degLie -- the first degree of a graded element in the LieAlgebra

Synopsis

Usage:
dl = degLie(g)
Inputs:
- g, a symbol, a generator of the Lie algebra
- g, an integer, a generator of the Lie algebra
- g, an indexed variable, a generator of the Lie algebra
- g, an array, a monomialLie
- g, a list, a generalExpressionLie element or a list of generalExpressionLie elements
Outputs:
- dl, an integer, the first degree of the element or a list of first degrees

Description

The degLie of [] is defined to be 0. However, the degree of [] should be thought of as arbitrary since, in the example below, the element [b,b] has degLie 2 and is equal to [] in L.

i1 : L=lieAlgebra({a,b,c},{},genWeights => {{1,1},{1,1},{2,2}})

o1 = L

o1 : LieAlgebra

i2 : degLie(a)

o2 = 1

i3 : degLie([a,a,c])

o3 = 4

i4 : g={{1,-1},{[a,c],[b,c]}}

o4 = {{1, -1}, {[a, c], [b, c]}}

o4 : List

i5 : degLie g

o5 = 3

i6 : m=indexFormLie g

o6 = mb       - mb
       {3, 2}     {3, 3}

o6 : QQ[mb      , mb      , mb      , mb      , mb      , mb      , mb      , mb      ]
          {1, 0}    {1, 1}    {2, 0}    {2, 1}    {3, 0}    {3, 1}    {3, 2}    {3, 3}

i7 : (degree m)_0

o7 = 3

i8 : degLie {[],[b,b],{{1,2},{[c],[a,b]}}}

o8 = {0, 2, 2}

o8 : List

Ways to use `degLie` :

degLie(Array)
degLie(IndexedVariable)
degLie(List)
degLie(Symbol)
degLie(ZZ)

degLie -- the first degree of a graded element in the LieAlgebra

Synopsis

Description

See also

Ways to use degLie :

Ways to use `degLie` :