Theorems · Theorem · algebraic geometry
WeierstrassCurve.Projective.nonsingular_iff_of_Y_eq_negY
∀ {F : Type u} [inst : Field F] {W : WeierstrassCurve.Projective F} {P : Fin 3 → F},
P 2 ≠ 0 → P 1 = W.negY P → (W.Nonsingular P ↔ W.Equation P ∧ (MvPolynomial.eval P) W.polynomialX ≠ 0)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 116 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Field
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- RingHomstatement · cited by 10,189
- Fieldstatement and proof · cited by 7,404
- Finsuppstatement · cited by 5,255
- MvPolynomialstatement · cited by 2,140
- MulZeroClass.zero_mulproof · cited by 1,625
- sub_selfproof · cited by 996
- WeierstrassCurve.a₁proof · cited by 272
- WeierstrassCurve.Projectivestatement and proof · cited by 244
- WeierstrassCurve.a₃proof · cited by 210
- MvPolynomial.evalstatement and proof · cited by 157
- WeierstrassCurve.Projective.Equationstatement and proof · cited by 88
Cited by1
Results whose statement or proof uses this declaration.
- WeierstrassCurve.Projective.dblU_ne_zero_of_Y_eqproof · cited by 1