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 |