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7.7.3.0. checkRoot2
Procedure from library dmod.lib (see dmod_lib).
- Usage:
- checkRoot2(I,f,a [,eng]); I an ideal, f a poly, alpha a number, eng an optional int
- Assume:
- I is the annihilator of f^s in D[s], basering is D[s],
that is basering and I are the output os Sannfs-like procedure,
f is a polynomial in K[_x] and alpha is a rational number.
- Return:
- int, the multiplicity of -alpha as a root of the BS polynomial of f.
- Purpose:
- check whether a rational number alpha is a root of the global Bernstein-
Sato polynomial of f and compute its multiplicity from the known Ann F^s in D[s]
- Note:
- If -alpha is not a root, the output is 0.
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*y*z;
printlevel = 0;
def A = Sannfs(F);
setring A;
poly F = imap(r,F);
checkRoot2(LD,F,1); // -1 is a root of bs with multiplicity 3
==> 3
checkRoot2(LD,F,1/3); // -1/3 is not a root
==> 0
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