Theorems · Definition · commutative algebra
MvPolynomial.pderiv
{R : Type u} → {σ : Type v} → [inst : CommSemiring R] → σ → Derivation R (MvPolynomial σ R) (MvPolynomial σ R)pderiv i p is the partial derivative of p with respect to i
- Defined in
- Mathlib.Algebra.MvPolynomial.PDeriv
- Cited by
- 71 results in Mathlib
- Foundations
- Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommSemiringstatement and proof · cited by 10,911
- Finsuppstatement · cited by 5,255
- MvPolynomialstatement · cited by 2,140
- Pi.singleproof · cited by 518
- Derivationstatement · cited by 293
- MvPolynomial.mkDerivationproof · cited by 6
Cited by79
Results whose statement or proof uses this declaration.
- WeierstrassCurve.Projective.polynomialXproof · cited by 19
- MvPolynomial.pderiv_Xstatement · cited by 16
- WeierstrassCurve.Jacobian.polynomialYproof · cited by 10
- WeierstrassCurve.Projective.polynomialYproof · cited by 10
- WeierstrassCurve.Jacobian.polynomialXproof · cited by 9
- Algebra.PreSubmersivePresentation.jacobiMatrix_applystatement and proof · cited by 9
- MvPolynomial.pderiv_Cstatement and proof · cited by 8
- MvPolynomial.pderiv_X_of_nestatement · cited by 8
- MvPolynomial.pderiv_mapstatement and proof · cited by 8
- WeierstrassCurve.Jacobian.polynomialZproof · cited by 7
- WeierstrassCurve.Projective.polynomialZproof · cited by 7
- MvPolynomial.pderiv_X_selfstatement · cited by 7