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GradedLieAlgebras :: signLie

signLie -- returns the sign of a graded Lie element.

Synopsis

Description

The signs of the generators, see genSigns define the sign of an arbitrary expression. The sign of [] is defined to be 0. However, the sign of [] should be thought of as arbitrary since, in the example below, the element [a1,a1,a1] has sign 1 and is still equal to [] in L.

i1 : L = lieAlgebra( {a_1,a_2}, {}, genSigns => {1,0})

o1 = L

o1 : LieAlgebra
i2 : prod=multLie([a_1,a_1],[a_2])

o2 = {{-1}, {[a , a , a ]}}
               2   1   1

o2 : List
i3 : signLie oo

o3 = 0
i4 : signLie{[a_2],[a_1,a_1,a_1],{{1,2},{[a_1,a_2,a_2],[a_2,a_2,a_1]}}}

o4 = {0, 1, 1}

o4 : List
i5 : indexFormLie prod

o5 = -mb
        {3, 0}

o5 : QQ[mb      , mb      , mb      , mb      , mb      , mb      ]
          {1, 0}    {1, 1}    {2, 0}    {2, 1}    {3, 0}    {3, 1}
i6 : signLie oo

o6 = 0

Ways to use signLie :