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7.5.2.0. bfctOneGB
Procedure from library bfun.lib (see bfun_lib).
- Usage:
- bfctOneGB(f [,s,t]); f a poly, s,t optional ints
- Return:
- list of ideal and intvec
- Purpose:
- computes the roots of the Bernstein-Sato polynomial b(s) for the
hypersurface defined by f, using only one GB computation
- Assume:
- The basering is commutative and of characteristic 0.
- Background:
- In this proc, the initial Malgrange ideal is computed based on the
algorithm by Masayuki Noro and combined with an elimination ordering.
- Note:
- In the output list, the ideal contains all the roots and the intvec
their multiplicities.
If s<>0, std is used for the GB computation, otherwise,
and by default, slimgb is used.
If t<>0, a matrix ordering is used for GB computations,
otherwise, and by default, a block ordering is used.
- Display:
- If printlevel=1, progress debug messages will be printed,
if printlevel>=2, all the debug messages will be printed.
Example:
| LIB "bfun.lib";
ring r = 0,(x,y),dp;
poly f = x^2+y^3+x*y^2;
bfctOneGB(f);
==> [1]:
==> _[1]=-5/6
==> _[2]=-1
==> _[3]=-7/6
==> [2]:
==> 1,1,1
bfctOneGB(f,1,1);
==> [1]:
==> _[1]=-5/6
==> _[2]=-1
==> _[3]=-7/6
==> [2]:
==> 1,1,1
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