Minimalizes first, then replaces each of the values of a hash table H by its remainder on the division by the remaining values H.
If values H constitute a Groebner basis of the ideal they generate, this method returns a reduced Groebner basis.
i1 : R = ZZ/101[a,b,c]; |
i2 : T = tgb( ideal "abc+c2,ab2-b3c+ac,b2",2) 3 o2 = 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 o2 : HashTable |
i3 : reduce T o3 = 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 o3 : HashTable |
Polynomials are normalized so that the leading coefficient is 1. Note that keys of non-minimal entries are retained, and the corresponding table value is null.
The object reduce is a method function.