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D.6.5.1 complexClassify

Procedure from library classify2.lib (see classify2_lib).

Usage:
complexClassify(fl); fl Poly

Assume:
fl is a bivariate polynomial defining a curve singularity at (0,0) of modality <=2 and corank <=2. The ordering of the basering must be local.

Return:
A normal form equation g for fl represented by an element of type NormalFormEquation.

Note: So far the final scaling step is not implemented, so to obtain a normal form equation it may be necessary to do a transformation of the form x->lambda1*x, y->lambda2*y

Note: Case X9 is not implemented yet. In this case an error is returned stating that it is case X9.

g.normalFormEquation.in stores the polynomial ring containing the normal form equation.

g.normalFormEquation.value is the normal form equation.

To access the normal form equation as a polynomial do:

def S = g.normalFormEquation.in;
setring S;
poly nf = g.normalFormEquation.value;

Example:
 
LIB "classify2.lib";
ring R = 0,(x,y),ds;
Poly f = -16065*y^9*x-5103*y^9-128*x^7-595*y^9*x^4+6*y^5-21*y^9*x^5-2187*y^7+4*x^2*y^2+12*x*y^3-5102*y^8-4480*x^6*y^2-45359*x^4*y^4-54431*x^2*y^6-19152*x^5*y^3-64258*x^3*y^5-25515*y^7*x-14490*y^9*x^2-4830*y^9*x^3-27208*x*y^8-77490*x^3*y^6-25872*x^5*y^4+20*y^3*x^3+4*x^4*y^2-15116*x^4*y^3+8*x^3*y^2-6384*x^6*y^3+y^6+28*y^3*x^2-6048*x^5*y^2+28*y^4*x+30*y^4*x^2-1344*x^6*y-2835*y^10-51555*x^3*y^7-4235*y^8*x^4-17185*x^4*y^7-22668*x^3*y^4-84*y^5*x^7-5040*y^4*x^6-560*y^3*x^7-280*y^4*x^7-19320*y^5*x^5-2380*y^5*x^6-672*x^6*y^6-40880*x^4*y^6-8610*x^5*y^6-2289*x^5*y^7-38717*y^8*x^2-20384*y^8*x^3+x^8*y^8-x^7*y^7-14*x^7*y^6-105*x^6*y^7-280*x^5*y^8+21*x^6*y^8+8*x^7*y^8+14*y^5*x-20402*y^5*x^2-10204*y^6*x-5670*y^10*x-3234*y^10*x^2-630*y^10*x^3-35*y^10*x^4-189*y^12-945*y^11-y^14-1197*y^11*x-21*y^13-399*y^11*x^2-140*y^12*x-35*y^11*x^3-21*y^12*x^2-7*y^13*x-61803*y^7*x^2-57960*y^5*x^4-448*x^7*y+9*y^4-672*x^7*y^2;
NormalFormEquation F = complexClassify(f);
F;
==> Corank = 2
==> Normalform equation of type = Y[7,8]
==> Normalform equation = x2y2-x7+y8
==> Milnor number = 16
==> Modality = 1
==> Parameter term = x2y2
==> Determinacy <= 8
==> 
def S = F.normalFormEquation.in;
setring S;
poly nf = F.normalFormEquation.value;