Theorems · Definition · commutative algebra
PolynomialModule.eval
{R : Type u_2} →
{M : Type u_3} →
[inst : CommRing R] → [inst_1 : AddCommGroup M] → [inst_2 : Module R M] → R → PolynomialModule R M →ₗ[R] MEvaluate a polynomial p : PolynomialModule R M at r : R.
- Defined in
- Mathlib.Algebra.Polynomial.Module.Basic
- Cited by
- 17 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingAddCommGroupModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- LinearMapstatement · cited by 10,215
- Finsupp.sumproof · cited by 481
- PolynomialModulestatement and proof · cited by 76
- PolynomialModule.coeffproof · cited by 27
Cited by20
Results whose statement or proof uses this declaration.
- taylorWithinEvalproof · cited by 27
- PolynomialModule.eval_singlestatement · cited by 9
- PolynomialModule.compproof · cited by 6
- taylor_within_zero_evalproof · cited by 6
- taylorWithinEval_succproof · cited by 6
- PolynomialModule.comp_applystatement · cited by 3
- Derivation.apply_aeval_eq'statement and proof · cited by 2
- PolynomialModule.eval_smulstatement and proof · cited by 2
- Differential.deriv_aeval_eqproof · cited by 2
- PolynomialModule.comp_evalstatement and proof · cited by 1
- PolynomialModule.comp_singleproof · cited by 1
- PolynomialModule.eval_lsinglestatement · cited by 1