Points for products of projective spaces

This class builds on the projective space class and its point and morphism classes.

EXAMPLES:

We construct products projective spaces of various dimensions over the same ring.:

sage: P1xP1.<x,y, u,v> = ProductProjectiveSpaces(QQ, [1,1])
sage: P1xP1([2,1, 3,1])
(2 : 1 , 3 : 1)
class sage.schemes.product_projective.point.ProductProjectiveSpaces_point_ring(parent, polys, check=True)

Bases: sage.schemes.generic.morphism.SchemeMorphism_point

The class of points on products of projective spaces. The components are projective space points.

EXAMPLES:

sage: T.<x,y,z,w,u> = ProductProjectiveSpaces([2,1],QQ)
sage: T.point([1,2,3,4,5]);
(1/3 : 2/3 : 1 , 4/5 : 1)
change_ring(R, check=True)

Returns a new ProductProjectiveSpaces_point which is self coerced to R.

If check is True, then the initialization checks are performed.

INPUT:

  • R – a ring
  • check – Boolean (optional)

OUTPUT:

ProductProjectiveSpaces_point

EXAMPLES:

sage: T.<x,y,z,u,v,w> = ProductProjectiveSpaces([1,1,1],ZZ)
sage: P = T.point([5,3,15,4,2,6]);
sage: P.change_ring(GF(3))
(1 : 0 , 0 : 1 , 1 : 0)
normalize_coordinates()

Removes common factors (componentwise) from the coordinates of self (including -1).

OUTPUT:

None.

EXAMPLES:

sage: T.<x,y,z,u,v,w> = ProductProjectiveSpaces([2,2],ZZ)
sage: P = T.point([5,10,15,4,2,6]);
sage: P.normalize_coordinates()
sage: P
(1 : 2 : 3 , 2 : 1 : 3)
scale_by(t)

Scale the coordinates of the point self by t, done componentwise.

A TypeError occurs if the point is not in the base ring of the codomain after scaling.

INPUT:

  • t – a ring element

EXAMPLES:

sage: T.<x,y,z,u,v,w> = ProductProjectiveSpaces([1,1,1],ZZ)
sage: P = T.point([5,10,15,4,2,6]);
sage: P.scale_by([2,1,1])
sage: P
(10 : 20 , 15 : 4 , 2 : 6)

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