"Source: Text/Geometry/Lseries.text";
"Line: 2951";
"Date: Thu Sep 25 14:47:45 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Geometry/Lseries.text, line: 2951
// Example: H139E36 ()
print "Example: H139E36";
ei := GetEchoInput();
SetEchoInput(true);
H := HypergeometricData([1,1,1],[2,2,2]);
L := LSeries(H,2 : BadPrimes:=[<2,8,1>],SaveEuler:=10000);
LSetPrecision(L,5);
assert IsOrthogonal(L); // degree 3 weight 2
S3 := Symmetrization(L,[3] : BadPrimes:=[<2,26,1>]);
[Degree(x[1]) : x in Factorization(S3)];
CFENew(S3); // 2^18 for deg 7 factor
O3 := OrthogonalSymmetrization(L,[3] : BadPrimes:=[<2,18,1>]);
Degree(O3);
CFENew(O3); // L-coeffs already computed, thanks to SaveEuler
LSetPrecision(L,20);
S21 := Symmetrization(L,[2,1] : BadPrimes:=[<2,20,1>]); // deg 8
CFENew(S21);
LT := Translate(L,2);
CFENew(S21/LT);
D := Determinant(L); D;
O2 := OrthogonalSymmetrization(L,[2] : BadPrimes:=[<2,10,1>]);
CFENew(O2);
TP := TensorProduct(O2,D : BadPrimes:=[<2,12,1>]);
Q := Translate(S21/LT,2);
P := PrimesUpTo(100);
assert &and[EulerFactor(TP,p) eq EulerFactor(Q,p) : p in P];
CFENew(S21/LT/D);       // the product of these
CFENew(LT/D);           // last two is ~ 10^(-12)
S := Symmetrization(L,[1,1] :  BadPrimes:=[<2,8,1>]);
DL := TensorProduct(D,L : BadPrimes:=[<2,8,1>]);
T := Translate(DL,-2);
assert &and[EulerFactor(T,p)  eq EulerFactor(S,p) : p in P];
SetEchoInput(ei);
