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jstoobysmith merged 1 commit into from
Jun 29, 2026
Merged

Add criticality transfer API to PhyslibAlpha #1314

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60 changes: 60 additions & 0 deletions PhyslibAlpha/ClassicalFieldTheory/Local/TotalDivergenceEquivalence.lean
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Original file line number Diff line number Diff line change
Expand Up @@ -29,6 +29,7 @@ which facts are data and which facts are proved.

- `ClassicalFieldTheory.Local.HasTotalDivergenceDifference`
- `ClassicalFieldTheory.Local.IsEulerLagrangeEquivalent`
- `ClassicalFieldTheory.Local.IsEulerLagrangeEquivalent.eulerLagrangeOp_eq_zero_iff`
- `ClassicalFieldTheory.Local.IsEulerLagrangeEquivalent.isCritical_iff`
- `ClassicalFieldTheory.Local.TotalDivergenceEquivalence`
- `ClassicalFieldTheory.Local.TotalDivergenceEquivalence.isCritical_iff`
Expand Down Expand Up @@ -96,6 +97,18 @@ lemma trans {L1 L2 L3 : Lagrangian d m k}
intro f
exact (h23 f).trans (h12 f)

lemma eulerLagrangeOp_eq {source target : Lagrangian d m k}
(h : IsEulerLagrangeEquivalent source target)
(f : Space d → EuclideanSpace ℝ (Fin m)) :
eulerLagrangeOp target f = eulerLagrangeOp source f :=
h f

lemma eulerLagrangeOp_eq_zero_iff {source target : Lagrangian d m k}
(h : IsEulerLagrangeEquivalent source target)
(f : Space d → EuclideanSpace ℝ (Fin m)) :
eulerLagrangeOp target f = 0 ↔ eulerLagrangeOp source f = 0 := by
rw [h.eulerLagrangeOp_eq f]

lemma isCritical_iff {source target : Lagrangian d m k}
(h : IsEulerLagrangeEquivalent source target)
(f : Space d → EuclideanSpace ℝ (Fin m))
Expand All @@ -110,6 +123,28 @@ lemma isCritical_iff {source target : Lagrangian d m k}
source f hsourcef hsource,
h f]

lemma isCritical_target_of_source {source target : Lagrangian d m k}
(h : IsEulerLagrangeEquivalent source target)
(f : Space d → EuclideanSpace ℝ (Fin m))
(hsourcef : IsAdmissibleForAction source f)
(htargetf : IsAdmissibleForAction target f)
(hsource : Lagrangian.SmoothInCoordinates source)
(htarget : Lagrangian.SmoothInCoordinates target)
(hcrit : IsCritical source f) :
IsCritical target f :=
(h.isCritical_iff f hsourcef htargetf hsource htarget).2 hcrit

lemma isCritical_source_of_target {source target : Lagrangian d m k}
(h : IsEulerLagrangeEquivalent source target)
(f : Space d → EuclideanSpace ℝ (Fin m))
(hsourcef : IsAdmissibleForAction source f)
(htargetf : IsAdmissibleForAction target f)
(hsource : Lagrangian.SmoothInCoordinates source)
(htarget : Lagrangian.SmoothInCoordinates target)
(hcrit : IsCritical target f) :
IsCritical source f :=
(h.isCritical_iff f hsourcef htargetf hsource htarget).1 hcrit

end IsEulerLagrangeEquivalent

/-!
Expand Down Expand Up @@ -152,6 +187,11 @@ lemma eulerLagrangeOp_eq (E : TotalDivergenceEquivalence d m k)
eulerLagrangeOp E.target f = eulerLagrangeOp E.source f :=
E.sameEulerLagrangeOp f

lemma eulerLagrangeOp_eq_zero_iff (E : TotalDivergenceEquivalence d m k)
(f : Space d → EuclideanSpace ℝ (Fin m)) :
eulerLagrangeOp E.target f = 0 ↔ eulerLagrangeOp E.source f = 0 :=
E.sameEulerLagrangeOp.eulerLagrangeOp_eq_zero_iff f

lemma isCritical_iff (E : TotalDivergenceEquivalence d m k)
(f : Space d → EuclideanSpace ℝ (Fin m))
(hsourcef : IsAdmissibleForAction E.source f)
Expand All @@ -161,6 +201,26 @@ lemma isCritical_iff (E : TotalDivergenceEquivalence d m k)
IsCritical E.target f ↔ IsCritical E.source f := by
exact E.sameEulerLagrangeOp.isCritical_iff f hsourcef htargetf hsource htarget

lemma isCritical_target_of_source (E : TotalDivergenceEquivalence d m k)
(f : Space d → EuclideanSpace ℝ (Fin m))
(hsourcef : IsAdmissibleForAction E.source f)
(htargetf : IsAdmissibleForAction E.target f)
(hsource : Lagrangian.SmoothInCoordinates E.source)
(htarget : Lagrangian.SmoothInCoordinates E.target)
(hcrit : IsCritical E.source f) :
IsCritical E.target f :=
E.sameEulerLagrangeOp.isCritical_target_of_source f hsourcef htargetf hsource htarget hcrit

lemma isCritical_source_of_target (E : TotalDivergenceEquivalence d m k)
(f : Space d → EuclideanSpace ℝ (Fin m))
(hsourcef : IsAdmissibleForAction E.source f)
(htargetf : IsAdmissibleForAction E.target f)
(hsource : Lagrangian.SmoothInCoordinates E.source)
(htarget : Lagrangian.SmoothInCoordinates E.target)
(hcrit : IsCritical E.target f) :
IsCritical E.source f :=
E.sameEulerLagrangeOp.isCritical_source_of_target f hsourcef htargetf hsource htarget hcrit

end TotalDivergenceEquivalence

end Local
Expand Down
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