Theorems · Theorem · field theory
Polynomial.eval_zero
∀ {R : Type u} [inst : Semiring R] {x : R}, Polynomial.eval x 0 = 0- Defined in
- Mathlib.Algebra.Polynomial.Eval.Defs
- Cited by
- 36 results in Mathlib
- Foundations
- Depth 85 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.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- RingHom.idproof · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- Polynomialstatement · cited by 5,681
- Polynomial.evalstatement · cited by 796
- Polynomial.eval₂_zeroproof · cited by 14
Cited by36
Results whose statement or proof uses this declaration.
- Polynomial.Splits.exists_eval_eq_zeroproof · cited by 14
- Polynomial.isEquivalent_atTop_divproof · cited by 5
- Polynomial.isEquivalent_atTop_leadproof · cited by 5
- Polynomial.div_tendsto_atTop_zero_of_degree_ltproof · cited by 5
- Polynomial.logMahlerMeasure_eq_log_MahlerMeasureproof · cited by 4
- Polynomial.resultant_eq_prod_evalproof · cited by 3
- Polynomial.zero_lt_eval_of_roots_lt_of_leadingCoeff_nonnegproof · cited by 3
- Polynomial.coeff_mul_invOneSubPow_eq_hilbertPoly_evalproof · cited by 3
- evalRingHom_mapMatrix_comp_polyToMatrixproof · cited by 2
- bernsteinPolynomial.iterate_derivative_at_0proof · cited by 2
- Polynomial.isBigO_atTop_of_degree_leproof · cited by 2
- Polynomial.isEquivalent_cobounded_leading_monomialproof · cited by 2