Theorems · Theorem · field theory
Polynomial.eval_neg
∀ {R : Type u} [inst : Ring R] (p : Polynomial R) (x : R), Polynomial.eval x (-p) = -Polynomial.eval x p- Defined in
- Mathlib.Algebra.Polynomial.Eval.Defs
- Cited by
- 30 results in Mathlib
- Foundations
- Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Ring
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
- Ringstatement and proof · cited by 7,463
- Polynomialstatement and proof · cited by 5,681
- Polynomial.evalstatement · cited by 796
- Polynomial.eval₂_negproof · cited by 3
Cited by30
Results whose statement or proof uses this declaration.
- WeierstrassCurve.Affine.nonsingular_negAddproof · cited by 4
- Matrix.eval_charpolyproof · cited by 2
- Polynomial.abs_tendsto_atBotproof · cited by 2
- Polynomial.zero_lt_negOnePow_mul_eval_of_lt_roots_of_leadingCoeff_nonnegproof · cited by 2
- WeierstrassCurve.Affine.equation_negAddproof · cited by 2
- Module.reflection_mul_reflection_pow_applyproof · cited by 2
- Module.reflection_mul_reflection_zpow_applyproof · cited by 1
- FiniteField.exists_root_sum_quadraticproof · cited by 1
- Matrix.eval_charpolyRevproof · cited by 1
- Polynomial.eval_lt_zero_of_roots_lt_of_leadingCoeff_nonposproof · cited by 1
- Polynomial.isEquivalent_atBot_leadproof · cited by 1
- polynomialFunctions.comap_compRightAlgHom_iccHomeoIproof · cited by 1