Fixed a bug in tate resolution.
Merge pull request #15 from sebasguts/master

Danke Markus, danke Sebastian


$ gap P2.g 

#I  Overwriting already installed help book 'convex not loaded'.

┌───────┐   GAP, Version 4.5.6 of 16-Sep-2012 (free software, GPL)

│  GAP  │http://www.gap-system.org

└───────┘   Architecture: x86_64-apple-darwin12.2.0-gcc-default64

 Libs used:  gmp

 Loaded workspace: /Users/mo/software/gap/gap4r5/bin/wsgap4

 Components: trans 1.0, prim 2.1, small* 1.0, id* 1.0

 Packages:   AClib 1.2, Alnuth 3.0.0, AtlasRep 1.5.0, AutPGrp 1.5, Browse 1.8.2, CRISP 1.3.5, Cryst 4.1.10, CrystCat 1.1.6, CTblLib 1.2.1, 

             EDIM 1.3.1, FactInt 1.5.3, FGA 1.1.1, GAPDoc 1.5.1, IO 4.2, IRREDSOL 1.2.1, LAGUNA 3.6.1, Polenta 1.3.1, Polycyclic 2.10.1, 

             RadiRoot 2.6, ResClasses 3.1.1, Sophus 1.23, TomLib 1.2.2

 Try '?help' for help. See also  '?copyright' and  '?authors'

----------------------------------------------------------------

Loading  AutoDoc 2012.10.26

by Sebastian Gutsche (http://wwwb.math.rwth-aachen.de/~gutsche/)

Type:

  ?AutoDoc:        ## for the contents of the manual

  ?AutoDoc:x       ## for chapter/section/topic x

----------------------------------------------------------------

----------------------------------------------------------------

Loading  ToolsForHomalg 2012.10.27

by Mohamed Barakat (http://www.mathematik.uni-kl.de/~barakat/)

   Sebastian Gutsche (http://wwwb.math.rwth-aachen.de/~gutsche/)

   Markus Lange-Hegermann (http://wwwb.math.rwth-aachen.de/~markus/)

Type:

  ?ToolsForHomalg:        ## for the contents of the manual

  ?ToolsForHomalg:x       ## for chapter/section/topic x

----------------------------------------------------------------

----------------------------------------------------------------

Loading  homalg 2012.10.28

by Mohamed Barakat (http://www.mathematik.uni-kl.de/~barakat/)

   Sebastian Gutsche (http://wwwb.math.rwth-aachen.de/~gutsche/)

   Markus Lange-Hegermann (http://wwwb.math.rwth-aachen.de/~markus/)

Type:

  ?homalg:                   ## for the contents of the manual

  ?homalg:x                  ## for chapter/section/topic x

  ExamplesForHomalg();       ## for a guide to create a ring

----------------------------------------------------------------

----------------------------------------------------------------

Loading  MatricesForHomalg 2012.10.25

by Mohamed Barakat (http://www.mathematik.uni-kl.de/~barakat/)

   Markus Lange-Hegermann (http://wwwb.math.rwth-aachen.de/~markus/)

Type:

  ?MatricesForHomalg:        ## for the contents of the manual

  ?MatricesForHomalg:x       ## for chapter/section/topic x

----------------------------------------------------------------

----------------------------------------------------------------

Loading  HomalgToCAS 2012.10.22

by Mohamed Barakat (http://www.mathematik.uni-kl.de/~barakat/)

   Thomas Breuer (http://www.math.rwth-aachen.de/~Thomas.Breuer/)

   Simon Görtzen (http://wwwb.math.rwth-aachen.de/~simon/)

   Sebastian Gutsche (http://wwwb.math.rwth-aachen.de/~gutsche/)

   Frank Lübeck (http://www.math.rwth-aachen.de/~Frank.Luebeck/)

For help, type: ?HomalgToCAS package 

----------------------------------------------------------------

----------------------------------------------------------------

Loading  Modules 2012.10.27

by Thomas Bächler (http://wwwb.math.rwth-aachen.de/~thomas/)

   Mohamed Barakat (http://www.mathematik.uni-kl.de/~barakat/)

   Florian Diebold ()

   Sebastian Gutsche (http://wwwb.math.rwth-aachen.de/~gutsche/)

   Markus Lange-Hegermann (http://wwwb.math.rwth-aachen.de/~markus/)

Type:

  ?Modules:                  ## for the contents of the manual

  ?Modules:x                 ## for chapter/section/topic x

  ExamplesForHomalg();       ## for a guide to create a ring

----------------------------------------------------------------

----------------------------------------------------------------

Loading  RingsForHomalg 2012.10.25

by Mohamed Barakat (http://www.mathematik.uni-kl.de/~barakat/)

   Simon Goertzen (http://wwwb.math.rwth-aachen.de/goertzen/)

   Markus Kirschmer (http://www.math.rwth-aachen.de/~Markus.Kirschmer/)

   Markus Lange-Hegermann (http://wwwb.math.rwth-aachen.de/~markus/)

   Oleksandr Motsak (http://www.mathematik.uni-kl.de/~motsak/)

   Max Neunhöffer (http://www-groups.mcs.st-and.ac.uk/~neunhoef/)

   Daniel Robertz (http://wwwb.math.rwth-aachen.de/~daniel/)

   Hans Schönemann (http://www.mathematik.uni-kl.de/~hannes/)

   Andreas Steenpaß ()

For help, type: ?RingsForHomalg package 

----------------------------------------------------------------

----------------------------------------------------------------

Loading  GradedRingForHomalg 2012.10.25

by Mohamed Barakat (http://www.mathematik.uni-kl.de/~barakat/)

   Sebastian Gutsche (http://wwwb.math.rwth-aachen.de/~gutsche/)

   Markus Kirschmer (http://www.math.rwth-aachen.de/~Markus.Kirschmer/)

   Sebastian Jambor (http://wwwb.math.rwth-aachen.de/~sebastian/)

   Markus Lange-Hegermann (http://wwwb.math.rwth-aachen.de/~markus/)

   Daniel Robertz (http://wwwb.math.rwth-aachen.de/~daniel/)

Type:

  ?GradedRingForHomalg:      ## for the contents of the manual

  ?GradedRingForHomalg:x     ## for chapter/section/topic x

----------------------------------------------------------------

----------------------------------------------------------------

Loading  IO_ForHomalg 2012.10.22

by Thomas Bächler (http://wwwb.math.rwth-aachen.de/~thomas/)

   Mohamed Barakat (http://www.mathematik.uni-kl.de/~barakat/)

   Sebastian Gutsche (http://wwwb.math.rwth-aachen.de/~gutsche/)

   Max Neunhöffer (http://www-groups.mcs.st-and.ac.uk/~neunhoef/)

   Daniel Robertz (http://wwwb.math.rwth-aachen.de/~daniel/)

For help, type: ?IO_ForHomalg package 

----------------------------------------------------------------

================================================================

                     SINGULAR                                 /  Development

 A Computer Algebra System for Polynomial Computations       /   version 3-1-5

                                                           0<

 by: W. Decker, G.-M. Greuel, G. Pfister, H. Schoenemann     \   Jul 2012

FB Mathematik der Universitaet, D-67653 Kaiserslautern        \

// ** executing /Users/mo/software/singular/Singular/LIB/.singularrc

================================================================

================================================================

                     SINGULAR::SCA

The SINGULAR Subsystem for Super-Commutative Algebras

     by: G.-M. Greuel, O. Motsak, H. Schoenemann

FB Mathematik der Universitaet, D-67653 Kaiserslautern

================================================================

----------------------------------------------------------------

Loading  GradedModules 2012.10.26

by Mohamed Barakat (http://www.mathematik.uni-kl.de/~barakat/)

   Sebastian Gutsche (http://wwwb.math.rwth-aachen.de/~gutsche/)

   Sebastian Jambor (http://wwwb.math.rwth-aachen.de/~sebastian/)

   Markus Lange-Hegermann (http://wwwb.math.rwth-aachen.de/~markus/)

   Arne Lorenz (http://wwwb.math.rwth-aachen.de/~arne/)

   Oleksandr Motsak (http://www.mathematik.uni-kl.de/~motsak/)

Type:

  ?GradedModules:            ## for the contents of the manual

  ?GradedModules:x           ## for chapter/section/topic x

----------------------------------------------------------------

total:  48 35 24 15  8  3  1  3  8 15 24  ?  ?

---------|--|--|--|--|--|--|--|--|--|--|--|--|

    2:  48 35 24 15  8  3  .  .  .  .  .  0  0

    1:   *  .  .  .  .  .  .  1  .  .  .  .  0

    0:   *  *  .  .  .  .  .  .  .  3  8 15 24

---------|--|--|--|--|--|--|--|--|--S--|--|--|

twist:  -7 -6 -5 -4 -3 -2 -1  0  1  2  3  4  5

----------------------------------------------

Euler:  48 35 24 15  8  3  0 -1  0  3  8 15 24

gap> TateResolution(O(0)+O(1),-5,5); 

<An acyclic cocomplex containing 10 morphisms of graded left modules at degrees [ -5 .. 5 ]>

gap> Display( BettiDiagram( last ) );

total:  25 16  9  4  2  4  9 16 25 36 49  ?  ?

---------|--|--|--|--|--|--|--|--|--|--|--|--|

    2:  25 16  9  4  1  .  .  .  .  .  .  0  0

    1:   *  .  .  .  .  .  .  .  .  .  .  .  0

    0:   *  *  .  .  .  .  1  4  9 16 25 36 49

---------|--|--|--|--|--|--|--S--|--|--|--|--|

twist:  -7 -6 -5 -4 -3 -2 -1  0  1  2  3  4  5

----------------------------------------------

Euler:  25 16  9  4  1  0  1  4  9 16 25 36 49

gap> TateResolution(O(0)+O(1)+O(3),-5,5);

<An acyclic cocomplex containing 10 morphisms of graded left modules at degrees [ -5 .. 5 ]>

gap> Display( BettiDiagram( last ) );    

total:  28 17 10  7  8 14 24 37 53 72 94  ?  ?

---------|--|--|--|--|--|--|--|--|--|--|--|--|

    2:  28 17  9  4  1  .  .  .  .  .  .  0  0

    1:   *  .  .  .  .  .  .  .  .  .  .  .  0

    0:   *  *  .  .  1  3  7 14 24 37 53 72 94

---------|--|--|--|--|--|--|--S--|--|--|--|--|

twist:  -7 -6 -5 -4 -3 -2 -1  0  1  2  3  4  5

----------------------------------------------

Euler:  28 17  9  4  2  3  7 14 24 37 53 72 94

gap> TateResolution(O(0)+O(1)+O(3),-7,7);

Error, no method found! For debugging hints type ?Recovery from NoMethodFound

Error, no 1st choice method found for `ListOp' on 2 arguments called from

CallFuncList( ListOp, arg ) called from

List( i, HomalgElementToInteger ) called from

func( C[i] ) called from

List( old_degrees, function ( i )

      return List( i, HomalgElementToInteger );

  end ) called from

CallFuncList( Functor!.OnObjects, arguments_of_functor ) called from

...  at line 5 of *stdin*

you can 'quit;' to quit to outer loop, or

you can 'return;' to continue

brk> 

gap> TateResolution(O(0)+O(1)+O(3),-7,7);

Error, no method found! For debugging hints type ?Recovery from NoMethodFound

Error, no 1st choice method found for `ListOp' on 2 arguments called from

CallFuncList( ListOp, arg ) called from

List( i, HomalgElementToInteger ) called from

func( C[i] ) called from

List( old_degrees, function ( i )

      return List( i, HomalgElementToInteger );

  end ) called from

CallFuncList( Functor!.OnObjects, arguments_of_functor ) called from

...  at line 5 of *stdin*

you can 'quit;' to quit to outer loop, or

you can 'return;' to continue

brk> 

gap>
MaximalGradedLeftIdeal and ResidueClassRingAsGradedLeftModule are now attributes

together with their "Right" versions
installed GradedLeftSubmodule and GradedRightSubmodule for IsHomalgGradedRingElementRep

with caching, analogous to Left/RightSubmodule in Modules v2012.08.10
declared and installed JacobianIdeal for graded modules and "homogeneous" ring elements

WARNING: we don't check if the elements of the graded ring are homogeneous
installed FittingIdeal

(needs Modules v2013.02.05)
improved ResidueClassRing
installed MinimalParametrization
renamed KaehlerDifferentials -> ModuleOfKaehlerDifferentials