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GradedLieAlgebras :: intersectionLie

intersectionLie -- computes a basis for the intersection of subspaces of a given degree

Synopsis

Description

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

o1 = L

o1 : LieAlgebra
i2 : computeLie 4

o2 = {3, 3, 8, 18}

o2 : List
i3 : basisLie 4

o3 = {[a, a, b, a], [b, a, b, a], [c, a, b, a], [b, b, b, a], [c, b, b, a],
     ------------------------------------------------------------------------
     [a, c, b, a], [b, c, b, a], [c, c, b, a], [a, a, c, a], [b, a, c, a],
     ------------------------------------------------------------------------
     [c, a, c, a], [b, b, c, a], [c, b, c, a], [b, c, c, a], [c, c, c, a],
     ------------------------------------------------------------------------
     [b, b, c, b], [c, b, c, b], [c, c, c, b]}

o3 : List
i4 : d=defLie(mb_{4,2}+mb_{4,1})

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

o4 : List
i5 : intersectionLie(4,{{[b, a, b, a], [c, a, b, a]},{[c,b,b,a],d}})

o5 = {{{1, 1}, {[b, a, b, a], [c, a, b, a]}}}

o5 : List
i6 : indexFormLie oo

o6 = {mb       + mb      }
        {4, 1}     {4, 2}

o6 : List

Ways to use intersectionLie :