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https://github.com/allaunthefox/SilverSight.git
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allaun
48ee7f7fdb
C: stack_overflow test now uses AVM_MAX_STACK+10 fuel Octave: test creates AVM() instance and calls methods on it
55 lines
1.6 KiB
Text
55 lines
1.6 KiB
Text
import CoreFormalism.BraidStateN
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import CoreFormalism.FixedPoint
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open SilverSight.BraidStateN
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open SilverSight.FixedPoint
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namespace SilverSight.HopfFibration
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structure Quaternion where
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a : Q16_16
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b : Q16_16
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c : Q16_16
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d : Q16_16
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deriving Repr
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namespace Quaternion
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def conj (q : Quaternion) : Quaternion :=
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{ a := q.a, b := Q16_16.neg q.b, c := Q16_16.neg q.c, d := Q16_16.neg q.d }
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def sumSq (q : Quaternion) : Q16_16 :=
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let sq (x : Q16_16) := Q16_16.mul x x
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Q16_16.add (Q16_16.add (sq q.a) (sq q.b)) (Q16_16.add (sq q.c) (sq q.d))
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def isUnit (q : Quaternion) : Prop :=
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sumSq q = Q16_16.one
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def ofChiralLabel (label : ChiralLabel) : Quaternion :=
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match label with
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| ChiralLabel.achiral_stable => { a := Q16_16.one, b := 0, c := 0, d := 0 }
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| ChiralLabel.left_handed_mass_bias => { a := 0, b := Q16_16.one, c := 0, d := 0 }
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| ChiralLabel.right_handed_vector_bias => { a := 0, b := 0, c := Q16_16.one, d := 0 }
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| ChiralLabel.chiral_scarred => { a := 0, b := 0, c := 0, d := Q16_16.one }
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theorem ofChiralLabel_isUnit (label : ChiralLabel) : isUnit (ofChiralLabel label) := by
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unfold isUnit ofChiralLabel sumSq
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simp
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end Quaternion
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structure PointS7 where
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q1 : Quaternion
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q2 : Quaternion
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deriving Repr
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def braidToS7 (s : BraidStateN 8) : PointS7 :=
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let a0 := (s.strands ⟨0, by decide⟩).residue
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let a1 := (s.strands ⟨2, by decide⟩).residue
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let a2 := (s.strands ⟨4, by decide⟩).residue
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let a3 := (s.strands ⟨6, by decide⟩).residue
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{ q1 := { a := a0, b := a1, c := 0, d := 0 }
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, q2 := { a := a2, b := a3, c := 0, d := 0 }
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}
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end SilverSight.HopfFibration
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