We can give any names we like to the variables in a Weyl algebra, provided we specify the correspondence between the variables and the derivatives, with the WeylAlgebra option, as follows.
i1 : R = QQ[x,y,dx,dy,t,WeylAlgebra => {x=>dx, y=>dy}] o1 = R o1 : PolynomialRing, 2 differential variables |
i2 : dx*dy*x*y o2 = x*y*dx*dy + x*dx + y*dy + 1 o2 : R |
i3 : dx*x^5 5 4 o3 = x dx + 5x o3 : R |
i4 : dx*x o4 = x*dx + 1 o4 : R |
i5 : matrix{{dx}} * matrix{{x}} o5 = | xdx | 1 1 o5 : Matrix R <--- R |