[was@modular was]$ [was@modular was]$ Magma V2.8-2      Wed Jan 16 2002 20:54:02 on modular  [Seed = 2448130872]
Type ? for help.  Type <Ctrl>-D to quit.

Loading startup file "/home/was/magma/local/emacs.m"

Loading "/home/was/magma/local/init.m"
> C := HyperellipticCurve([x^3 + x + 1, x^5 - x ]);
> P := C![0,-1];
> C19 := ChangeRing(C,GF(19));

>> C19,pi := ChangeRing(C,GF(19));
          ^
Runtime error in :=: Expected to assign 2 value(s) but only computed 1 value(s)
> C19 := ChangeRing(C,GF(19));
> P19 := C19!P;
n> Order(P19);

>> Order(P19);
        ^
Runtime error in 'Order': Bad argument types
Argument types given: PtHyp
> J := Jacobian(C);
> J19 := ChangeRing(J,GF(19));

>> J19 := ChangeRing(J,GF(19));
                    ^
Runtime error in 'ChangeRing': Bad argument types
Argument types given: JacHyp, FldFin
> J19 := Jacobian(C19);
> P19 := J19!(C19!P);

>> P19 := J19!(C19!P);
             ^
Runtime error in '!': RHS must be either 0 or a sequence of two polynomials
LHS: JacHyp
RHS: PtHyp
> Z := C![0,0];
>  P19 := J19![C19!P,C19!Z];
> Order(P19);
123
>


>Cbig := ChangeRing(C,GF(NextPrime(10^6)));
> 
> Jbig := Jacobian(Cbig);
> Pbig := Jbig![Cbig!P,Cbig!Z];
> Pbig;
(x^2, 1000002, 2)
> Csim,phi := SimplifiedModel(Cbig);
> phi(Pbig);
(x^2, x + 1000002, 2)
> Psim := phi(Pbig);
> Psim;
(x^2, x + 1000002, 2)
> Order(Psim);
333087389997
> time Order(Psim);
333087389997
Time: 0.010