invSyzygies -- compute involutive basis of syzygies

i1 : R = QQ[x,y,z];

i2 : I = ideal(x,y,z);

o2 : Ideal of R

i3 : J = janetBasis I

     +-+---------+
o3 = |z|{z}      |
     +-+---------+
     |y|{z, y}   |
     +-+---------+
     |x|{z, y, x}|
     +-+---------+

o3 : InvolutiveBasis

i4 : invSyzygies J

     +----------+---------+
o4 = |{1} | x  ||{z, y, x}|
     |{1} | 0  ||         |
     |{1} | -z ||         |
     +----------+---------+
     |{1} | y  ||{z, y}   |
     |{1} | -z ||         |
     |{1} | 0  ||         |
     +----------+---------+
     |{1} | 0  ||{z, y, x}|
     |{1} | x  ||         |
     |{1} | -y ||         |
     +----------+---------+

o4 : InvolutiveBasis