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GradedLieAlgebras :: defLie

defLie -- returns a LieElement corresponding to input

Synopsis

Description

The set of linear polynomials in L.cache.mbRing, see mbRing, gives a representation of the elements in the Lie algebra L. The function defLie gives back the standard output and indexFormLie goes in the other direction.

i1 : L = lieAlgebra{a,b}

o1 = L

o1 : LieAlgebra
i2 : b3 = basisLie 3

o2 = {(a b a), (b b a)}

o2 : List
i3 : Q = L.cache.mbRing

o3 = Q

o3 : PolynomialRing
i4 : gens Q

o4 = {mb      , mb      , mb      , mb      , mb      }
        {1, 0}    {1, 1}    {2, 0}    {3, 0}    {3, 1}

o4 : List
i5 : c3 = indexFormLie b3

o5 = {mb      , mb      }
        {3, 0}    {3, 1}

o5 : List
i6 : defLie indexFormLie a a b

o6 =  - (a b a)

o6 : L
i7 : defLie mb_{3,0}

o7 = (a b a)

o7 : L
i8 : defLie (mb_{3,0}+2*mb_{3,1})

o8 = (a b a) + 2 (b b a)

o8 : L
i9 : indexFormLie oo

o9 = mb       + 2mb
       {3, 0}      {3, 1}

o9 : Q

See also

Ways to use defLie :