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
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i2 : A = koszulComplexDGA(R)
o2 = {Ring => R }
Underlying algebra => R[T ..T ]
1 4
Differential => {a, b, c, d}
o2 : DGAlgebra
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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
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The object getBasis is a method function with options.