If the argument of multVar is an object of class InvolutiveBasis, then the i-th set in m consists of the multiplicative variables for the i-th generator in J.
If the arguments of multVar are a chain complex and an integer, where C is the result of either janetResolution or resolution called with the optional argument 'Strategy => Involutive', then the i-th set in m consists of the multiplicative variables for the i-th generator in the n-th differential of C.
If the argument of multVar is an object of class FactorModuleBasis, then the i-th set in m consists of the multiplicative variables for the i-th monomial cone in F.
i1 : R = QQ[x,y]; |
i2 : I = ideal(x^3,y^2); o2 : Ideal of R |
i3 : J = janetBasis I; |
i4 : multVar J
o4 = {set {y}, set {y}, set {x, y}, set {y}}
o4 : List
|
i5 : R = QQ[x,y,z]; |
i6 : I = ideal(x,y,z); o6 : Ideal of R |
i7 : C = res(I, Strategy => Involutive)
1 3 3 1
o7 = R <-- R <-- R <-- R <-- 0
0 1 2 3 4
o7 : ChainComplex
|
i8 : multVar(C, 2)
o8 = {set {x, y, z}, set {x, y, z}, set {y, z}}
o8 : List
|
i9 : R = QQ[x,y,z]; |
i10 : M = matrix {{x*y,x^3*z}};
1 2
o10 : Matrix R <--- R
|
i11 : J = janetBasis M
+---+---------+
o11 = |x*y|{z, y} |
+---+---------+
| 2 | |
|x y|{z, y} |
+---+---------+
| 3 | |
|x z|{z, x} |
+---+---------+
| 3 | |
|x y|{z, y, x}|
+---+---------+
o11 : InvolutiveBasis
|
i12 : F = factorModuleBasis J
+--+------+
o12 = |1 |{z, y}|
+--+------+
|x |{z} |
+--+------+
| 2| |
|x |{z} |
+--+------+
| 3| |
|x |{x} |
+--+------+
o12 : FactorModuleBasis
|
i13 : basisElements F
o13 = | 1 x x2 x3 |
1 4
o13 : Matrix R <--- R
|
i14 : multVar F
o14 = {set {y, z}, set {z}, set {z}, set {x}}
o14 : List
|