The key maxDeg is by default 5. If computeLie n is executed for n>L.cache.maxDeg, then the program changes the key to n+5. The value of maxDeg defines the internal representation of Lie elements in the polynomial ring "L.cache.lieRing", 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 |