\vec{d})$ where A ...
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### induced group actions in GAP

Suppose $G$ is a permutation group acting on some set (for example, $G$ could be the automorphism group of a graph, acting on its vertices). Suppose $G$ also acts on some collection $\Sigma$ of ...
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### Computing group cohomology in magma?

I don't how to construct a group module in MAGMA. Can someone show me how to compute group cohomology using MAGMA? For example, I am interested in the action of finite p-groups on abelian p-groups, ...
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### standard notation to handle representation of a real number on a computer

Is there a standard notation to handle the effective representation of some real number $x$ on a finite machine ? I have in mind some kind of braces, but I am not sure it is appropriate. Let me try to ...
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### How to calculate the polynomial coefficients of a fraction of polynomials?

I have a polynomial fraction which results in a polynomial $$\frac{f(x)}{g(x)}=q(x)$$ with $f$ $g$ and $q$ being polynomials. I have formulas for the coefficients of $f(x)$ and $g(x)$ dependent on 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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I'm wondering if anyone can let me know advantages to installing/setting up Sage on my computer for doing computational math (work in groups, finite fields, and combinatorics, along with some search ...
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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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### Determining equations for Lie symmetries

Am I right that using methods of the 1-forms (that usually implemented in system of computer algebra for Lie Symmetries), we can always generate determining equations for ODE, that solved for highest ...
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### Can SAGE or othe software compute or guess growth rates of infinite discrete groups?

I am interested in the growth rate of some finitely generated (infinite, non-abelian) discrete groups. Knowing very little about geometric group theory, I am wondering if I can plug them into sage and ...
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### signature function of Weyl group element in LieArt

I am currently using LieArt Mathematica package for some calculations in Lie algebra, I am wondering if there is a way to know what is the signature of a Weyl group element, it seems the package can ...
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### 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 ...
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### Maxima CAS and programmatically defining a function with a variable number of arguments. -?

This is a very simplified question of what I had asked. In Maxima, how can I include a for-loop counter in the left-hand side of an assignment, e.g. ...
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### Any mathematical software to verify no unique products.

Let $D^3= D \times D \times D$ where $D = D_\infty$ where we see $D$ as the group generated by $\mathbb{Z}$ and element $0^*$ of order $2$ such that $0^*n0^*=-n$ for all $n \in \mathbb{Z}$. Letting ...
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### Help with Math software (macaulay 2)

I just started working with Macaulay 2 and need some help. I need to find the number of solutions of a system of equations. I am having difficulty imputing this into the software so please be specific ...