There are two strategies for constructing w-adapted resolutions. The first strategy is to construct a Schreyer resolution in the homogenized Weyl algebra and then dehomogenize. The second strategy is to homogenize with respect to the weight vector. These strategies are described in the paper 'Algorithims for D-modules' by Oaku-Takayama(1999).
i1 : R = QQ[x_1,x_2,D_1,D_2,WeylAlgebra=>{x_1=>D_1,x_2=>D_2}] o1 = R o1 : PolynomialRing, 2 differential variables |
i2 : I = ideal(x_1*D_1+3*x_2*D_2-1, D_1^3-D_2) 3 o2 = ideal (x D + 3x D - 1, D - D ) 1 1 2 2 1 2 o2 : Ideal of R |
i3 : Dresolution(I,{-1,-1,1,1}) 1 5 6 2 o3 = R <-- R <-- R <-- R <-- 0 0 1 2 3 4 o3 : ChainComplex |
The object Dresolution is a method function with options.