#4513: Action of MatrixGroup on a MPolynomialRing
-------------------------+--------------------------------------------------
Reporter: SimonKing | Owner: tbd
Type: enhancement | Status: new
Priority: major | Milestone:
Component: algebra | Keywords: matrix group, action, polynomial ring
-------------------------+--------------------------------------------------
A group of n by n matrices over a field K acts on a polynomial ring with n
variables over K. However, this is not implemented yet.
Off list, David Joyner suggested to implement it with a `__call__` method
in `matrix_group_element.py`. Then, the following should work:
{{{
sage: M=Matrix(GF(3),[[1,2],[1,1]])
sage: G=MatrixGroup([M])
sage: g=G.0
sage: p=x*y^2
sage: g(p)
x^3 + x^2*y - x*y^2 - y^3
sage: _==(x+2*y)*(x+y)^2
True
}}}
Although it concerns `matrix_group_element.py`, I believe this ticket
belongs to Commutative Algebra, for two reasons:
1. An efficient implementation probably requires knowledge of the guts of
MPolynomialElement.
2. My long-term goal is to re-implement my algorithms for the computation
of non-modular invariant rings. The current implementation is in the
`finvar.lib` library of Singular -- the slow Singular interpreter
sometimes is a bottle necks.
One more general technical question: It is `matrix_group_element.py`,
hence seems to be pure python. Is it possible to define an additional
method in some `.pyx` file using Cython? I don't know if this would be
reasonable to do here, but perhaps this could come in handy at some
point...
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/4513>
Sage <http://sagemath.org/>
Sage - Open Source Mathematical Software: Building the Car Instead of
Reinventing the Wheel
--~--~---------~--~----~------------~-------~--~----~
You received this message because you are subscribed to the Google Groups
"sage-trac" group.
To post to this group, send email to [email protected]
To unsubscribe from this group, send email to [EMAIL PROTECTED]
For more options, visit this group at
http://groups.google.com/group/sage-trac?hl=en
-~----------~----~----~----~------~----~------~--~---
