Theorems · Theorem · algebraic geometry
WeierstrassCurve.Affine.evalEval_polynomial
∀ {R : Type r} [inst : CommRing R] {W : WeierstrassCurve.Affine R} (x y : R),
Polynomial.evalEval x y W.polynomial = y ^ 2 + W.a₁ * x * y + W.a₃ * y - (x ^ 3 + W.a₂ * x ^ 2 + W.a₄ * x + W.a₆)- Cited by
- 4 results in Mathlib
- Foundations
- Depth 108 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.
- DFunLike.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Polynomial.Xproof · cited by 1,639
- Polynomial.Cproof · cited by 1,598
- Polynomial.evalproof · cited by 796
- add_assocproof · cited by 746
- add_mulproof · cited by 363
- WeierstrassCurve.a₁statement and proof · cited by 272
- WeierstrassCurve.a₂statement and proof · cited by 216
- WeierstrassCurve.a₃statement and proof · cited by 210
- WeierstrassCurve.a₄statement and proof · cited by 187
- WeierstrassCurve.Affinestatement and proof · cited by 174
Cited by4
Results whose statement or proof uses this declaration.
- WeierstrassCurve.Affine.equation_iff'proof · cited by 3
- WeierstrassCurve.Affine.evalEval_polynomial_zeroproof · cited by 1
- WeierstrassCurve.Projective.eval_polynomial_of_Z_ne_zeroproof · cited by 0
- WeierstrassCurve.Jacobian.eval_polynomial_of_Z_ne_zeroproof · cited by 0