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Theorems · Theorem · algebraic geometry

WeierstrassCurve.Projective.addX_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 → Q 2 = 0 → W'.addX P Q = -(Q 1 ^ 2 * P 2) * P 0
Defined in
Mathlib.AlgebraicGeometry.EllipticCurve.Projective.Formula
Cited by
2 results in Mathlib
Foundations
Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommRingNoZeroDivisors
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WeierstrassCurve.Projective.addY_of_Z_eq_zero_right · cited by 1Projective.addY_of_Z_eq_z…WeierstrassCurve.Projective.addXYZ_of_Z_eq_zero_right · cited by 1Projective.addXYZ_of_Z_eq…CommRing · cited by 17173CommRingNat.cast_zero · cited by 1870Nat.cast_zeroNoZeroDivisors · cited by 545NoZeroDivisorsWeierstrassCurve.a₁ · cited by 272WeierstrassCurve.a₁WeierstrassCurve.Projective · cited by 244WeierstrassCurve.Projecti…WeierstrassCurve.a₂ · cited by 216WeierstrassCurve.a₂WeierstrassCurve.a₃ · cited by 210WeierstrassCurve.a₃WeierstrassCurve.a₄ · cited by 187WeierstrassCurve.a₄WeierstrassCurve.a₆ · cited by 153WeierstrassCurve.a₆WeierstrassCurve.Projective.Equation · cited by 88Projective.EquationWeierstrassCurve.Projective.addX · cited by 21Projective.addXWeierstrassCurve.Projective.X_eq_zero_of_Z_eq_zero · cited by 12Projective.X_eq_zero_of_Z…Projective.addX_of_Z_eq_zero_…CITED BYCITES

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