[string1 string2]  ring_of_differential_difference operators
This command is used to define a ring of differential-difference operators 
with the macros define_ring, weight_vector and elimination_order.
string1 is a set of variables for differential operators.
string2 is a set of variables for difference operators.
The user cannot use the variable names h, e, H and E.
cf. show_ring, system_variable --- CurrentRing
    print_switch_status, switch_function
Example: [[(x,y) (s)] ring_of_differential_difference_operators 
          [[(Es) 1] [(s) 1]] weight_vector 0] define_ring
         Dx and Dy are corresponding differential operators to the 
         space variables x and y.  Try show_ring to see the commutation
Example: contiguity of 1F1. Eb b = (b-1) Eb
 [ [(x) (a,b)] ring_of_differential_difference_operators 
  [[(Dx) 1]] weight_vector 0] define_ring 
 [ ( x Dx (x Dx+b-1) -x (x Dx+a) ). 
 ( (x Dx +b-1) - (b-1) Eb ). ] /ff set 
 ff {dehomogenize homogenize} map /ff2 set 
 [ff2] groebner /gg set 
 gg dehomogenize 0 get /gg set 
 gg [(Dx)] eliminatev /gg2 set 
 gg2 pmat

Nobuki Takayama 2020-11-24