Descend issue

[edgarcosta]

Something goes wrong when one tries to compute endomorphisms over the base:

> R<x> := PolynomialRing(Rationals());
> F<z> := NumberFieldExtra(x^2-x+1:prec:=300);
> z3 := -z;
> assert z3^2+z3+1 eq 0;
> R<a,b,c> := PolynomialRing(F,3);
> f := a^4 + (z3-1)*a^3*b + (3*z3+2)*a^3*c -3*a^2*c^2 + (2*z3+2)*a*b^3 -
> 3*z3*a*b^2*c + 3*z3*a*b*c^2 - 2*z3*a*c^3 - z3*b^3*c + 3*z3*b^2*c^2 +
> (-z3+1)*b*c^3 + (z3+1)*c^4;
> C := Curve(ProjectiveSpace(R),f);
> HeuristicEndomorphismRepresentation(C : Geometric:=true);
[ [*
[1 0 0]
[0 1 0]
[0 0 1],

[1 0 0 0 0 0]
[0 1 0 0 0 0]
[0 0 1 0 0 0]
[0 0 0 1 0 0]
[0 0 0 0 1 0]
[0 0 0 0 0 1]
*], [*
[     0 -z + 1 -z + 1]
[     z      0      z]
[     z -z + 1      0],

[ 1  0  2  0  1  0]
[ 1 -1  2 -1  0 -1]
[ 0  1  0  0  1  0]
[ 0  0 -1  1  1  0]
[ 0  0  0  0 -1  1]
[ 1  0  0  2  2  0]
*], [*
[    0    -z     1]
[z - 1     0     1]
[    1     1     0],

[-1  2  2  0  2  1]
[-1  1  1 -2  0  1]
[ 1 -1  0 -1 -1  0]
[ 0 -1 -1 -1 -1  1]
[ 1  0  0  2  1 -1]
[ 1  0  0  2  1  0]
*] ]
> HeuristicEndomorphismRepresentation(C : Geometric:=false);

HeuristicEndomorphismRepresentation(
X: Curve over L defined by a^4 + (-z - 1)*a^3*b + (-3*z + 2)*a^...
)
EndomorphismRepresentation(
GeoEndoRep: [ [* [1 0 0] [0 1 0] [0 0 1],  [1 0 0 0 0 0] [0 1 0 0 0 0] [...,
K: Rational Field,
h: Mapping from: Rational Field to FldNum: L
)
EndomorphismRepresentation(
GeoEndoRep: [ [* [1 0 0] [0 1 0] [0 0 1],  [1 0 0 0 0 0] [0 1 0 0 0 0] [...,
GalK: [* { (1, 2) }, Mapping from: GrpPerm: $, Degree 2, Order 2 t...
)
In file "/Users/edgarcosta/projects/CHIMP/endomorphisms/endomorphisms/magma/heuristic/OverField.m", line 49, column 9:
>>         assert test;
           ^
Runtime error in assert: Assertion failed
>

reported by @AashrayaJha

[edgarcosta]

This is basically the other issue mentioned in #58