#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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Changes (by SimonKing):
* owner: malb => SimonKing
* summary: [with patch, needs work] Action of MatrixGroup on a
MPolynomialRing => [with patch, needs review]
Action of MatrixGroup on a MPolynomialRing
Comment:
Some changes:
Nicolas Thiéry suggested to implement the action of matrix groups by a
method for polynomials (I call the method `left_matrix_action`), and, for
convenience, also provide a `__call__` method for MatrixGroupElement that
refers to `left_matrix_action`.
This has several advantages:
* The `__call__` works for any class that has a `left_matrix_action`
method, hence, it is not a-priori restricted to polynomials.
* I've put `left_matrix_action` into `multi_polynomial.pyx`, hence, I can
use Cython.
I have two Cython concerns left:
1. The innerst loop is
{{{
prod([Im[k]**X[k] for k in xrange(n)])
}}}
where `k` is c'defined as `int`. Should this better be done in a for-
loop, rather then creating a list and calling `prod`?
2. The variable `X` is of type `polydict.ETuple`, so I can not directly
c'define `X`. One could do
{{{
cdef tuple X
for i from 0<i<l:
X = tuple(Expo[i])
}}}
But would this be faster?
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/4513#comment:4>
Sage <http://sagemath.org/>
Sage - Open Source Mathematical Software: Building the Car Instead of
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