If the argument of basisElements is an instance of the type InvolutiveBasis, then the columns of B are generators for the module spanned by the involutive basis. These columns form a Gr\"obner basis for this module.
If the argument of basisElements is an instance of the type FactorModuleBasis, then the columns of B are generators for the monomial cones in the factor module basis.
i1 : R = QQ[x,y]; |
i2 : I = ideal(x^3,y^2); o2 : Ideal of R |
i3 : J = janetBasis I; |
i4 : basisElements J
o4 = | y2 xy2 x3 x2y2 |
1 4
o4 : Matrix R <--- R
|
i5 : R = QQ[x,y,z]; |
i6 : M = matrix {{x*y,x^3*z}};
1 2
o6 : Matrix R <--- R
|
i7 : J = janetBasis M; |
i8 : F = factorModuleBasis J
+--+------+
o8 = |1 |{z, y}|
+--+------+
|x |{z} |
+--+------+
| 2| |
|x |{z} |
+--+------+
| 3| |
|x |{x} |
+--+------+
o8 : FactorModuleBasis
|
i9 : basisElements F
o9 = | 1 x x2 x3 |
1 4
o9 : Matrix R <--- R
|
i10 : multVar F
o10 = {set {y, z}, set {z}, set {z}, set {x}}
o10 : List
|