[was@modular wooley]$ [was@modular wooley]$ Magma V2.8-2      Mon Dec  3 2001 16:43:25 on modular  [Seed = 2744413716]
Type ? for help.  Type <Ctrl>-D to quit.

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

Loading "/home/was/magma/local/init.m"
> A<x,y> := AffinePlane(Rationals());
> X := Scheme(x^2+y^2-1);

>> X := Scheme(x^2+y^2-1);
              ^
Runtime error in 'Scheme': Bad argument types
Argument types given: RngMPolElt
> X := Scheme(A, x^2+y^2-1);
> X;
Scheme over Rational Field defined by
x^2 + y^2 - 1
> Z := ProjectiveClosure(X);
> Z;
Scheme over Rational Field defined by
$.1^2 + $.2^2 - $.3^2
> C := Curve(Z);
> GeometricGenus(C);
0
> X := Scheme(A, x^5+3*x^4*y+y^5-1);
> Z := ProjectiveClosure(X);
> C := Curve(Z);
> GeometricGenus(C);
6
> Type(C);
Crv
> Attach("12-03-01.m");
> C,g := RandomCurve(5);

In file "/home/was/people/wooley/12-03-01.m", line 13, column 9:
>>    Z := ProjectiveCluse(X);
           ^
Runtime error: Undefined reference 'ProjectiveCluse' in package "/home/was/people/wooley/12-03-01.m"
> C,g := RandomCurve(5);

RandomCurve(
d: 5
)
In file "/home/was/people/wooley/12-03-01.m", line 12, column 15:
>>    X := Scheme(f);
                 ^
Runtime error in 'Scheme': Bad argument types
Argument types given: RngMPolElt
> C,g := RandomCurve(5);
> g;
0
> C,g := RandomCurve(5);

RandomCurve(
d: 5
)
GeometricGenus(
C: C
)
In file "/usr/local/Magma2.8/package/AlgGeom/curve/singularity.m", line 9, column 17:
>>     return Genus(C);
                   ^
Runtime error in 'Genus': Genus cannot be computed
> c;

>> c;
   ^
User error: Identifier 'c' has not been declared or assigned
> C;
Curve over Rational Field defined by
$.1^5 + $.1^4*$.2 - $.1^3*$.2^2 - $.1^2*$.2^3 + $.1*$.2^4 + 2*$.2^5
> C,g := RandomCurve(5);

RandomCurve(
d: 5
)
GeometricGenus(
C: C
)
In file "/usr/local/Magma2.8/package/AlgGeom/curve/singularity.m", line 9, column 17:
>>     return Genus(C);
                   ^
Runtime error in 'Genus': Genus cannot be computed
> C,g := RandomCurve(5);
C =  Curve over Rational Field defined by
$.1^4*$.2 + 1/2*$.1^3*$.2^2 + 1/2*$.1^2*$.2^3 + $.2^5

RandomCurve(
d: 5
)
GeometricGenus(
C: C
)
In file "/usr/local/Magma2.8/package/AlgGeom/curve/singularity.m", line 9, column 17:
>>     return Genus(C);
                   ^
Runtime error in 'Genus': Genus cannot be computed
> C,g := RandomCurve(5);

RandomCurve(
d: 5
)
In file "/home/was/people/wooley/12-03-01.m", line 14, column 6:
>>    PP<X,Y,Z> := Parent(Z);
        ^
Runtime error in 'AssignNames': Bad argument types
Argument types given: PowerStructure ~, SeqEnum[MonStgElt]
> C,g := RandomCurve(5);

RandomCurve(
d: 5
)
In file "/home/was/people/wooley/12-03-01.m", line 15, column 14:
>>    C := Curve(Z);
                ^
Runtime error in 'Curve': Bad argument types
Argument types given: RngMPolElt
> C,g := RandomCurve(5);
C =  Curve over Rational Field defined by
x^5 + x^4*y - x^3*y^2 - 2*x^2*y^3 + x*y^4 + 2*y^5

RandomCurve(
d: 5
)
GeometricGenus(
C: C
)
In file "/usr/local/Magma2.8/package/AlgGeom/curve/singularity.m", line 9, column 17:
>>     return Genus(C);
                   ^
Runtime error in 'Genus': Genus cannot be computed
> C,g := RandomCurve(5);
C =  Curve over Rational Field defined by
x^5*y^5 - 2*x^5*y^4*z + x^5*y^3*z^2 + x^5*y^2*z^3 + 2*x^5*y*z^4 + 2*x^5*z^5 + x^4*y^5*z - x^4*y^4*z^2 - x^4*y^3*z^3 - 2*x^4*y^2*z^4 + 2*x^4*y*z^5 - 2*x^4*z^6 - 2*x^3*y^4*z^3 - 2*x^3*y^3*z^4 + x^3*y^2*z^5 - 2*x^3*z^7 + 2*x^2*y^5*z^3 - x^2*y^3*z^5 + x^2*y^2*z^6 - x^2*y*z^7 - x^2*z^8 + x*y^5*z^4 + x*y^4*z^5 - 2*x*y^3*z^6 - x*y^2*z^7 + x*z^9 + 2*y^5*z^5 - 2*y^4*z^6 + 2*y^3*z^7 + y^2*z^8 + 2*y*z^9 + 2*z^10
> g;
16
> C,g := RandomCurve(5);
C =  Curve over Rational Field defined by
2*x^4*z + x^3*y^2 + x^3*y*z - x^3*z^2 + 2*x^2*y^3 + x^2*y^2*z - 2*x^2*z^3 + 2*x*y^4 + 2*x*y^3*z + x*y^2*z^2 - x*z^4 - y^5 + y^4*z - 2*y^3*z^2 + 2*y^2*z^3 - 2*y*z^4 + z^5
> g;
6
> C,g := RandomCurve(5);
C =  Curve over Rational Field defined by
x^5 - x^4*y + x^3*y^2 + x^3*y*z - x^3*z^2 + x^2*y^3 + 2*x^2*y^2*z - 2*x^2*y*z^2 - x^2*z^3 + x*y^4 - 2*x*y^3*z - 2*x*y^2*z^2 + 2*x*y*z^3 + x*z^4 + y^5 - 2*y^4*z + 2*y^3*z^2 + y*z^4 + 2*z^5
> g;
6
> C,g := RandomCurve(5);
C =  Curve over Rational Field defined by
x^5 + x^4*y + 1/2*x^3*y^2 + x^3*y*z + 1/2*x^3*z^2 - x^2*y^3 + 1/2*x^2*y^2*z + 1/2*x*y^4 - x*y^3*z - x*y^2*z^2 + x*y*z^3 + x*z^4 + y^5 - y^2*z^3 + y*z^4 + z^5
> g;
6
> C,g := RandomCurve(5);
C =  Curve over Rational Field defined by
x^5 - x^4*z + 2*x^3*y^2 - x^3*y*z + 2*x^3*z^2 - x^2*y^3 - x^2*y^2*z + 2*x^2*y*z^2 + 2*x*y^4 - 2*x*y^3*z + x*y^2*z^2 - x*y*z^3 + x*z^4 - 2*y^5 - y^3*z^2 - y^2*z^3 + 2*z^5
> g;
6
> C,g := RandomCurve(5 : range := 10);
C =  Curve over Rational Field defined by
x^5 + 4*x^4*y - x^3*y^2 - 5*x^3*y*z - 4*x^3*z^2 - 1/2*x^2*y^3 - 7/2*x^2*y^2*z - 7/2*x^2*y*z^2 + 5/2*x^2*z^3 - 2*x*y^4 - 2*x*y^3*z + 3/2*x*y^2*z^2 + 9/2*x*y*z^3 + 9/2*x*z^4 + 5*y^5 + 5/2*y^4*z - y^3*z^2 + 1/2*y^2*z^3 - 2*y*z^4
> g;
6
> C,g := RandomCurve(6 : range := 10);
C =  Curve over Rational Field defined by
x^6 + 2/3*x^5*y + 7/6*x^5*z - 5/6*x^4*y^2 - 2/3*x^4*y*z + 5/3*x^4*z^2 + 5/6*x^3*y^3 - x^3*y^2*z + 3/2*x^3*y*z^2 + 5/6*x^3*z^3 + x^2*y^4 - 5/3*x^2*y^3*z + 1/3*x^2*y^2*z^2 + 4/3*x^2*y*z^3 - 1/6*x^2*z^4 - 5/6*x*y^5 + 4/3*x*y^4*z + 1/2*x*y^3*z^2 + 1/6*x*y^2*z^3 - 1/2*x*y*z^4 + 1/3*x*z^5 - y^6 - 5/3*y^5*z + 1/2*y^4*z^2 - 1/2*y^3*z^3 - 3/2*y^2*z^4 + 4/3*y*z^5 + 5/3*z^6
> C;
Curve over Rational Field defined by
x^6 + 2/3*x^5*y + 7/6*x^5*z - 5/6*x^4*y^2 - 2/3*x^4*y*z + 5/3*x^4*z^2 + 5/6*x^3*y^3 - x^3*y^2*z + 3/2*x^3*y*z^2 + 5/6*x^3*z^3 + x^2*y^4 - 5/3*x^2*y^3*z + 1/3*x^2*y^2*z^2 + 4/3*x^2*y*z^3 - 1/6*x^2*z^4 - 5/6*x*y^5 + 4/3*x*y^4*z + 1/2*x*y^3*z^2 + 1/6*x*y^2*z^3 - 1/2*x*y*z^4 + 1/3*x*z^5 - y^6 - 5/3*y^5*z + 1/2*y^4*z^2 - 1/2*y^3*z^3 - 3/2*y^2*z^4 + 4/3*y*z^5 + 5/3*z^6
> g;
10
> ;
> C,g := RandomCurve(6 : range := 10);
> g;
10
> C;
Curve over Rational Field defined by
x^6 - 3/2*x^5*y + 1/3*x^5*z - 1/2*x^4*y*z - 2/3*x^4*z^2 - 5/3*x^3*y^3 - 5/3*x^3*y^2*z - 7/6*x^3*y*z^2 + 1/2*x^3*z^3 - 1/2*x^2*y^3*z + 1/6*x^2*y^2*z^2 + 3/2*x^2*y*z^3 - 4/3*x^2*z^4 + 5/6*x*y^5 + 5/3*x*y^4*z + 4/3*x*y^3*z^2 + 1/3*x*y^2*z^3 - 1/6*x*y*z^4 + 1/2*x*z^5 - 5/6*y^6 + 7/6*y^5*z - y^4*z^2 + 4/3*y^3*z^3 + 1/6*y^2*z^4 + 5/6*y*z^5 - 5/6*z^6
> DefiningPolynomial(C);
x^6 - 3/2*x^5*y + 1/3*x^5*z - 1/2*x^4*y*z - 2/3*x^4*z^2 - 5/3*x^3*y^3 - 5/3*x^3*y^2*z - 7/6*x^3*y*z^2 + 1/2*x^3*z^3 - 1/2*x^2*y^3*z + 1/6*x^2*y^2*z^2 + 3/2*x^2*y*z^3 - 4/3*x^2*z^4 + 5/6*x*y^5 + 5/3*x*y^4*z + 4/3*x*y^3*z^2 + 1/3*x*y^2*z^3 - 1/6*x*y*z^4 + 1/2*x*z^5 - 5/6*y^6 + 7/6*y^5*z - y^4*z^2 + 4/3*y^3*z^3 + 1/6*y^2*z^4 + 5/6*y*z^5 - 5/6*z^6
> Parent($1);
Polynomial ring of rank 3 over Rational Field
Lexicographical Order
Variables: x, y, z
> 23+1-2*Sqrt(23);
14.408336953374560916805123871875216307
> C,g := RandomCurve(6 : range := 15);
> C;
Curve over Rational Field defined by
x^6 - 13*x^5*y + 2*x^5*z + 6*x^4*y^2 - 3*x^4*y*z - 14*x^4*z^2 - x^3*y^3 + 11*x^3*y^2*z + 3*x^3*y*z^2 - 4*x^3*z^3 + 2*x^2*y^4 - 8*x^2*y^3*z + 9*x^2*y^2*z^2 - 6*x^2*y*z^3 + 13*x^2*z^4 + 4*x*y^5 + 4*x*y^4*z + 11*x*y^3*z^2 - 7*x*y^2*z^3 + x*y*z^4 + 14*x*z^5 - 4*y^6 - 15*y^5*z + 3*y^4*z^2 - 13*y^3*z^3 - 14*y^2*z^4 - 4*y*z^5 + 6*z^6
> g;
10
> 2*6-2;
10
> 2*7-2;
12
> C,g := RandomCurve(5);
> g;
6
> C;
Curve over Rational Field defined by
x^5 + x^4*y - 2*x^4*z + 2*x^3*y^2 - 2*x^2*y^3 - 2*x^2*y*z^2 + 2*x^2*z^3 - 2*x*y^4 - x*y^3*z + y^5 + y^4*z + 2*y^3*z^2 - 2*y^2*z^3 - 2*y*z^4 - 2*z^5
> ;

In file "/home/was/people/wooley/12-03-01.m", line 23, column 4:
>>    for t in y do
      ^
User error: bad syntax
> ;

In file "/home/was/people/wooley/12-03-01.m", line 24, column 42:
>>       phi := hom<Parent(F) -> R | R.1,t,1);
                                            ^
User error: bad syntax
> ;
> C;
Curve over Rational Field defined by
x^5 + x^4*y - 2*x^4*z + 2*x^3*y^2 - 2*x^2*y^3 - 2*x^2*y*z^2 + 2*x^2*z^3 - 2*x*y^4 - x*y^3*z + y^5 + y^4*z + 2*y^3*z^2 - 2*y^2*z^3 - 2*y*z^4 - 2*z^5
> SolvablePoint(C,[1]);

>> SolvablePoint(C,[1]);
                ^
Runtime error in 'SolvablePoint': Bad argument types
Argument types given: Crv, SeqEnum[RngIntElt]
> SolvablePoint(C,[1]);
Permutation group acting on a set of cardinality 5
(1, 2, 3, 4, 5)
(1, 2)
[ 7, 6, 3, 2*w + 9, 9*w + 9 ]
11
0
> SolvablePoint(C,[1]);
120
0
> SolvablePoint(C,[i : i in [1..10]]);
120
120
120
120
120
120
120
120
120
120
0
> ;

In file "/home/was/people/wooley/12-03-01.m", line 19, column 34:
>> intrinsic GaloisGroup(C::Crv, y::RngRatElt) -> .
                                    ^
User error: Unknown type 'RngRatElt'
> ;

In file "/home/was/people/wooley/12-03-01.m", line 19, column 34:
>> intrinsic GaloisGroup(C::Crv, y::RngRatElt) -> Grp
                                    ^
User error: Unknown type 'RngRatElt'
> ;
> GaloisGroup(C,1/5);

In file "/home/was/people/wooley/12-03-01.m", line 23, column 36:
>>    phi := hom<Parent(F) -> R | R.1,t,1>;
                                      ^
Runtime error: Undefined reference 't' in package "/home/was/people/wooley/12-03-01.m"
> GaloisGroup(C,1/5);
Permutation group acting on a set of cardinality 5
(1, 2, 3, 4, 5)
(1, 2)
[ 1, 21*w + 33, 20*w + 33, 3*w + 32, 38*w + 32 ]
41
> #$1;
1
> GaloisGroup(C,1/5);
Permutation group acting on a set of cardinality 5
(1, 2, 3, 4, 5)
(1, 2)
[ 1, 21*w + 33, 20*w + 33, 3*w + 32, 38*w + 32 ]
41
> #$1;
120
> ;
> #G2(C,1/5);
120
> G2(C,1/5);
Permutation group acting on a set of cardinality 5
(1, 2, 3, 4, 5)
(1, 2)
[ 1, 21*w + 33, 20*w + 33, 3*w + 32, 38*w + 32 ]
41
> K<a> := NumberField(x^2+1);

>> K<a> := NumberField(x^2+1);
                      ^
Runtime error in 'NumberField': Bad argument types
Argument types given: RngMPolElt
> R<x> := PolynomialRing(Rationals());
> > K<a> := NumberField(x^2+1);
> G := G2(C,a);
Permutation group acting on a set of cardinality 5
(1, 2, 3, 4, 5)
(1, 2)
[ 8, 8*w + 8, 9*w + 8, 11*w + 4, 6*w + 4 ]
Prime Ideal
Two element generators:
[17, 0]
[13, 1]
> #$1;
120
> G := G2(C,a);
> G;
Permutation group G acting on a set of cardinality 5
(1, 2, 3, 4, 5)
(1, 2)
> IsSolvable(G);
false
> K<a> := NumberField(x^3+17);
> G := GaloisGroup(C,a);
> G;
Permutation group G acting on a set of cardinality 5
(1, 2, 3, 4, 5)
(1, 2)
> IsSolvable(G);
false
> ;
> SolvablePoint(C,20);

>> SolvablePoint(C,20);
                ^
Runtime error in 'SolvablePoint': Bad argument types
Argument types given: Crv, RngIntElt
> SolvablePoint(C,10,20);

SolvablePoint(
C: C,
ymin: 10,
ymax: 20
)
In file "/home/was/people/wooley/12-03-01.m", line 39, column 58:
>>    return [y : y in [ymin..ymax] | IsSolvable(GaloisGroup(C, y))];
                                                            ^
Runtime error in 'GaloisGroup': Bad argument types
Argument types given: Crv, RngIntElt
> ;
> SolvablePoint(C,10,20);

SolvablePoint(
C: C,
ymin: 10,
ymax: 20
)
In file "/home/was/people/wooley/12-03-01.m", line 40, column 58:
>>    return [y : y in [ymin..ymax] | IsSolvable(GaloisGroup(C, y))];
                                                            ^
Runtime error in 'GaloisGroup': Bad argument types
Argument types given: Crv, RngIntElt
> SolvablePoint(C,10,20);
[]
> SolvablePoint(C,10,20);
[]
> SolvablePoint(C,10,20);
[]
> G := GaloisGroup(C,a);
> G;
Permutation group G acting on a set of cardinality 5
(1, 2, 3, 4, 5)
(1, 2)
> SolvablePoint(C,20,30);
[]
> SolvablePoint(C,50,60);
[]
> SolvablePoint(C,100,120);
[]
> SolvablePoint(C,1,100,5);
[]
> SolvablePoint(C,1,100,7);
[]
> C,g := RandomCurve(5);
> C,g := RandomCurve(4);
> g;
3
> SolvablePoint(C,1,100,7);

SolvablePoint(
C: C,
ymin: 1,
ymax: 100,
denom: 7
)
GaloisGroup(
C: C,
y: 1
)
In file "/home/was/people/wooley/12-03-01.m", line 34, column 12:
>>    f := phi(F);
              ^
Runtime error in map application: Coefficient ring coercion fail
> C;
Curve over Rational Field defined by
x^4 - 1/2*x^3*y + 1/2*x^3*z - 1/2*x^2*y^2 - 1/2*x^2*z^2 - 1/2*x*y^3 - x*y^2*z - 1/2*x*y*z^2 - x*z^3 + y^2*z^2 - 1/2*y*z^3 + z^4
> FractionField;

>> FractionField;
   ^
User error: Identifier 'FractionField' has not been declared or assigned
> SolvablePoint(C,1,100,7);
[ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100 ]
> C,g := RandomCurve(5);
> C;
Curve over Rational Field defined by
x^4*y - 2*x^4*z + x^3*y^2 - 2*x^3*z^2 + 2*x^2*y^3 - 2*x^2*y^2*z + 2*x^2*y*z^2 - x^2*z^3 + x*y^4 + 2*x*y^3*z - x*y*z^3 - y^5 + 2*y^4*z - y^3*z^2 - y*z^4
> g;
6
> SolvablePoint(C,1,40,7);

SolvablePoint(
C: C,
ymin: 1,
ymax: 40,
denom: 7
)
GaloisGroup(
C: C,
y: 1
)
In file "/home/was/people/wooley/12-03-01.m", line 35, column 22:
>>    return GaloisGroup(f);
                        ^
Runtime error in 'GaloisGroup': Argument 1 is not irreducible
> SymmetricGroup(3);
Symmetric group acting on a set of cardinality 3
Order = 6 = 2 * 3
> &*[SymmetricGroup(3), SymmetricGroup(4)];

>> &*[SymmetricGroup(3), SymmetricGroup(4)];
   ^
Runtime error in '&*': Universe has no multiplication algorithm
> SymmetricGroup(3) * SymmetricGroup(4);

>> SymmetricGroup(3) * SymmetricGroup(4);
                     ^
Runtime error in '*': Could not find a covering group
> SolvablePoint(C,1,40,7);
[ 1/7, 2/7, 3/7, 4/7, 5/7, 6/7, 1, 8/7, 9/7, 10/7, 11/7, 12/7, 13/7, 2, 15/7, 16/7, 17/7, 18/7, 19/7, 20/7, 3, 22/7, 23/7, 24/7, 25/7, 26/7, 27/7, 4, 29/7, 30/7, 31/7, 32/7, 33/7, 34/7, 5, 36/7, 37/7, 38/7, 39/7, 40/7 ]
> C;
Curve over Rational Field defined by
x^4*y - 2*x^4*z + x^3*y^2 - 2*x^3*z^2 + 2*x^2*y^3 - 2*x^2*y^2*z + 2*x^2*y*z^2 - x^2*z^3 + x*y^4 + 2*x*y^3*z - x*y*z^3 - y^5 + 2*y^4*z - y^3*z^2 - y*z^4
> g;
6
> SolvablePoint(C,1,40,1);
[ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40 ]
> SolvablePoint(C,1,5,1);
x - 1
x^3 + 11/2*x^2 + 15*x - 5
x^4 + 7*x^3 + 41*x^2 + 132*x - 111
x^4 + 7*x^3 + 103/2*x^2 + 190*x - 290
x^4 + 23/3*x^3 + 209/3*x^2 + 290*x - 2005/3
[ 1, 2, 3, 4, 5 ]
> SolvablePoint(C,1,5,1);
-x^4 - x^3 + x^2 + 2*x - 1
x - 1
2*x^3 + 11*x^2 + 30*x - 10
x^3 + 11/2*x^2 + 15*x - 5
x^4 + 7*x^3 + 41*x^2 + 132*x - 111
x^4 + 7*x^3 + 41*x^2 + 132*x - 111
2*x^4 + 14*x^3 + 103*x^2 + 380*x - 580
x^4 + 7*x^3 + 103/2*x^2 + 190*x - 290
3*x^4 + 23*x^3 + 209*x^2 + 870*x - 2005
x^4 + 23/3*x^3 + 209/3*x^2 + 290*x - 2005/3
[ 1, 2, 3, 4, 5 ]
> C;
Curve over Rational Field defined by
x^4*y - 2*x^4*z + x^3*y^2 - 2*x^3*z^2 + 2*x^2*y^3 - 2*x^2*y^2*z + 2*x^2*y*z^2 - x^2*z^3 + x*y^4 + 2*x*y^3*z - x*y*z^3 - y^5 + 2*y^4*z - y^3*z^2 - y*z^4
> C,g := RandomCurve(5);
> C;
Curve over Rational Field defined by
x^5 - 2*x^4*y - 2*x^4*z - 2*x^3*y^2 - 2*x^3*y*z + x^3*z^2 - 2*x^2*y^3 + x^2*y^2*z + x^2*y*z^2 - 2*x^2*z^3 + 2*x*y^4 - x*y^3*z - 2*x*y*z^3 + y^5 + 2*y^4*z - 2*z^5
> g;
6
> C;
Curve over Rational Field defined by
x^5 - 2*x^4*y - 2*x^4*z - 2*x^3*y^2 - 2*x^3*y*z + x^3*z^2 - 2*x^2*y^3 + x^2*y^2*z + x^2*y*z^2 - 2*x^2*z^3 + 2*x*y^4 - x*y^3*z - 2*x*y*z^3 + y^5 + 2*y^4*z - 2*z^5
> SolvablePoint(C,1,5,1);
x^5 - 4*x^4 - 3*x^3 - 2*x^2 - x + 1
x^5 - 4*x^4 - 3*x^3 - 2*x^2 - x + 1
x^5 - 6*x^4 - 11*x^3 - 12*x^2 + 20*x + 62
x^5 - 6*x^4 - 11*x^3 - 12*x^2 + 20*x + 62
x^5 - 8*x^4 - 23*x^3 - 44*x^2 + 129*x + 403
x^5 - 8*x^4 - 23*x^3 - 44*x^2 + 129*x + 403
x^5 - 10*x^4 - 39*x^3 - 110*x^2 + 440*x + 1534
x^5 - 10*x^4 - 39*x^3 - 110*x^2 + 440*x + 1534
x^5 - 12*x^4 - 59*x^3 - 222*x^2 + 1115*x + 4373
x^5 - 12*x^4 - 59*x^3 - 222*x^2 + 1115*x + 4373
[]
> SolvablePoint(C,1,5,1);
[]
> SolvablePoint(C,1,5,7);
[]
> SolvablePoint(C,1,11,13);
[]
> SolvablePoint(C,1,11,19);
[]
> SolvablePoint(C,1,11,31);
[]
> SolvablePoint(C,1,100,31);
[]
> SolvablePoint(C,-1,1,31);
[]
> C,g := RandomCurve(4);
> C;
Curve over Rational Field defined by
x^4 + x^3*y + 1/2*x^3*z + 1/2*x^2*y^2 - x^2*y*z + 1/2*x^2*z^2 - x*y^3 + x*y^2*z + x*y*z^2 + x*z^3 + y^4 + 1/2*y^2*z^2 + y*z^3 + 1/2*z^4
> g;
3
> SolvablePoint(C,1,5,1);
[ 1, 2, 3, 4, 5 ]
> > R<x> := PolynomialRing(Rationals());
> K<a> := NumberField(x^3+1);
> IsSolvable(GaloisGroup(C,a));

> 
>>   K<a> := NumberField(x^3+1);
                        ^
Runtime error in 'NumberField': Argument 1 is not irreducible
> true
> > > R<x> := PolynomialRing(Rationals());
> K<a> := NumberField(x^3+x^2+1);
> #GaloisGroup(C,a);

> > 24
> >