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# isUnmixed -- checks whether an ideal is unmixed

- Usage:
    `isUnmixed I`
- Inputs:
  - I, an ideal,
- Outputs:
  - a Boolean value,

## Description

A function that checks whether an ideal $I \subseteq R$ is unmixed, that is, whether the ideal $I$ satisfies $\dim(R/I) = \dim(R/P)$ for all associated primes $P \in {\rm Ass}_R(R/I)$.

The following example uses [SM, Example 1.6].

    i1 : R = QQ[x_1..x_5];

    i2 : I = ideal(x_1*x_3, x_1*x_4, x_1*x_5, x_2*x_3, x_2*x_4, x_2*x_5);

    o2 : Ideal of R

    i3 : isUnmixed I

    o3 = false

## References

[SM] Hero Saremi and Amir Mafi. Unmixedness and arithmetic properties of matroidal ideals. Arch. Math. 114 (2020), no. 3 299–-304.

## See also

- CheckUnmixed -- check whether ideals encountered are unmixed
- isGVD -- checks whether an ideal is geometrically vertex decomposable
- IsIdealUnmixed -- specify whether an ideal is unmixed
- isLexCompatiblyGVD -- checks whether an ideal is <-compatibly geometrically vertex decomposable for a given order
- isWeaklyGVD -- checks whether an ideal is weakly geometrically vertex decomposable

## Ways to use isUnmixed:

- `isUnmixed(Ideal)`

## For the programmer

The object isUnmixed is a method function.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/GeometricDecomposability.m2:1363:0.