TODO-QPA1.txt

List of all things that are documented in the manual for QPA1 (version 1.26),
with information about whether the same functionality is implemented in QPA2.

[function] -- no              means [function] is not implemented in QPA2
[function] -- same            means [function] is implemented in QPA2, with exactly the same name
[function] -> [replacement]   means [function] is implemented in QPA2, but under the name/syntax [replacement]


CHAPTER 3: QUIVERS

InfoQuiver                 -- no
OrderedBy( quiver, ordering) -- no
Q.name -> Q[ vertex_label ], Q.arrow_label
OrderingOfQuiver( quiver ) -- no
OrderingOfQuiver( quiver ) -- no
IsZeroPath( obj ) -- no, there are no zero paths

CHAPTER 4: PATH ALGEBRAS

OrderingOfAlgebra( FQ ) -> no
FQ.name -> FQ[ vertex_label ], FQ.arrow_label
a < b -- no (needed?)
MakeUniformOnRight( elems ) -- no (check if needed, see NthPowerOfArrowIdeal)
MappedExpression( expr, gens1, gens2 ) -- no (not needed)
AssignGeneratorVariables( A ) -- no (should be ported)
elt in I -- same
IsIdealInPathAlgebra( I ) -- no (check if needed)
ProductOfIdeals( I, J ) -- no (should be ported)
QuadraticPerpOfPathAlgebraIdeal( rels ) -- no (should be ported)
IsAdmissibleQuotientOfPathAlgebra( A ) -- no (should be ported)
IsNormalForm( element ) -- no (needed?)
a < b (documented twice in QPA1 manual) -- no (needed?)
OriginalPathAlgebra( algebra ) -> PathAlgebra( algebra ) (TODO: should change to OriginalPathAlgebra ) 
IsQuiverProductDecomposition( obj ) -- no (not needed)
IsEnvelopingAlgebra( A ) -- no (needed?)
TrivialExtensionOfQuiverAlgebra( A ) -- no (should be ported)
ReadAlgebra( file ) -- no (should be ported)
SaveAlgebra( A, file, option ) -- no (should be ported)

CHAPTER 5: GROEBNER BASIS

QPA1 has a category IsGroebnerBasis; in QPA2 we just use plain lists
to represent Groebner bases.  Should probably define the category
IsGroebnerBasis as in QPA1.
InfoGroebnerBasis -- no
IsCompletelyReducedGroebnerBasis( gb ) -- no
IsCompleteGroebnerBasis( gb ) -- no
IsGroebnerBasis( obj ) -- no
IsHomogeneousGroebnerBasis( gb ) -- no
IsTipReducedGroebnerBasis( gb ) -- no
AdmitsFinitelyManyNontips( GB ) -- no
CompletelyReduceGroebnerBasis( GB ) -- no
Enumerator( GB ) -- no
IsPrefixOfTipInTipIdeal( GB, R ) -- no
Iterator( GB ) -- no
Nontips( GB ) -- no
NontipSize( GB ) -- no
TipReduce( GB, a ) -- no
TipReduceGroebnerBasis( GB ) -> no
IsRightGroebnerBasis( obj ) -- no
RightGroebnerBasis( I ) -- no
RightGroebnerBasisOfIdeal( I ) -- no

CHAPTER 6: RIGHT MODULES OVER PATH ALGEBRAS

IsDirectSumOfModules( M ) -- no (should be ported)
IsZero( M ) -- same (undocumented)
SubRepresentation( M, gens ) -- no (use Source( SubmoduleInclusion( M,gens ) )) 
ElementOfIndecProjective( A, m, s ) -- no (implemented more generally in QPA2)
RestrictionViaAlgebraHomomorphism( f, M ) -- no (restriction implemented as functor on representation level)
[ 6.7 Vertex projective modules and submodules thereof ] -- no (should be ported)

CHAPTER 7: HOMOMORPHISMS OF RIGHT MODULES OVER PATH ALGEBRAS

CoKernelOfWhat( f ) -- no (not needed?)
ImageElm( f, elem ) -- same (undocumented)
ImagesSet( f, elts ) -- no (not needed?)
ImageOfWhat( f ) -- no (not needed?)
KernelOfWhat( f ) -- no (not needed?)
PathAlgebraOfMatModuleMap( f ) -- no (not needed)
Zero( f ) -- no (applicable method installed in GAP, but it does not give what we want; should be fixed)
HomomorphismFromImages( M, N, genImages ) -- no (should be ported)
EndOfModuleAsQuiverAlgebra( M ) -- no (should be ported)
HomFromProjective( m, M ) -- implemented on representation level, same name
ImageProjectionInclusion( f ) -- no (not needed)

CHAPTER 8: HOMOLOGICAL ALGEBRA

[ everything from homological algebra ] -- no
a few exceptions, from CAP:
PushOut -> Pushout
PullBack -> FiberProduct (make synonym with Pullback)

CHAPTER 9: AUSLANDER-REITEN THEORY

[ everything from Auslander-Reiten theory ] -- no

CHAPTER 10: CHAIN COMPLEXES

Should be in a separate package.
Either improve the `complex' package or use `ComplexesForCAP' by Kamal Saleh
(Saleh's package is based on `complex', but seems to be more complete.)

CHAPTER 11: PROJECTIVE RESOLUTIONS AND THE BOUNDED DERIVED CATEGORY

[ everything from Projective resolutions and the bounded derived category ] -- no

CHAPTER 13: DEGENERATION ORDER FOR MODULES IN FINITE TYPE

[ everything from Degeneration order for modules in finite type ] -- no

New functions:

AllIndecModulesOfLengthAtMost -- no
AllModulesOfLengthAtMost -- no
AllSimpleSubmodulesOfModule -- no
AllSubmodulesOfModule -- no
BlocksOfAlgebra -- no
BrauerAlgebra -- no
BongartzTest -- no
DecomposeModuleProbabilistic -- no
DecomposeModuleViaCharPoly -- no
DecomposeModuleViaTop -- no
FrobeniusForm -- no
FrobeniusLinearFunctional -- no
FromIdentityToDoubleStarHomomorphism -- no
LeftApproximationByAddM -- no
MatrixOfHomomorphismBetweenProjectives -- no
PreprojectiveAlgebra -- no
ProjectiveResolutionOfSimpleModuleOverEndo -- no
QuiverAlgebraOfAmodAeA -- no
QuiverAlgebraOfeAe -- no
RadicalRightApproximationByAddM -- no
RestrictionViaAlgebraHomomorphismMap -- ?
RightApproximationByAddM -- no


Check for bugs fixed/code change in the functions:

AlgebrasAsQuiverAlgebra
AllSubmodulesOfModule
BlockSplittingIdempotents
Center
Complex
CotiltingModule
DualOfAlgebraAsModuleOverEnvelopingAlgebra
DualOfModule
ExtOverAlgebra
HaveFiniteCoresolutionInAddM
HaveFiniteResolusionInAddM
ImageProjectiveInclusion
IsCotiltingModule
IsFiniteTypeAlgebra
IsSymmetricAlgebra
ElementOfQuotientPathAlgebra
LiftingMorphismFromProjective
LiftTwoOrthogonalIdempotents
Kernel  
NthSyzygy
Poset
QuiverAlgebraOfAmodAeA
RightModuleOverPathAlgebra
SaveAlgebra
StarOfModuleHomomorphism
TauOfComplex