Theorems · Theorem · algebraic geometry

WeierstrassCurve.Projective.add_of_X_ne

∀ {F : Type u} [inst : Field F] {W : WeierstrassCurve.Projective F} [inst_1 : DecidableEq F] {P Q : Fin 3 → F},
  W.Equation P →
    W.Equation Q →
      P 2 ≠ 0 →
        Q 2 ≠ 0 →
          P 0 * Q 2 ≠ Q 0 * P 2 →
            W.add P Q =
              W.addZ P Q •
                ![W.toAffine.addX (P 0 / P 2) (Q 0 / Q 2)
                    (W.toAffine.slope (P 0 / P 2) (Q 0 / Q 2) (P 1 / P 2) (Q 1 / Q 2)),
                  W.toAffine.addY (P 0 / P 2) (Q 0 / Q 2) (P 1 / P 2)
                    (W.toAffine.slope (P 0 / P 2) (Q 0 / Q 2) (P 1 / P 2) (Q 1 / Q 2)),
                  1]

Defined in

Mathlib.AlgebraicGeometry.EllipticCurve.Projective.Point

Cited by

3 results in Mathlib

Foundations

Depth 103 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldDecidableEq