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 - ToricDivisorrepresenting- self- EXAMPLES: - 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 - >>> 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 - xis a toric rational divisor class.- INPUT: - x– anything
 - OUTPUT: - Trueif- xis a toric rational divisor class,- Falseotherwise- EXAMPLES: - 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 - >>> 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