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.


Compute Hom(M,N) as a vector spaceNot Done
Compute Hom(M,N) using tensor product methodNot Done
Compute M\otimes N as a vector spaceNot Done
Compute the functor -\otimes B, when B is a bimoduleNot Done
Compute Hom(M,N) as a End(M)-End(N)-bimoduleNot Done
Compute Ext^n(M,N) as a vectorspace, modules over End(M) and End(N), and bimodule over theseNot Done
Compute Tor^n(M,N) as a vectorspace, modules over End(M) and End(N), and bimodule over theseNot Done
Compute Hom-underline and Hom-overlineNot Done
Compute the adjuntion isomorphismNot Done
Compute the Auslander-Reiten formulaNot Done
Compute the Hom(T,-) and Ext(T,-) for a tilting module TNot Done
Coxeter like operations, functorsNot Done


Is an algebra a (quotient of a) poset-algebraNot Done
Tests for finite type of an algebraPartially Done
Is an algebra Gorenstein?Not Done
Compute the representation dimension of an algebraNot Done
Find the Auslander algebra of an algebra of finite typeNot Done
Compute trivial extension, one-point extensionsSoon Done
Find matrix constructions of new ringsNot Done
Compute the ring structure of Ext^*(M,M) for a module MPartially Done
Find non-nilpotent elements of an algebraNot Done
Find the (graded) center of an algebraNot Done
Check if an graded algebra is Koszul, D-Koszul? Not Done
Predefined classes of quivers and path algebras, Dynkin, extended Dynkin quivers, preprojective algebras, special biserial algebrasNot Done
Quiver of an algebra, algebra given by structure constants, find quiverNot Done
Hilbert series, Poincare seriesNot Done
Compute the Hochschild cohomology ring of an algebraNot Done
Coverings of an algebra, fundamental group of a quiverNot Done


Predefined classes of modules for the predefined classes of algebrasNot 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 modulesPartially Done
Find the multiplicity of an indecomposable module in a given moduleNot Done
Is a module preprojective?Not Done
Is a module preinjective?Not Done
Is a module regular? Not Done
Is a module DTr-periodic, TrD-periodic, eventually periodic?Not Done
Given a A-B-bimodule M, view it as a module over A or B.Not Done
Given a A-A-bimodule M such that as a right and a left A-module 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 moduleNot Done
Compute the support variety of a moduleNot Done
Degenerations of modules?Not Done


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 moduleDone using linear algebra, only partially using Groebner basis
Injective resolutions of a moduleNot Done
Minimalization of non-minimal projective and injective resolutionsNot Done
Injective resolution of the algebraNot 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 algebrasNot Done
Quasi-isomorphism test for morphisms of complexesNot Done
Hom-spaces of complexesNot Done
Endomorphism rings of complexesNot Done
Approximations/mutations of complexesNot Done
AR-triangles of complexesNot Done
Tilting complex testNot Done


Euler formNot Done
Knitting in the Auslander-Reiten quiverNot Done
Include the combinatorial structures and functionality from CREPStarted, not done


Latex output for every objectNot Done

Oyvind.Solberg (at) math ntnu no