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GradedLieAlgebras :: lieRing

lieRing -- the internal ring for representation of Lie elements

Synopsis

Description

lieRing is the internal polynomial ring representation of Lie elements, which cannot be used by the user but can be looked upon by writing "L.cache.lieRing". The Lie monomials are represented as commutative monomials in this ring. The number of generators in lieRing is the number of generators in the Lie algebra times the internal counter "maxdeg" which initially is set to 5 and is changed to n+5 if dimsLie n is performed with n>maxdeg.

i1 : L=lieAlgebra{a,b}/{a a a b,b b b a}

o1 = L

o1 : LieAlgebra
i2 : dimsLie 4

o2 = {2, 1, 2, 1}

o2 : List
i3 : peek L.cache

o3 = CacheTable{bas => MutableHashTable{...5...}                                        }
                bound => MutableHashTable{}
                cyc => MutableHashTable{}
                deglist => MutableHashTable{...4...}
                dims => MutableHashTable{...5...}
                genslie => {a, b}
                gr => MutableHashTable{...4...}
                lieRing => QQ[aR , aR , aR , aR , aR , aR , aR , aR , aR , aR ]
                                0    1    2    3    4    5    6    7    8    9
                maxDeg => 5
                mbRing => QQ[mb      , mb      , mb      , mb      , mb      , mb      ]
                               {1, 0}    {1, 1}    {2, 0}    {3, 0}    {3, 1}    {4, 0}
                opL => MutableHashTable{}
i4 : dimsLie 6

o4 = {2, 1, 2, 1, 2, 1}

o4 : List
i5 : L.cache.lieRing

o5 = QQ[aR , aR , aR , aR , aR , aR , aR , aR , aR , aR , aR  , aR  , aR  , aR  , aR  , aR  , aR  , aR  , aR  , aR  , aR  , aR  ]
          0    1    2    3    4    5    6    7    8    9    10    11    12    13    14    15    16    17    18    19    20    21

o5 : PolynomialRing
i6 : dimsLie 10

o6 = {2, 1, 2, 1, 2, 1, 2, 1, 2, 1}

o6 : List
i7 : L.cache.lieRing

o7 = QQ[aR , aR , aR , aR , aR , aR , aR , aR , aR , aR , aR  , aR  , aR  , aR  , aR  , aR  , aR  , aR  , aR  , aR  , aR  , aR  ]
          0    1    2    3    4    5    6    7    8    9    10    11    12    13    14    15    16    17    18    19    20    21

o7 : PolynomialRing

See also

For the programmer

The object lieRing is a symbol.