feat(AlgebraicGeometry/AffineSpace): affine space is smooth

[justus-springer]

Show that affine space 𝔸(n; S) is smooth over S (or relative dimension Nat.card n) . Also remove the LocallyOfFinitePresentation instance, as it can be inferred automatically from smoothness.

• depends on: feat(RingTheory/): MvPolynomial is standard smooth #39709

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[github-actions]

PR summary 2eecea44be

Import changes exceeding 2%

%	File
+9.52%	Mathlib.AlgebraicGeometry.AffineSpace

Import changes for modified files

Dependency changes

File	Base Count	Head Count	Change
Mathlib.AlgebraicGeometry.AffineSpace	2458	2692	+234 (+9.52%)

Import changes for all files

Files	Import difference
Mathlib.AlgebraicGeometry.AffineSpace	234

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Declarations diff

+ IsStandardSmoothOfRelativeDimension.mvPolynomial
+ IsStandardSmoothOfRelativeDimension.mvPolynomial_fin
+ dimension_mvPolynomial
+ instance [Finite n] : Smooth (𝔸(n; S) ↘ S) := (smoothOfRelativeDimension n S).smooth
+ jacobian_mvPolynomial
+ smoothOfRelativeDimension
+ smoothOfRelativeDimension_fin
+++ mvPolynomial
- instance [Finite n] : LocallyOfFinitePresentation (𝔸(n; S) ↘ S)

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.

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No changes to strong technical debt.

No changes to weak technical debt.

Current commit 2eecea44be
Reference commit f6eb107aa5

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/): MvPolynomial is standard smooth #39709
  By Dependent Issues (🤖). Happy coding!

[mathlib-merge-conflicts]

This pull request has conflicts, please merge master and resolve them.

[mathlib-merge-conflicts]

This pull request has conflicts, please merge master and resolve them.