Hi David,
On Nov 24, 10:38 pm, "David Joyner" <[EMAIL PROTECTED]> wrote:
> The commands at
> http://www.singular.uni-kl.de/Manual/latest/sing_1083.htm#SEC1142
> are a good example to start.
In my previous post, i explained how one might use invariant_ring (for
getting a Hironaka decomposition) or invariant_algebra_reynolds (for
getting minimal sub-algebra generators).
For completeness, i explain here what one may do in the special case
of a permutation group, and would like to combine it with another
question on the correct use of the Singular interface.
Let IR be the invariant ring of a non-modular representation of a
permutation group. We will compute a minimal set of sub-algebra
generators for IR.
A permutation group is given by a list of generators, where each
generator is presented by a list of disjoint cycles, where each cycle
is a list of integers. So, for the natural action of the cyclic group
of order 9 in characteristic 2, you would write
sage: singular.LIB("finvar.lib")
sage: R=singular.ring(2,'(x(1..9))','dp')
sage:
K=singular.list((singular.list('1,2,3,4,5,6,7,8,9').list()).list())
And then, you get a minimal set of generators by
sage: IR=K.invariant_algebra_perm()
In this innocent-looking example, there are minimally 119 (!)
generators, so IR is a 1x119 Singular matrix.
Here is my question about the use of the Singular interface. Above, i
define
sage:
K=singular.list((singular.list('1,2,3,4,5,6,7,8,9').list()).list())
which is not exactly elegant. Is there a better way to do in sage what
in Singular was
def K = list(list(list(1,2,3,4,5,6,7,8,9)))
?
Yours
Simon
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