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# firstDegree -- get the degree of an element

## Description

The degree of an element $x$ in a Lie algebra or an Ext-algebra is the first degree of the homogeneous element $x$. The zero element has degree 0; however, its degree should be thought of as arbitrary. The degree of a Lie derivation $d$ is the first degree of $d$ considered as a graded map.

## Synopsis

• Usage:
n=firstDegree(x)
• Inputs:
• Outputs:
• n, an integer, the first degree of $x$

## Synopsis

• Usage:
n=firstDegree(x)
• Inputs:
• Outputs:
• n, an integer, the first degree of $x$

## Synopsis

• Usage:
n=firstDegree(d)
• Inputs:
• Outputs:
• n, an integer, the first degree of $d$
 i1 : L = lieAlgebra({a,b,c},Weights=>{1,2,3}) o1 = L o1 : LieAlgebra i2 : firstDegree(c a b+a b c) o2 = 6 i3 : E = extAlgebra(5,L) o3 = E o3 : ExtAlgebra i4 : apply(gens E,firstDegree) o4 = {1, 2, 3} o4 : List i5 : d=lieDerivation({a c b,b b c,c c b}) o5 = d o5 : LieDerivation i6 : firstDegree d o6 = 5