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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

See also

Ways to use weight:

  • weight(ExtElement)
  • weight(LieDerivation)
  • weight(LieElement)

For the programmer

The object weight is a method function.

The source of this document is in GradedLieAlgebras/doc2.m2:443:0.