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ThreadedGB :: Minimal

Minimal -- Option to specify whether the end Groebner basis should be a minimal Groebner basis

Synopsis

Description

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{(((0-1)-0)-0) => null}
               ((0-1)-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{(((0-1)-0)-0) => -c    }
                                2
               ((0-1)-0) => -a*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{(((0-1)-0)-0) => null}
               ((0-1)-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

Functions with optional argument named Minimal :

For the programmer

The object Minimal is a symbol.