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Theorems · Theorem · algebraic geometry

WeierstrassCurve.Projective.add_of_Z_eq_zero_right

∀ {R : Type r} [inst : CommRing R] {W' : WeierstrassCurve.Projective R} [NoZeroDivisors R] {P Q : Fin 3 → R},
  W'.Equation Q → P 2 ≠ 0 → Q 2 = 0 → W'.add P Q = -(Q 1 ^ 2 * P 2) • P
Defined in
Mathlib.AlgebraicGeometry.EllipticCurve.Projective.Point
Cited by
3 results in Mathlib
Foundations
Depth 104 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommRingNoZeroDivisors
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Around this declaration

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WeierstrassCurve.Projective.Point.toAffine_add · cited by 1Point.toAffine_addWeierstrassCurve.Projective.nonsingular_add · cited by 1Projective.nonsingular_addWeierstrassCurve.Projective.addMap_of_Z_eq_zero_right · cited by 0Projective.addMap_of_Z_eq…CommRing · cited by 17173CommRingNoZeroDivisors · cited by 545NoZeroDivisorsWeierstrassCurve.Projective · cited by 244WeierstrassCurve.Projecti…WeierstrassCurve.Projective.Equation · cited by 88Projective.EquationWeierstrassCurve.Projective.add · cited by 20Projective.addWeierstrassCurve.Projective.add_of_not_equiv · cited by 6Projective.add_of_not_equ…WeierstrassCurve.Projective.not_equiv_of_Z_eq_zero_right · cited by 2Projective.not_equiv_of_Z…WeierstrassCurve.Projective.addXYZ_of_Z_eq_zero_right · cited by 1Projective.addXYZ_of_Z_eq…Projective.add_of_Z_eq_zero_r…CITED BYCITES

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Cited by3

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