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Dimensions of the concrete coefficient space

Lax342547.CoordinateCounts · concepts/Lax342547/CoordinateCounts.lean · lax-342547

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    Natural Language Statement

    Theorem

    The selector dimension counts squarefree monomials by cardinality. The base coordinates comprise g² ordinary blocks and three common blocks, each of length n; the coefficient space has one extra constant coordinate.

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    Proven claimDefinitionThis conceptRelated conceptA → B: B builds on A
    Evidence

    Each proof establishes this claim relative to its assumptions.

    Lean source view on GitHub

    1import Lax342547.ConcreteGeometry
    2
    3/-!
    4---
    5title: Dimensions of the concrete coefficient space
    6type: theorem
    7---
    8The selector dimension counts squarefree monomials by cardinality.
    9The base coordinates comprise g² ordinary blocks and three common blocks,
    10each of length n; the coefficient space has one extra constant coordinate.
    11-/
    12
    13namespace Lax342547.CoordinateCounts
    14
    15open Lax342547.MomentSpace Lax342547.TagGeometry Lax342547.ConcreteGeometry
    16
    17axiom coordinate_dimensions (k n b degree : ℕ) :
    18 Fintype.card (SelectorCoordinates b degree) = ∑ j ∈ Finset.range (degree + 1), b.choose j ∧
    19 Fintype.card (Base k n) = ((2 * k + 1) ^ 2 + 3) * n ∧
    20 Fintype.card (Coordinate k n b degree) =
    21 (∑ j ∈ Finset.range (degree + 1), b.choose j) * (1 + ((2 * k + 1) ^ 2 + 3) * n)
    22
    23end Lax342547.CoordinateCounts
    24
    Show Proof
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    From Mathlib

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