Theorems · Definition · algebraic geometry
WeierstrassCurve.Projective.Equation
{R : Type r} → [CommRing R] → WeierstrassCurve.Projective R → (Fin 3 → R) → PropThe proposition that a projective point representative (x, y, z) lies in a Weierstrass curve
W.
In other words, it satisfies the homogeneous Weierstrass equation W(X, Y, Z) = 0.
- Cited by
- 88 results in Mathlib
- Foundations
- Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- WeierstrassCurve.Projectivestatement and proof · cited by 244
- MvPolynomial.evalproof · cited by 157
- WeierstrassCurve.Projective.polynomialproof · cited by 10
Cited by89
Results whose statement or proof uses this declaration.
- WeierstrassCurve.Projective.Nonsingularproof · cited by 37
- WeierstrassCurve.Projective.X_eq_zero_of_Z_eq_zerostatement and proof · cited by 12
- WeierstrassCurve.Projective.equation_iffstatement · cited by 8
- WeierstrassCurve.Projective.nonsingular_smulproof · cited by 5
- WeierstrassCurve.Projective.isUnit_addZ_of_X_nestatement and proof · cited by 4
- WeierstrassCurve.Projective.isUnit_dblZ_of_Y_ne'statement and proof · cited by 4
- WeierstrassCurve.Projective.neg_of_Z_eq_zerostatement and proof · cited by 3
- WeierstrassCurve.Projective.Y_ne_negY_of_Y_ne'statement and proof · cited by 3
- WeierstrassCurve.Projective.addZ_eq'statement and proof · cited by 3
- WeierstrassCurve.Projective.add_of_X_nestatement and proof · cited by 3
- WeierstrassCurve.Projective.add_of_Y_eqstatement and proof · cited by 3
- WeierstrassCurve.Projective.add_of_Y_nestatement and proof · cited by 3