feat(RingTheory/Polynomial/Hilbert): given a natural number d and a polynomial p : ℤ[X], proved the key property of the Hilbert polynomial in terms of d and p

[FMLJohn]

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• depends on: [Merged by Bors] - feat(RingTheory/Polynomial/HilbertPoly): the definition and key property of Polynomial.hilbertPoly p d for p : F[X] and d : ℕ, where F is a field. #19303

In this pull request, we have proved the key property of the Hilbert polynomial in terms of a natural number d and a polynomial p : ℤ[X] (Polynomial.coeff_mul_invOneSubPow_eq_hilbert_eval), i.e. for any term of p * (invOneSubPow ℤ d) whose degree is large enough, its coefficient can be obtained by evaluating the Hilbert polynomial.

The codes are much longer than needed. Further editing is needed.

[github-actions]

PR summary 24b0b96bf5

Import changes exceeding 2%

%	File
+4.59%	Mathlib.RingTheory.Polynomial.HilbertPoly

Import changes for modified files

Dependency changes

File	Base Count	Head Count	Change
Mathlib.RingTheory.Polynomial.HilbertPoly	1046	1094	+48 (+4.59%)

Import changes for all files

Files	Import difference
Mathlib.RingTheory.Polynomial.HilbertPoly	48

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Declarations diff

+ exists_unique_hilbertPoly

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:

• [Merged by Bors] - feat(RingTheory/Polynomial/HilbertPoly): the definition and key property of Polynomial.hilbertPoly p d for p : F[X] and d : ℕ, where F is a field. #19303
  By Dependent Issues (🤖). Happy coding!