11
$\begingroup$

Let $V$ be a polynomial representation of the general linear group $\Gamma:=\DeclareMathOperator{\Gl}{Gl}\Gl_n(\newcommand{\C}{\mathbb C}\C)$.

In chapter 4.6 of his book "Algorithms in Invariant Theory", Bernd Sturmfels describes an algorithm he calls Hilbert's Algorithm, which calculates a finite set of generators for the ring of invariants $$\C[V]^\Gamma = \left\{~ f\in\C[V] ~:~ \forall\gamma\in\Gamma:~ \gamma.f=f ~\right\}.$$ My question: Are there any software implementations of this algorithm (or, of any algorithm that does the same thing) in computer algebra systems? I would prefer free software, but if the only implementation is in a commercial product, I'd still use it.

Improve this question
$\endgroup$
1
  • 1
    $\begingroup$ I have no useful comment on this very interesting question (although I think I heard people talking about implementing this recently at a Macaulay2 conference -- but it's not there yet), but I thought it might be worth remarking that this appears to me to be the 5000th question in ag.algebraic-geometry. $\endgroup$
    – Karl Schwede
    Commented Sep 11, 2012 at 4:14

3 Answers 3

Reset to default
3
$\begingroup$

Magma (not free, unfortunately) is capable of this. The method FundamentalInvariants(R) : RngInvar -> RngMPol should do what you need.

Improve this answer
$\endgroup$
1
$\begingroup$

http://arxiv.org/abs/1101.0622

Improve this answer
$\endgroup$
1
$\begingroup$

I dont know whether this helps : http://www.sciencedirect.com/science/article/pii/S074771711200079X

Improve this answer
$\endgroup$

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .