"Source: Text/Ring/FldFunG.text";
"Line: 5678";
"Date: Fri Sep 26 13:15:42 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Ring/FldFunG.text, line: 5678
// Example: H46E34 ()
print "Example: H46E34";
ei := GetEchoInput();
SetEchoInput(true);
PR<x> := FunctionField(Rationals());
P<y> := PolynomialRing(PR);
FR1<a> := FunctionField(y^3 - x + 1/x^3);
P<y> := PolynomialRing(FR1);
FR2<c> := FunctionField(y^2 - a/x^3*y + 1);
I := ideal<MaximalOrderFinite(FR2) | 
[ x^9 + 1639*x^8 + 863249*x^7 + 148609981*x^6 + 404988066*x^5 + 567876948*x^4 + 
468363837*x^3 + 242625823*x^2 + 68744019*x + 8052237, x^9 + 1639*x^8 + 
863249*x^7 + 148609981*x^6 + 404988066*x^5 + 567876948*x^4 + 468363837*x^3 +
242625823*x^2 + 68744019*x + 8052237, (x^15 + 1639*x^14 + 863249*x^13 + 
148609981*x^12 + 404988066*x^11 + 567876948*x^10 + 468363837*x^9 + 
242625823*x^8 + 68744019*x^7 + 8052237*x^6)*c, (x^15 + 1639*x^14 + 
863249*x^13 + 148609981*x^12 + 404988066*x^11 + 567876948*x^10 + 
468363837*x^9 + 242625823*x^8 + 68744019*x^7 + 8052237*x^6)*c ]>;
I;
J := ideal<MaximalOrderFinite(FR2) | 
[ x^3 + 278*x^2 + 164*x + 742, x^3 + 278*x^2 + 164*x + 742, (x^9 + 278*x^8 + 
164*x^7 + 742*x^6)*c, (x^9 + 278*x^8 + 164*x^7 + 742*x^6)*c ]>;
J;
Generators(J);
TwoElement(J);
Minimum(I);
Basis(J);
Basis(I);
I eq J;
assert not $1;
II, d := IntegralSplit(I);
II;
d;
assert $1 eq 1;
IsIntegral(I);
assert $1;
GCD(I, J)*LCM(I, J) eq I*J;
assert $1;
SetEchoInput(ei);
