HI Nicolas,
> Hmm. I would need to better know the mathematics behind to give any
> useful answer. My (little) understanding was that the main point of
> the Zumbroich basis was to avoid such dependencies.
see my answer above.
> > 1. if I want to use the category Fields as well, I get the following
> > TypeError:
>
> > TypeError: metaclass conflict: the metaclass of a derived class
> > must be a (non-strict) subclass of the metaclasses of all its bases
>
> Please send me the smallest piece of code that triggers this, for me
> to investigate.
class FieldAndFreeModule(CombinatorialFreeModule):
def __init__(self):
CombinatorialFreeModule.__init__(self, QQ, ['a'],
category=Fields)
causes already the error.
> > 3. the __div__ method in the Element class seem to explain how
> > division by coefficients should work, not how basis elements interact,
> > right?
>
> As far as I know, it should handle the division of two general
> elements of the field. By the way, maybe it is sufficient to just
> implement __invert__.
Maybe, but the category Fields did not work yet. As the UCF is only a
CombinatorialFreeModule, I get
sage: F =
UniversalCyclotomicField()
sage: F.Element.__div__?
...
Division by coefficients
and __invert__ is not yet there.
> > 4. the embedding into CC does not yet work: in the constructor, I
> > define the following module_morphism:
> > def on_basis( x ):
> > return (2 * CLF.pi() * CLF.gen() * x[1] /x[0]).exp()
>
> > g = self.module_morphism( on_basis=on_basis, codomain=CLF )
> > self.register_embedding( g )
>
> > but this morphism returns an error:
> > sage: F = UniversalCyclotomicField()
> > sage: CC( E(6) )
> > TypeError: unsupported operand parent(s) for '+': 'Complex Lazy
> > Field' and '<type 'NoneType'>'
>
> Probably just a glitch. I would need to run the code to debug.
The code should be on the track server, ticket 8327.
> Infinite families indeed don't have a __contains__ by default. In that
> case, it would be possible in principle to define one, by checking
> that the element is in the field, and has a single term. In practice,
> this would require using special families for basis of vector spaces.
> How useful a feature would this be?
I thought that, having a vector space with a concrete basis, it would
be natural to be able to check if some object I have is in the basis.
In our case, to check if some pair (n,k) is in the ZumbroichBasis(n,1)
without reconstructing it. I will find a workaround for that...
Thanks and best_2, Christian
--
You received this message because you are subscribed to the Google Groups
"sage-combinat-devel" group.
To post to this group, send email to sage-combinat-de...@googlegroups.com.
To unsubscribe from this group, send email to
sage-combinat-devel+unsubscr...@googlegroups.com.
For more options, visit this group at
http://groups.google.com/group/sage-combinat-devel?hl=en.
