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 of n_1 + \cdots + n_r multi-homogeneous polynomials, all of which should have the same parent
  • domain – a projective scheme embedded in P^{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).