#C(x,y)[Dx,Dy]-module of G2(a1,a2,b1,b2,x,y) with basis [G1, DxG1, DyG1], reason to choose this basis is it saves some computation when computing matrices in M.

M:=[[x, y], [Dx, Dy], [Matrix(3, 3, {(1, 2) = a1*(b2-a2*y-(b2+a2)*x*y)/((x*y+x^2*y-1-x)*x), (1, 3) = a1*a2/(1-x*y), (2, 1) = 1, (2, 2) = -(x*y+x^2*y-1-x+b2*x^2*y-b2*x-b1*x*y+b1+a2*x^2*y+a2*x*y+a1*x^2*y-a1*x)/((x+1)*x*(x*y-1)), (2, 3) = -a2*x/(x*y-1), (3, 2) = -a1*(y+1)*y/((x*y+x^2*y-1-x)*x), (3, 3) = -a1*y/(x*y-1)}, datatype = anything, storage = rectangular, order = Fortran_order, shape = []), Matrix(3, 3, {(1, 2) = a1*a2/(1-x*y), (1, 3) = a2*(b1-a1*x-(b1+a1)*x*y)/((x*y+x*y^2-1-y)*y), (2, 2) = -a2*x/(x*y-1), (2, 3) = -a2*(x+1)*x/((x*y+x*y^2-1-y)*y), (3, 1) = 1, (3, 2) = -a1*y/(x*y-1), (3, 3) = -(x*y+x*y^2-1-y-b2*x*y+b2+y^2*b1*x-y*b1+y^2*a2*x-a2*y+y^2*x*a1+y*x*a1)/((x*y-1)*y*(y+1))}, datatype = anything, storage = rectangular, order = Fortran_order, shape = [])]]:





# G2 = (a1)m(a2)n(b1)n-m(b2)m-n/m!n! x^m*y^n
# order = 3
# Arguments: [1,1,1,1,x,u*x],[-a-b+c,-b-d,-c+b,-c],[[1,-1,1,0,0,0],[0,0,1,1,0,0],[0,1,-1,0,1,0],[0,1,0,0,0,1]]
# Notes on A-hypergeometric function by Frits Beukers. P7
# reducible: a1 or a2 or a1+b1 or a2+b2 or b1+b2 is an integer
# A-hypergeometric function and theri Monodromy