Theorems · Theorem · commutative algebra
MvPolynomial.smul_eval
∀ {R : Type u} {σ : Type u_1} [inst : CommSemiring R] (x : σ → R) (p : MvPolynomial σ R) (s : R),
(MvPolynomial.eval x) (s • p) = s * (MvPolynomial.eval x) p- Defined in
- Mathlib.Algebra.MvPolynomial.Eval
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- CommSemiringstatement and proof · cited by 10,911
- RingHomstatement · cited by 10,189
- Finsuppstatement · cited by 5,255
- MvPolynomialstatement and proof · cited by 2,140
- MvPolynomial.Cproof · cited by 400
- MvPolynomial.evalstatement and proof · cited by 157
- RingHom.map_mulproof · cited by 45
- MvPolynomial.eval_Cproof · cited by 20
- MvPolynomial.smul_eq_C_mulproof · cited by 6
Cited by1
Results whose statement or proof uses this declaration.
- MvPolynomial.map_restrict_dom_evalₗproof · cited by 1