Multivariate polynomials over fields #
This file contains basic facts about multivariate polynomials over fields, for example that the
dimension of the space of multivariate polynomials over a field is equal to the cardinality of
finitely supported functions from the indexing set to ℕ.
theorem
MvPolynomial.quotient_mk_comp_C_injective
(σ : Type u)
(K : Type v)
[Field K]
(I : Ideal (MvPolynomial σ K))
(hI : I ≠ ⊤)
:
Function.Injective ⇑((Ideal.Quotient.mk I).comp MvPolynomial.C)
theorem
MvPolynomial.rank_mvPolynomial
{σ : Type u}
{K : Type u}
[Field K]
:
Module.rank K (MvPolynomial σ K) = Cardinal.mk (σ →₀ ℕ)