 LIB "classify.lib";
ring r=0,(x,y,z),ds;
poly p=singularity("E[6k+2]",2)[1];
p=p+z^2;
p;
==> z2+x3+xy6+y8
// We received an E_14 singularity in normal form
// from the database of normal forms. Since only the residual
// part is saved in the database, we added z^2 to get an E_14
// of embedding dimension 3.
//
// Now we apply a coordinate change in order to deal with a
// singularity which is not in normal form:
map phi=r,x+y,y+z,x;
poly q=phi(p);
// Yes, q really looks ugly, now:
q;
==> x2+x3+3x2y+3xy2+y3+xy6+y7+6xy5z+6y6z+15xy4z2+15y5z2+20xy3z3+20y4z3+15xy2z\
4+15y3z4+6xyz5+6y2z5+xz6+yz6+y8+8y7z+28y6z2+56y5z3+70y4z4+56y3z5+28y2z6+8\
yz7+z8
// Classification
classify(q);
==> About the singularity :
==> Milnor number(f) = 14
==> Corank(f) = 2
==> Determinacy <= 12
==> Guessing type via Milnorcode: E[6k+2]=E[14]
==>
==> Computing normal form ...
==> I have to apply the splitting lemma. This will take some time....:)
==> Arnold step number 9
==> The singularity
==> x39/4x4+27/4x5189/8x6+737/8x7+6x6y+15x5y2+20x4y3+15x3y4+6x2y5+xy624\
089/64x8x7y+11/2x6y2+26x5y3+95/2x4y4+47x3y5+53/2x2y6+8xy7+y8+104535/64x9\
+27x8y+135/2x7y2+90x6y3+135/2x5y4+27x4y5+9/2x3y6940383/128x10405/4x9y2\
025/8x8y2675/2x7y32025/8x6y4405/4x5y5135/8x4y6+4359015/128x11+1701/4x\
10y+8505/8x9y2+2835/2x8y3+8505/8x7y4+1701/4x6y5+567/8x5y682812341/512x12\
15333/8x11y76809/16x10y225735/4x9y378525/16x8y416893/8x7y58799/16x6\
y6198x5y7495/4x4y855x3y933/2x2y103xy111/4y12
==> is Requivalent to E[14].
==> Milnor number = 14
==> modality = 1
==> 2z2+x3+xy6+y8
// The library also provides routines to determine the corank of q
// and its residual part without going through the whole
// classification algorithm.
corank(q);
==> 2
morsesplit(q);
==> y39/4y4+27/4y5189/8y6+737/8y7+6y6z+15y5z2+20y4z3+15y3z4+6y2z5+yz624089\
/64y8y7z+11/2y6z2+26y5z3+95/2y4z4+47y3z5+53/2y2z6+8yz7+z8+104535/64y9+27\
y8z+135/2y7z2+90y6z3+135/2y5z4+27y4z5+9/2y3z6940383/128y10405/4y9z2025\
/8y8z2675/2y7z32025/8y6z4405/4y5z5135/8y4z6+4359015/128y11+1701/4y10z\
+8505/8y9z2+2835/2y8z3+8505/8y7z4+1701/4y6z5+567/8y5z682812341/512y1215\
333/8y11z76809/16y10z225735/4y9z378525/16y8z416893/8y7z58799/16y6z6\
198y5z7495/4y4z855y3z933/2y2z103yz111/4z12
