Dates: 07.08. - 11.08.
Place: 48/582
Start: 07.08., 10:00
End: 11.08. 12:00

Topics:

* Division with remainder, orderings:
* normal form of polynomials and vectors w.r.t. local orderings, https://github.com/oscar-system/Oscar.jl/issues/2477 (DONE in Singular.jl, TODO in Oscar.jl)
* complete_reduction option for reduce, https://github.com/oscar-system/Oscar.jl/issues/2233 (DONE in Singular.jl, TODO in Oscar.jl)
* Definition of is_global(ordering) does not match how it is used internally, https://github.com/oscar-system/Oscar.jl/issues/1697
* ~~Oscar seems to spend a lot of time comparing monomial orderings for lookups in dictionaries,~~ https://github.com/oscar-system/Oscar.jl/issues/2498
This should be largely resolved already by https://github.com/oscar-system/Oscar.jl/pull/2535 and https://github.com/oscar-system/Oscar.jl/pull/2499
* Coercion:
* Oscar Singular coercion ambiguities, https://github.com/oscar-system/Oscar.jl/issues/976
* Printing of abelian group elements
* ~~remove "graded by"~~
* Free resolutions:
* ~~sres does not work with Oscar's free_resolution, Gröbner bases in free_resolution,~~ https://github.com/oscar-system/Oscar.jl/issues/2501
keep only fres and apply the above to fres
* ~~Zero rows in free resolutions~~
https://github.com/oscar-system/Oscar.jl/issues/2471
This is a bug which only appears due to another bug, indicative of a missing check.
* ~~Free resolution broken in some settings~~
Start with Gröbner basis for fres
attach properly to presentation
* adjust mres (transformation)
* ~~adjust printing (direction, print as in textbook, betti diagrams)~~ Fixed after Hecke release
* minimize free resolutions
* ~~minimal Betti table from non-minimal free resolution~~
* ~~Computations over non-simple number fields:~~
* ~~Radical over number field segmentation fault~~, https://github.com/oscar-system/Oscar.jl/issues/2435
* ~~not specific to non-simple, it will apply to all non-AnticNumberField~~~~
* ~~Hilbert Series~~:
* Integer overflow when computing Hilbert polynomial and degree, https://github.com/oscar-system/Oscar.jl/issues/2411
* Unify code for affine algebras
* denominator in factorized form
* Improve Multi-Hilbert function; in particular, use GB with respect to a different ordering if thus a GB is already there
* extend to modules
* Computing Gröbner bases:
* ~~groebner_basis(...,algorithm=:f4) does not work over FiniteField(), https://github.com/oscar-system/Oscar.jl/issues/2221,~~ fixed in AlgebraicSolving.jl via PR #17
* Feature request: degree truncated Gröbner bases, https://github.com/oscar-system/Oscar.jl/issues/1430 (there is a function `function _groebner_basis(I::MPolyIdeal, d::Int; ..._` in Oscar.jl that implements this, but needs a nicer interface)
* Reducing usage of or even removing groebner_assure, oscar_assure, singular_assure, https://github.com/oscar-system/Oscar.jl/issues/1920
Note https://github.com/oscar-system/Oscar.jl/issues/1914 which should be fixed first.
Partially resolved in https://github.com/oscar-system/Oscar.jl/pull/2646
* Use of modular Gröbner bases computations; partially resolved in https://github.com/oscar-system/Oscar.jl/pull/2632 (up to some heuristic when to use it)
* Avoid double Gröbner bases computations (examples? perhaps Wolfram knows?)
* IdealGens/Gröbner bases:
* ~~equality of Gröbner bases~~, https://github.com/oscar-system/Oscar.jl/issues/2019
Fix exists, PR to be done
* Preferred ordering for ideal computations, https://github.com/oscar-system/Oscar.jl/issues/1487
Note that a polynomial rings has now a default ordering https://github.com/oscar-system/Oscar.jl/pull/2535
* ~~Oscar silently changes orderings of ideal gens~~, https://github.com/oscar-system/Oscar.jl/issues/1914
Fix exists here https://github.com/oscar-system/Oscar.jl/pull/2109 but leads to segfault
See also https://github.com/oscar-system/Oscar.jl/pull/1489 which leads to a silent change, possibly more spots.
This is done in the following PR (one issue remaining)
https://github.com/oscar-system/Oscar.jl/pull/2683
https://github.com/oscar-system/Oscar.jl/pull/2673
https://github.com/oscar-system/Oscar.jl/pull/2670
https://github.com/oscar-system/Oscar.jl/pull/2663
* Modules:
* is_surjective sometimes broken for module homomorphisms, https://github.com/oscar-system/Oscar.jl/issues/1883
See also https://github.com/oscar-system/Oscar.jl/pull/1879
* Generic kernel, https://github.com/oscar-system/Oscar.jl/pull/2234
code available, segfault over Q[x]/(0)
* Ideals:
* allow ishomogeneous for ideals https://github.com/oscar-system/Oscar.jl/issues/908
* ~~Documentation: katsura https://github.com/oscar-system/Oscar.jl/issues/1694~~, fixed via PR #2594
* Absolute primary decomposition:
* ~~fix bug, see decide_du_val_singularity: Ideal does not describe a single K-point~~, https://github.com/oscar-system/Oscar.jl/issues/2531
* better structures for primary decompositions? -> needs further discussion
* Eliminate
* Provide in addition preimage under inclusion map
* Subring with inclusion
* Quotient rings:
* Role of zero ideal when passing to Singular (might be that some segfaults occur when working with a ring modulo the zero ideal)
* Tensor product of polynomial ring (e.g. assign suitable blocker orderings)
* then use it for e.g. the coordinate ring of varieties
* degree & co: return as integers?
dim, degree(Variety), ...
possibly: dim() -> Int, dim(ZZRingElem, ...) -> ZZRingElem
degree defaults???
degree(Module(in the MPoly setting)), degree(MPolyQuo)??
in groups: order(...) -> ZZRingElem, order(Int, ...)
Try to be consistent ...
* Reduce and GBs for modules?
* ~~Speedups~~ (for tests? and in general?(is_zero, == 0, dot, ...))
* Truncations of ~~ideals~~, ~~modules~~, rings (later), see https://github.com/oscar-system/Oscar.jl/pull/2660
* Regularity (needs minimal resolutions) see https://github.com/oscar-system/Oscar.jl/pull/2666 multigraded cases still to be done