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refactor: Change in contraction notation

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jstoobysmith 2025-01-24 06:39:30 +00:00
parent 6701ee7b37
commit 321e69e52e
5 changed files with 326 additions and 324 deletions
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28
HepLean/PerturbationTheory/WickContraction/UncontractedList.lean
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@ -281,7 +281,16 @@ lemma take_uncontractedIndexEquiv_symm (k : c.uncontracted) :
rw [hl]
rw [uncontractedIndexEquiv_symm_eq_filter_length]
simp
/-!
## Uncontracted List get
-/
def uncontractedListGet {φs : List 𝓕.States} (φsΛ : WickContraction φs.length) :
List 𝓕.States := φsΛ.uncontractedList.map φs.get
scoped[WickContraction] notation "[" φsΛ "]ᵘᶜ" => uncontractedListGet φsΛ
/-!
## uncontractedStatesEquiv
@ -291,20 +300,21 @@ lemma take_uncontractedIndexEquiv_symm (k : c.uncontracted) :
/-- The equivalence between the type `Option c.uncontracted` for `WickContraction φs.length` and
`Option (Fin (c.uncontractedList.map φs.get).length)`, that is optional positions of
`c.uncontractedList.map φs.get` induced by `uncontractedIndexEquiv`. -/
def uncontractedStatesEquiv (φs : List 𝓕.States) (c : WickContraction φs.length) :
Option c.uncontracted ≃ Option (Fin (c.uncontractedList.map φs.get).length) :=
Equiv.optionCongr (c.uncontractedIndexEquiv.symm.trans (finCongr (by simp)))
def uncontractedStatesEquiv (φs : List 𝓕.States) (φsΛ : WickContraction φs.length) :
Option φsΛ.uncontracted ≃ Option (Fin [φsΛ]ᵘᶜ.length) :=
Equiv.optionCongr (φsΛ.uncontractedIndexEquiv.symm.trans
(finCongr (by simp [uncontractedListGet])))
@[simp]
lemma uncontractedStatesEquiv_none (φs : List 𝓕.States) (c : WickContraction φs.length) :
(uncontractedStatesEquiv φs c).toFun none = none := by
lemma uncontractedStatesEquiv_none (φs : List 𝓕.States) (φsΛ : WickContraction φs.length) :
(uncontractedStatesEquiv φs φsΛ).toFun none = none := by
simp [uncontractedStatesEquiv]
lemma uncontractedStatesEquiv_list_sum [AddCommMonoid α] (φs : List 𝓕.States)
(c : WickContraction φs.length) (f : Option (Fin (c.uncontractedList.map φs.get).length) → α) :
∑ (i : Option (Fin (c.uncontractedList.map φs.get).length)), f i =
∑ (i : Option c.uncontracted), f (c.uncontractedStatesEquiv φs i) := by
rw [(c.uncontractedStatesEquiv φs).sum_comp]
(φsΛ : WickContraction φs.length) (f : Option (Fin [φsΛ]ᵘᶜ.length) → α) :
∑ (i : Option (Fin [φsΛ]ᵘᶜ.length)), f i =
∑ (i : Option φsΛ.uncontracted), f (φsΛ.uncontractedStatesEquiv φs i) := by
rw [(φsΛ.uncontractedStatesEquiv φs).sum_comp]
/-!