This is a quick list of things that is implemented in the latest
version of QPA. For further information see the manual
of QPA.
Between the different releases, updates are made, and if you want
to take advantage of these updates, you should make a copy or a
clone of the GIT-repository at SourceForge.net. Give the command
If you have suggestions of computations that you want to
see implemented and it is not on the list, please contact us.
| Check if an ideal is monomial | Done |
| Check if an ideal is admissible | Done |
| Test for distributivity of an algebra | Done |
| Tests for finite type of an algebra | Partially Done |
| Compute the product of two ideals | Done |
| Compute the opposite algebra | Done |
| Compute the tensor product of two algebras | Done |
| Compute the enveloping an algebra | Done |
| Compute the trivial extension of an algebra | Done |
| Check if an algebra is distributive? | Done |
| Check if an algebra is gentle? | Done |
| Check if an algebra is selfinjective | Partially done |
| Check if an algebra is special biserial | Done |
| Check if an algebra is a string algebra | Done |
| Check if an algebra is a Schurian algebra | Done |
| Check if an algebra symmetric? | Done |
| Check if an algebra weakly symmetric? | Done |
| Find the center of an algebra | Partially Done |
| Find a minimal generating set of an admissible ideal | Done |
| Find the Loewy length of an algebra | Done |
| Nakayama automorphism for selfinjective algebras | Done |
| Dynkin quivers (simply laced) | Done |
| Canonical algebra, predefined class | Done |
| Kronecker algebra, predefined class | Done |
| Nakayama algebra, predefined class | Done |
| Truncated path algebras | Done |
| Compute an estimate of the complexity of an algebra | Done |
| Compute the dominant dimension of an algebra | Done |
| Compute the Koszul dual | Done |
| Compute the ring structure of Ext^*(M,M) for a module M | Partially Done |
| Find the dimension vector of a module | Done |
| Construct the direct sum of two representations | Done |
| Find the submodule of a module generated by a set of elements | Done |
| Find the intersection of two submodules of a module | Done |
| Find the sum of two submodules of a module | Done |
| Find the radical of a module | Done |
| Find the socle of a module | Done |
| Find the top of a module | Done |
| Find a minimal set of generators a module | Done |
| Find the radical series of a module | Done |
| Find the socle series of a module | Done |
| Find the Loewy length of a module | Done |
| Find all indecomposable projective modules over an algebra | Done |
| Find all indecomposable injective modules over an algebra | Done |
| Find all simple modules over an algebra | Done |
| Make the algebra a module over the enveloping algebra | Done |
| Make the dual of the algebra a module over the enveloping algebra | Done |
| Test if a module is simple. | Done |
| Test if a module is semisimple. | Done |
| Test if a module is projective. | Done |
| Test if a module is injective. | Done |
| Test if a module is Omega periodic. | Done |
| Test if two modules are isomorphic. | Done |
| Find an isomorphism between isomorphic modules | Done |
| Test if a module is a direct summand in another. | Done |
| Find a common direct summand in two given modules. | Done |
| Find the maximal common direct summand in two given modules. | Done |
| Test if a module is in the additive closure of another module. | Done |
| Test if a module as a finite resolution or coresolution in the additive closure of another module. | Done |
| Test if a module is tilting/cotilting module. | Done |
| Find the left and right mutation of an almost complete tilting/cotilting module. | Done |
| Find the number of complements of an almost complete tilting/cotilting module. | Done
|
| Find all complements of an almost complete tilting/cotilting module given one complement. | Done |
| Find the annihilator of a module | Done |
| Find the basic version of a module | Done (over finite fields) |
| Decomposition of modules | Partially Done (over finite fields) |
| Decomposition of modules with multiplicities | Partially Done (over finite fields) |
| Block decomposition and blocksplitting idempotents of a module | Done |
| Compute an estimate of the complexity of a module | Done |
| Find a projective presentation of a module over the corresponding path algebra | Done |
| Compute the almost split sequence ending in an indecomposable module | Done |
| Compute the predecessor of an indecomposable module in the AR-quiver | Done |
| Degeneration order for modules of (some) algebras of finite type | Done |
| Represent maps between representations | Done |
| Compute kernel, image and cokernel of a map between modules | Done |
| Compute the image and the preimage of an element for a map between modules | Done |
| Check if a map between modules is one-to-one, onto, isomorphism and zero | Done |
| Composition and addition of maps between representations | Done |
| Compute pushouts and pullbacks | Done |
| Given a commutative diagram of homomorphisms of
modules, compute the homomorphisms induced on kernels and cokernels. | Done |
| Given an epimorphism g and a homomorphism f from a
direct sum of indecomposable projective modules to the range of
g, finds a lifting of f to the source of g. | Done |
| Find the endomorphism ring of a module | Done |
| Test if a map is split epi. | Done |
| Test if a map is split mono. | Done |
| Test if a map is left or right minimal. | Done |
| Given a homomorphism between two modules, find the left and the right minimal version of this homomorphism. | Done |
| Compute minimal left/right approximations of a module X with respect to another module M | Done |
| Compute the trace of a module M in another module N | Done |
| Compute Fac(M) and Sub(M) left/right approximations of modules | Done |
| Find the projective cover of a module. | Done |
| Find the first syzygy of a module. | Done (using linear algebra) |
| Find the n-th syzygy of a module. | Done (using linear algebra) |
| Find the first extension group for two modules. | Done |
| Find the injective and the projective dimension of a module. | Done |
| Find the global dimension of an algebra. | Done |
| Find the dominant dimension of a module | Done |
| Find the faithful dimension of a module | Done |
| Data structures for complexes of finitely generated modules and morphisms between such | Done |
| Truncations of complexes, splicing of complexes, acyclicity test | Done |
| Mapping cones of morphisms of complexes | Done |
| Check if a complex is a perfect complex | Done |
| Check if a complex is a coperfect complex | Done |
| Projective resolutions of bounded complexes of finitely generated modules | Done |
| Compute tau of a finite complex of projectives | Done |
| Find a Iyama generator for a module | Done |