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 Hom-underline and Hom-overline | Not Done |
| Compute the adjuntion isomorphism | Not Done |
| Compute the Auslander-Reiten 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) poset-algebra | 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, one-point 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 non-nilpotent elements of an algebra | Not Done |
| Find the (graded) center of an algebra | Not 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 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 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 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 non-minimal 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 |
| Quasi-isomorphism test for morphisms of complexes | Not Done |
| Hom-spaces of complexes | Not Done |
| Endomorphism rings of complexes | Not Done |
| Approximations/mutations of complexes | Not Done |
| AR-triangles of complexes | Not Done |
| Tilting complex test | Not Done |
Invariants
| Euler form | Not Done |
| Knitting in the Auslander-Reiten quiver | Not Done |
| Include the combinatorial structures and functionality from CREP | Started, not done |
Miscellaneous
| Latex output for every object | Not Done |
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