Home Online Manual
Top
Back: jacoblift
Forward: H2basis
FastBack: kskernel_lib
FastForward: qhmoduli_lib
Up: mondromy_lib
Top: Singular Manual
Contents: Table of Contents
Index: Index
About: About this document

D.6.11.4 monodromyB

Procedure from library mondromy.lib (see mondromy_lib).

Usage:
monodromyB(f[,opt]); f poly, opt int

Assume:
The polynomial f in a series ring (local ordering) defines an isolated hypersurface singularity.

Return:
The procedure returns a residue matrix M of the meromorphic Gauss-Manin connection of the singularity defined by f or an empty matrix if the assumptions are not fulfilled. If opt=0 (default), exp(-2*pi*i*M) is a monodromy matrix of f, else, only the characteristic polynomial of exp(-2*pi*i*M) coincides with the characteristic polynomial of the monodromy of f.

Display:
The procedure displays more comments for higher printlevel.

Example:
 
LIB "mondromy.lib";
ring R=0,(x,y),ds;
poly f=x2y2+x6+y6;
matrix M=monodromyB(f);
print(M);
==> 7/6,0,  0,0,  0,  0,0,   0,-1/2,0,  0,  0,  0,   
==> 0,  7/6,0,0,  0,  0,-1/2,0,0,   0,  0,  0,  0,   
==> 0,  0,  1,0,  0,  0,0,   0,0,   0,  0,  0,  0,   
==> 0,  0,  0,4/3,0,  0,0,   0,0,   0,  0,  0,  0,   
==> 0,  0,  0,0,  4/3,0,0,   0,0,   0,  0,  0,  0,   
==> 0,  0,  0,0,  0,  1,0,   0,0,   0,  0,  0,  0,   
==> 0,  0,  0,0,  0,  0,5/6, 0,0,   0,  0,  0,  0,   
==> 0,  0,  0,0,  0,  0,0,   1,0,   0,  0,  0,  0,   
==> 0,  0,  0,0,  0,  0,0,   0,5/6, 0,  0,  0,  0,   
==> 0,  0,  0,0,  0,  0,0,   0,0,   2/3,0,  0,  0,   
==> 0,  0,  0,0,  0,  0,0,   0,0,   0,  2/3,0,  0,   
==> 0,  0,  0,0,  0,  0,0,   0,0,   0,  0,  1,  -1/3,
==> 0,  0,  0,0,  0,  0,0,   0,0,   0,  0,  3/4,0