|
 |
 |
 |
 |
 |
 |
 |
 |
 |
A.27 Fast lexicographical GB
Compute Groebner basis in lexicographical ordering
by using the FGLM algorithm (stdfglm)
and Hilbert driven Groebner (stdhilb).
The command stdfglm applies only for zero-dimensional ideals and
returns a reduced Groebner basis.
For the ideal below, stdfglm is more than 100 times
and stdhilb about 10 times faster than std.
ring r =32003,(a,b,c,d,e),lp;
ideal i=a+b+c+d, ab+bc+cd+ae+de, abc+bcd+abe+ade+cde,
abc+abce+abde+acde+bcde, abcde-1;
int t=timer;
ideal j1=stdfglm(i);
timer-t;
→ 0
size(j1); // size (no. of polys) in computed GB
→ 5
t=timer;
ideal j2=stdhilb(i);
timer-t;
→ 0
size(j2); // size (no. of polys) in computed GB
→ 158
// usual Groebner basis computation for lex ordering
t=timer;
ideal j0 =std(i);
timer-t;
→ 1
|