invSyzygies -- compute involutive basis of syzygies

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

o1 = R

o1 : PolynomialRing

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

o2 = ideal (x, y, z)

o2 : Ideal of R

i3 : G = gb I

o3 = GroebnerBasis[status: done; S-pairs encountered up to degree 0]

o3 : GroebnerBasis

i4 : J = janetBasis G

o4 = InvolutiveBasis{0 => | z y x |                                                }
                     1 => {HashTable{x => 0}, HashTable{x => 0}, HashTable{x => 1}}
                                     y => 0             y => 1             y => 1
                                     z => 1             z => 1             z => 1

o4 : InvolutiveBasis

i5 : invSyzygies J

o5 = InvolutiveBasis{0 => | x  y  0  |                                             }
                          | 0  -z x  |
                          | -z 0  -y |
                     1 => {HashTable{x => 1}, HashTable{x => 0}, HashTable{x => 1}}
                                     y => 1             y => 1             y => 1
                                     z => 1             z => 1             z => 1

o5 : InvolutiveBasis