Theorems · Theorem · number theory
IsNonarchimedean.eval_mvPolynomial_le
∀ {K : Type u_4} [inst : Field K] {ι : Type u_5} [Finite ι] {v : AbsoluteValue K ℝ},
IsNonarchimedean ⇑v →
∀ {p : MvPolynomial ι K} {N : ℕ},
p.IsHomogeneous N →
∀ (x : ι → K), v ((MvPolynomial.eval x) p) ≤ (⨆ s, v (MvPolynomial.coeff (↑s) p)) * (⨆ i, v (x i)) ^ N- Defined in
- Mathlib.NumberTheory.Height.MvPolynomial
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 121 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites44
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
- Realstatement and proof · cited by 25,697
- Finsetstatement and proof · cited by 13,712
- RingHomstatement · cited by 10,189
- Fieldstatement and proof · cited by 7,404
- Finsuppstatement and proof · cited by 5,255
- Finset.sumproof · cited by 5,195
- Finitestatement and proof · cited by 3,029
- iSupstatement and proof · cited by 2,415
- Finset.prodproof · cited by 2,356
- MvPolynomialstatement and proof · cited by 2,140
- le_reflproof · cited by 2,061
Cited by1
Results whose statement or proof uses this declaration.
- Height.mulHeight_eval_leproof · cited by 3