ToDoList
This is a quick list of things we want to implement. This is by no
means a complete list of which computations one can do in QPA
(hopefully), but an indication of what is possible in not so distant
future. If you have suggestions of computations that you want to see
implemented and it is not on the list, please contact us.
Functors
Compute Hom(M,N) as a vector space  Not Done 
Compute Hom(M,N) using tensor product method  Not Done 
Compute M\otimes N as a vector space  Not Done 
Compute the functor \otimes B, when B is a bimodule  Not Done 
Compute Hom(M,N) as a End(M)End(N)bimodule  Not Done 
Compute Ext^n(M,N) as a vectorspace, modules over End(M) and End(N), and bimodule over these  Not Done 
Compute Tor^n(M,N) as a vectorspace, modules over End(M) and End(N), and bimodule over these  Not Done 
Compute Homunderline and Homoverline  Not Done 
Compute the adjuntion isomorphism  Not Done 
Compute the AuslanderReiten formula  Not Done 
Compute the Hom(T,) and Ext(T,) for a tilting module T  Not Done 
Coxeter like operations, functors  Not Done 
Algebras
Is an algebra a (quotient of a) posetalgebra  Not Done 
Tests for finite type of an algebra  Partially Done 
Is an algebra Gorenstein?  Not Done 
Compute the representation dimension of an algebra  Not Done 
Find the Auslander algebra of an algebra of finite type  Not Done 
Compute trivial extension, onepoint extensions  Soon Done 
Find matrix constructions of new rings  Not Done 
Compute the ring structure of Ext^*(M,M) for a module M  Partially Done 
Find nonnilpotent elements of an algebra  Not Done 
Find the (graded) center of an algebra  Not Done 
Check if an graded algebra is Koszul, DKoszul?  Not Done 
Predefined classes of quivers and path algebras, Dynkin, extended Dynkin quivers, preprojective
algebras, special biserial algebras  Not Done 
Quiver of an algebra, algebra given by structure constants, find quiver  Not Done 
Hilbert series, Poincare series  Not Done 
Compute the Hochschild cohomology ring of an algebra  Not Done 
Coverings of an algebra, fundamental group of a quiver  Not Done 
Modules
Predefined classes of modules for the predefined classes of algebras  Not Done 
Given a ring homomorphism between two quotients
of path algebras and a module over the target of this
homomorphism, compute the induced module over the domain of the
ring homomorphism.  Not Done 
Decomposition of modules  Partially Done 
Find the multiplicity of an indecomposable module in a given module  Not Done 
Is a module preprojective?  Not Done 
Is a module preinjective?  Not Done 
Is a module regular?  Not Done 
Is a module DTrperiodic, TrDperiodic, eventually periodic?  Not Done 
Given a ABbimodule M, view it as a module over A or B.  Not Done 
Given a AAbimodule M such that as
a right and a left Amodule M is isomorphic to A,
find the automorphism of A such that M is isomorphic
to A twisted on the left with this automorphism.  Not Done 
Compute the almost split sequence starting in an indecomposable module  Not Done 
Compute the support variety of a module  Not Done 
Degenerations of modules?  Not Done 
Homomorphisms
Given n homomorphism from n modules to one module, or vica versa, construct the sum of these maps.  Not Done 
Resolutions/homological algebra
Projective resolutions of a module  Done using linear algebra, only partially using Groebner basis 
Injective resolutions of a module  Not Done 
Minimalization of nonminimal projective and injective resolutions  Not Done 
Injective resolution of the algebra  Not Done 
Projective resolution of dual of the algebra (all injectives)  Not Done 
Compute Ext^i(M,N) and Tor_i(M,N)  Not Done 
Graded resolutions for graded modules over graded algebras  Not Done 
Quasiisomorphism test for morphisms of complexes  Not Done 
Homspaces of complexes  Not Done 
Endomorphism rings of complexes  Not Done 
Approximations/mutations of complexes  Not Done 
ARtriangles of complexes  Not Done 
Tilting complex test  Not Done 
Invariants
Euler form  Not Done 
Knitting in the AuslanderReiten quiver  Not Done 
Include the combinatorial structures and functionality from CREP  Started, not done 
Miscellaneous
Latex output for every object  Not Done 
