Bug: RightDivide returns wrong output for Koszul dual rings defined over MAGMA.

[kamalsaleh]

The output of the operation RightDivide(a,b) for two matrices a,b is fail or a matrix x with x*b = a.

LoadPackage( "RingsForHomalg" );
Q := HomalgFieldOfRationalsInMAGMA( );
S := Q * "x0,x1";
A := KoszulDualRing( S );
a := HomalgMatrix( "[ [ e0*e1, 3*e0*e1 ] ]", 1, 2, A );
b := HomalgMatrix( "[ [ e0, e1 ] ]", 1, 2, A );
# x*b = a
x := RightDivide( a, b);
# <An unevaluated 1 x 1 matrix over an external ring>
x*b = a;
# false
Display( x );
# [3*e0 + e1]

If we define the field over Singular we get x = [ 3*e0 - e1] which satisfies x*b=a.

[mohamed-barakat]

This is a serious bug in the interface, i.e., the way we communicate with MAGMA.

[mohamed-barakat]

Everyone should please be cautious when using MAGMA's exterior algebra until I fix this bug (@zickgraf, @sebastianpos).

[mohamed-barakat]

Here is a minimal example that shows that the problem is in MAGMA (as far as I understand):

> E<e0,e1> := ExteriorAlgebra(Rationals(),2,"grevlex");
> A := Matrix(E,2,2,[ [ 0, e0*e1 ], [ e0,  e1 ] ] );
> B := Matrix(E,1,2,[ [ e0*e1, 3*e0*e1 ] ]);
> X := Solution( A, B );
> X * A;
[ -e0*e1 3*e0*e1]
> B;
[  e0*e1 3*e0*e1]

I will post a bug report.

[kamalsaleh]

For a future reference, this is caused by a bug and has been solved in magma V2.25-6.

[mohamed-barakat]

Please do not close the issue. I will close it with a commit.