# getBasis -- Get a basis for a particular homological degree of a DG algebra.

## Synopsis

• Usage:
M = getBasis(n,A)
• Inputs:
• Optional inputs:
• Limit => ..., default value -1, Option to specify the maximum number of basis elements to return
• Outputs:
• M, , The basis of the desired homological degree of the DG Algebra.

## Description

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

## For the programmer

The object getBasis is .