"Source: Text/Commut/Ideal.text";
"Line: 808";
"Date: Thu Sep 25 14:47:46 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Commut/Ideal.text, line: 808
// Example: H116E4 ()
print "Example: H116E4";
ei := GetEchoInput();
SetEchoInput(true);
P<x,y> := PolynomialRing(RationalField(), 2);
MilnorNumber((x^2 + y^2)^3 - 4*x^2*y^2); // 4-leaved rose
assert $1 eq 13;
[MilnorNumber(y^2 - x^n): n in [1 .. 5]];
P<x,y,z> := PolynomialRing(RationalField(), 3);  
[MilnorNumber(x*y*z + x^n + y^n + z^n): n in [1 .. 10]];
assert $1 eq [ 0, 1, 8, 11, 14, 17, 20, 23, 26, 29 ]; 
[TjurinaNumber(x*y*z + x^n + y^n + z^n): n in [1 .. 10]];
assert $1 eq [ 0, 1, 8, 10, 13, 16, 19, 22, 25, 28 ]; 
P<x,y> := PolynomialRing(RationalField(), 2);
f := y^2 - 2*x^28*y - 4*x^21*y^17 + 4*x^14*y^33 - 8*x^7*y^49 +               
     x^56 + 20*y^65 + 4*x^49*y^16;
time TjurinaNumber(f);
assert $1 eq 2260;
SetEchoInput(ei);
