On 2015-04-08, Nils Bruin <[email protected]> wrote:
> On Monday, February 23, 2015 at 1:35:16 AM UTC-8, Dima Pasechnik wrote:
>>
>> This is easy at least in the sense that this is the stabiliser of 
>> a set of subsets of the variables in the symmetric group S_n (assuming 
>> you have n variables). And GAP does this for you. 
>>
>
> You'd need to be a little more careful than that. The coefficients do 
> matter:

well, the examples were just sums of monomials.

More generally, one could speak about
finding the automorphism group of the edge-coloured hypergraph, with 
edges corresponding to monomials, and edge colours corresponding to 
the coefficients of the monomials.

How does one solve this in full generality, i.e. finding the
largest subgroup of GL(V) which leaves the polynomial invariant, 
I don't really know. (Unless one resorts to solving systems of 
polynomial equations).

Dima

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