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
 -- 0.000463751 seconds elapsed
 -- 0.000487142 seconds elapsed
 -- 0.000480842 seconds elapsed
 -- 0.000239735 seconds elapsed
 -- 0.00051792 seconds elapsed
 -- 0.000490696 seconds elapsed
 -- 0.000254131 seconds elapsed
 -- 0.000480388 seconds elapsed
 -- 0.000483511 seconds elapsed
 -- 0.00046508 seconds elapsed
 -- 0.000496457 seconds elapsed
 -- 0.000476474 seconds elapsed
 -- 0.000249622 seconds elapsed
 -- 0.000513025 seconds elapsed
 -- 0.00048202 seconds elapsed
 -- 0.000228913 seconds elapsed
 -- 0.000516215 seconds elapsed
 -- 0.000444728 seconds elapsed
 -- 0.000259883 seconds elapsed
 -- 0.000597528 seconds elapsed
 -- 0.000637391 seconds elapsed
 -- 0.000222872 seconds elapsed
 -- 0.000633865 seconds elapsed
 -- 0.000596471 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: