Top
Back: determineNormalForm
Forward: nondegeneratePart
FastBack:
FastForward:
Up: arnold_lib
Top: Singular Manual
Contents: Table of Contents
Index: Index
About: About this document

D.15.1.17 determineNormalFormEquation

Procedure from library arnold.lib (see arnold_lib).

Usage:
determineNormalFormEquation(N); N a NormalForm as given by @ref(NormalForm)

Return:
a normalform equation, stored in N.normalFormEquation, occuring in the normalform, stored in N.normalForm, of the polynomial, stored in N.phi.sourcegerm, as well as polynomials, stored in N.extension1 and N.extension2 (of type Poly), defining the parameters,
given as ring variables in N.normalFormEquation.

Example:
 
LIB "arnold.lib";
ring R=0,(x,y),ds;
poly g = x4+2*x2y2+y4+x^(10)+y^(10);
poly phix = x+y^2+x^2+x*y+x^2*y+x*y^3;
poly phiy = y+y^2+2*x^2+x*y+y*x^2+y^2*x+x*y^4;
map phi = R,phix,phiy;
g=phi(g);
Poly F = makePoly(g);
NormalForm N;
N = determineNormalForm(F);
determineNormalFormEquation(N);
==> Embedding dimension = 2
==> Corank of singularity = 2
==> Normalform of type = (0,34),(1,9),(2,2),(9,1),(34,0)
==> Normalform = (a(1))*x^2*y^2+x^9*y+x*y^9+x^34+y^34
==> Normalform equation =x34+y34+x9y+xy9+65536/25*x2y2e16
==> Minimal polynomial = (a2+1)
==> Polynomial of ring extension =(625/4294967296a)*v40+1
==> Polynomial of ring extension =ev-1
==> Milnor number = 33
==> Modality = 1
==> Monomials corresponding to moduli terms = x2y2
==> Delta invariant = 18
==> Number of branches = 4
==> Determinacy <= 16
==> Nondegenerate part = 0
==> Chain of transformations before Morse split of length 0
==> Chain of transformations after Morse split of length 16
==> 
==> 


Top Back: determineNormalForm Forward: nondegeneratePart FastBack: FastForward: Up: arnold_lib Top: Singular Manual Contents: Table of Contents Index: Index About: About this document
            User manual for Singular version 4.4.0, 2024, generated by texi2html.