Theorems · Definition · algebraic geometry
WeierstrassCurve.Affine.CoordinateRing.basis
{R : Type r} →
[inst : CommRing R] → (W' : WeierstrassCurve.Affine R) → Module.Basis (Fin 2) (Polynomial R) W'.CoordinateRingThe power basis {1, Y} for R[W] over R[X].
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 130 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.
Cites14
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
- Polynomialstatement · cited by 5,681
- Nontrivialproof · cited by 2,416
- Module.Basisstatement · cited by 1,477
- WeierstrassCurve.Affinestatement and proof · cited by 174
- subsingleton_or_nontrivialproof · cited by 161
- finCongrproof · cited by 78
- WeierstrassCurve.Affine.polynomialstatement · cited by 61
- Module.Basis.reindexproof · cited by 57
- PowerBasis.basisproof · cited by 54
- WeierstrassCurve.Affine.CoordinateRingstatement · cited by 39
- AdjoinRoot.powerBasis'proof · cited by 12
Cited by8
Results whose statement or proof uses this declaration.
- WeierstrassCurve.Affine.CoordinateRing.basis_onestatement · cited by 4
- WeierstrassCurve.Affine.CoordinateRing.basis_zerostatement · cited by 4
- WeierstrassCurve.Affine.CoordinateRing.norm_smul_basisproof · cited by 2
- WeierstrassCurve.Affine.CoordinateRing.basis_applystatement and proof · cited by 2
- WeierstrassCurve.Affine.CoordinateRing.exists_smul_basis_eqproof · cited by 2
- WeierstrassCurve.Affine.CoordinateRing.smul_basis_eq_zeroproof · cited by 1
- WeierstrassCurve.Affine.Point.toClass_eq_zeroproof · cited by 1
- WeierstrassCurve.Affine.CoordinateRing.coe_basisstatement · cited by 0