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 |