Theorems · Theorem · field theory
Polynomial.eval_sub
∀ {R : Type u} [inst : Ring 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
- 124 results in Mathlib
- Foundations
- Depth 93 from the axioms, rests on 1,864 definitions · 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_subproof · cited by 23
Cited by124
Results whose statement or proof uses this declaration.
- Polynomial.Splits.exists_eval_eq_zeroproof · cited by 14
- Polynomial.mem_nthRootsproof · cited by 9
- Polynomial.modByMonic_X_sub_C_eq_C_evalproof · cited by 7
- taylorWithinEval_succproof · cited by 6
- Matrix.det_eq_sign_charpoly_coeffproof · cited by 5
- WeierstrassCurve.Affine.evalEval_polynomialXproof · cited by 5
- Polynomial.mul_divByMonic_eq_iff_isRootproof · cited by 5
- bernstein_applyproof · cited by 4
- WeierstrassCurve.Affine.evalEval_polynomialproof · cited by 4
- spectrum.subset_polynomial_aevalproof · cited by 4
- WeierstrassCurve.Affine.nonsingular_negAddproof · cited by 4
- Polynomial.Chebyshev.T_eval_negproof · cited by 4