Theorems · Definition · functional analysis

FormalMultilinearSeries.order

{𝕜 : Type u} →
  {E : Type v} →
    {F : Type w} →
      [inst : Semiring 𝕜] →
        [inst_1 : AddCommMonoid E] →
          [inst_2 : Module 𝕜 E] →
            [inst_3 : TopologicalSpace E] →
              [inst_4 : ContinuousAdd E] →
                [inst_5 : ContinuousConstSMul 𝕜 E] →
                  [inst_6 : AddCommMonoid F] →
                    [inst_7 : Module 𝕜 F] →
                      [inst_8 : TopologicalSpace F] →
                        [inst_9 : ContinuousAdd F] →
                          [inst_10 : ContinuousConstSMul 𝕜 F] → FormalMultilinearSeries 𝕜 E F → ℕ

The index of the first non-zero coefficient in p (or 0 if all coefficients are zero). This is the order of the isolated zero of an analytic function f at a point if p is the Taylor series of f at that point.

Defined in

Mathlib.Analysis.Calculus.FormalMultilinearSeries

Cited by

13 results in Mathlib

Foundations

Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringAddCommMonoidModuleTopologicalSpaceContinuousAddContinuousConstSMulAddCommMonoidModuleTopologicalSpaceContinuousAddContinuousConstSMul