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D.15.1.3 arnoldNormalForm
Procedure from library arnoldclassify.lib (see arnoldclassify_lib).
- Usage:
- arnoldNormalForm( S [, l]), S string or singclass, l list
- Assume:
- If S is of type string, then S is the name of a singularity series
as listed by arnoldListAllSeries() and l may contain suitable
integer parameters k,r,s. Otherwise S of type singclass is a
singularity class from Arnol'd's list.
Optional suitable polynomial parameters a,b,c,d can be appended to l.
If a,b,c,d are not given, valid values are chosen automatically.
- Return:
- string NF is the normal form of the series S if no parameters given,
or poly NF is the normal form of the class S with parameters k,r,s.
Example:
| | LIB "arnoldclassify.lib";
ring R = 0, (x,y), ds;
poly a,b,c,d;
a= 1+y2;
c= 3+y;
int k = 5;
int r = 4;
int s = 3;
arnoldNormalForm ("W[12k+1]", k,r,s,a,b,c,d);
==> x4+x2y11+x2y13+xy16+3y22+y23
def f = _;
def sf = arnoldClassify( f );
arnoldNormalForm(sf, a,b,c,d);
==> x4+x2y11+x2y13+xy16+3y22+y23
arnoldNormalForm("W[12k+1]");
==> x4+x*y^(3*k+1)+y^(4*k+2)
arnoldNormalForm(sf);
==> x4+xy16+y22
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