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D.15.1.21 normalFormEquationUpToRescaling
Procedure from library arnold.lib (see arnold_lib).
- Usage:
- normalFormEquationUpToRescaling(N); N NormalForm of which the field N.normalFormEquation is filled using @ref(determineNormalForm) and using @ref(determineNormalFormEquation)
- Return:
- N.normalFormEquationUpToRescaling, a Poly which is right-equivalent to N.normalFormEquation, by the transformation x-->ax, y-->by, a,b complex numbers, such that its ring is minimal
Example:
| | LIB "arnold.lib";
ring R=0,(x,y),ds;
poly g = x^4+2*x^2*y^2+y^4+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);
N = determineNormalFormEquation(N);
normalFormEquationUpToRescaling(N);
==> x^2*y^2-5/256*x^9*y+5/256*x*y^9+x^34+y^34
==>
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