Theorems · Theorem · field theory
Polynomial.coeff_zero
∀ {R : Type u} [inst : Semiring R] (n : ℕ), Polynomial.coeff 0 n = 0- Defined in
- Mathlib.Algebra.Polynomial.Basic
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 83 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.
Cites3
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 · cited by 5,681
- Polynomial.coeffstatement · cited by 1,045
Cited by12
Results whose statement or proof uses this declaration.
- Polynomial.derivative_eq_zeroproof · cited by 4
- IsAlgebraic.of_smul_isIntegralproof · cited by 2
- Polynomial.expand_contractproof · cited by 2
- RingHom.isIntegralElem_leadingCoeff_mulproof · cited by 2
- Polynomial.comp_C_mul_X_eq_zero_iffproof · cited by 2
- MvPolynomial.isAlgebraic_of_mem_vars_of_forall_totalDegree_leproof · cited by 1
- Polynomial.coeff_pow_mul_natDegreeproof · cited by 1
- Polynomial.generalizedEisensteinproof · cited by 1
- AlgebraicClosure.toSplittingField_coeffproof · cited by 1
- Polynomial.coeff_divByMonic_X_sub_Cproof · cited by 0
- Ideal.jacobson_bot_polynomial_of_jacobson_botproof · cited by 0
- Polynomial.eq_zero_of_hasseDeriv_eq_zeroproof · cited by 0