Theorems · Theorem · field theory
Polynomial.coeff_C_zero
∀ {R : Type u} {a : R} [inst : Semiring R], (Polynomial.C a).coeff 0 = a- Defined in
- Mathlib.Algebra.Polynomial.Basic
- Cited by
- 58 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.
Cites7
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 · cited by 5,681
- Polynomial.Cstatement · cited by 1,598
- Polynomial.coeffstatement · cited by 1,045
- Polynomial.coeff_monomialproof · cited by 40
Cited by58
Results whose statement or proof uses this declaration.
- Polynomial.eq_C_of_degree_le_zeroproof · cited by 20
- Polynomial.isUnit_Cproof · cited by 19
- Polynomial.eq_X_add_C_of_degree_le_oneproof · cited by 5
- Polynomial.content_Cproof · cited by 5
- Polynomial.Splits.of_natDegree_le_one_of_invertibleproof · cited by 4
- Polynomial.resultant_C_rightproof · cited by 3
- X_pow_sub_C_irreducible_of_oddproof · cited by 3
- Polynomial.gaussNorm_Cproof · cited by 2
- IsLocalization.isAlgebraicproof · cited by 2
- Polynomial.eq_mul_mul_of_roots_quadratic_eq_pairproof · cited by 2
- Irreducible.isPrimitiveproof · cited by 2
- Polynomial.eq_neg_mul_add_of_roots_quadratic_eq_pairproof · cited by 2