feat: scalar multiplication as a CLM on D^n

[luigi-massacci]

Introduces for TestFunction the analogous results from SchwartzMap.

---

• depends on: feat: multiplication by a regular function in D^n as a CLM (bilin version) #41485
• depends on: feat: multiplication by a regular function in D^n_{K} as CLM (bilinear form version) #41324

[github-actions]

PR summary fe6c7c5d2f

Import changes for modified files

Dependency changes

File	Base Count	Head Count	Change
Mathlib.Analysis.Distribution.ContDiffMapSupportedIn	2395	2404	+9 (+0.38%)
Mathlib.Analysis.Distribution.TestFunction	2433	2440	+7 (+0.29%)

Import changes for all files

Files	Import difference
Mathlib.Analysis.Distribution.Distribution Mathlib.Analysis.Distribution.TestFunction	7
Mathlib.Analysis.Distribution.ContDiffMapSupportedIn	9

---

Declarations diff (regex)

+ bilinLeftCLM
+ instance : ContinuousConstSMul 𝕜 𝓓^{n}(Ω, F)
+ smulLeftCLM
+ smulLeftCLM_add
+ smulLeftCLM_apply
+ smulLeftCLM_apply_apply
+ smulLeftCLM_compL_smulLeftCLM
+ smulLeftCLM_const
+ smulLeftCLM_neg
+ smulLeftCLM_smul
+ smulLeftCLM_smulLeftCLM_apply
+ smulLeftCLM_sub
++ bilinLeftCLM_apply
- fderivCLM
- instance : LineDeriv E 𝓓(Ω, F) 𝓓(Ω, F)
- integralAgainstBilinCLM
- lineDerivCLM
- monoCLM
- ofSupportedInCLM
- originalTop
- postcompCLM
- toBoundedContinuousFunctionCLM

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)

✅ Lean-aware diff — post-build, computed from the Lean environment (commit fe6c7c5).

• +17 new declarations
• −0 removed declarations

+ContDiffMapSupportedIn.bilinLeftCLM
+ContDiffMapSupportedIn.bilinLeftCLM_apply
+ContDiffMapSupportedIn.mk.congr_simp
+TestFunction.bilinLeftCLM
+TestFunction.bilinLeftCLM.congr_simp
+TestFunction.bilinLeftCLM_apply
+TestFunction.instContinuousConstSMul
+TestFunction.smulLeftCLM
+TestFunction.smulLeftCLM_add
+TestFunction.smulLeftCLM_apply
+TestFunction.smulLeftCLM_apply_apply
+TestFunction.smulLeftCLM_compL_smulLeftCLM
+TestFunction.smulLeftCLM_const
+TestFunction.smulLeftCLM_neg
+TestFunction.smulLeftCLM_smul
+TestFunction.smulLeftCLM_smulLeftCLM_apply
+TestFunction.smulLeftCLM_sub

---

No changes to strong technical debt.

No changes to weak technical debt.

Current commit fe6c7c5d2f
Reference commit ed0d70fdcd

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).

[luigi-massacci]

I would like to get feedback most of all on the ContinuousConstSMul instance. I don't know if this is the proper way to do it, it feels a bit teleological. I'm unsure if this partially resolves the existing TODO for ContinuousSMul or is just an abomination. I needed the instance for smulLeftCLM_const.

[mathlib-dependent-issues]

This PR/issue depends on:

• feat: multiplication by a regular function in D^n as a CLM (bilin version) #41485
• feat: multiplication by a regular function in D^n_{K} as CLM (bilinear form version) #41324
  By Dependent Issues (🤖). Happy coding!