generators(SAGBIBasis) -- Returns a partial sagbi generating set

Synopsis

Function: generators
Usage:

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

Description

Returns the current list of sagbiGenerators of the underlying Subring. If the SAGBIBasis is not a complete sagbi basis (for example it is 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
 -- 0.000201146 seconds elapsed
 -- 0.000227597 seconds elapsed
 -- 0.000188313 seconds elapsed
 -- 0.000096942 seconds elapsed
 -- 0.000228207 seconds elapsed
 -- 0.000183142 seconds elapsed
 -- 0.000093054 seconds elapsed
 -- 0.000206226 seconds elapsed
 -- 0.000180038 seconds elapsed
 -- 0.000253324 seconds elapsed
 -- 0.000236402 seconds elapsed
 -- 0.000190427 seconds elapsed
 -- 0.000097411 seconds elapsed
 -- 0.000228539 seconds elapsed
 -- 0.000189785 seconds elapsed
 -- 0.000100408 seconds elapsed
 -- 0.000219541 seconds elapsed
 -- 0.000185307 seconds elapsed
 -- 0.000103353 seconds elapsed
 -- 0.000287358 seconds elapsed
 -- 0.000261269 seconds elapsed
 -- 0.000099727 seconds elapsed
 -- 0.000275586 seconds elapsed
 -- 0.000265847 seconds elapsed
timing raw subduction
timing raw subduction
timing raw subduction
timing raw subduction
timing raw subduction
timing raw subduction
timing raw subduction
timing raw subduction

o6 = true

i7 : isSAGBI SB

o7 = false

Ways to use this method: