Theorems · Theorem · commutative algebra
MvPolynomial.monomial_mul
∀ {R : Type u} {σ : Type u_1} [inst : CommSemiring R] {s s' : σ →₀ ℕ} {a b : R},
(MvPolynomial.monomial s) a * (MvPolynomial.monomial s') b = (MvPolynomial.monomial (s + s')) (a * b)- Defined in
- Mathlib.Algebra.MvPolynomial.Basic
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 82 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.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · 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
- MvPolynomialstatement · cited by 2,140
- MvPolynomial.monomialstatement · cited by 253
- AddMonoidAlgebra.single_mul_singleproof · cited by 20
Cited by15
Results whose statement or proof uses this declaration.
- MvPolynomial.monomial_add_singleproof · cited by 5
- MvPolynomial.monomial_single_addproof · cited by 3
- Algebra.Generators.map_toComp_kerproof · cited by 3
- MonomialOrder.sPolynomial_monomial_mulproof · cited by 3
- Algebra.Generators.H1Cotangent.δAux_mulproof · cited by 2
- MvPolynomial.monomial_dvd_monomialproof · cited by 2
- MvPolynomial.esymmAlgHomMonomial_addproof · cited by 2
- Matrix.toMvPolynomial_mulproof · cited by 1
- MvPolynomial.X_mul_pderiv_monomialproof · cited by 1
- MvPolynomial.dvd_monomial_mul_iff_existsproof · cited by 1
- MvPolynomial.restrictSupport_addproof · cited by 1
- MvPolynomial.irreducible_sumSMulXSMulYproof · cited by 0