Theorems · Theorem · field theory
Polynomial.mul_coeff_zero
∀ {R : Type u} [inst : Semiring R] (p q : Polynomial R), (p * q).coeff 0 = p.coeff 0 * q.coeff 0- Defined in
- Mathlib.Algebra.Polynomial.Coeff
- Cited by
- 37 results in Mathlib
- Foundations
- Depth 79 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.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- Polynomialstatement and proof · cited by 5,681
- Finset.sum_congrproof · cited by 2,323
- Polynomial.coeffstatement and proof · cited by 1,045
- Finset.sum_singletonproof · cited by 251
- Polynomial.coeff_mulproof · cited by 29
- Finset.HasAntidiagonal.antidiagonal_zeroproof · cited by 8
Cited by38
Results whose statement or proof uses this declaration.
- Polynomial.constantCoeffproof · cited by 15
- Polynomial.divX_mul_X_addproof · cited by 6
- Polynomial.eq_X_add_C_of_degree_le_oneproof · cited by 5
- Polynomial.cyclotomic_coeff_zeroproof · cited by 3
- Algebra.exists_aeval_invOf_eq_zero_of_idealMap_adjoin_sup_span_eq_topproof · cited by 3
- IsLocalization.isAlgebraicproof · cited by 2
- Polynomial.eq_mul_mul_of_roots_quadratic_eq_pairproof · cited by 2
- Polynomial.coeff_X_mul_zeroproof · cited by 2
- Polynomial.X_mul_divX_addproof · cited by 2
- Polynomial.irreducible_C_mul_X_add_Cproof · cited by 2
- Polynomial.coeff_isUnit_isNilpotent_of_isUnitproof · cited by 2
- Polynomial.natDegree_eq_oneproof · cited by 2