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);
==> x^2*y^2+(3*a+5/2)*x^3*y^2+(-3*a+5/2)*x^2*y^3+(13/4*a-15/16)*x^4*y^2+27/2*\
   x^3*y^3+(-13/4*a-15/16)*x^2*y^4+(-19/8*a-65/32)*x^6*y+(5/8*a-9/8)*x^5*y^2\
   +(169/16*a+231/32)*x^4*y^3+(-63/8*a+163/32)*x^3*y^4+(5/16*a-21/32)*x^2*y^\
   5+(19/8*a-65/32)*x*y^6+(-399/64*a+53/64)*x^7*y+(61/64*a-2455/128)*x^6*y^2\
   +(487/64*a-53/32)*x^5*y^3+(55/64*a+1513/256)*x^4*y^4+(5/4*a-155/64)*x^3*y\
   ^5+(-51/64*a-1295/64)*x^2*y^6+(419/64*a+19/32)*x*y^7+(271/256*a-157/512)*\
   x^8*y+(-2693/128*a-2497/128)*x^7*y^2+(5849/256*a-3421/256)*x^6*y^3+(543/2\
   56*a-1649/256)*x^5*y^4+(301/16*a-8633/512)*x^4*y^5+(-6193/256*a-2255/128)\
   *x^3*y^6+(4891/256*a-653/32)*x^2*y^7+(-13/8*a-327/512)*x*y^8+(1235/512*a-\
   1531/4096)*x^10+(329/1024*a+1381/256)*x^9*y+(-6803/1024*a+14159/2048)*x^8\
   *y^2+(3909/512*a-13727/512)*x^7*y^3+(12109/512*a+27775/2048)*x^6*y^4+(108\
   87/1024*a+1101/256)*x^5*y^5+(-755/256*a+19387/2048)*x^4*y^6+(-3623/512*a-\
   8933/256)*x^3*y^7+(-10135/1024*a+30775/4096)*x^2*y^8+(-1287/1024*a+1905/5\
   12)*x*y^9+(-1235/512*a-1531/4096)*y^10
==>