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GradedLieAlgebras :: sign

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

See also

Ways to use sign :