AutomorphismGroup

[jvoight]

Something up with relative extensions?

> _<x> := PolynomialRing(Rationals());
> X := HyperellipticCurve(x^5 - 3*x^4 + 5*x^3 + 27*x^2 + 18*x);
> Y := EllipticCurve(x^3 - 7*x^2 + 20*x + 4);
> K := NumberField(x^2+1);
> AllArithmetic2Gluings(Y,X);
[ [*
    4*x^4 - 39*x^2*y^2 - 94*x^2*y*z - 27*x^2*z^2 + 4*y^4 + 20*y^2*z^2 + 72*z^4,
    -188,
    t,
    [
        [
            1/682*(-3*$.1^4 + 84*$.1^3 - 937*$.1^2 + 4886*$.1 - 8468),
            1/1364*(3*$.1^4 - 84*$.1^3 + 937*$.1^2 - 5568*$.1 + 18016),
            1/1364*(3*$.1^4 - 84*$.1^3 + 937*$.1^2 - 4204*$.1 + 8468)
        ],
        [
            1/682*(7*$.1^4 - 196*$.1^3 + 1959*$.1^2 - 8218*$.1 + 11802),
            1/1364*(-3*$.1^5 + 98*$.1^4 - 1329*$.1^3 + 9486*$.1^2 - 34452*$.1 + 
                50884),
            1/1364*(3*$.1^5 - 112*$.1^4 + 1721*$.1^3 - 13404*$.1^2 + 50888*$.1 -
                67668)
        ]
    ]
*], [*
    9*x^4 - 8*x^2*y^2 + 36*x^2*y*z - 36*x^2*z^2 + 9*y^4 + 36*y^3*z - 72*y*z^3 - 
        81*z^4,
    234,
    t + 1,
    [
        [
            1/682*(-3*$.1^4 + 84*$.1^3 - 937*$.1^2 + 4886*$.1 - 8468),
            1/1364*(3*$.1^4 - 84*$.1^3 + 937*$.1^2 - 5568*$.1 + 18016),
            1/1364*(3*$.1^4 - 84*$.1^3 + 937*$.1^2 - 4204*$.1 + 8468)
        ],
        [
            1/341*(2*$.1^4 - 56*$.1^3 + 511*$.1^2 - 1666*$.1 + 1326),
            1/1364*(-3*$.1^5 + 101*$.1^4 - 1413*$.1^3 + 10423*$.1^2 - 40020*$.1 
                + 67536),
            1/1364*(3*$.1^5 - 109*$.1^4 + 1637*$.1^3 - 12467*$.1^2 + 46684*$.1 -
                60564)
        ]
    ]
*] ]
> AllArithmetic2Gluings(ChangeRing(Y,K),ChangeRing(X,K));

AllArithmetic2Gluings(
    X1: Elliptic Curve defined by y^2 = x^3 - 7*x^2 + 20*x + 4 over ...,
    X2: Hyperelliptic Curve defined by y^2 = x^5 - 3*x^4 + 5*x^3 + 2...
)
ApplyFormulaABRs(
    frs: $.1^3 - 7*$.1^2 + 20*$.1 + 4,
    fss: $.1^4 - 3*$.1^3 + 5*$.1^2 + 27*$.1 + 18,
    fab: $.1
)
CompatibleRootPairings(
    f1: $.1^3 - 7*$.1^2 + 20*$.1 + 4,
    f2: $.1^3 - 5*$.1^2 - 153*$.1 - 531
)
SplittingFieldWithAutomorphisms(
    f: $.1^3 - 7*$.1^2 + 20*$.1 + 4
)
In file "/Users/jvoight/Library/CloudStorage/Dropbox-Personal/github/CHIMP/glui\
ng/magma/interpolated/routines.m", line 58, column 34:
>> Gp, Ga, Gphi := AutomorphismGroup(L, K);
                                    ^
Runtime error in 'AutomorphismGroup': The first argument must be an extension of
the second argument