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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.

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

o1 = L

o1 : LieAlgebra
i2 : computeLie 4

o2 = {2, 1, 2, 1}

o2 : List
i3 : peek L.cache

o3 = CacheTable{bas => MutableHashTable{...5...}                                        }
                deglist => MutableHashTable{...4...}
                diffl => false
                dims => MutableHashTable{...5...}
                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 : L.cache.lieRing

o4 = QQ[aR , aR , aR , aR , aR , aR , aR , aR , aR , aR ]
          0    1    2    3    4    5    6    7    8    9

o4 : PolynomialRing
i5 : computeLie 6

o5 = {2, 1, 2, 1, 2, 1}

o5 : List
i6 : L.cache.maxDeg

o6 = 11
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
i8 : computeLie 10

o8 = {2, 1, 2, 1, 2, 1, 2, 1, 2, 1}

o8 : List
i9 : L.cache.lieRing

o9 = 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

o9 : PolynomialRing

See also

For the programmer

The object lieRing is a symbol.