This gives a basis (in positive degrees) up to the specified degree of ExtUL(k,k) where k=L.field or the basis in a specified first and last degree or multi-degree. The basis elements are the generators in the polynomial ring L.cache.extRepRing, see extRepRing.
i1 : L=lieAlgebra{a,b}/{a a b,b b a} o1 = L o1 : LieAlgebra |
i2 : extBasisLie 4 o2 = {ext , ext , ext , ext , ext } 0 1 2 3 4 o2 : List |
i3 : extTableLie 4 o3 = | 2 0 0 0 | | 0 0 2 0 | | 0 0 0 1 | | 0 0 0 0 | 4 4 o3 : Matrix ZZ <--- ZZ |
i4 : extBasisLie(3,2) o4 = {ext , ext } 2 3 o4 : List |
i5 : weightExtLie(ext_2-3*ext_3) o5 = {3, 2} o5 : List |
i6 : ext_2 o6 = ext 2 o6 : QQ[ext , ext , ext , ext , ext ] 0 1 2 3 4 |
i7 : signExtLie ext_2 o7 = 0 |