# sign -- get the sign of a homogeneous element

## Description

The sign of a homogeneous Lie (or Ext) element $x$ is obtained as sign(x). The zero element has sign equal to 0; however, its sign should be thought of as arbitrary. The sign of a derivation $d$ is the sign of $d$ as a graded map and may also be obtained as d#sign.

## Synopsis

• Usage:
s=sign(x)
• Inputs:
• x, an instance of the type LieElement, an element of type $L$ where $L$ is of type LieAlgebra
• 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 : sign x o4 = 1

## Synopsis

• Usage:
s=sign(x)
• Inputs:
• x, an instance of the type ExtElement, an element of type $E$ where $E$ is of type ExtAlgebra
• Outputs:
 i5 : E=extAlgebra(5,D) o5 = E o5 : ExtAlgebra i6 : b=basis(5,E) o6 = {ext_4, ext_5} o6 : List i7 : apply(b,sign) o7 = {1, 1} o7 : List

## Synopsis

• Usage:
s=sign(d)
• Inputs:
• Outputs:
 i8 : sign differential D o8 = 1