Theorems · Definition · algebraic geometry
WeierstrassCurve.Affine.CoordinateRing.mk
{R : Type r} → [inst : CommRing R] → (W' : WeierstrassCurve.Affine R) → Polynomial (Polynomial R) →+* W'.CoordinateRingThe natural ring homomorphism mapping R[X][Y] to R[W].
- Cited by
- 25 results in Mathlib
- Foundations
- Depth 104 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.
Cites7
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
- RingHomstatement · cited by 10,189
- Polynomialstatement · cited by 5,681
- WeierstrassCurve.Affinestatement and proof · cited by 174
- WeierstrassCurve.Affine.polynomialstatement and proof · cited by 61
- AdjoinRoot.mkproof · cited by 50
- WeierstrassCurve.Affine.CoordinateRingstatement · cited by 39
Cited by27
Results whose statement or proof uses this declaration.
- WeierstrassCurve.Affine.CoordinateRing.XClassproof · cited by 5
- WeierstrassCurve.Affine.CoordinateRing.basis_onestatement and proof · cited by 4
- WeierstrassCurve.Affine.CoordinateRing.YClassproof · cited by 3
- WeierstrassCurve.Affine.CoordinateRing.smulstatement · cited by 3
- WeierstrassCurve.Affine.CoordinateRing.exists_smul_basis_eqstatement · cited by 2
- WeierstrassCurve.Affine.CoordinateRing.map_mkstatement and proof · cited by 2
- WeierstrassCurve.Affine.CoordinateRing.mk_ψ₂_sqstatement and proof · cited by 2
- WeierstrassCurve.Affine.CoordinateRing.norm_smul_basisstatement and proof · cited by 2
- WeierstrassCurve.Affine.CoordinateRing.C_addPolynomialstatement · cited by 1
- WeierstrassCurve.Affine.CoordinateRing.C_addPolynomial_slopestatement and proof · cited by 1
- WeierstrassCurve.Affine.CoordinateRing.XYIdeal_add_eqstatement and proof · cited by 1
- WeierstrassCurve.Affine.CoordinateRing.XYIdeal_eq₁proof · cited by 1