Krull dimension of an ideal

Introduction

AlgebraicSolving allows to compute the Krull dimension for the ideal spanned by given input generators over finite fields of characteristic smaller $2^{31}$ and over the rationals.

The underlying engine is provided by msolve.

Functionality

AlgebraicSolving.dimension — Method

dimension(I::Ideal{T}) where T <: MPolyRingElem

Compute the Krull dimension of a given polynomial ideal I.

Note: This requires a Gröbner basis of I, which is computed internally if not alraedy known.

Examples

julia> using AlgebraicSolving

julia> R, (x, y, z) = polynomial_ring(QQ, ["x", "y", "z"]);

julia> I = Ideal([x*y,x*z,y*z]);

julia> dimension(I)
1

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