* `factorisations` -> `factorizations`

* comment and docu fixes

* Add `centraliser` -> `centralizer` deprecation

* `neighbour` -> `neighbor`

#3369)

Add type assertions to their getindex methods to improve type stability.
Similarly ensure that the return value of `size` is recognized as Tuple{Int}.

Silly microbenchmark, before:

    julia> v = PointVector{ZZRingElem}(matrix(ZZ, [1 2 3 ; ]));

    julia> @Btime prod(v)
      1.217 μs (21 allocations: 336 bytes)

After:

    julia> @Btime prod(v);
      288.449 ns (5 allocations: 80 bytes)

* some debuggging

* add fix to upgrade tests, and fix code regression

* updates johnson matrices, and always adds the refs to s.refs

... the quick and dirty way to have a stable API

(cherry picked from commit d0aad4e)

from PR #3298

* Remove deprecated use of `Frac`

* Remove deprecated use of `chi`

* Remove deprecated use of `MPolyElem`

* feat: Use new linear algebra functionality

* Adjust to deleted deprecations/aliases Hecke edition

* fixed

* fix for symmetric intersections test

* back to the roots

* revert

* Apply suggestions from code review

Co-authored-by: Benjamin Lorenz <benlorenz@users.noreply.github.com>

---------

Co-authored-by: Tommy Hofmann <thofma@gmail.com>
Co-authored-by: Benjamin Lorenz <benlorenz@users.noreply.github.com>
(cherry picked from commit 7433548)

- fix error because `Indent` was undefined
- remove extra newline at end
- add a missing `Lowercase`
- simplify the code
- make output order less random

(cherry picked from commit aefcd0a)

* Typos
* Make the "show source" buttons in the docs work again
* Enable the "Edit page on GitHub" buttons

(cherry picked from commit 56b8182)

* fix is_normal call after removed deprecations

* galois_group: add test from the book

(cherry picked from commit a73b844)

* Rename `vec` for AbstractAlgebra matrices to `_vec`

* Move `_vec` to src

* Adapt callsites

(cherry picked from commit 0b282fb)

(cherry picked from commit eb7bbdf)

(cherry picked from commit 0bc8558)

* Rename `is_exterior_power` to `is_exterior_power_with_data` (and friends)

* Revert "Rename `is_exterior_power` to `is_exterior_power_with_data` (and friends)"

This reverts commit b19369b.

* Make `is_exterior_power` internal

* the same for similar functions

(cherry picked from commit 9d88a8f)

(cherry picked from commit 6408748)

* fixers for phylogenetic adjacency tree

* get rid of whitespace

* fix for tests

(cherry picked from commit c65cb77)

* added cayley-omega.jl

* made omegap a separate function

* updates reynolds__ - need to fix det denominator

* First attempt for SLn

* fixed the bug

* Added direct product and tensor

* removed a loop from generators

* small fix - reduce_gens_

* deleted cayley omega

* coefficient bug fixed

* Created object Reductive Groups in file InvariantRings_ReductiveGroups

* small fixes in InvariantRings_ReductiveGroups.jl

* callable derksen_ideal and hilbert_ideal in InvariantRings_ReductiveGroups

* export functions in InvariantRings_ReductiveGroups

* printing of direct sum of vector stpaces in InvariantRings_ReductiveGroups

* mu_star, reynolds_operator added to Inv Rings Red Grps

* added file InvariantRings_ReductiveGroups

* deleted redundant folder

* Some tweaks

* edits to make the code more efficient in InvariantTheory.jl

* minor edits in InvariantTheory.jl

* fixed coefficient problem in InvariantTheory.jl

* added comments and minor edits. Lazy computation of InvariantRing in InvariantTheory.jl

* minor edits to InvariantTheory.jl

* added export functions in InvariantTheory.jl

* typo in InvariantTheory.jl

* minor edits in InvaraintTheory.jl, few tests in tests.jl

* finished tests.jl for invariant theory of SLm

* removed factorise in InvariantTheory.jl

* more efficient rep_mat_ function in InvariantTheory.jl

* chenged degree_basis function

* pretty(io) in InvariantTheory.jl

* minor change in reductive group constructor

* evaluate func in generators func in InvariantTheory.jl

* started with adding Torus to reductive groups

* incorporating tori with fast algorithm to InvariantTheory.jl

* removed show functions, added test in invariant theory

* field error for reductive groups

* minor type changes

* added test for invariants of tori

* direct product and tensor for representations

* tests for direct sum, tensor of representaions, minor fix in construction function of reductive groups

* minor modification

* minor edits in InvariantTheory.jl

* Update experimental/InvariantTheory/src/InvariantTheory.jl

Co-authored-by: Max Horn <max@quendi.de>

* Update experimental/InvariantTheory/src/InvariantTheory.jl

Co-authored-by: Max Horn <max@quendi.de>

* minor changes discussed in pull request

* removed goto in torus invariants function

* removed import statement

* changed name of representation_from_forms

* torus of rank

* minor changes from pull request

* minor edits from pr comments

* minor changes in show commands

* started file for torus fast

* shifted torus to new file TorusInvariantsFast

* minor change in fundtion degree basis

* fixed typo

* added comments, removed extra output of generators(..)

* renamed InvariantRing to RedGrpInvRing

* minor changes

* fixed all texts except torus

* no internal constructor needed

* fixed tests, changed names

* print field for LinearlyReductiveGroup

* changed RedGrpInvRing to attributes. Other minor changes

* added error messages for @Req, fixed typo

* added export functions to torus groups

* fixed export functions in InvariantTheory.jl

* minor changes suggested in pr implemented

* fixed test

* exported direct_sum, tensor

* included file TorusInvariantsFast.jl

---------

Co-authored-by: Max Horn <max@quendi.de>
(cherry picked from commit 7da4224)

* Remove :task from sub methods for modules.

* Introduce new function submodule.

* Remove all deprecated uses of sub.

* Export submodule.

* Fix tests.

* Fix tests again.

* Register morphisms in general.

* Rebase network of natural maps on WeakKeyIdDicts.

* Clean up the morphisms network and dont store the actual morphisms.

* Some small fix for Wolfram.

* Some fixes and marking the test as broken again.

* Fix documentation.

* Another small fix for Wolfram.

* Fix the fix.

* Fix method selection.

* Introduce kw argument for caching morphisms.

* Redirect previous usages.

* Adjust tests.

* submodule -> sub_object.

* Fix docstrings and signatures for quo.

* Fix methods for quo.

* Adjust documentation.

* Fix up usages of quo.

* Export new functions.

* Some fixes.

* Fix tests.

* Fix tests.

* Fix tests.

* Fix tests.

* Fix tests.

* Fix tests.

* Squashed changes.

* Fix tests.

* Fix up the truncation.

* New rebase.

* Fix tests.

* WIP with debug messages.

* Progress in debugging.

* WIP on debugging.

* Write truely generic presentation and kernel methods [no ci].

* Repair graded_map to accept zero entries.

* Add tensor decomposition function to return value.

* Add some assertions.

* Repair kernel routine.

* Rewrite hom methods for modules.

* Add generic method for simplification of SubquoModuleElems.

* Add missing check argument.

* Fix or disable brittle tests.

* Fix faulty merge.

* Go back to old hom.

* Switch tests to old hom.

* Clean up some deprecated assertions.

* Repair truncate.

* Disable internal checks.

* Update docs/src/CommutativeAlgebra/ModulesOverMultivariateRings/free_modules.md

* Revert "Go back to old hom."

This reverts commit a6b7c15.

* Revert "Switch tests to old hom."

This reverts commit 178eaf3.

* Disable duplicate method.

* Adjust printing.

* Fix tests.

* Fix keyword argument for duals.

* Fix doctests.

* Fix tests.

* Fix doctests.

* Delete some falsely added files.

* Remove deprecated code.

* Another round of disabling internal checks.

* Disable various internal checks.

* Disable further internal checks.

* Set random seeds in tests.

* Adjust use of keyword argument.

* Fix more random seeds.

* Fix the generic simplify method for SubquoModuleElems.

* Revert "Remove deprecated code."

This reverts commit 190256b.

* Repair revert to old hom.

* Repair preimage function.

* Repair degree function.

* Adjust tests to use of repaired old hom.

* Add dummy simplify function for FreeModuleElems.

* Fix doctests.

* Repair simplify.

* Fix documentation.

* Fix doctests.

* Some tuning.

* Fix tests.

* Bugfix from running book code run.

* Remove some debugging artifacts.

* Fix faulty merge.

* Restrict signature.

* Update flattenings of modules over towers of polynomial rings to make the tests run again.

* Small fix.

* Disable the superfluous kernel routine.

* Restrict some further signatures to cases Singular can handle.

* Add tests for flattenings of modules.

* Readd methods which are not superfluous, yet.

---------

Co-authored-by: Lars Göttgens <lars.goettgens@rwth-aachen.de>
Co-authored-by: Lars Göttgens <lars.goettgens@gmail.com>
(cherry picked from commit cfb3413)

* `ordering` -> `internal_ordering` for polynomial rings
* Adjust to unexported symbols from Hecke
* `find_name` now lives in `PrettyPrinting`

(cherry picked from commit d32efdd)

* Corrected defn of deg(ideal); correction from W Decker

* Removed spaces at end of lines (to force GitHub to try again)

(cherry picked from commit 290734f)

* some progress on serializing dicts

* saving

* serialization: add helpers to deconstruct polymake bigobject to dict

currently with a few warnings that might be removed later

* updates

* starting on load

* fix type string for saving

* adds work around for vector{Int}

* use new qualified bigobject name

* serialize dicts

* still need to work out loading

* can load polyhedral object over different fields

* some updates

* add helpers for conversion from oscar graphs back to polymake

* tiny improvement

* fix inner types, store coeff only once

* polymake: improve matrix conversion helpers, allow float in some places

* adds serialzation for sets

* adds test for dicts

* adds test for sets

* replace johnson matrices with Johnson solids

* replace johnson matrices with solids

* pretty print the rest of the Johnson Solids

* pretty print

* padding, + file extension and not pretty printed

* fixes polyhedral test

* update file version tag

* file version tag + add extension for surface files

* fix surface loading

* fix typo

* adds fix for polyhedron of floats and adds test

* fix typo

* better padding implementation

* adds catch for unsupported loading types

* remove Nothing type for coeff inputs, and fixed vector collect

* adds tests for serializing polyhdral objects over oscar fields

* fixes to MILP

* MILP: add missing specialization for QQ to avoid saving other fields for now

* polymake: change warnings to debug when saving unsupported polymake properties

* polyhedral: add missing field for loading milp

* fix for polyhedron with floats

* serialization: fix load distinction between different fields, fix loading float polytopes

* Update test/Serialization/PolyhedralGeometry.jl

* Apply suggestions from code review

Co-authored-by: Lars Kastner <lkastner@users.noreply.github.com>

---------

Co-authored-by: Benjamin Lorenz <lorenz@math.tu-berlin.de>
Co-authored-by: Benjamin Lorenz <benlorenz@users.noreply.github.com>
Co-authored-by: Lars Kastner <lkastner@users.noreply.github.com>
(cherry picked from commit 52c1236)

(cherry picked from commit 376b3f0)

Do not just verify that certain `exterior_algebra` invocations don't error
out; also check that the returned values satisfy certain properties.

Also disable two `@test_broken` tests for now, because (a) the underlying
issue is fixed in a Singular PR, but this causes OscarCI failures there.. (b)
even if the underlying issue is fixed, those test were wrong, because
`exterior_algebra` doesn't return a boolean, but the return value was used in
a context where it must be boolean (namely as "argument" for `@test_broken`).

…ish (#3392)

* `behaviour` -> `behavior`

* `labelled` -> `labeled`

* `modelled` -> `modeled`

* `cancelled` -> `canceled`

* `cancellation` -> `cancelation`

* `regocnise` -> `recognize`

* More `-ise-` -> `-ize-`

* `-re` -> `-er`

(cherry picked from commit 898f41a)

* Small docs improvements

* Adapt so interface

* Add sp Lie algebra

* Adapt to `vec` renaming

* Don't assume anything about the kernel structure

* Apply suggestions from code review

Co-authored-by: Max Horn <max@quendi.de>

---------

Co-authored-by: Max Horn <max@quendi.de>
(cherry picked from commit db3dc1f)