Lax Lean Archive

Constructible differentially algebraic series

Lax825748.CDA · concepts/Lax825748/CDA.lean · lax-825748

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    Natural Language Statement

    Definition

    A commutative formal power series is constructible differentially algebraic (CDA) if it belongs to a finitely generated unital real subalgebra stable under every ordinary partial derivative. Auxiliary generators are allowed; their number need not equal the number of independent variables.

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    Lean source view on GitHub

    1import Lax825748.FormalSeries
    2import Mathlib.RingTheory.Adjoin.FG
    3
    4/-!
    5---
    6title: Constructible differentially algebraic series
    7type: definition
    8---
    9A commutative formal power series is constructible differentially algebraic
    10(CDA) if it belongs to a finitely generated unital real subalgebra stable
    11under every ordinary partial derivative. Auxiliary generators are allowed;
    12their number need not equal the number of independent variables.
    13-/
    14
    15noncomputable section
    16
    17namespace Lax825748.CDA
    18
    19open FormalSeries
    20
    21def DerivativeStable {d : ℕ} (C : Subalgebra ℝ (StateSeries d)) : Prop :=
    22 ∀ (i : Fin d) (f : StateSeries d), f ∈ C → MvPowerSeries.pderiv ℝ i f ∈ C
    23
    24def IsCDA {d : ℕ} (f : StateSeries d) : Prop :=
    25 ∃ C : Subalgebra ℝ (StateSeries d), C.FG ∧ DerivativeStable C ∧ f ∈ C
    26
    27end Lax825748.CDA
    28
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