Top
Back: bfctVarIn
Forward: SannfsVar
FastBack: dmodapp_lib
FastForward: fpadim_lib
Up: dmodvar_lib
Top: Singular Manual
Contents: Table of Contents
Index: Index
About: About this document
7.7.6.0. bfctVarAnn
Procedure from library dmodvar.lib (see dmodvar_lib).

Usage:
bfctVarAnn(F[,gid,eng]); F an ideal, gid,eng optional ints

Return:
list of an ideal and an intvec

Purpose:
computes the roots of the Bernstein-Sato polynomial and their multiplicities for an affine algebraic variety defined by F = F[1],..,F[r].

Assume:
The basering is commutative and over a field in char 0.

Note:
In the output list, the ideal contains all the roots and the intvec their multiplicities.
If gid<>0, the ideal is used as given. Otherwise, and by default, a heuristically better suited generating set is used.
If eng<>0, std is used for GB computations, otherwise, and by default, slimgb is used.
Computational remark: The time of computation can be very different depending on the chosen generators of F, although the result is always the same.
Further note that in this proc, the annihilator of f^s in D[s] is computed and then a system of linear equations is solved by linear reductions in order to find the minimal polynomial of S = s(1)(1) + ... + s(P)(P). The resulted is shifted by 1-codim(Var(F)) following (BMS06).

Display:
If printlevel=1, progress debug messages will be printed,
if printlevel=2, all the debug messages will be printed.

Example:
 
LIB "dmodvar.lib";
ring R = 0,(x,y,z),Dp;
ideal F = x^2+y^3, z;
bfctVarAnn(F);
==> [1]:
==>    _[1]=-5/6
==>    _[2]=-1
==>    _[3]=-7/6
==> [2]:
==>    1,1,1


Top Back: bfctVarIn Forward: SannfsVar FastBack: dmodapp_lib FastForward: fpadim_lib Up: dmodvar_lib Top: Singular Manual Contents: Table of Contents Index: Index About: About this document
            User manual for Singular version 4-0-3, 2016, generated by texi2html.