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 |