generators(SAGBIBasis) -- Returns generators of a SAGBIBasis computation object

Synopsis

Function: generators
Usage:

result = gens S
Inputs:
- S, a SAGBIBasis,
Optional inputs:
- CoefficientRing => a Boolean value, default value null, unused option
Outputs:
- result, a matrix,

Description

Returns a list of subalgebra generators of the Subring underlying the SAGBIBasis. If the subalgebra generators do not form a complete subalgebra basis (for example if they were obtained from a partial computation), then the generators obtained from this command may not be a generating set for the original subring.

i1 : R = QQ[x,y];

i2 : S = subring {x*y, x^2*y, x^3*y};

i3 : gens S

o3 = | xy x2y x3y |

             1      3
o3 : Matrix R  <-- R

i4 : SB = sagbi(S, Limit => 3);

i5 : gens SB

o5 = | xy x2y |

             1      2
o5 : Matrix R  <-- R

i6 : isSAGBI S

o6 = true

i7 : isSAGBI SB

o7 = false

Ways to use this method: