          ##### 7.5.4.0. annfspecialOld
Procedure from library `dmod.lib` (see dmod_lib).

Usage:
annfspecialOld(I,F,mir,n); I an ideal, F a poly, int mir, number n

Return:
ideal

Purpose:
compute the annihilator ideal of F^n in the Weyl Algebra
for the given rational number n

Assume:
The basering is D[s] and contains 's' explicitly as a variable,
the ideal I is the Ann F^s in D[s] (obtained with e.g. SannfsBM),
the integer 'mir' is the minimal integer root of the BS polynomial of F,
and the number n is rational.

Note:
We compute the real annihilator for any rational value of n (both
generic and exceptional). The implementation goes along the lines of
the Algorithm 5.3.15 from Saito-Sturmfels-Takayama, which has a bug.
This procedure is correct for integer values of n.

Display:
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; poly F = x3-y2; def B = annfs(F); setring B; minIntRoot(BS,0); ==> -1 // So, the minimal integer root is -1 setring r; def A = SannfsBM(F); setring A; poly F = x3-y2; annfspecialOld(LD,F,-1,3/4); // generic root ==> _=4*x*Dx+6*y*Dy-9 ==> _=3*x^2*Dy+2*y*Dx ==> _=18*x*y*Dy^2-8*y*Dx^2-33*x*Dy ==> _=54*y^2*Dy^3+16*y*Dx^3+66*x*Dx*Dy-9*y*Dy^2+66*Dy annfspecialOld(LD,F,-1,-2); // integer but still generic root ==> _=2*x*Dx+3*y*Dy+12 ==> _=3*x^2*Dy+2*y*Dx ==> _=9*x*y*Dy^2-4*y*Dx^2+33*x*Dy ==> _=27*y^2*Dy^3+8*y*Dx^3-66*x*Dx*Dy+144*y*Dy^2-66*Dy annfspecialOld(LD,F,-1,1); // exceptional integer root ==> _=Dx*Dy ==> _=2*x*Dx+3*y*Dy-6 ==> _=Dy^3 ==> _=y*Dy^2-Dy ==> _=3*x*Dy^2+Dx^2 ==> _=3*x^2*Dy+2*y*Dx ==> _=Dx^3+3*Dy^2 ==> _=y*Dx^2+3*x*Dy ```          User manual for Singular version 4.3.2, 2023, generated by texi2html.