isUnmixed -- checks whether an ideal is unmixed

Usage:

isUnmixed I
Inputs:
- I, an ideal, a homogeneous ideal $I$ of the polynomial ring $S=K[x_1,\ldots,x_n]$, with $K$ a field
Outputs:
- b, a Boolean value, whether the ideal $I$ is unmixed

Description

For a homogeneous ideal $I\subset S$, the function checks if the $i$th unmixed layer of $I$, $U_i(I)$ is zero for all $1\leq i < d$, where $d=\dim S/I$ and if $U_d(I)=S/I$.

i1 : S = QQ[x_1..x_10,y_1..y_10];

i2 : E = {{1,2},{1,3},{1,4},{1,5},{1,6},{1,7},{1,8},{1,9},{1,10},{6,7},{8,9},{8,10},{9,10}};

i3 : J=ideal(for e in E list x_(e#0)*y_(e#1)-x_(e#1)*y_(e#0));

o3 : Ideal of S

i4 : isUnmixed J

o4 = false

Ways to use isUnmixed:

isUnmixed(Ideal)

For the programmer

The object isUnmixed is a method function.

The source of this document is in SCMAlgebras.m2:481:0.

isUnmixed -- checks whether an ideal is unmixed

Description

See also

Ways to use isUnmixed:

For the programmer