# initialDegree -- return the initial degree of a given graded ideal

## Synopsis

• Usage:
initialDegree I
• Inputs:
• I, a graded ideal of a polynomial ring
• Outputs:
• an integer, the initial degree of the ideal I

## Description

The initial degree of a graded ideal I is the least degree of a homogeneous generator of I.

Example:

 i1 : S=QQ[x_1..x_4] o1 = S o1 : PolynomialRing i2 : initialDegree ideal {x_1*x_2,x_2*x_3*x_4} o2 = 2 i3 : initialDegree ideal {x_1*x_3*x_4} o3 = 3

## Ways to use initialDegree :

• "initialDegree(Ideal)"

## For the programmer

The object initialDegree is .