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7.7.3.0. annfsBMI
Procedure from library dmod.lib (see dmod_lib).
- Usage:
- annfsBMI(F [,eng]); F an ideal, eng an optional int
- Return:
- ring
- Purpose:
- compute the D-module structure of basering[1/f]*f^s where
f = F[1]*..*F[P], according to the algorithm by Briancon and Maisonobe.
- Note:
- activate the output ring with the
setring command. In this ring,
- the ideal LD is the needed D-mod structure,
- the list BS is the Bernstein ideal of a polynomial f = F[1]*..*F[P].
If eng <>0, std is used for Groebner basis computations,
otherwise, and by default slimgb is used.
If printlevel=1, progress debug messages will be printed,
if printlevel>=2, all the debug messages will be printed.
Example:
| LIB "dmod.lib";
ring r = 0,(x,y),Dp;
ideal F = x,y,x+y;
printlevel = 0;
def A = annfsBMI(F);
setring A;
LD;
==> LD[1]=x*Dx+y*Dy-s(1)-s(2)-s(3)
==> LD[2]=x*y*Dy+y^2*Dy-x*s(2)-y*s(2)-y*s(3)
==> LD[3]=y^2*Dx*Dy-y^2*Dy^2+y*Dy*s(1)-y*Dx*s(2)+2*y*Dy*s(2)-y*Dx*s(3)+y*Dy*s\
(3)-s(1)*s(2)-s(2)^2-s(2)*s(3)-s(2)
BS;
==> [1]:
==> _[1]=s(1)+1
==> _[2]=s(2)+1
==> _[3]=s(1)+s(2)+s(3)+4
==> _[4]=s(1)+s(2)+s(3)+2
==> _[5]=s(1)+s(2)+s(3)+3
==> _[6]=s(3)+1
==> [2]:
==> 1,1,1,1,1,1
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