Theorems · Theorem · field theory
Polynomial.coeff_one_zero
∀ {R : Type u} [inst : Semiring R], Polynomial.coeff 1 0 = 1- Defined in
- Mathlib.Algebra.Polynomial.Basic
- Cited by
- 21 results in Mathlib
- Foundations
- Depth 100 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
- Polynomialstatement · cited by 5,681
- Polynomial.coeffstatement · cited by 1,045
- Polynomial.coeff_oneproof · cited by 10
Cited by22
Results whose statement or proof uses this declaration.
- Polynomial.constantCoeffproof · cited by 15
- Polynomial.cyclotomic_coeff_zeroproof · cited by 3
- Polynomial.resultant_eq_prod_evalproof · 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
- Polynomial.isUnit_resultant_iff_isCoprimeproof · cited by 2
- Polynomial.coeff_isUnit_isNilpotent_of_isUnitproof · cited by 2
- Polynomial.resultant_prod_leftproof · cited by 2
- isIntegral_of_isIntegral_adjoin_of_mul_eq_oneproof · cited by 1
- PrimeSpectrum.isIntegral_of_isClosedMap_comap_mapRingHomproof · cited by 1
- Polynomial.coeff_pow_mul_natDegreeproof · cited by 1
- Polynomial.coeff_pow_of_natDegree_leproof · cited by 1