Theorems · Definition · algebraic geometry

WeierstrassCurve.Projective.addMap

{R : Type r} →
  [inst : CommRing R] →
    WeierstrassCurve.Projective R →
      WeierstrassCurve.Projective.PointClass R →
        WeierstrassCurve.Projective.PointClass R → WeierstrassCurve.Projective.PointClass R

The addition of two projective point classes on a Weierstrass curve W. If P and Q are two projective point representatives on W, then W.addMap ⟦P⟧ ⟦Q⟧ is definitionally equivalent to W.add P Q.

Defined in: Mathlib.AlgebraicGeometry.EllipticCurve.Projective.Point
Cited by: 7 results in Mathlib
Foundations: Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing

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Cites6

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

CommRingstatement and proof · cited by 17,173
WeierstrassCurve.Projectivestatement and proof · cited by 244
WeierstrassCurve.Projective.PointClassstatement and proof · cited by 21
WeierstrassCurve.Projective.addproof · cited by 20
Quotient.map₂proof · cited by 3
WeierstrassCurve.Projective.add_equivproof · cited by 0

Cited by7

Results whose statement or proof uses this declaration.

WeierstrassCurve.Projective.addMap_eqstatement · cited by 4
WeierstrassCurve.Projective.nonsingularLift_addMapstatement · cited by 0
WeierstrassCurve.Projective.addMap_of_Y_eqstatement · cited by 0
WeierstrassCurve.Projective.addMap_of_Z_eq_zero_rightstatement · cited by 0
WeierstrassCurve.Projective.addMap_of_Z_ne_zerostatement · cited by 0
WeierstrassCurve.Projective.Point.add_pointstatement · cited by 0
WeierstrassCurve.Projective.addMap_of_Z_eq_zero_leftstatement · cited by 0