Singular

7.7.4.0. Sannfs

Usage:

Sannfs(f [,S,eng]); f a poly, S a string, eng an optional int

Return:

ring

Purpose:

compute the D-module structure of basering[f^s] with the algorithm
given in S and with the Groebner basis engine given in eng

Note:

activate the output ring with the setring command.
The value of a string S can be
'bm' (default) - for the algorithm of Briancon and Maisonobe,
'lot' - for the Levandovskyy's modification of the algorithm of OT,
'ot' - for the algorithm of Oaku and Takayama.
If eng <>0, std is used for Groebner basis computations,
otherwise, and by default slimgb is used.
In the output ring:
- the ideal LD is the needed D-module structure.

Display:

If printlevel=1, progress debug messages will be printed,
if printlevel>=2, all the debug messages will be printed.

LIB "dmod.lib";
ring r = 0,(x,y,z),Dp;
poly F = x^3+y^3+z^3;
printlevel = 0;
def A  = Sannfs(F); // here, the default BM algorithm will be used
setring A;
LD;
==> LD[1]=z^2*Dy-y^2*Dz
==> LD[2]=x*Dx+y*Dy+z*Dz-3*s
==> LD[3]=z^2*Dx-x^2*Dz
==> LD[4]=y^2*Dx-x^2*Dy