feat (RingTheory/HahnSeries): algebra homomorphism from PowerSeries to HahnSeries.

[ScottCarnahan]

This PR defines the R-algebra homomorphism from PowerSeries R to HahnSeries Γ R that takes X to some positive-order element, and extends formally to infinite sums.

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• depends on: feat: SMul with Top #21316

[github-actions]

PR summary 48d1555dcd

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference
8 files Mathlib.Algebra.Vertex.HVertexOperator Mathlib.Algebra.Vertex.VertexOperator Mathlib.RingTheory.HahnSeries.HEval Mathlib.RingTheory.HahnSeries.Multiplication Mathlib.RingTheory.HahnSeries.PowerSeries Mathlib.RingTheory.HahnSeries.Summable Mathlib.RingTheory.HahnSeries.Valuation Mathlib.RingTheory.LaurentSeries	1
Mathlib.Algebra.Order.SMulWithTop (new file)	224

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Declarations diff

+ SMulTop
+ SMulTop.coe_SMul
+ SMulTop.coe_ne_smultop
+ SMulTop.coe_smul_eq_top_iff
+ SMulTop.le_iff
+ SMulTop.le_top
+ SMulTop.lt_iff
+ SMulTop.lt_top_iff_ne_top
+ SMulTop.of
+ SMulTop.of_symm_top
+ SMulTop.of_top
+ SMulTop.rec
+ SMulTop.smul_coe_eq_top_iff
+ SMulTop.smul_eq_top
+ SMulTop.smul_lt_top
+ SMulTop.smul_ne_top
+ SMulTop.smul_top
+ SMulTop.smultop_ne_coe
+ SMulTop.top_SMul
+ SMulTop.top_le_iff
+ coeff_heval
+ coeff_heval_zero
+ given
+ heval
+ heval_mul
+ heval_unit
+ instance (priority := 10) [LE P] : LE (SMulTop P)
+ instance (priority := 10) [LT P] : LT (SMulTop P)
+ instance : Top (SMulTop P)
+ instance [LE G] [LE P] [IsOrderedSMul G P] :
+ instance [SMul G P] : SMul (WithTop G) (SMulTop P)
+ orderTop_add_le_mul
+ orderTop_nsmul_le_orderTop_pow
+ orderTop_of_Subsingleton
+ orderTop_vAdd_le_orderTop_smul

You can run this locally as follows

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

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

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

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No changes to technical debt.

You can run this locally as

./scripts/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).

[mathlib4-dependent-issues-bot]

This PR/issue depends on:

• feat: SMul with Top #21316
  By Dependent Issues (🤖). Happy coding!