The result represents a collection of finitely many cones of monomials, each cone being the set of multiples of a certain monomial by all monomials in certain variables; the generating monomials are accessed by basisElements; the sets of variables for each cone are obtained from multVar.
i1 : R = QQ[x,y,z]; |
i2 : M = matrix {{x*y,x^3*z}};
1 2
o2 : Matrix R <--- R
|
i3 : J = janetBasis M; |
i4 : F = factorModuleBasis J
+--+------+
o4 = |1 |{z, y}|
+--+------+
|x |{z} |
+--+------+
| 2| |
|x |{z} |
+--+------+
| 3| |
|x |{x} |
+--+------+
o4 : FactorModuleBasis
|
i5 : basisElements F
o5 = | 1 x x2 x3 |
1 4
o5 : Matrix R <--- R
|
i6 : multVar F
o6 = {set {y, z}, set {z}, set {z}, set {x}}
o6 : List
|
i7 : R = QQ[x,y]; |
i8 : M = matrix {{x*y-y^3, x*y^2, x*y-x}, {x, y^2, x}};
2 3
o8 : Matrix R <--- R
|
i9 : J = janetBasis M
+--------------+------+
o9 = || y3-x | |{y} |
|| 0 | | |
+--------------+------+
|| xy-x | |{y} |
|| x | | |
+--------------+------+
|| x2y-x2 | |{y} |
|| x2 | | |
+--------------+------+
|| x3 | |{y, x}|
|| x2 | | |
+--------------+------+
|| -x | |{y} |
|| xy-y2+x | | |
+--------------+------+
|| x2 | |{y} |
|| y3 | | |
+--------------+------+
|| -x2 ||{y} |
|| x2y-xy2+x2 || |
+--------------+------+
|| 0 | |{y, x}|
|| x3+2x2+y2 | | |
+--------------+------+
o9 : InvolutiveBasis
|
i10 : F = factorModuleBasis J
+------+--+
o10 = || 1 | |{}|
|| 0 | | |
+------+--+
|| y | |{}|
|| 0 | | |
+------+--+
|| y2 ||{}|
|| 0 || |
+------+--+
|| x | |{}|
|| 0 | | |
+------+--+
|| x2 ||{}|
|| 0 || |
+------+--+
|| 0 | |{}|
|| 1 | | |
+------+--+
|| 0 | |{}|
|| y | | |
+------+--+
|| 0 ||{}|
|| y2 || |
+------+--+
|| 0 | |{}|
|| x | | |
+------+--+
|| 0 ||{}|
|| x2 || |
+------+--+
o10 : FactorModuleBasis
|
i11 : basisElements F
o11 = | 1 y y2 x x2 0 0 0 0 0 |
| 0 0 0 0 0 1 y y2 x x2 |
2 10
o11 : Matrix R <--- R
|
i12 : multVar F
o12 = {set {}, set {}, set {}, set {}, set {}, set {}, set {}, set {}, set {}, set {}}
o12 : List
|
The object factorModuleBasis is a method function.