Monomial ideal

In algebra, a monomial ideal is an ideal generated by some monomials in a multivariate polynomial ring over a field.

A toric ideal is an ideal generated by differences of monomials (provided the ideal is a prime ideal). An affine or projective algebraic variety defined by a toric ideal or a homogeneous toric ideal is an affine or projective toric variety, possibly non-normal.

The computer algebra system Macaulay 2 has commands that handle monomial ideals.

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