Singular

7.7.4.0. annfsParamBM

Usage:

annfsParamBM(f [,eng]); f a poly, eng an optional int

Return:

ring

Purpose:

compute the generic Ann F^s and exceptional parametric constellations
of a polynomial with parametric coefficients with the BM algorithm

Note:

activate the output ring with the setring command. In this ring,
- the ideal LD is the D-module structure oa Ann F^s
- the ideal Param contains special parameters as entries
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.

LIB "dmod.lib";
ring r = (0,a,b),(x,y),Dp;
poly F = x^2 - (y-a)*(y-b);
printlevel = 0;
def A = annfsParamBM(F);  setring A;
LD;
==> LD[1]=2*y*Dx+2*x*Dy+(-a-b)*Dx
==> LD[2]=x^2*Dy-y^2*Dy+(a+b)*y*Dy+2*y*s+(-a*b)*Dy+(-a-b)*s
==> LD[3]=4*x^2*Dx+4*x*y*Dy+(-2*a-2*b)*x*Dy-8*x*s+(a^2-2*a*b+b^2)*Dx
Param;
==> Param[1]=(a-b)
setring r;
poly G = x2-(y-a)^2; // try the exceptional value b=a of parameters
def B = annfsParamBM(G); setring B;
LD;
==> LD[1]=y*Dx+x*Dy+(-a)*Dx
==> LD[2]=x*Dx+y*Dy+(-a)*Dy-2*s
==> LD[3]=x^2*Dy-y^2*Dy+(2*a)*y*Dy+2*y*s+(-a^2)*Dy+(-2*a)*s
Param;
==> Param[1]=0