[was@laptop mlogs]$ [was@laptop mlogs]$ Magma V2.9-19     Fri Nov  8 2002 08:51:14 on laptop   [Seed = 4245356983]
Type ? for help.  Type <Ctrl>-D to quit.

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

Loading "/home/was/magma/local/init.m"
> K<a> := QuadraticField(23);
> O := MaximalOrder(K);
> I := 3*O + (2*a+3)*O;
> I;
Principal Ideal of O
Generator:
1
> I := (2*a+3)*O;
> I;
Principal Ideal of O
Generator:
2*$.2 + 3
> Q := QuadraticForms(23*4);
> Q;
Binary quadratic forms of discriminant 92
> ClassGroup(Q);
Abelian Group of order 1
Mapping from: Abelian Group of order 1 to QuadBin: Q given by a rule [no inverse]
> FundamentalUnit(O);
5*$.2 + 24
> Norm($1);
1
> Q;
Binary quadratic forms of discriminant 92
> Q := QuadraticForms(23*4);
> Q![1,2,3];

>> Q![1,2,3];
    ^
Runtime error in '!': Quadratic form has incorrect discriminant
LHS: QuadBin
RHS: [RngIntElt]
> Q.1;

>> Q.1;
    ^
Runtime error in '.': Bad argument types
Argument types given: QuadBin, RngIntElt
> f := PrimeForm(Q,2);
<2,2,-11>
> g := Identity(Q);
<1,8,-7>
> f := PrimeForm(Q,2);
> g := Identity(Q);
> IsEquivalent(f,g);
true
> Ideal(f);
Ideal of O
Two element generators:
2
$.2 - 1
> Ideal(g);
Ideal of O
Two element generators:
1
$.2
> f, b:=IsEquivalent(f,g);

>> f, b:=IsEquivalent(f,g);
                     ^
Runtime error in 'IsEquivalent': Tranformation matrix can only be given for negative discriminants
> f := PrimeForm(Q,23);
> f;
<23,0,-1>
> PrimeForm;
Intrinsic 'PrimeForm'

Signatures:

(<QuadBin> M, <RngIntElt> p) -> QuadBinElt

The prime form whose first coefficient is p, in the magma of quadratic forms M


> f := Q![-23,0,1];
> f;
<-23,0,1>
> Discriminant(f);
92
> IsEquivalent(f,g);
true
> g;
<1,8,-7>
> g := Q![-1,0,23];
> IsEquivalent(f,g);
true
> Reduce(f);

>> Reduce(f);
         ^
Runtime error in 'Reduce': Bad argument types
Argument types given: QuadBinElt
> Reduction(f);
<1,8,-7>
> Reduction(g);
<-1,8,7>
> IsEquivalent(f,g);
true
>