refactor: Slight adjustments to doc-strings
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15 changed files with 64 additions and 30 deletions
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@ -291,9 +291,15 @@ lemma insert_fin_eq_self (φ : 𝓕.FieldOp) {φs : List 𝓕.FieldOp}
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Wick contractions of `φs` with `φ` inserted at `i` is equal to the sum over Wick contractions
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`φsΛ` of just `φs` and the sum over optional uncontracted elements of the `φsΛ`.
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In other words, `∑ (φsΛ : WickContraction (φs.insertIdx i φ).length), f φsΛ` is equal to
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`∑ (φsΛ : WickContraction φs.length), ∑ (k : Option φsΛ.uncontracted), f (φsΛ ↩Λ φ i k) `.
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where `(φs.insertIdx i φ)` is `φs` with `φ` inserted at position `i`. -/
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In other words,
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`∑ (φsΛ : WickContraction (φs.insertIdx i φ).length), f φsΛ`
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where `(φs.insertIdx i φ)` is `φs` with `φ` inserted at position `i`. is equal to
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`∑ (φsΛ : WickContraction φs.length), ∑ k, f (φsΛ ↩Λ φ i k) `.
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where the sum over `k` is over all `k` in `Option φsΛ.uncontracted`. -/
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lemma insertLift_sum (φ : 𝓕.FieldOp) {φs : List 𝓕.FieldOp}
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(i : Fin φs.length.succ) [AddCommMonoid M] (f : WickContraction (φs.insertIdx i φ).length → M) :
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∑ c, f c =
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@ -22,7 +22,8 @@ open FieldStatistic
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/-- Given a Wick contraction `c : WickContraction n` and `i1 i2 : Fin n` the finite set
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of elements of `Fin n` between `i1` and `i2` which are either uncontracted
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or are contracted but are contracted with an element occurring after `i1`.
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I.e. the elements of `Fin n` between `i1` and `i2` which are not contracted with before `i1`.
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In other words, the elements of `Fin n` between `i1` and `i2` which are not
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contracted with before `i1`.
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One should assume `i1 < i2` otherwise this finite set is empty. -/
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def signFinset (c : WickContraction n) (i1 i2 : Fin n) : Finset (Fin n) :=
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Finset.univ.filter (fun i => i1 < i ∧ i < i2 ∧
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