WeilPairing.lean`

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1 declarations, 1 contain sorry, 0 declared as axioms

The Weil pairing

Let E be an elliptic curve over a separably closed field k and let n be a natural number which is nonzero in k. This file states the existence of the Weil pairing, a bilinear pairing on the n-torsion of E(k) with values in the n-th roots of unity of k.

Imports (3)

Imported by 2 files

def WeierstrassCurve.weilPairing The Weil pairing on the n-torsion of an elliptic curve E over a separably closed field k, a bilinear pairing with values in the n-th roots of unity of k sorry line 38 source
Source documentation
The Weil pairing on the n-torsion of an elliptic curve E over a separably closed field k, a bilinear pairing with values in the n-th roots of unity of k.

depends on sorry what this means
Statement uses: Field, DecidableEq, WeierstrassCurve, Nat, AddMonoidHom, Subtype, WeierstrassCurve.Affine.Point, WeierstrassCurve.Affine.baseChange, Membership.mem, AddSubgroup, AddSubgroup.torsionBy, Int, Additive, Units, Subgroup, rootsOfUnity
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous, OfNat.ofNat
60 instances, coercions and auxiliary constants left out.
```
def WeierstrassCurve.weilPairing :
    AddSubgroup.torsionBy (E⁄k).Point (n : ℤ) →+
    AddSubgroup.torsionBy (E⁄k).Point (n : ℤ) →+
    Additive (rootsOfUnity n k) :=
…
```