Use Minimal=>True as an argument in the function tgb for ensure the resulting Groebner basis is minimalized. Lineages of non-minimal Groebner basis elements that were added to the basis during the distributed computation are saved, with the corresponding entry in the table being null.
i1 : S = ZZ/101[a,b,c]; |
i2 : T = tgb( ideal "abc+c2,ab2-b3c+ac,b2",2, Minimal=>true)
o2 = HashTable{((0-2)-0) => null}
2
((1-2)-0) => c
(0-1) => null
(0-2) => null
(1-2) => a*c
0 => null
1 => null
2
2 => b
o2 : HashTable
|
By default, the option is false. The basis can also be minimalized after the distributed computation is finished:
i3 : T = tgb( ideal "abc+c2,ab2-b3c+ac,b2",2)
3
o3 = HashTable{((0-2)-0) => -c }
2
((1-2)-0) => -c
2
(0-1) => a c
2
(0-2) => b*c
(1-2) => -a*c
2
0 => a*b*c + c
3 2
1 => - b c + a*b + a*c
2
2 => b
o3 : HashTable
|
i4 : minimalize T
o4 = HashTable{((0-2)-0) => null}
2
((1-2)-0) => c
(0-1) => null
(0-2) => null
(1-2) => a*c
0 => null
1 => null
2
2 => b
o4 : HashTable
|