feat(DiscreteConvolution): add ring convolution definitions and properties

[IlPreteRosso]

Continuation of PR #34191

Adds ring convolution and its elementary properties.

Aligns the API with Day convolution structure. Although no idea how to bridge them right now.

[github-actions]

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[github-actions]

PR summary 623375f76c

Import changes for modified files

Dependency changes

File	Base Count	Head Count	Change
Mathlib.Topology.Algebra.InfiniteSum.DiscreteConvolution	1305	1306	+1 (+0.08%)

Import changes for all files

Files	Import difference
Mathlib.Topology.Algebra.InfiniteSum.DiscreteConvolution	1

---

Declarations diff (regex)

+ add_ringConvolution
+ convolutionExists_of_hasMulAntidiagonal
+ convolution_eq_sum_mulAntidiagonal
+ delta
+ delta_ringConvolution
+ mulFiber_eq_mulAntidiagonal
+ mulFiber_finite
+ mulLinearMap
+ mulLinearMap_apply
+ ringConvolution
+ ringConvolution_add
+ ringConvolution_apply
+ ringConvolution_comm
+ ringConvolution_delta
+ ringConvolution_eq_sum_mulAntidiagonal
+ ringConvolution_smul
+ ringConvolution_zero
+ smul_ringConvolution
+ zero_ringConvolution

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 623375f).

• +36 new declarations
• −0 removed declarations

+DiscreteConvolution.addConvolutionExists_of_hasAntidiagonal
+DiscreteConvolution.addConvolution_eq_sum_antidiagonal
+DiscreteConvolution.addDelta
+DiscreteConvolution.addDelta_addRingConvolution
+DiscreteConvolution.addFiber_finite
+DiscreteConvolution.addRingConvolution
+DiscreteConvolution.addRingConvolution_add
+DiscreteConvolution.addRingConvolution_addDelta
+DiscreteConvolution.addRingConvolution_apply
+DiscreteConvolution.addRingConvolution_comm
+DiscreteConvolution.addRingConvolution_eq_sum_antidiagonal
+DiscreteConvolution.addRingConvolution_smul
+DiscreteConvolution.addRingConvolution_zero
+DiscreteConvolution.add_addRingConvolution
+DiscreteConvolution.add_ringConvolution
+DiscreteConvolution.convolutionExists_of_hasMulAntidiagonal
+DiscreteConvolution.convolution_eq_sum_mulAntidiagonal
+DiscreteConvolution.delta
+DiscreteConvolution.delta_ringConvolution
+DiscreteConvolution.mulFiber_finite
+DiscreteConvolution.mulLinearMap
+DiscreteConvolution.mulLinearMap_apply
+DiscreteConvolution.ringConvolution
+DiscreteConvolution.ringConvolution_add
+DiscreteConvolution.ringConvolution_apply
+DiscreteConvolution.ringConvolution_comm
+DiscreteConvolution.ringConvolution_delta
+DiscreteConvolution.ringConvolution_eq_sum_mulAntidiagonal
+DiscreteConvolution.ringConvolution_smul
+DiscreteConvolution.ringConvolution_zero
+DiscreteConvolution.smul_addRingConvolution
+DiscreteConvolution.smul_ringConvolution
+DiscreteConvolution.zero_addRingConvolution
+DiscreteConvolution.zero_ringConvolution
+DiscreteConvolution.«term_⋆ᵣ_»
+DiscreteConvolution.«term_⋆ᵣ₊_»

---

No changes to strong technical debt.

No changes to weak technical debt.

Current commit 623375f76c
Reference commit 2d8c533bd0

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).