minimumDimension -- computes the minimum dimension of $I$.

Synopsis

Usage:

minimumDimension I
Inputs:
- I, an ideal, a homogeneous ideal of the polynomial ring $S=K[x_1,\ldots,x_n]$, with $K$ a field
Outputs:
- k, an integer, the minimum dimension of $I$

Description

Let $S=K[x_1,\ldots,x_n]$ be a polynomial ring. Given a homogeneous ideal $I\subset S$, it returns the minimum dimension, defined as the minimum integer $k$ such that the filter ideal $I^{<k>}$ differs from $I$.

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 : minimumDimension J

o4 = 11

Ways to use minimumDimension:

minimumDimension(Ideal)

For the programmer

The object minimumDimension is a method function.

minimumDimension -- computes the minimum dimension of $I$.

Synopsis

Description

See also

Ways to use minimumDimension:

For the programmer