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