Hi all,
Sorry for asking a somewhat related question to one I asked a while ago,
but I find myself in the situation of trying to expand a certain
multivariate symmetric series (polynomial after cutoff) in certain classes
of symmetric functions and can't seem to get it working.
The following
Dan,
Before giving any sage advice I need to know how bad the
real denominators will get.
A special trick can be used if the denominators are limited to
(x_i - x_j).
Your toy example involves (1 - t x_i y_j)^{-1}
which is no problem at all using geometric series in an extra variable.
--Mark
Hey Dan,
The reason why you're getting the symbolic ring error is because you are
saying the matrix should have coeff in SR (the symbolic ring) but the
matrix coeff you've specified are in the power series ring. So it should
work if you change SR to S in the M = matrix(...) line (I suspect
Dan,
Someone correct me if I am ignorant, but
even after fixing syntax errors, the problem will be that multivariate
polynomials
don't know when they are divisible by things like x_i - x_j.
--Mark
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Hi Mark,
Someone correct me if I am ignorant, but
even after fixing syntax errors, the problem will be that multivariate
polynomials
don't know when they are divisible by things like x_i - x_j.
Really?
sage: P
Multivariate Polynomial Ring in x, y over Rational Field
sage:
Um, Sorry!
In preparation for converting to symmetric polynomials I had
used an iterated polynomial ring
Rt = QQ['t']
Ry = Rt['y1,y2,y3']
R = Ry['x1,x2,x3']
and the fraction field of the ring R is not smart enough to divide by x1-x2
in general.
If you use the polynomial ring
S =
On Tuesday, March 4, 2014 5:16:14 PM UTC+1, Mark Shimozono wrote:
Dan,
Before giving any sage advice I need to know how bad the
real denominators will get.
A special trick can be used if the denominators are limited to
(x_i - x_j).
The denominators are mostly vandermondes.
Hi Mark, Travis and Darij,
@ Travis: Thanks for catching the SR bug and for pointing me to the fact
pfaffian is now implemented in sage. Last time I checked (not so recently),
it wasn't:)
@ Mark: As I said, the denominators that *are not* power series are
vandermondes or C Weyl denominators.
Dan,
The denominators are mostly vandermondes. However, there is something in
type C (symplectic) which will have a vandermonde in the x's and a Weyl
type C denominator in the y's. But that's probably a subject for a
different email altogether, because multivariate Laurent power series are
Nicolas,
I covet your thoughts on the following.
It seems mostly hopeless to implement tensor products for random modules
since this involves infinitely many generators and infinitely many relations.
Therefore I will limit this discussion to ModulesWithBasis(R) for R a
commutative ring with 1.
Is CombinatorialFreeModule_Tensor the only class that actually builds tensor
products,
rather than delegating?
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On Wed, Mar 05, 2014 at 12:18:36AM -0500, Mark Shimozono wrote:
Is CombinatorialFreeModule_Tensor the only class that actually builds tensor
products,
rather than delegating?
At this point, yes, I think so.
Cheers,
Nicolas
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Nicolas M. Thiéry Isil
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