Theorems · Theorem · commutative algebra
PolynomialModule.aeval_equivPolynomial
∀ {R : Type u_2} [inst : CommRing R] {S : Type u_8} [inst_1 : CommRing S] [inst_2 : Algebra S R]
(f : PolynomialModule S S) (x : R),
(Polynomial.aeval x) (PolynomialModule.equivPolynomial f) =
(PolynomialModule.eval x) ((PolynomialModule.map R (Algebra.linearMap S R)) f)- Defined in
- Mathlib.Algebra.Polynomial.Module.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 111 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites26
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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- CommRingstatement and proof · cited by 17,173
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- LinearMapstatement · cited by 10,215
- Polynomialstatement and proof · cited by 5,681
- Algebra.algebraMapproof · cited by 4,706
- LinearEquivstatement · cited by 3,317
- AlgHomstatement · cited by 3,236
- mul_commproof · cited by 2,262
- map_zeroproof · cited by 1,614
- map_addproof · cited by 964
Cited by1
Results whose statement or proof uses this declaration.
- Differential.deriv_aeval_eqproof · cited by 2