[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 relations. 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