[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.

[FMLJohn]

Given any field F, polynomial p : F[X] and natural number d, we have defined Polynomial.hilbertPoly p d : F[X]. If F is of characteristic zero, then for any large enough n : ℕ, PowerSeries.coeff F n (p * (invOneSubPow F d)) equals (hilbertPoly p d).eval (n : F) (see Polynomial.coeff_mul_invOneSubPow_eq_hilbertPoly_eval).

[github-actions]

PR summary fe4cf0e8c1

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference
Mathlib.RingTheory.Polynomial.HilbertPoly (new file)	1043

---

Declarations diff

+ ascFactorial_eq_prod_range
+ ascPochhammer_nat_eq_natCast_ascFactorial
+ ascPochhammer_nat_eq_natCast_descFactorial
+ coeff_mul_invOneSubPow_eq_hilbertPoly_eval
+ hilbertPoly
+ hilbertPoly_X_pow_succ
+ hilbertPoly_poly_succ
+ hilbertPoly_poly_zero
+ hilbertPoly_zero_nat
+ invOneSubPow_inv_zero_eq_one
+ preHilbertPoly
+ preHilbertPoly_eq_choose_sub_add
- invOneSubPow_inv_eq_one_of_eq_zero

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.

---

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).

[kbuzzard]

Thanks a lot for your work on this!

maintainer merge

[github-actions]

🚀 Pull request has been placed on the maintainer queue by kbuzzard.

[mathlib-bors]

✌️ FMLJohn can now approve this pull request. To approve and merge a pull request, simply reply with bors r+. More detailed instructions are available here.

[FMLJohn]

bors r+

[mathlib-bors]

Pull request successfully merged into master.

Build succeeded:

• Build
• Lint style