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InvolutiveBases :: basisElements

basisElements -- extract the matrix of generators from an involutive basis or factor module basis

Synopsis

Description

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

See also

Ways to use basisElements :