Dynamical systems for products of projective spaces¶
This class builds on the prouct projective space class.
The main constructor functions are given by DynamicalSystem
and
DynamicalSystem_projective
. The constructors function can take either
polynomials or a morphism from which to construct a dynamical system.
The must be specified.
EXAMPLES:
sage: P1xP1.<x,y,u,v> = ProductProjectiveSpaces(QQ, [1, 1])
sage: DynamicalSystem_projective([x^2*u, y^2*v, x*v^2, y*u^2], domain=P1xP1)
Dynamical System of Product of projective spaces P^1 x P^1 over Rational Field
Defn: Defined by sending (x : y , u : v) to
(x^2*u : y^2*v , x*v^2 : y*u^2).
-
sage.dynamics.arithmetic_dynamics.product_projective_ds.
DynamicalSystem_product_projective
¶ The class of dynamical systems on products of projective spaces.
Warning
You should not create objects of this class directly because no type or consistency checking is performed. The preferred method to construct such dynamical systems is to use
DynamicalSystem_projective()
function.INPUT:
polys
– a list ofn_1 + \cdots + n_r
multi-homogeneous polynomials, all of which should have the same parentdomain
– a projective scheme embedded inP^{n_1-1} \times \cdots \times P^{n_r-1}
EXAMPLES:
sage: T.<x,y,z,w,u> = ProductProjectiveSpaces([2, 1], QQ) sage: DynamicalSystem_projective([x^2, y^2, z^2, w^2, u^2], domain=T) Dynamical System of Product of projective spaces P^2 x P^1 over Rational Field Defn: Defined by sending (x : y : z , w : u) to (x^2 : y^2 : z^2 , w^2 : u^2).