Commit 2024-12-02 18:04 561e0504
View on Github →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)
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
).