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GradedLieAlgebras :: defLie

defLie -- returns a general Lie expression corresponding to input

Synopsis

Usage:
a=defLie(r)
l=defLie(r)
ll=defLie(rl)
Inputs:
- r, a ring element, element in mbRing
- rl, a list, of elements in mbRing
Outputs:
- a, an array, if r is a variable, then the monomialLie corresponding to r is returned
- l, a list, if r is not a variable, but a linear combination of variables, then a generalExpressionLie is returned
- ll, a list, the list of all values of defLie on the elements in rl is returned

Description

i1 : L = lieAlgebra( {a,b}, {})

o1 = L

o1 : LieAlgebra

i2 : b3 = basisLie 3

o2 = {[a, b, a], [b, b, a]}

o2 : List

i3 : L.cache.mbRing

o3 = QQ[mb      , mb      , mb      , mb      , mb      ]
          {1, 0}    {1, 1}    {2, 0}    {3, 0}    {3, 1}

o3 : PolynomialRing

i4 : c3 = indexFormLie b3

o4 = {mb      , mb      }
        {3, 0}    {3, 1}

o4 : List

i5 : defLie oo

o5 = {[a, b, a], [b, b, a]}

o5 : List

i6 : defLie mb_{3,0}

o6 = [a, b, a]

o6 : Array

i7 : defLie (mb_{3,0}+2*mb_{3,1})

o7 = {{1, 2}, {[a, b, a], [b, b, a]}}

o7 : List

i8 : indexFormLie oo

o8 = mb       + 2mb
       {3, 0}      {3, 1}

o8 : QQ[mb      , mb      , mb      , mb      , mb      ]
          {1, 0}    {1, 1}    {2, 0}    {3, 0}    {3, 1}

See also

indexFormLie -- returns an element in the ring representation corresponding to the input
mbRing -- the ring representation of the Lie algebra used as output

Ways to use `defLie` :

defLie(List)
defLie(RingElement)