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Theorems · Theorem · field theory

Polynomial.eval_list_prod

∀ {R : Type u} [inst : CommSemiring R] (l : List (Polynomial R)) (x : R),
  Polynomial.eval x l.prod = (List.map (Polynomial.eval x) l).prod

Polynomial evaluation commutes with List.prod

Defined in
Mathlib.Algebra.Polynomial.Eval.Defs
Cited by
1 results in Mathlib
Foundations
Depth 107 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommSemiring
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Polynomial.evalEval_list_prod · cited by 0Polynomial.evalEval_list_…CommSemiring · cited by 10911CommSemiringPolynomial · cited by 5681PolynomialPolynomial.eval · cited by 796Polynomial.evalmap_list_prod · cited by 35map_list_prodPolynomial.evalRingHom · cited by 29Polynomial.evalRingHomPolynomial.eval_list_prodCITED BYCITES

Cites5

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by1

Results whose statement or proof uses this declaration.