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Dear friends, I recently answered a query concerning the action of the automorphism group of the Petersen graph on its edges at stackexchange.com. The algorithm that I present is quite naive, but it does produce the desired result. I thought I would share it here because it makes a nice Maple programming exercise e.g. for a talented student at high school level. ...

I consider a polynomial $P(x)$ such that their coefficients are in $\mathbb{Q}(u_1,\cdots,u_k)$ where $u_1,\cdots,u_k$ are complex parameters. I use in Maple the command $galois(p(x),x)$ and I obtain a fixed Galois group solution.  Fortunately, when I give explicit values (randomly chosen) to the $(u_i)_i$, I obtain always the previous group as Galois group. I think that Maple considers that the $(u_i)_i$ satisfy no algebraic equations, that is the $(u_i)_i$ are generic....

Is there a possibility in Maple to define a set of elements using a rule or semanticdescription. The problem is that  I need to define a set of numbers of the concrete form (e.g. of the form a+b\sqrt[3](2)). Or more complecated task: the set of pairs (a,b) where a,b::integer. And then I need to define an abstract operation on that set. I explain: my global task is to create a procedure to define whether a set with an operation is a group (where a set is defined using a rule).

A simple question. I have this:

k*(2x+y-3z+2)+s*(5x+5y-4z+3)=0

And I want to group it by x, y, z, so that I would get:

x*(2k+5s)+y(k+5s)...=0

I'm using Maple 11.

I'm trying to make a Cayley table with a group of permutations (Specifically S₃ and A₄) and can't figure it out.  I've been looking through the help without much success.  Here is the code I have so far:

Matrix(nops(permgroup(6, {[[1, 2]], [[2, 3]]})), proc (i, j) options operator, arrow; multperms(i, j, permgroup(6, {[[1, 2]], [[2, 3]]})) end proc)

Thanks