Theorems · Theorem · field theory
Polynomial.eval_add
∀ {R : Type u} [inst : Semiring R] {p q : Polynomial R} {x : R},
Polynomial.eval x (p + q) = Polynomial.eval x p + Polynomial.eval x q- Defined in
- Mathlib.Algebra.Polynomial.Eval.Defs
- Cited by
- 84 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 and proof · cited by 5,681
- Polynomial.evalstatement · cited by 796
- Polynomial.eval₂_addproof · cited by 22
Cited by85
Results whose statement or proof uses this declaration.
- Polynomial.eval_compproof · cited by 29
- Polynomial.eval₂_eq_eval_mapproof · cited by 29
- WeierstrassCurve.Affine.evalEval_polynomialXproof · cited by 5
- WeierstrassCurve.Affine.evalEval_polynomialYproof · cited by 5
- Polynomial.levalproof · cited by 4
- Polynomial.taylor_evalproof · cited by 4
- WeierstrassCurve.Affine.evalEval_polynomialproof · cited by 4
- Polynomial.eval_C_mulproof · cited by 4
- WeierstrassCurve.Affine.nonsingular_negAddproof · cited by 4
- Matrix.GeneralLinearGroup.IsParabolic.smul_eq_self_iffproof · cited by 3
- Matrix.adjugate_mul_distribproof · cited by 3
- Polynomial.hasStrictDerivAtproof · cited by 3