# 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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### 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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### How does GAP understand $SL_2(\mathbb{F}_3)$?

When one is asking for " IrreducibleRepresentations(SL(2,3))" it makes sense that the matrices it returns are over the complex field as thats the field on which the representations are. There GAP uses ...
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### ”lesser known” rules to calculate the derivative

I was reading through the online help of WolframAlpha (link) and found this statement: Wolfram|Alpha calls Mathematica's $D$ function, which uses a table of identities much larger than one would ...
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### Practical applications of computer algebra systems

(Sorry if this is not the correct place for the question) Are there practical applications of symbolic computation systems like Mathematica, Sage, Maxima and the like in software development? To ...
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### Given the graph below, use Dijkstra’s algorithm to find the shortest path (More details included)

So I've found out a few things and was wondering if someone could verify if I'm doing this correctly. So here is an example I've been given: Here is the solution to that example: Now here is the ...
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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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### 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 {1.5+...
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### Generating a 2D coordinate from a 1D Index

Imagine you have a 5x5 matrix (zero indexed), where only the upper right coordinates are valid. I am unsure if this is the terminology to use, so the following coordinates should be the valid ones: <...
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### What is the difference between Set, and Class in object oriented languages?

What is the difference between Set in set theory, and Class in object oriented languages?
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### Understanding BlowUp Computation in Singular

Many of us might know that "Singular" is a computer algebra system for Algebraic Geometry, Commutative Algebra and Non-commutative algebra. This is a procedure in "Singular" for computing blowups. ...
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### 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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### Is there any Software package to confirm correctness of your derivation steps?

Suppose I made a very complicated (not necessarily difficult) derivations in which it is very likely for anyone to make some silly mistakes, e.g., incorrect sign, overlooking a term, and so on. I ...
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### 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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### Algorithms for generating $A_n$ and $S_n$ from specific generators

Is there a simple algorithm to generate the elements of the alternating group $A_n$ in terms of some small set of generators? For example, when $n = 4$, I'm looking for an algorithm whose output is a ...
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### Is there any efficient progam or software to calculate the fractional chromatic number?

The fractional chromatic number $\chi_f(G)$ is a generation of the chromatic number of a graph $G$. It can be formulated as a linear programming question: Let $\mathcal{I}(G)$ be the set of all ...
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### Improvement of Buchberger's Algorithm (second part)

Suppose $S_j$ is a homogeneous syzygy of multidegree $\gamma_j$ in $S(G)$, where $G=\{g_1,\dots,g_t\}$. Show that $S_j G=\Sigma_{i=1}^{t} c_ix^{\alpha(i)}g_i$ has multidegree $< \gamma_j$. Now, I ...
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 $l_1$ ...