Theorems · Theorem · field theory
Polynomial.coeff_mul_monomial
∀ {R : Type u} [inst : Semiring R] (p : Polynomial R) (n d : ℕ) (r : R),
(p * (Polynomial.monomial n) r).coeff (d + n) = p.coeff d * r- Defined in
- Mathlib.Algebra.Polynomial.Coeff
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 107 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.
Cites14
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 and proof · cited by 5,681
- mul_assocproof · cited by 1,667
- Polynomial.Xproof · cited by 1,639
- Polynomial.Cproof · cited by 1,598
- Polynomial.coeffstatement and proof · cited by 1,045
- Polynomial.monomialstatement · cited by 256
- Polynomial.C_mul_X_pow_eq_monomialproof · cited by 53
- Polynomial.coeff_mul_Cproof · cited by 20
Cited by2
Results whose statement or proof uses this declaration.
- Polynomial.coeff_mul_monomial_zeroproof · cited by 0
- Polynomial.succ_signVariations_X_sub_C_mul_monomialproof · cited by 0