Singular

D.15.1.2 arnoldShowSeries

Usage:

arnoldShowSeries( S ); S string

Assume:

S is the name of a singularity series listed by arnoldListAllSeries().

Return:

data of the singularity series S of type singseries including
- Milnor number of S,
- Corank of S,
- Milnor code of S (see [Bac01]),
- normal form of S as string with parameters k,r,s and a,b,c,d,
- restrictions on parameters in the normal form in SINGULAR syntax,
- normal form with special (valid) parameters.

LIB "arnoldclassify.lib";
arnoldShowSeries("Z[k,12k+6r]");
==> Series=Z[k,12k+6r]
==> NormalForm=(x + a(y)*y^k)*(x^3 + x*y^(2*k+2*r+1) +
==>         b(y)* y^(3*k+3*r+2))
==> SpecialForm=(x + y^k)*(x^3 + x*y^(2*k+2*r+1) +y^(3*k+3*r+2))
==> Modality=3*k+r-2
==> Corank=2
==> MilnorNumber=12*k+6r
==> MilnorCode=1,1,2k-1,2k-1+2*r,2k+2*r
==> Restrictions= (k>1)&&(r>=0)&&(deg(a)<=(k-2))&&(jet(a,0)!=0)&&
==>         (jet(b,0)!=0)&&(deg(b)<=(2*k+r-2))