Theorems · Theorem · field theory
Polynomial.coeff_mul_C
∀ {R : Type u} [inst : Semiring R] (p : Polynomial R) (n : ℕ) (a : R), (p * Polynomial.C a).coeff n = p.coeff n * a- Defined in
- Mathlib.Algebra.Polynomial.Coeff
- Cited by
- 20 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_mul_single_zeroproof · cited by 1
Cited by20
Results whose statement or proof uses this declaration.
- Polynomial.taylor_coeffproof · cited by 4
- coeff_minpolyDivproof · cited by 2
- exists_isTranscendenceBasis_and_isSeparable_of_linearIndepOn_powproof · cited by 2
- Polynomial.coeff_mul_monomialproof · cited by 2
- Polynomial.integralNormalization_mul_C_leadingCoeffproof · cited by 2
- Field.primitive_element_inf_auxproof · cited by 1
- Polynomial.X_sub_C_scaleRootsproof · cited by 1
- IsPrimitiveRoot.sum_eq_zero_iff_forall_eqproof · cited by 1
- isStronglyTranscendental_mk_of_mem_minimalPrimesproof · cited by 1
- Polynomial.coeff_X_add_C_powproof · cited by 1
- Polynomial.X_add_C_scaleRootsproof · cited by 1
- Polynomial.coeff_mul_natCastproof · cited by 1