Singular Manual: annfs2

| ##### 7.5.4.0. annfs2 Procedure from library `dmod.lib` (see dmod_lib). Usage: annfs2(I, F [,eng]); I an ideal, F a poly, eng an optional int Return: ring Purpose: compute the annihilator ideal of f^s in the Weyl Algebra, based on the output of Sannfs-like procedure annfs2 uses shorter expressions in the variable s (the idea of Noro). Note: activate the output ring with the `setring` command. In this ring, - the ideal LD (which is a Groebner basis) is the annihilator of f^s, - the list BS contains the roots with multiplicities of the BS polynomial. If eng <>0, `std` is used for Groebner basis computations, otherwise and by default `slimgb` is used. 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,z),Dp;
    poly F = x^3+y^3+z^3;
    printlevel = 0;
    def A = SannfsBM(F);
    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
    poly F = imap(r,F);
    def B  = annfs2(LD,F);
    setring B;
    LD;
    ==> LD[1]=x*Dx+y*Dy+z*Dz+6
    ==> LD[2]=z^2*Dy-y^2*Dz
    ==> LD[3]=z^2*Dx-x^2*Dz
    ==> LD[4]=y^2*Dx-x^2*Dy
    ==> LD[5]=x^3*Dz+y^3*Dz+z^3*Dz+6*z^2
    ==> LD[6]=x^3*Dy+y^3*Dy+y^2*z*Dz+6*y^2
    BS;
    ==> [1]:
    ==>    _[1]=-2
    ==>    _[2]=-5/3
    ==>    _[3]=-4/3
    ==>    _[4]=-1
    ==> [2]:
    ==>    1,1,1,2

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