|  |  7.5.6.0. annihilatorMultiFs Procedure from librarydmodideal.lib(see  dmodideal_lib).
 
Example:Usage:
annihilatorMultiFs(F [,eng,us,ord]); F an ideal, eng, us, ord optional ints
Return:
ring
Purpose:
compute Ann(F[1]^s(1)*...*F[P]^s(P))
with the multivariate algorithm by Briancon and Maisonobe.
 
Assume:
basering is a commutative polynomial ring in characteristic 0
Note:
activate the output ring with the setringcommand. In this ring,
the ideal annFs is the annihilator of F[1]^s_1*..*F[P]^s_p.
If eng <>0,stdis used for Groebner basis computations,
otherwise, and by defaultslimgbis used.
If us<>0, then syzygies-driven method is used additionally.
If specified, ord describes the desired order from the following choices:
0 - 'dp'1 - elimination order for x, 'dp' in the parts
 2 - elimination order for s, 'dp' in the parts
 3 - elimination order for x and s, 'dp' in the parts
 4 - elimination order for x and D, 'dp' in the parts
 (used for the further work in the Bernstein-Sato ideal)
If printlevel=1, progress debug messages will be printed,
if printlevel>=2, all the debug messages will be printed.
 
 |  | LIB "dmodideal.lib";
ring R = 0,(x,y),dp;
ideal F = x^2-y,y;
def S = annihilatorMultiFs(F,0,0,0);
setring S;
annFs;
==> annFs[1]=-2*x*y*Dy-y*Dx+2*x*s(2)
==> annFs[2]=-x*Dx-2*y*Dy+2*s(1)+2*s(2)
groebner(annFs);
==> _[1]=x*Dx+2*y*Dy-2*s(1)-2*s(2)
==> _[2]=2*x*y*Dy+y*Dx-2*x*s(2)
==> _[3]=4*y^2*Dy^2-y*Dx^2-4*y*Dy*s(1)-8*y*Dy*s(2)+2*y*Dy+4*s(1)*s(2)+4*s(2)^\
   2+2*s(2)
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