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Monodromy
Task: Compute a matrix M such that is a monodromy matrix of the singularity f.

ring R=0,(x,y),ds;
poly f=x5+y5+x2y2; // A'Campo example

To compute the Jordan data of M, we can use:

LIB "gaussman.lib"; monodromy(f);
==>
 [1]:   // the eigenvalues of M
     _[1]=1/2  _[2]=7/10  _[3]=9/10  _[4]=1  _[5]=11/10  _[6]=13/10

 [2]:   // the Block sizes
     2,1,1,1,1,1

 [3]:   // the multiplicities
     1,2,2,1,2,2
Alternatively, we can compute the Jordan normal form of the monodromy matrix (directly) by using Brieskorn's algorithm:

LIB "mondromy.lib";
LIB "linalg.lib";
matrix M = monodromyB(f); // using Brieskorn algorithm
print(jordannf(M));

Note that the monodromy matrix has a Jordan block of size 2.

Sao Carlos, 08/02 http://www.singular.uni-kl.de