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Revision 66031d5da1579950542857d7fd87288b3d6fe116 authored by Mohamed Barakat on 30 September 2015, 13:56:13 UTC, committed by Mohamed Barakat on 30 September 2015, 14:08:55 UTC 
fixed CommonHomalgTableForSingularTools.MulMat bug for nonconstant ring elements
 
From: Sebastian Posur <sebastian.posur@rwth-aachen.de>
Subject: Re: Skalarmultiplikation in MatricesForHomalg
Date: 30. September 2015 10:20:29 MESZ
To: Mohamed Barakat <mohamed.barakat@rwth-aachen.de>
Cc: Sebastian Gutsche <gutsche@momo.math.rwth-aachen.de>

Ein weiterer Bug in diesem Zusammenhang: Die Linksmultiplikation
mit einem Weylalgebra Element wird als Rechtsmultiplikation ausgeführt.

LoadPackage( "RingsForHomalg" );;

LoadPackage( "Modules" );;

Qx := HomalgFieldOfRationalsInDefaultCAS( ) * "x";;
A1 := RingOfDerivations( Qx, "d" );;

x := IndeterminateCoordinatesOfRingOfDerivations( A1 )[1];;
d := IndeterminateDerivationsOfRingOfDerivations( A1 )[1];;

M := HomalgMatrix( [ [ d ] ], 1, 1, A1 );;

gap> x*d;
x*d
gap> Display( x * M );
x*d+1
1 parent ba74531
Raw File
CompleteNonProjective.g 
LoadPackage( "ToricVarieties" );

## Lets have a look at the toric variety that is complete but not projective

rays := [ [1,0,0], [-1,0,0], [0,1,0], [0,-1,0], [0,0,1], [0,0,-1],
          [2,1,1], [1,2,1], [1,1,2], [1,1,1] ];

cones := [ [1,3,6], [1,4,6], [1,4,5], [2,3,6], [2,4,6], [2,3,5], [2,4,5],
           [1,5,9], [3,5,8], [1,3,7], [1,7,9], [5,8,9], [3,7,8],
           [7,9,10], [8,9,10], [7,8,10] ];

F := Fan( rays, cones );

T := ToricVariety( F );

IsComplete( T );

IsAffine( T );

SetIsProjective( T, false );

Dimension( T );

HasTorusfactor( T );

IsSmooth( T );

ClassGroup( T );

PicardGroup( T );

CoxRing( T, "x" );

Display( ClassGroup ( T ) );

Display( ByASmallerPresentation( ClassGroup( T ) ) );

CoxRing( T );

# MorphismFromCoxVariety( T );
# 
# IsMorphism( last );
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