Enhance global_height functionality for other fields

[b11e3d19-0e1d-4b36-b44b-4e039832fbf9]

Currently we cannot calculate the global height of an element that is not already an explicit element of QQ, QQbar, or NumberField. For example,

sage: P.<x,y> = ProjectiveSpace(AlgebraicRealField(), 1)
sage: Q = P(10)
sage: Q.global_height()

currently fails, when we should be able to calculate the global heights for a point in any field that can be embedded into QQbar. We use coercion to QQbar in the global_height() function to solve this problem. There are also numerous instances in the projective_ds file where a check is made on the base field for the sole purpose of safely calling the global_height() function. We have removed these checks in favor of a single check in the global_height() function.

CC: @bhutz

Component: dynamics

Keywords: SI2019

Author: Talia Blum, Trevor Hyde, Joey Lupo, Matt Torrence

Branch/Commit: 667039f

Reviewer: Shuofeng Xu, Max Weinreich, Brandon Gontmacher, Heidi Benham, Ben Hutz

Issue created by migration from https://trac.sagemath.org/ticket/28071

[b11e3d19-0e1d-4b36-b44b-4e039832fbf9]

Changed author from Trevor Hyde, Joey Lupo, Matt Torrence to Talia Blum, Trevor Hyde, Joey Lupo, Matt Torrence

[b11e3d19-0e1d-4b36-b44b-4e039832fbf9]

Description changed:

--- 
+++ 
@@ -1,9 +1,9 @@
-Currently we cannot calculate the global height of an element that is not already an explicit element of QQ, QQbar, or NumberField. For example,
+Currently we cannot calculate the global height of an element that is not already an explicit element of `QQ`, `QQbar`, or `NumberField`. For example,

-P.<x,y> = ProjectiveSpace(AlgebraicRealField(), 1) -Q = P(10) -Q.global_height() +sage: P.<x,y> = ProjectiveSpace(AlgebraicRealField(), 1) +sage: Q = P(10) +sage: Q.global_height()

-currently fails, when we should be able to calculate the global heights for a point in any field that can be embedded into QQbar. We use coercion to QQbar in the global_heights function to solve this problem. There are also numerous instances in the projective_ds file where a check is made on the base field for the sole purpose of safely calling the global_height() function. We have removed these checks in favor of a single check in the global_height function.
+currently fails, when we should be able to calculate the global heights for a point in any field that can be embedded into `QQbar`. We use coercion to `QQbar` in the `global_height()` function to solve this problem. There are also numerous instances in the `projective_ds` file where a check is made on the base field for the sole purpose of safely calling the `global_height()` function. We have removed these checks in favor of a single check in the `global_height()` function.

[b11e3d19-0e1d-4b36-b44b-4e039832fbf9]

Commit: 01747de

[b11e3d19-0e1d-4b36-b44b-4e039832fbf9]

Branch: u/gh-Torrencem/28071_global_height

[b11e3d19-0e1d-4b36-b44b-4e039832fbf9]

New commits:

01747de

28071: fix global height checks

[39bf98b2-f392-42d4-a7cb-688d50feb567]

Reviewer: Shuofeng Xu, Max Weinreich, Brandon Gontmacher, Heidi Benham

[bhutz]

comment:5

Two questions here:

1) Can the new ``except'' trap a specific error?

2) It would be better if the example had elements actually in the field you are defining instead of just over QQ.

[vbraun]

Changed branch from u/gh-Torrencem/28071_global_height to 01747de

[vbraun]

Changed commit from 01747de to none

[4edfbb98-6b40-4472-8655-ea92584e13fe]

Changed branch from 01747de to u/gh-Torrencem/28071_global_height

[4edfbb98-6b40-4472-8655-ea92584e13fe]

comment:8

The latest commit should fix these issues Ben

---

New commits:

01747de	28071: fix global height checks
667039f	28071: Change example, more specific except

[4edfbb98-6b40-4472-8655-ea92584e13fe]

Commit: 667039f

[bhutz]

Changed reviewer from Shuofeng Xu, Max Weinreich, Brandon Gontmacher, Heidi Benham to Shuofeng Xu, Max Weinreich, Brandon Gontmacher, Heidi Benham, Ben Hutz

[vbraun]

Changed branch from u/gh-Torrencem/28071_global_height to 667039f