#4513: [with patch, needs review] Action of MatrixGroup on a MPolynomialRing
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Reporter: SimonKing | Owner: SimonKing
Type: enhancement | Status: new
Priority: major | Milestone: sage-3.2.1
Component: commutative algebra | Resolution:
Keywords: matrix group, action, polynomial ring |
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Comment (by SimonKing):
Replying to [comment:6 SimonKing]:
> One observation:
> Reverse the outer loop
> {{{
> for i from l>i>=0:
> X = tuple(Expo[i])
> c = Coef[i]
> for k from 0<=k<n:
> if X[k]:
> c *= Im[k]**X[k]
> q += c
> }}}
> It results in a further improvement of computation time. Is this
coincidence? Or is it since summation of polynomials should better start
with the smallest summands?
I made a couple of tests, and there was a small but consistent
improvement. So, in the third patch (to be applied after the other two) I
did it in that way.
The `left_matrix_action` shall eventually be used for computing the
Reynolds operator of a group action; moreover, the Reynolds operator
should be applicable on a ''list'' of polynomials. Then, the function
would repeatedly compute the image of the ring variables under the action
of some group element. But then it would be better to compute that image
only ''once'' and pass it to `left_matrix_action`. The new patch provides
this functionality. Example (continuing the original example):
{{{
sage: L=[X.left_matrix_action(g) for X in R.gens()]
sage: p.left_matrix_action(L)
x^3 + x^2*y - x*y^2 - y^3
}}}
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/4513#comment:7>
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Sage - Open Source Mathematical Software: Building the Car Instead of
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