| import OAI.AlgebraicGeometry.CharacterVarieties.Frames.Mirror |
| import OAI.AlgebraicGeometry.CharacterVarieties.Frames.NamedSeams |
| import OAI.AlgebraicGeometry.CharacterVarieties.Cutting.MarkedDiagram |
|
|
| namespace OAI |
|
|
| noncomputable section |
| namespace IntegralCharacterVarieties.SurfacePresentation.Diagram |
| open scoped Classical Matrix |
| open OccurrenceIncidence MatrixExpression NamedBandGrades |
| variable {F S V K : Type} {arity : S → ℕ} [Field K] |
| (D : Diagram F S V arity) (q : S) [Finite V] |
| (g : (e : D.Generator) → (Matrix (Fin (D.generatorRank e)) (Fin (D.generatorRank e)) K)ˣ) |
| (J : (Matrix (Fin (D.rank (D.ports.facet ⟨q,none⟩))) |
| (Fin (D.rank (D.ports.facet ⟨q,none⟩))) K)ˣ) |
| /-- A simultaneous splitting for arbitrary original generator coordinates, including the circle- |
| gauged coordinates of the surface equation. -/ |
| opaque cutGeneratorWitness : IdentifiedBand (D.childDim q) |
| (D.namedSeamFrame q (g (.frame q false))) |
| (((D.namedSeamFrame q (g (.frame q false))).trans (D.namedParentLinear q g)).trans |
| (MatrixIso.unit J).linearEquiv.symm) := |
| identifiedBand (D.namedSeamFrame q (g (.frame q false))) |
| (((D.namedSeamFrame q (g (.frame q false))).trans (D.namedParentLinear q g)).trans |
| (MatrixIso.unit J).linearEquiv.symm) |
| end IntegralCharacterVarieties.SurfacePresentation.Diagram |
| end |
|
|
| noncomputable section |
| namespace IntegralCharacterVarieties.SurfacePresentation.Diagram |
| open scoped Classical Matrix |
| open OccurrenceIncidence MatrixExpression NamedBandGrades |
| variable {F S V K : Type} {arity : S → ℕ} [Field K] |
| (D : Diagram F S V arity) (q : S) [Finite V] |
| {f h : (((i : Fin (arity q)) × Fin (D.childDim q i)) → K) ≃ₗ[K] |
| (Fin (D.rank (D.ports.facet ⟨q,none⟩)) → K)} |
| (w : IdentifiedBand (D.childDim q) f h) |
| (hproper : D.Proper) (hmax : ∀ f,D.rank f≤D.rank (D.ports.facet ⟨q,none⟩)) |
| (old : D.PortFrames (R:=K)) |
| (T : MatrixIso K (Fin (D.rank (D.ports.facet ⟨q,none⟩))) |
| (Fin (D.rank (D.ports.facet ⟨q,none⟩)))) |
|
|
| def markedCutFrames : (D.refinedMarkedDiagram q w.shape rfl w.rowRanks w.colRanks hproper hmax).PortFrames (R:=K) := |
| D.namedCutPortFrames q w old T |
|
|
| lemma markedCutFrames_holds |
| (hold : ∀ v,(VertexTable.LocalRanks.comparison (D.ports.kind v) (D.vertexRanks v) |
| (fun p => old ⟨v,p⟩)).Holds) : |
| ∀ v,(VertexTable.LocalRanks.comparison |
| ((D.refinedMarkedDiagram q w.shape rfl w.rowRanks w.colRanks hproper hmax).ports.kind v) |
| ((D.refinedMarkedDiagram q w.shape rfl w.rowRanks w.colRanks hproper hmax).vertexRanks v) |
| (fun p => D.markedCutFrames q w hproper hmax old T ⟨v,p⟩)).Holds := |
| D.namedCutPortFrames_holds q w old T hold |
|
|
| lemma marked_values_vertexHolds |
| (oldHolds : ∀ v,(VertexTable.LocalRanks.comparison (D.ports.kind v) (D.vertexRanks v) |
| (fun p => old ⟨v,p⟩)).Holds) |
| (s : (D.refinedMarkedDiagram q w.shape rfl w.rowRanks w.colRanks hproper hmax).SideValues (R:=K)) |
| (hh : (D.refinedMarkedDiagram q w.shape rfl w.rowRanks w.colRanks hproper hmax).HandleValues (R:=K)) : |
| (D.refinedMarkedDiagram q w.shape rfl w.rowRanks w.colRanks hproper hmax).VertexHolds |
| ((D.refinedMarkedDiagram q w.shape rfl w.rowRanks w.colRanks hproper hmax).valuesFromPorts |
| (D.markedCutFrames q w hproper hmax old T) s hh) := by |
| exact @vertexHolds_valuesFromPorts _ _ _ K _ _ |
| (D.refinedMarkedDiagram q w.shape rfl w.rowRanks w.colRanks hproper hmax) |
| (D.markedCutFrames q w hproper hmax old T) s hh |
| (D.markedCutFrames_holds q w hproper hmax old T oldHolds) |
| end IntegralCharacterVarieties.SurfacePresentation.Diagram |
| end |
|
|
| end OAI |
|
|
