isUnmixed -- checks whether an ideal is unmixed

Synopsis

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) 299–304.

Ways to use isUnmixed :

isUnmixed(Ideal)

For the programmer

The object isUnmixed is a method function.