refactor(Analysis): golf Mathlib/Analysis/Analytic/OfScalars

[yuanyi-350]

• simplifies ofScalars_series_injective by evaluating the equality on the constant 1 tuple
• rewrites ofScalars_add and ofScalars_smul with ext/simp, removing the transparency workaround

Extracted from #37968

[yuanyi-350]

!bench

[leanprover-radar]

Benchmark results for a548273 against 36a9746 are in. No significant results found. @yuanyi-350

• ✅ build//instructions: -14.2G (-0.01%)

Small changes (2✅)

• ✅ build/module/Mathlib.Tactic.Explode.Pretty//instructions: -397.9M (-12.84%)
• ✅ build/module/Mathlib.Topology.Algebra.Module.StrongTopology//instructions: -366.7M (-6.78%)

[github-actions]

PR summary 36a97460d7

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference

---

Declarations diff

No declarations were harmed in the making of this PR! 🐙

You can run this locally as follows

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

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

The doc-module for scripts/pr_summary/declarations_diff.sh contains some details about this script.

---

Decrease in tech debt: (relative, absolute) = (2.00, 0.00)

Current number	Change	Type
6204	-2	backward.isDefEq.respectTransparency

Current commit 8b14f261d9
Reference commit 36a97460d7

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).

[yuanyi-350]

I ran a profiler comparison for the changed declarations in this PR.

Results (seconds):

• FormalMultilinearSeries.ofScalars_series_injective: 0.106365 -> 0.100783 (-5.2%)
• FormalMultilinearSeries.ofScalars_add: 0.111418 -> 0.150578 (+35.1%)
• FormalMultilinearSeries.ofScalars_smul: 0.078849 -> 0.093558 (+18.7%)

Overall:

• ofScalars_series_injective is slightly faster.
• ofScalars_add and ofScalars_smul regress, with the larger slowdown on ofScalars_add.

[themathqueen]

Suggested change

	intro c c' h
	funext n
	intro _ _ h
	ext n

[themathqueen]

Suggested change

	ext n x
	simp [ofScalars, add_smul]
	ext; simp [ofScalars, add_smul]

[themathqueen]

Suggested change

	ext n y
	simp [ofScalars, smul_smul]
	ext; simp [ofScalars, smul_smul]