LIB "classify.lib";
ring r=0,(x,y,z),ds;
poly f=(x2+3y-2z)^2+xyz-(x-y3+x2*z3)^3;
classify(f);
→ About the singularity :
→           Milnor number(f)   = 4
→           Corank(f)          = 2
→           Determinacy       <= 5
→ Guessing type via Milnorcode:   D[k]=D[4]
→ 
→ Computing normal form ...
→ I have to apply the splitting lemma. This will take some time....:-)
→    Arnold step number 4
→ The singularity
→    -x3+3/2xy2+1/2x3y-1/16x2y2+3x2y3
→ is R-equivalent to D[4].
→    Milnor number = 4
→    modality      = 0
→ 2z2+x2y+y3
init_debug(3);
→ Debugging level change from  0  to  3
classify(f);
→ Computing Basicinvariants of f ...
→ About the singularity :
→           Milnor number(f)   = 4
→           Corank(f)          = 2
→           Determinacy       <= 5
→ Hcode: 1,2,1,0,0
→ Milnor code :  1,1,1
→ Debug:(2):  entering HKclass3_teil_1 1,1,1
→ Debug:(2):  finishing HKclass3_teil_1
→ Guessing type via Milnorcode:   D[k]=D[4]
→ 
→ Computing normal form ...
→ I have to apply the splitting lemma. This will take some time....:-)
→ Debug:(3):  Split the polynomial below using determinacy:  5
→ Debug:(3):  9y2-12yz+4z2-x3+6x2y-4x2z+xyz+x4+3x2y3
→ Debug:(2):  Permutations: 3,2,1
→ Debug:(2):  Permutations: 3,2,1
→ Debug:(2):  rank determined with Morse rg= 1
→ Residual singularity f= -x3+3/2xy2+1/2x3y-1/16x2y2+3x2y3
→ Step 3
→    Arnold step number 4
→ The singularity
→    -x3+3/2xy2+1/2x3y-1/16x2y2+3x2y3
→ is R-equivalent to D[4].
→    Milnor number = 4
→    modality      = 0
→ Debug:(2):  Decode:
→ Debug:(2):  S_in= D[4]   s_in= D[4]                          
→ Debug:(2):  Looking for Normalform of  D[k] with (k,r,s) = ( 4 , 0 , 0 )
→ Debug:(2):  Opening Singalarity-database:  
→  DBM: NFlist
→ Debug:(2):  DBMread( D[k] )= x2y+y^(k-1) .
→ Debug:(2):  S= f = x2y+y^(k-1);  Tp= x2y+y^(k-1) Key= I_D[k]
→ Polynom f= x2y+y3   crk= 2   Mu= 4  MlnCd= 1,1,1
→ Debug:(2):  Info= x2y+y3
→ Debug:(2):  Normal form NF(f)= 2*x(3)^2+x(1)^2*x(2)+x(2)^3
→ 2z2+x2y+y3