Theorems · Definition · field theory
Polynomial.constantCoeff
{R : Type u} → [inst : Semiring R] → Polynomial R →+* RconstantCoeff p returns the constant term of the polynomial p,
defined as coeff p 0. This is a ring homomorphism.
- Defined in
- Mathlib.Algebra.Polynomial.Coeff
- Cited by
- 15 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.
Cites6
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
- RingHomstatement · cited by 10,189
- Polynomialstatement and proof · cited by 5,681
- Polynomial.coeffproof · cited by 1,045
- Polynomial.mul_coeff_zeroproof · cited by 37
- Polynomial.coeff_one_zeroproof · cited by 21
Cited by15
Results whose statement or proof uses this declaration.
- Polynomial.isUnit_Cproof · cited by 19
- Polynomial.constantCoeff_applystatement and proof · cited by 6
- LinearMap.not_hasEigenvalue_zero_tfaestatement and proof · cited by 2
- Irreducible.isPrimitiveproof · cited by 2
- ringKrullDim_succ_le_ringKrullDim_polynomialproof · cited by 2
- LinearMap.hasEigenvalue_zero_tfaestatement and proof · cited by 2
- LinearMap.finrank_maxGenEigenspace_zero_eqproof · cited by 2
- Polynomial.natTrailingDegree_eq_zero_of_constantCoeff_ne_zerostatement and proof · cited by 1
- LinearMap.charpoly_constantCoeff_eq_zero_iffstatement and proof · cited by 1
- LieAlgebra.engel_isBot_of_isMinproof · cited by 1
- minpoly.natSepDegree_eq_one_iff_eq_X_sub_C_powproof · cited by 1
- Polynomial.constantCoeff_surjectivestatement · cited by 0