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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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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Splitting even degree polynomials

I have an octic equation (degree $8$) and a sextic equation (degree $6$) in $\Bbb Z[x]$ with very large coefficients (size several hundred bits) that I know splits into two quartics and two cubics ...
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91 views

Advantages to learning Sage?

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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2answers
42 views

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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22 views

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 ...
2
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29 views

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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1answer
49 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 ...
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35 views

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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62 views

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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71 views

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 ...
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20 views

factor out of an expression, a couple principal ideals, software?

I have an expression, $f$, consisting of a few rational fractions of large multivariate numerators, $n1,\,n2,\ldots \in \mathbb{Q}[a1,a2,b1,b2;Q]$ and large multivariate denominators, $d1,\,d2,\ldots ...
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42 views

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 ...
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2answers
75 views

”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 ...
2
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1answer
77 views

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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1answer
101 views

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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1answer
46 views

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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72 views

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 ...
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49 views

How does the factor command on the TI-89 works?

So to put my question in context, I am working on the following problem. Let $N=1291233941$. Eve's magic box tells her the following three encryption/decryption pairs for $N$: $$(1103927639, ...
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24 views

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: ...
3
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1answer
122 views

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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48 views

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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34 views

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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43 views

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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29 views

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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23 views

Derivative with respect to matrix X of Tr(A Exp(-iX)) where A in another matrix

How could I numerically evaluate $\nabla_\mathbf{X} \textrm{Tr}\left(\mathbf{A} \exp(-i \mathbf{X})\right)$? Is there a simple expression for it?
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50 views

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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100 views

finding roots of polynomial in MAGMA or GAP

Please hint me. I want to find the roots of $x^3+(1-2n)x^2-(1+4n)x+8n^2-10n-1$ with Magma or GAP. In Magma: $P<x> := PolynomialRing(Rationals())$; $P<n>:= ...
2
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1answer
75 views

do we have any special algorithms or software to find all 2-sylow subgroups of a group?

I am working on a project that involves 2-sylow subgroups of groups,one thing that I need to do is to find all 2-sylow subgroups of a group and check that it is cyclic or not, now my question is that ...
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31 views

Is there some database or software to look for patterns in polynomials?

Like if I am looking at these polynomials, $$x^8-8x^6+20x^4-16x^2+3$$ $$x^{10}-12x^8+48x^6-72x^4+33x^2$$ $$x^{12}-16x^{10}+88x^8-192x^6+138x^4$$ And I want to know if they are members of some ...
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36 views

Lower bounds on possible integer relations from the PSLQ algorithm

For the equation: $$ \sum_{i=1}^na_ix_i=0 $$ where all $x_i$ are real numbers and all $a_i$ are integers, the PSLQ algorithm can either find an integer relation or give lower bounds on the norm of ...
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368 views

How to efficiently represent and manipulate polynomials in software?

I've started to work on a package (written in matlab for now) that among other things must be able to represent and manipulate (compare, add, multiply, differentiate, etc) polynomials in several ...
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3rd order non linear differential equation

$2f'''+f.f''=0$ The boundary conditions are given as $f(0)=r, f'(0)=0, f'(∞)=1$ , where $r$ is a constant . How can I solve this differential equation using Matlab or Mathematica ??
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66 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 ...
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59 views

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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148 views

Computing a nasty integral (probably with computer algebra system)

I'm trying to do this integral, not sure if it is possible: $$ \int_{1}^{\infty}\int_{0}^{\infty} \exp\left(\, -\,{x^{2} \over y^{2}}\,\right) \exp\left(\,-\,{y^{2} \over z^{2}}\,\right) \exp\left(\, ...
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2answers
953 views

Nspire cx CAS - Laplace inverse fails

I'm trying to calculate that easy integral but I get undef. When I replaced $\infty$ with $1000$, I got the right answer. ($e^{-1000}$ is zero roughly). Although this calculator knows that ...
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44 views

What is the “cost” of computation of two special CAS algorithms

Suppose I have an integer $n$ with e.g. a large number of say decimal digits. I would like to get some information about the runtime "cost" of standard CAS algorithm which factors $n$ into primes ...
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1answer
36 views

Interpolating transformation matrices

I read not to interpolate transformation matrices by linearly interpolating. Can someone explain to me why interpolating transformation matrices by linearly interpolating the matrix components is a ...
0
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1answer
51 views

Get the closed form of Taylor series with Maple

Is it possible to get the closed form of Taylor series with Maple? The series command can give any given number of terms, but the question is about the closed form ...
3
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38 views

Tool for construction of graph with specified properties

Is there a tool (class of algorithms for graph generation) that can construct graph with specified properties. E.g. construct graph who is homeomorphic with both to K5 and K3,3. Construct planar graph ...
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1answer
277 views

Solve nolinear system of equaion with c/c++ [closed]

My system of equation is like this: (x-a1)^2 + (y-b1)^2 = c1 (x-a2)^2 + (y-b2)^2 = c2 I know it is simple using matlab: ...
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1answer
17 views

Verification of $F(m)^{d} \pmod n \equiv m$ with very large inputs, where $F(m)=m^e$

Does anyone have the computational power to check whether or not $F(m)^{d} \pmod n \equiv m$, where the values of the variables are found below. According to Wolfram Alpha, I found the result of the ...
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1answer
65 views

Any algorithm or theorem to decide whether two functions are equivalent? [duplicate]

Any algorithm or theorem to decide whether two functions that are polynomials,rationals and analytic over $\mathbb{N}$ or $\mathbb{Q}$ or $\mathbb{R}$ or $\mathbb{C}$ are equivalent ?
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119 views

MuPAD - complicated solve() solutions

I am trying to solve an equation for one variable as shown in the picture: Judging from the output of the second command, I should be able to get an expression for $\ddot{\theta}$. I tried ...
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1answer
178 views

MuPAD - rearrange an equation

I have a huge expression, say $f(x_1,x_2,x_3) = 0,$ and I want MuPAD to try to express $x_1 $ in terms of $x_2$ and $x_3$ Is this possible?
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2answers
66 views

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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20 views

defining an upper bound for n-tuple

Let we have $n-tuple ~~like ~ a=(a_1,...a_n) \in N_0^n ~and ~every ~a_j < (2^{m_j} -1). $ and let suppose we have another n-tuple like $b:=(b_1,...,b_n)$ such that $ b_i \leq (2^{m_j} -1)$. I ...
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1answer
39 views

Variance of discrete probability distribution

I was wondering how I should calculate the variance of the following discrete probability distribution: $$P(y = 0|X) = w + (1-w)e^{-\mu}$$ $$P(y = j|X) = (1-w)e^{-\mu}\mu^{y}/y! \qquad j=1,2...$$ ...
2
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26 views

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 ...