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
 -- 0.000191167 seconds elapsed
 -- 0.00022899 seconds elapsed
 -- 0.000188844 seconds elapsed
 -- 0.000098745 seconds elapsed
 -- 0.000227707 seconds elapsed
 -- 0.000208861 seconds elapsed
 -- 0.000098745 seconds elapsed
 -- 0.00021392 seconds elapsed
 -- 0.000192881 seconds elapsed
 -- 0.000185567 seconds elapsed
 -- 0.000231404 seconds elapsed
 -- 0.000183565 seconds elapsed
 -- 0.00010188 seconds elapsed
 -- 0.00023513 seconds elapsed
 -- 0.0001923 seconds elapsed
 -- 0.00009649 seconds elapsed
 -- 0.000225903 seconds elapsed
 -- 0.000181088 seconds elapsed
 -- 0.000110215 seconds elapsed
 -- 0.000298189 seconds elapsed
 -- 0.000270116 seconds elapsed
 -- 0.000099646 seconds elapsed
 -- 0.000271429 seconds elapsed
 -- 0.000279924 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: