Merge branch 'master' into bl/posets

Project.toml

@@ -25,22 +25,22 @@ UUIDs = "cf7118a7-6976-5b1a-9a39-7adc72f591a4"
 cohomCalg_jll = "5558cf25-a90e-53b0-b813-cadaa3ae7ade"
 
 [compat]
-AbstractAlgebra = "0.41.3"
-AlgebraicSolving = "0.5.0"
+AbstractAlgebra = "0.42.0"
+AlgebraicSolving = "0.5.1"
 Distributed = "1.6"
 GAP = "0.10.2"
-Hecke = "0.32.0"
+Hecke = "0.33.0"
 JSON = "^0.20, ^0.21"
 JSON3 = "1.13.2"
 LazyArtifacts = "1.6"
 Markdown = "1.6"
-Nemo = "0.45.5"
+Nemo = "0.46.0"
 Pkg = "1.6"
-Polymake = "0.11.14"
+Polymake = "0.11.19"
 Random = "1.6"
 RandomExtensions = "0.4.3"
 Serialization = "1.6"
-Singular = "0.23.1"
+Singular = "0.23.4"
 TOPCOM_jll = "0.17.8"
 UUIDs = "1.6"
 cohomCalg_jll = "0.32.0"

docs/doc.main

@@ -23,9 +23,10 @@
      "Groups/grouphom.md",
      "Groups/autgroup.md",
      "Groups/grouplib.md",
-     "Hecke/abelian/introduction.md",
+     "Hecke/manual/abelian/introduction.md",
      "Groups/group_characters.md",
      "Groups/recog.md",
+     "Groups/tom.md",
   ],
 
   "Rings" => [
@@ -50,8 +51,8 @@
      "Fields/intro.md",
      "AbstractAlgebra/field.md",
      "Rings/rational.md",
-     "Hecke/FacElem.md",
-     "Hecke/class_fields/intro.md",
+     "Hecke/manual/misc/FacElem.md",
+     "Hecke/manual/number_fields/class_fields.md",
      "AbstractAlgebra/fraction.md",
      "Local Fields" => [
         "Nemo/padic.md",
@@ -64,7 +65,7 @@
 
   "Linear Algebra" => [
      "LinearAlgebra/intro.md",
-     "Hecke/sparse/intro.md",
+     "Hecke/manual/misc/sparse.md",
      "AbstractAlgebra/matrix.md",
      "AbstractAlgebra/matrix_algebras.md",
      "Modules" => [
@@ -76,23 +77,23 @@
         "AbstractAlgebra/module_homomorphism.md",
      ],
      "Quadratic and Hermitian forms" => [
-        "Hecke/quad_forms/introduction.md",
-        "Hecke/quad_forms/basics.md",
-        "Hecke/quad_forms/lattices.md",
-        "Hecke/quad_forms/genusherm.md",
-        "Hecke/quad_forms/integer_lattices.md",
-        "Hecke/quad_forms/Zgenera.md",
-        "Hecke/quad_forms/discriminant_group.md"
+        "Hecke/manual/quad_forms/introduction.md",
+        "Hecke/manual/quad_forms/basics.md",
+        "Hecke/manual/quad_forms/lattices.md",
+        "Hecke/manual/quad_forms/genusherm.md",
+        "Hecke/manual/quad_forms/integer_lattices.md",
+        "Hecke/manual/quad_forms/Zgenera.md",
+        "Hecke/manual/quad_forms/discriminant_group.md"
      ],
   ],
 
   "Number Theory" => [
      "NumberTheory/intro.md",
      "Number Fields" => [
-        "Hecke/number_fields/intro.md",
-        "Hecke/number_fields/fields.md",
-        "Hecke/number_fields/elements.md",
-        "Hecke/number_fields/internal.md",
+        "Hecke/manual/number_fields/intro.md",
+        "Hecke/manual/number_fields/fields.md",
+        "Hecke/manual/number_fields/elements.md",
+        "Hecke/manual/number_fields/internal.md",
      ],
      "Orders" => [
         "Hecke/orders/introduction.md",

docs/oscar_references.bib

@@ -386,6 +386,16 @@ @Article{Bis96
   doi           = {10.1112/S0025579300011773}
 }
 
+@Book{Bur55,
+  author        = {Burnside, W.},
+  title         = {Theory of groups of finite order},
+  mrnumber      = {69818},
+  note          = {2d ed},
+  publisher     = {Dover Publications, Inc., New York},
+  pages         = {xxiv+512},
+  year          = {1955}
+}
+
 @Book{C-MLS20,
   author        = {Cisneros Molina, Jose Luis and Le, Dung Trang and Seade, Jose},
   title         = {Handbook of Geometry and Topology of Singularities {I}},
@@ -1657,6 +1667,15 @@ @Book{Loo84
   year          = {1984}
 }
 
+@Misc{MNP24,
+  author        = {Merkwitz, Thomas and Naughton, Liam and Pfeiffer, Götz},
+  title         = {TomLib, The GAP Library of Tables of Marks, Version 1.2.11},
+  note          = {GAP package},
+  year          = {2024},
+  month         = {1},
+  url           = {https://gap-packages.github.io/tomlib/}
+}
+
 @Article{MR20,
   author        = {Markwig, Thomas and Ren, Yue},
   title         = {Computing tropical varieties over fields with valuation},
@@ -2219,6 +2238,19 @@ @Article{Wit88
   reportnumber  = {IASSNS-HEP-88/7}
 }
 
+@Article{Wit97,
+  author        = {Witten, Edward},
+  title         = {{On flux quantization in M theory and the effective action}},
+  journal       = {J. Geom. Phys.},
+  volume        = {22},
+  pages         = {1--13},
+  year          = {1997},
+  doi           = {10.1016/S0393-0440(96)00042-3},
+  eprint        = {hep-th/9609122},
+  archiveprefix = {arXiv},
+  reportnumber  = {IASSNS-HEP-96-96}
+}
+
 @Article{Yam18,
   author        = {Yamagishi, Ryo},
   title         = {On smoothness of minimal models of quotient singularities by finite subgroups of ${\rm SL}_n(\mathbb

docs/src/AlgebraicGeometry/ToricVarieties/CohomologyClasses.md

@@ -54,14 +54,14 @@ polynomial(ring::MPolyQuoRing, c::CohomologyClass)
 ## Methods
 
 ```@docs
-integrate(c::CohomologyClass)
+integrate(c::CohomologyClass; check::Bool = true)
 ```
 
 
 ## Special attributes of toric varieties
 
 ```@docs
-cohomology_ring(v::NormalToricVarietyType)
+cohomology_ring(v::NormalToricVarietyType; check::Bool = true)
 volume_form(v::NormalToricVariety)
 intersection_form(v::NormalToricVariety)
 ```

docs/src/AlgebraicGeometry/ToricVarieties/NormalToricVarieties.md

@@ -16,6 +16,46 @@ the affine and non-affine case:
     Transformations for non-standard lattices will have to be done by the user.
 
 
+## Equality of Normal Toric Varieties
+
+!!! warning
+    Equality of normal toric varieties is computationally very demanding.
+    We have therefore made special design decisions for the `==` method.
+
+In OSCAR, the `==` operator is reserved to check if two normal toric varieties are identical,
+meaning their underlying polyhedral fans are the same. However, this check is computationally
+challenging due to several reasons:
+
+- The ray generators might be scaled.
+- The ray generators might be stored in different orders.
+- The maximal (polyhedral) cones of the polyhedral fan might be stored in different orders.
+- If we fall back on polyhedral fan equality, lineality of the cones must also be considered.
+
+To avoid this computational bottleneck, we have specially designed the `==` method.
+It checks if the memory locations of the two objects in question are identical. If 
+so, our `==` method returns `true`. Otherwise, it raise an error.
+
+Note that triple equality `===` (i.e. the check of equal the memory locations) is always
+supported for normal toric varieties. We recommend using it.
+
+However, if you truly need to check for two normal toric varieties to be mathematically
+identical, then you will need to add a custom method. This method could look as follows:
+
+```julia
+function slow_equal(tv1::NormalToricVariety, tv2::NormalToricVariety)
+  tv1 === tv2 && return true
+  ambient_dim(tv1) == ambient_dim(tv2) || return false
+  f_vector(tv1) == f_vector(tv2) || return false
+  return Set(maximal_cones(tv1)) == Set(maximal_cones(tv2))
+end
+```
+
+Please note that this method `slow_equal` is not performant, that we currently (summer 2024)
+have no intentions in adding this function to OSCAR nor to make improvements to its performance.
+Rather, expect this method to be slow, potentially painfully so.
+
+
+
 ## Constructors
 
 ### Affine Toric Varieties

docs/src/AlgebraicGeometry/ToricVarieties/ToricLineBundles.md

@@ -31,6 +31,7 @@ the inverse by invoking `inv`.
 anticanonical_bundle(v::NormalToricVarietyType)
 canonical_bundle(v::NormalToricVarietyType)
 structure_sheaf(v::NormalToricVarietyType)
+trivial_line_bundle(v::NormalToricVarietyType)
 ```
 
 

docs/src/Combinatorics/matroids.md

@@ -31,6 +31,7 @@ bond_matroid(g::Graph)
 cocycle_matroid(g::Graph)
 Matroid(pm_matroid::Polymake.BigObjectAllocated, E::GroundsetType=Vector{Integer}(1:pm_matroid.N_ELEMENTS))
 matroid_from_revlex_basis_encoding(rvlx::String, r::IntegerUnion, n::IntegerUnion)
+matroid_from_matroid_hex(str::AbstractString)
 ```
 
 ## Examples
@@ -112,6 +113,7 @@ reduced_characteristic_polynomial(M::Matroid)
 revlex_basis_encoding(M::Matroid)
 is_isomorphic(M1::Matroid, M2::Matroid)
 is_minor(M::Matroid, N::Matroid)
+matroid_hex(M::Matroid)
 automorphism_group(M::Matroid)
 matroid_base_polytope(M::Matroid)
 ```

docs/src/Combinatorics/phylogenetic_trees.md

@@ -19,7 +19,7 @@ phylogenetic_tree
 
 ```@docs
 adjacency_tree
-equidistant
+is_equidistant
 cophenetic_matrix
 taxa
 newick

docs/src/Groups/group_characters.md

@@ -101,6 +101,7 @@ characteristic(tbl::GAPGroupCharacterTable)
 Base.mod(tbl::GAPGroupCharacterTable, p::Int)
 quo(tbl::GAPGroupCharacterTable, nclasses::Vector{Int})
 all_character_table_names
+is_character_table_name
 ```
 
 ## Attributes of group characters
@@ -130,14 +131,14 @@ class_names(tbl::GAPGroupCharacterTable)
 class_parameters
 conjugacy_classes(tbl::GAPGroupCharacterTable)
 decomposition_matrix
-identifier
+identifier(tbl::GAPGroupCharacterTable)
 induced_cyclic(tbl::GAPGroupCharacterTable)
 is_duplicate_table
 maxes
 names_of_fusion_sources
-class_lengths
+class_lengths(tbl::GAPGroupCharacterTable)
 orders_centralizers
-orders_class_representatives
+orders_class_representatives(tbl::GAPGroupCharacterTable)
 ordinary_table(tbl::GAPGroupCharacterTable)
 trivial_character(tbl::GAPGroupCharacterTable)
 regular_character(tbl::GAPGroupCharacterTable)
@@ -208,7 +209,8 @@ arithmetic operations:
   where the group of `chi` is a subgroup of the group of `tbl`.
 
 ```@docs
-scalar_product
+scalar_product(chi::GAPGroupClassFunction, psi::GAPGroupClassFunction)
+tensor_product(chi::GAPGroupClassFunction, psi::GAPGroupClassFunction)
 coordinates(chi::GAPGroupClassFunction)
 multiplicities_eigenvalues
 induce(chi::GAPGroupClassFunction, tbl::GAPGroupCharacterTable)

docs/src/Groups/permgroup.md

@@ -39,6 +39,7 @@ In OSCAR, every permutation group has a degree `n`, that corresponds to the size
 
 ```@docs
 degree(x::PermGroup)
+smaller_degree_permutation_representation(G::PermGroup)
 ```