implement height functions for product points

[raghukul01]

Currently local_height() and global_height() function are not present in the product projective points.

CC: @bhutz @raghukul01

Component: algebraic geometry

Keywords: gsoc2018

Author: Raghukul Raman

Branch/Commit: af73f95

Reviewer: Ben Hutz

Issue created by migration from https://trac.sagemath.org/ticket/25821

[raghukul01]

Branch: u/raghukul01/implement_height_functions_for_product_points

[raghukul01]

Commit: 44a8782

[raghukul01]

Author: Raghukul Raman

[raghukul01]

New commits:

44a8782

25821: Added global_height and local height for product points

[bhutz]

comment:3

Concept is fine, but the code can be made more readable

return max([self[i].global_height(prec=prec) \
                     for i in range(self.codomain().ambient_space().num_components())])

to

return max([t.global_height(prec=prec) for t in self])

I think more explanation is warranted in the docs as well. i.e., that you are taking the max of the heights of the component points.

and similarly for local height.

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

af73f95

25821: Updated docstring

[sagetrac-git]

Changed commit from 44a8782 to af73f95

[raghukul01]

comment:5

I think return max([t.global_height(prec=prec) for t in self] won't work since __iter__() function iterates over all coordinates, but here we need to iterate over all components. If we take max over all coordinates then we need to add a function to convert the space defined over QQbar to NumberField, as done in projective_point.

I have made it more readable though.

Replying to @bhutz:

Concept is fine, but the code can be made more readable

return max([self[i].global_height(prec=prec) \
                     for i in range(self.codomain().ambient_space().num_components())])

to

return max([t.global_height(prec=prec) for t in self])

I think more explanation is warranted in the docs as well. i.e., that you are taking the max of the heights of the component points.

and similarly for local height.

[bhutz]

Reviewer: Ben Hutz

[vbraun]

Changed branch from u/raghukul01/implement_height_functions_for_product_points to af73f95