"Source: Text/Geometry/CrvHyp.text";
"Line: 2298";
"Date: Fri Sep 26 09:12:34 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Geometry/CrvHyp.text, line: 2298
// Example: H137E14 ()
print "Example: H137E14";
ei := GetEchoInput();
SetEchoInput(true);
_<x> := PolynomialRing(Rationals());
C := HyperellipticCurve( (x^2+1)*(x^6+7) );
J := Jacobian(C);
Ptors := J![x^2+1, 0];
Ptors;
Ptors1 := elt< J | [x^2+1, 0], 2 >;
Ptors eq Ptors1;  // Are they the same?
assert $1;
2*Ptors;
$1 eq J!0;  // Is the previous result really the trivial point on J?
assert $1;
Order(Ptors);  // Just to be absolutely sure ...
assert $1 eq 2;
Ptors2 := J![x^6+7,0];
SetEchoInput(ei);
