LIB "arnold.lib";
ring R = 0,(x,y,z),ds;
poly g = (x^2+y^2)^2+5*x^(10)+y^(11)+z^2;
g = x^2*y^4+y^2*x^4+5*x^(10)+y^(11)+x^4*y^3+z^2;
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;
poly phiz = z+2*x+x^2+y^4*x;
map phi = R,phix,phiy,phiz;
g = phi(g);
Poly F = makePoly(g);
NormalForm N;
N=determineNormalForm(F);
normalForm(F);
==> (a(4))*x^4*y^2+(a(5))*x^3*y^3+(a(6))*x^2*y^4+(a(2))*x^4*y^3+(a(3))*x^3*y^\
   4+x^7*y+(a(1))*x^4*y^4+y^11+x^35
==> 
normalForm(N);
==> (a(4))*x^4*y^2+(a(5))*x^3*y^3+(a(6))*x^2*y^4+(a(2))*x^4*y^3+(a(3))*x^3*y^\
   4+x^7*y+(a(1))*x^4*y^4+y^11+x^35
==>