feat(RingTheory): compute the height of the ideal spanning a (sub)set of variables in a polynomial ring

[vlad902]

---

• depends on: feat(RingTheory): Ideal.span corollaries of Krull's height theorem #41401
• depends on: feat(MvPolynomial): ideal generated by variables is prime over a domain #41399

[github-actions]

PR summary c8e03ad561

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference
Mathlib.RingTheory.MvPolynomial.Height (new file)	1917

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Declarations diff (regex)

+ RingHom.height_le_height_comap_of_surjective
+ X_mem_ideal_span_X_image_iff
+ height_span_X_image_eq
+ le_height_span_X_image
+ le_height_span_X_image_of_isDomain

You can run this locally as follows

## from your `mathlib4` directory:
git clone https://github.com/leanprover-community/mathlib-ci.git ../mathlib-ci

## summary with just the declaration names:
../mathlib-ci/scripts/pr_summary/declarations_diff.sh <optional_commit>

## more verbose report:
../mathlib-ci/scripts/pr_summary/declarations_diff.sh long <optional_commit>

The doc-module for scripts/pr_summary/declarations_diff.sh in the mathlib-ci repository contains some details about this script.

Declarations diff (Lean -- pending)

Computed after the build finishes.

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No changes to strong technical debt.

No changes to weak technical debt.

Current commit c8e03ad561
Reference commit 85ce110e6b

This script lives in the mathlib-ci repository. To run it locally, from your mathlib4 directory:

git clone https://github.com/leanprover-community/mathlib-ci.git ../mathlib-ci
../mathlib-ci/scripts/reporting/technical-debt-metrics.sh pr_summary

• The relative value is the weighted sum of the differences with weight given by the inverse of the current value of the statistic.
• The absolute value is the relative value divided by the total sum of the inverses of the current values (i.e. the weighted average of the differences).

[mathlib-dependent-issues]

This PR/issue depends on:

• feat(RingTheory): Ideal.span corollaries of Krull's height theorem #41401
• feat(MvPolynomial): ideal generated by variables is prime over a domain #41399
  By Dependent Issues (🤖). Happy coding!