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
 -- 0.000202176 seconds elapsed
 -- 0.000229868 seconds elapsed
 -- 0.000198239 seconds elapsed
 -- 0.00010716 seconds elapsed
 -- 0.000227434 seconds elapsed
 -- 0.000189262 seconds elapsed
 -- 0.00009618 seconds elapsed
 -- 0.000216655 seconds elapsed
 -- 0.000181629 seconds elapsed
 -- 0.000182129 seconds elapsed
 -- 0.00021462 seconds elapsed
 -- 0.000186257 seconds elapsed
 -- 0.000099746 seconds elapsed
 -- 0.000222545 seconds elapsed
 -- 0.000191166 seconds elapsed
 -- 0.000098393 seconds elapsed
 -- 0.00022022 seconds elapsed
 -- 0.000184854 seconds elapsed
 -- 0.000097802 seconds elapsed
 -- 0.000271365 seconds elapsed
 -- 0.000260866 seconds elapsed
 -- 0.000098764 seconds elapsed
 -- 0.000265315 seconds elapsed
 -- 0.000268611 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: