* Add QQBar docs to the manual

* Update field overview list

(cherry picked from commit 7164435)

(cherry picked from commit 5f86803)

* fix bugs in `all_OD_infos`

* added a test

(cherry picked from commit 3672388)

* Rename Spec -> AffineScheme

Use `AffineScheme` only for the type, not the function.

* Rename proj for toric divisors to projectivization

As was recommended by Martin Bies and Wolfram Decker.

* Function ProjectiveScheme to projective_scheme and proj

* Fix: spec now extends the constructor AffineScheme

In particular, spec allows the argument to be a quotient ring or localized ring. Similarly for proj. Probably the tests would not have passed in the previous commit because of this

* add support for projective_scheme and affine_scheme

---------

Co-authored-by: Simon Brandhorst <brandhorst@math.uni-sb.de>
(cherry picked from commit b00d5e4)

(cherry picked from commit 8afc6a8)

... to ensure rank of the free group is set.

(cherry picked from commit 4cea177)

(cherry picked from commit 6308dd7)

…g a single int or int range (#3404)

(cherry picked from commit 83f0575)

For `all_small_groups` we allow specifying the order as a single
integer or abstract vector, followed by any number of additional
filters. For transitive and primitive groups, we also allowed
specifying the degree as a single integer or abstract vector, but
this then could not be followed by filters. With this patch the
additional filters work in all cases.

(cherry picked from commit dd7913b)

* support `gen(G::GAPGroup, 0)`

This was already supported for `FinGenAbGroup`.

(The delegations between methods are not the same:
For `FinGenAbGroup`, there is special code for `getindex(A, i)`,
and `gen(A, i)` calls `getindes(A, i)`.
For `GAPGroup`, there is special code for `gen(G, i)`,
and the generic `getindex` method from AbstractAlgebra calls `gen(G, i)`.)

* support negative indices, meaning inverses

(cherry picked from commit 58566cc)

(cherry picked from commit bb7fe08)

(cherry picked from commit 52a2a88)

* uses new divrem from Singular, fits Singular's reduce

* adds test case from issue #3105

* bump Singular to v0.22.4 for divrem2

* fixes doctests

(cherry picked from commit 2cc5013)

* Add test example to PR #3412 as requested by @thofma

* docu invariants tori

* readd algebraic.md

* typo

* Update docs/doc.main

* add one more functions and corrections

* correction

* correction

* addressing review

* forgot to add corrected file

---------

Co-authored-by: Lars Göttgens <lars.goettgens@rwth-aachen.de>
(cherry picked from commit 3c5f7fe)

* Fix printing of of affine schemes.

(cherry picked from commit 2a87512)

(cherry picked from commit 95a1e27)

(cherry picked from commit 62d3c12)

(cherry picked from commit 318a2c5)

---------

Co-authored-by: Max Horn <max@quendi.de>
Co-authored-by: Lars Göttgens <lars.goettgens@gmail.com>
(cherry picked from commit f468cca)

and character value access by class names

(cherry picked from commit e86fe09)

(cherry picked from commit e45ff24)

* add `conductor` for class functions

* add `:constituents` key (if available)

to the dictionaries returned by `all_atlas_group_infos`

* support `min_char` in `isomorphic_group_over_finite_field`

i.e., prescribe a minimal characteristic for the returned group,
in order to guarantee that the reduction of an irreducible group
is also irreducible

* better handling of quadratic fields

- improve coercion from quadratic fields into `QQAbField`;
  the check for `is_quadratic_field` is not general enough,
  and evaluation of a field element requires not just some polynomial ring
  but the underlying polynomial ring of the number field
- and add `_embedding` of `QQ` into `QQAbField`, for convenience

* added `orbits_group_automorphisms` and helpers

* add `od_from_atlas_group` and helper

* add p-group criterion

- add `known_class_fusions`
- add optional argument to `induced_cyclic`
- add `od_from_p_subgroup`
- add helper `possible_permutation_characters_from_sylow_subgroup`

* adjust to the changes in Oscar since November

* now the tests pass again

* `FiniteField` does no longer exist

* use `number_of_conjugacy_classes`

* omit some tests that require AtlasRep at least 2.1.7

* for the moment, leave out tests that need web access

(cherry picked from commit 556be5a)

…3443)

Co-authored-by: Johannes Schmitt <schmitt@mathematik.uni-kl.de>
(cherry picked from commit 73ba787)

(cherry picked from commit c58c7eb)

(cherry picked from commit 0e19721)

…rstrass (#3458)

* Export weierstrass_chart_on_minimal_model.

* Repair transform_to_weierstrass.

(cherry picked from commit 1a8e8e3)

(cherry picked from commit 189a55f)

* Added comment on convention

* Update experimental/InvariantTheory/src/InvariantTheory.jl

Co-authored-by: Johannes Schmitt <schmitt@mathematik.uni-kl.de>

---------

Co-authored-by: Johannes Schmitt <schmitt@mathematik.uni-kl.de>
(cherry picked from commit 21d13c9)

…A::FinGenAbGroup)` (#3457)

* Prepare for renaming of rank(A::FinGenAbGroup)

... to torsion_free_rank(A::FinGenAbGroup), see also
<thofma/Hecke.jl#1224>.

* Use is_z_graded in _regularity_bound

* more rank -> torsion_free_rank

* more

* more more

* Update experimental/GModule/Cohomology.jl

* more more more

* bump Hecke

---------

Co-authored-by: Tommy Hofmann <thofma@gmail.com>
Co-authored-by: Lars Göttgens <lars.goettgens@gmail.com>
(cherry picked from commit 8b863ed)

* TorGrpInvRing to attributes, added test for affine_algebra for tori

* graded affine algebra ring

* fix to doctest

(cherry picked from commit b6f11d0)