Toric rational divisor classes¶

This module is a part of the framework for toric varieties.

AUTHORS:

Volker Braun and Andrey Novoseltsev (2010-09-05): initial version.

class sage.schemes.toric.divisor_class.ToricRationalDivisorClass[source]¶

Bases: Vector_rational_dense

Create a toric rational divisor class.

Warning

You probably should not construct divisor classes explicitly.

INPUT:

same as for Vector_rational_dense.

OUTPUT: toric rational divisor class

lift()[source]¶

Return a divisor representing this divisor class.

OUTPUT: an instance of ToricDivisor representing self

EXAMPLES:

Sage

sage: X = toric_varieties.Cube_nonpolyhedral()
sage: D = X.divisor([0,1,2,3,4,5,6,7]); D
V(z1) + 2*V(z2) + 3*V(z3) + 4*V(z4) + 5*V(z5) + 6*V(z6) + 7*V(z7)
sage: D.divisor_class()
Divisor class [29, 6, 8, 10, 0]
sage: Dequiv = D.divisor_class().lift(); Dequiv
15*V(z1) - 11*V(z2) - 9*V(z5) + 19*V(z6) + 10*V(z7)
sage: Dequiv == D
False
sage: Dequiv.divisor_class() == D.divisor_class()
True

Python

>>> from sage.all import *
>>> X = toric_varieties.Cube_nonpolyhedral()
>>> D = X.divisor([Integer(0),Integer(1),Integer(2),Integer(3),Integer(4),Integer(5),Integer(6),Integer(7)]); D
V(z1) + 2*V(z2) + 3*V(z3) + 4*V(z4) + 5*V(z5) + 6*V(z6) + 7*V(z7)
>>> D.divisor_class()
Divisor class [29, 6, 8, 10, 0]
>>> Dequiv = D.divisor_class().lift(); Dequiv
15*V(z1) - 11*V(z2) - 9*V(z5) + 19*V(z6) + 10*V(z7)
>>> Dequiv == D
False
>>> Dequiv.divisor_class() == D.divisor_class()
True

sage.schemes.toric.divisor_class.is_ToricRationalDivisorClass(x)[source]¶

Check if x is a toric rational divisor class.

INPUT:

x – anything

OUTPUT: True if x is a toric rational divisor class, False otherwise

EXAMPLES:

Sage

sage: from sage.schemes.toric.divisor_class import is_ToricRationalDivisorClass
sage: is_ToricRationalDivisorClass(1)
False
sage: dP6 = toric_varieties.dP6()
sage: D = dP6.rational_class_group().gen(0); D
Divisor class [1, 0, 0, 0]
sage: is_ToricRationalDivisorClass(D)
True

Python

>>> from sage.all import *
>>> from sage.schemes.toric.divisor_class import is_ToricRationalDivisorClass
>>> is_ToricRationalDivisorClass(Integer(1))
False
>>> dP6 = toric_varieties.dP6()
>>> D = dP6.rational_class_group().gen(Integer(0)); D
Divisor class [1, 0, 0, 0]
>>> is_ToricRationalDivisorClass(D)
True