Theorems · Theorem · field theory
Polynomial.coeff_monomial
∀ {R : Type u} {a : R} {m n : ℕ} [inst : Semiring R], ((Polynomial.monomial n) a).coeff m = if n = m then a else 0- Defined in
- Mathlib.Algebra.Polynomial.Basic
- Cited by
- 40 results in Mathlib
- Foundations
- Depth 98 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.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- RingHom.idstatement · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- LinearMapstatement · cited by 10,215
- Polynomialstatement · cited by 5,681
- Polynomial.coeffstatement · cited by 1,045
- AddMonoidAlgebra.coeffproof · cited by 365
- Polynomial.monomialstatement · cited by 256
- Finsupp.single_applyproof · cited by 99
- Polynomial.toFinsupp_monomialproof · cited by 13
Cited by40
Results whose statement or proof uses this declaration.
- Polynomial.coeff_C_zeroproof · cited by 58
- Polynomial.coeff_X_zeroproof · cited by 48
- Polynomial.coeff_Cproof · cited by 33
- Polynomial.coeff_scaleRootsproof · cited by 20
- Polynomial.coeff_Xproof · cited by 12
- Polynomial.coeff_X_oneproof · cited by 12
- Polynomial.coeff_expandproof · cited by 11
- Polynomial.coeff_oneproof · cited by 10
- Polynomial.coeff_C_mul_X_powproof · cited by 10
- MvPolynomial.optionEquivLeft_coeff_some_coeff_noneproof · cited by 7
- Polynomial.integralNormalization_coeffproof · cited by 6
- Polynomial.leadingCoeff_monomialproof · cited by 6