Theorems · Theorem · field theory
Polynomial.coeff_C_mul
∀ {R : Type u} {a : R} {n : ℕ} [inst : Semiring R] (p : Polynomial R), (Polynomial.C a * p).coeff n = a * p.coeff n- Defined in
- Mathlib.Algebra.Polynomial.Coeff
- Cited by
- 55 results in Mathlib
- Foundations
- Depth 101 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 · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- RingHomstatement · cited by 10,189
- Polynomialstatement and proof · cited by 5,681
- Polynomial.Cstatement · cited by 1,598
- Polynomial.coeffstatement and proof · cited by 1,045
- AddMonoidAlgebraproof · cited by 649
- AddMonoidAlgebra.singleproof · cited by 250
- Polynomial.casesOnproof · cited by 15
- AddMonoidAlgebra.coeff_single_zero_mulproof · cited by 1
Cited by55
Results whose statement or proof uses this declaration.
- Polynomial.coeff_mapproof · cited by 114
- Polynomial.coeff_derivativeproof · cited by 14
- Polynomial.C_mul'proof · cited by 12
- Polynomial.smul_eq_C_mulproof · cited by 9
- Polynomial.coeff_comp_degree_mul_degreeproof · cited by 7
- Polynomial.coeff_freeMonicproof · cited by 6
- MvPolynomial.finSuccEquiv_coeff_coeffproof · cited by 5
- Polynomial.resultant_C_mul_rightproof · cited by 5
- Polynomial.associated_content_C_mulproof · cited by 4
- Polynomial.coeff_eq_esymm_roots_of_cardproof · cited by 4
- Polynomial.Monic.isPrimitiveproof · cited by 4
- Polynomial.resultant_eq_prod_evalproof · cited by 3