Let be a ring and
be elements of .
The left -module

is called the syzygy among . The following script computes the generators of the syzygy among

in the homogenized Weyl algebra.

%% syz.sm1 [ (x,y) ring_of_differential_operators [[(Dx) 1 (Dy) 1]] weight_vector 0 ] define_ring [ (x Dx + y Dy). (Dx^2 + Dy^2). ] /ff set ff { [[(h). (1).]] replace homogenize} map /ff2 set [ff2 [(needBack) (needSyz)]] groebner /ans set ; (Syzygies are ...) message ans 2 get ::The 0-th element of

Nobuki Takayama 2020-11-24