Theorems · Theorem · commutative algebra
MvPolynomial.pderiv_monomial
∀ {R : Type u} {σ : Type v} {a : R} {s : σ →₀ ℕ} [inst : CommSemiring R] {i : σ},
(MvPolynomial.pderiv i) ((MvPolynomial.monomial s) a) = (MvPolynomial.monomial (s - fun₀ | i => 1)) (a * ↑(s i))- Defined in
- Mathlib.Algebra.MvPolynomial.PDeriv
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 95 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.
Cites25
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- RingHom.idstatement · cited by 18,349
- CommSemiringstatement and proof · cited by 10,911
- LinearMapstatement · cited by 10,215
- Finsuppstatement and proof · cited by 5,255
- mul_oneproof · cited by 3,885
- MvPolynomialstatement and proof · cited by 2,140
- MulZeroClass.mul_zeroproof · cited by 2,091
- Nat.cast_zeroproof · cited by 1,870
- Finsupp.singlestatement and proof · cited by 943
- Finsupp.supportproof · cited by 828
- Pi.singleproof · cited by 518
Cited by4
Results whose statement or proof uses this declaration.
- MvPolynomial.X_mul_pderiv_monomialproof · cited by 1
- MvPolynomial.IsWeightedHomogeneous.pderivproof · cited by 1
- MvPolynomial.coeff_pderivproof · cited by 0
- MvPolynomial.pderiv_monomial_singleproof · cited by 0