[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
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erdOne
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d and a polynomial p : ℤ[X]d and a polynomial p : ℤ[X]
d and a polynomial p : ℤ[X]d and a polynomial p : ℤ[X]
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erdOne
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kbuzzard
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d and a polynomial p : ℤ[X]d and a polynomial p : F[X], where F is a field with characteristic 0.
kbuzzard
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kbuzzard
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d and a polynomial p : F[X], where F is a field with characteristic 0.Polynomial.hilbert p d for a natural number d and a polynomial p : F[X].
Polynomial.hilbert p d for a natural number d and a polynomial p : F[X].Polynomial.hilbert p d for a natural number d and a polynomial p : F[X], where F is a field.
Polynomial.hilbert p d for a natural number d and a polynomial p : F[X], where F is a field.Polynomial.hilbert p d, where F is a field, p : F[X] and d : ℕ.
kbuzzard
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Thanks a lot for your work on this! maintainer merge |
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🚀 Pull request has been placed on the maintainer queue by kbuzzard. |
erdOne
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Polynomial.hilbert p d for p : F[X] and d : ℕ, where F is a field.RatFunc.Polynomial.hilbert p d for p : F[X] and d : ℕ, where F is a field.
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RatFunc.Polynomial.hilbert p d for p : F[X] and d : ℕ, where F is a field.Polynomial.hilbertPoly p d for p : F[X] and d : ℕ, where F is a field.
Polynomial.hilbertPoly p d for p : F[X] and d : ℕ, where F is a field.Polynomial.hilbertPoly p d for p : F[X] and d : ℕ, where F is a field.
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…rty 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`).
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Polynomial.hilbertPoly p d for p : F[X] and d : ℕ, where F is a field.Polynomial.hilbertPoly p d for p : F[X] and d : ℕ, where F is a field.
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Given any field
F, polynomialp : F[X]and natural numberd, we have definedPolynomial.hilbertPoly p d : F[X]. IfFis of characteristic zero, then for any large enoughn : ℕ,PowerSeries.coeff F n (p * (invOneSubPow F d))equals(hilbertPoly p d).eval (n : F)(seePolynomial.coeff_mul_invOneSubPow_eq_hilbertPoly_eval).