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D.15.1.19 germWithNNB
Procedure from library arnold.lib (see arnold_lib).
- Usage:
- germWithNNB(N); N NormalForm as given by @ref(determineNormalForm)
- Return:
- a germ with a nondegenerate Newton boundary, returned as type Poly, that is stable equivalent to N.phi.sourcegerm.value, if possible, or an ERROR message otherwise
Example:
| LIB "arnold.lib";
ring R = 0,(x,y),ds;
poly g = (x^2+y^2)^2+5*x^(10)+y^(11);
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 = determineNormalForm(F);
germWithNNB(N);
==> x2y2+(3a+5/2)*x3y2+(-3a+5/2)*x2y3+(13/4a-15/16)*x4y2+27/2*x3y3+(-13/4a-15\
/16)*x2y4+(-19/8a-65/32)*x6y+(5/8a-9/8)*x5y2+(169/16a+231/32)*x4y3+(-63/8\
a+163/32)*x3y4+(5/16a-21/32)*x2y5+(19/8a-65/32)*xy6+(-399/64a+53/64)*x7y+\
(61/64a-2455/128)*x6y2+(487/64a-53/32)*x5y3+(55/64a+1513/256)*x4y4+(5/4a-\
155/64)*x3y5+(-51/64a-1295/64)*x2y6+(419/64a+19/32)*xy7+(271/256a-157/512\
)*x8y+(-2693/128a-2497/128)*x7y2+(5849/256a-3421/256)*x6y3+(543/256a-1649\
/256)*x5y4+(301/16a-8633/512)*x4y5+(-6193/256a-2255/128)*x3y6+(4891/256a-\
653/32)*x2y7+(-13/8a-327/512)*xy8+(1235/512a-1531/4096)*x10+(329/1024a+13\
81/256)*x9y+(-6803/1024a+14159/2048)*x8y2+(3909/512a-13727/512)*x7y3+(121\
09/512a+27775/2048)*x6y4+(10887/1024a+1101/256)*x5y5+(-755/256a+19387/204\
8)*x4y6+(-3623/512a-8933/256)*x3y7+(-10135/1024a+30775/4096)*x2y8+(-1287/\
1024a+1905/512)*xy9+(-1235/512a-1531/4096)*y10
==>
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