Theorems · Theorem · field theory
Polynomial.coeff_X_zero
∀ {R : Type u} [inst : Semiring R], Polynomial.X.coeff 0 = 0- Defined in
- Mathlib.Algebra.Polynomial.Basic
- Cited by
- 48 results in Mathlib
- Foundations
- Depth 99 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.
Cites4
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
- Polynomial.Xstatement · cited by 1,639
- Polynomial.coeffstatement · cited by 1,045
- Polynomial.coeff_monomialproof · cited by 40
Cited by48
Results whose statement or proof uses this declaration.
- 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
- Polynomial.coprime_of_root_cyclotomicproof · cited by 2
- 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
- GaloisField.finrankproof · cited by 2
- Polynomial.natDegree_eq_oneproof · cited by 2