#9337: Add toric divisors
----------------------------------+-----------------------------------------
Reporter: vbraun | Owner: AlexGhitza
Type: enhancement | Status: needs_info
Priority: major | Milestone: sage-4.6
Component: algebraic geometry | Keywords:
Author: Volker Braun | Upstream: N/A
Reviewer: Andrey Novoseltsev | Merged:
Work_issues: |
----------------------------------+-----------------------------------------
Comment(by vbraun):
The `ToricDivisorGroup` is the group of T-Weil divisors. They are
`FormalSums` of monomials, whereas a `Divisor_generic` is a formal sum of
(homogeneous) polynomials. A `ToricDivisor_generic` is a valid element of
its base class `Divisor_generic`, but not the other way round. If you want
non-toric divisors then you can already do
{{{
sage: from sage.schemes.generic.divisor_group import DivisorGroup
sage: dP6 = toric_varieties.dP6()
sage: dP6.inject_variables()
Defining x, u, y, v, z, w
sage: Div = DivisorGroup(toric_varieties.dP6()); Div
Group of ZZ-Divisors on 2-d CPR-Fano toric variety covered by 6 affine
patches
sage: Div(x^2+u) # does not know how to check homogeneity
x^2 + u
sage: type(_)
<class 'sage.schemes.generic.divisor.Divisor_generic'>
}}}
The `ToricDivisorGroup` should probably print `Group of toric ZZ-Weil
divisors` to be more explicit. I was trying to not print "T-Weil divisor"
all the time in the output to make things easier to read. I'll change the
`ToricDivisorGroup` output but leave its elements as "Divisor x", if in
doubt you can always use `parent()` or `type()` to find out what you are
working with.
I don't see much use to have separate `ToricVariety_field.divisor_group()`
and `.toric_divisor_group()` methods, I think newcomers would only be
tempted into constructing the generic divisor group and then be
disappointed that there is no toric functionality there.
In your last line, `G(x+y)` should have returned `G(x)+G(y)`, that is,
linear polynomials get converted to the analogous sum of T-Weil divisors,
but you found a bug. Although this is potentially dangerous it provides a
useful shorthand to define the T-Weil divisors.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/9337#comment:16>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
--
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.
