D.5.6.5 H2basis

Procedure from library mondromy.lib (see mondromy_lib).

Usage:

H2basis(f); f poly

Assume:

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

Return:

The procedure returns a list of representatives of a C{f}-basis of the Brieskorn lattice H”=Omega^(n+1)/df^dOmega^(n-1).

Theory:

H” is a free C{f}-module of rank milnor(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;
H2basis(f);
→ [1]:
→    x4
→ [2]:
→    x2y2
→ [3]:
→    y4
→ [4]:
→    x3
→ [5]:
→    x2y
→ [6]:
→    xy2
→ [7]:
→    y3
→ [8]:
→    x2
→ [9]:
→    xy
→ [10]:
→    y2
→ [11]:
→    x
→ [12]:
→    y
→ [13]:
→    1