Theorems · Theorem · algebraic geometry
WeierstrassCurve.Affine.equation_iff_variableChange
∀ {R : Type r} [inst : CommRing R] {W : WeierstrassCurve.Affine R} (x y : R),
W.Equation x y ↔ (WeierstrassCurve.toAffine ({ u := 1, r := x, s := 0, t := y } • W)).Equation 0 0- Cited by
- 2 results in Mathlib
- Foundations
- Depth 111 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.
Cites21
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
- Unitsstatement and proof · cited by 2,804
- Nat.cast_oneproof · cited by 2,501
- Units.valproof · cited by 1,966
- inv_oneproof · cited by 301
- WeierstrassCurve.a₁proof · cited by 272
- WeierstrassCurve.a₂proof · cited by 216
- WeierstrassCurve.a₃proof · cited by 210
- WeierstrassCurve.a₄proof · cited by 187
- WeierstrassCurve.Affinestatement and proof · cited by 174
- neg_eq_zeroproof · cited by 171
- WeierstrassCurve.a₆proof · cited by 153
Cited by2
Results whose statement or proof uses this declaration.
- WeierstrassCurve.Affine.nonsingular_iff_variableChangeproof · cited by 1
- WeierstrassCurve.Affine.equation_iff_nonsingular_of_Δ_ne_zeroproof · cited by 1