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Theorems · Theorem · commutative algebra

Polynomial.coeff_coe

∀ {R : Type u_1} [inst : Semiring R] (φ : Polynomial R) (n : ℕ), (PowerSeries.coeff n) ↑φ = φ.coeff n
Defined in
Mathlib.RingTheory.PowerSeries.Basic
Cited by
25 results in Mathlib
Foundations
Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
Semiring

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

PowerSeries.IsWeierstrassDivisorAt.isWeierstrassDivisionAt_div_mod · cited by 10IsWeierstrassDivisorAt.is…Polynomial.coe_monomial · cited by 5Polynomial.coe_monomialPolynomial.gaussNorm_coe_powerSeries · cited by 4Polynomial.gaussNorm_coe_…PowerSeries.trunc_trunc_mul · cited by 4PowerSeries.trunc_trunc_m…Polynomial.coe_add · cited by 4Polynomial.coe_addPolynomial.le_gaussNorm · cited by 4Polynomial.le_gaussNormPolynomial.coeff_mul_invOneSubPow_eq_hilbertPoly_eval · cited by 3Polynomial.coeff_mul_invO…Polynomial.polynomial_map_coe · cited by 3Polynomial.polynomial_map…Polynomial.coe_mul · cited by 3Polynomial.coe_mulPolynomial.gaussNorm_eq_zero_iff · cited by 2Polynomial.gaussNorm_eq_z…PowerSeries.trunc_trunc_of_le · cited by 2PowerSeries.trunc_trunc_o…PowerSeries.IsWeierstrassDivision.isUnit_of_map_ne_zero · cited by 2IsWeierstrassDivision.isU…PowerSeries.IsWeierstrassDivisorAt.coeff_seq_mem · cited by 2IsWeierstrassDivisorAt.co…PowerSeries.coeff_coe_trunc_of_lt · cited by 2PowerSeries.coeff_coe_tru…PowerSeries.normalized_count_X_eq_of_coe · cited by 1PowerSeries.normalized_co…DFunLike.coe · cited by 62936DFunLike.coeRingHom.id · cited by 18349RingHom.idSemiring · cited by 13802SemiringLinearMap · cited by 10215LinearMapPolynomial · cited by 5681PolynomialPolynomial.coeff · cited by 1045Polynomial.coeffPowerSeries · cited by 797PowerSeriesPowerSeries.coeff · cited by 324PowerSeries.coeffFinsupp.single_eq_same · cited by 171Finsupp.single_eq_samePolynomial.toPowerSeries · cited by 96Polynomial.toPowerSeriesPolynomial.coeff_coeCITED BYCITES

Cites10

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by25

Results whose statement or proof uses this declaration.