This function is to allow for the retrieval of a basis of a particular homological degree of a DGAlgebra when the underlying algebra A.natural is multigraded. In the code, the homological grading is always the first integer in the degree tuple, and so this function returns a matrix consisting of all monomials in homological degree n.
i1 : R = ZZ/101[a..d, Degrees=>{1,1,1,2}] o1 = R o1 : PolynomialRing |
i2 : A = koszulComplexDGA(R) o2 = {Ring => R } Underlying algebra => R[T ..T ] 1 4 Differential => {a, b, c, d} o2 : DGAlgebra |
i3 : getBasis(3,A) o3 = | T_1T_2T_3 T_1T_2T_4 T_1T_3T_4 T_2T_3T_4 | 1 4 o3 : Matrix (R[T ..T ]) <--- (R[T ..T ]) 1 4 1 4 |
The object getBasis is a method function with options.