# weight -- get the weight of a homogeneous element

## Description

The weight of a homogeneous Lie (or Ext) element $x$ is obtained as weight(x). The zero element of a Lie algebra has weight equal to a list of zeroes of length equal to the degree length of the Lie algebra; however, its weight should be thought of as arbitrary. The weight of a derivation $d$ is the weight of $d$ as a graded map and may also be obtained as d#weight.

## Synopsis

• Usage:
w=weight(x)
• Inputs:
• Outputs:
 i1 : L = lieAlgebra({a,b,c},Weights=>{{1,0},{2,1},{3,2}}, LastWeightHomological=>true, Signs => 1) o1 = L o1 : LieAlgebra i2 : D=differentialLieAlgebra{0_L,a a,a b}/{a a b, a a c, b a b} o2 = D o2 : LieAlgebra i3 : x=a b c+2 c b a o3 = - 2 (b a c) - (a b c) o3 : D i4 : weight x o4 = {6, 3} o4 : List i5 : weight 0_D o5 = {0, 0} o5 : List

## Synopsis

• Usage:
w=weight(x)
• Inputs:
• Outputs:
 i6 : E=extAlgebra(5,D) o6 = E o6 : ExtAlgebra i7 : b=basis(5,E) o7 = {ext_4, ext_5} o7 : List i8 : apply(b,weight) o8 = {{5, 4}, {5, 4}} o8 : List

## Synopsis

• Usage:
w=weight(d)
• Inputs:
• Outputs:
 i9 : weight differential D o9 = {0, -1} o9 : List