Backports for 1.1.0

Project.toml

@@ -1,7 +1,7 @@
 name = "Oscar"
 uuid = "f1435218-dba5-11e9-1e4d-f1a5fab5fc13"
 authors = ["The OSCAR Team <[email protected]>"]
-version = "1.1.0-DEV"
+version = "1.1.0"
 
 [deps]
 AbstractAlgebra = "c3fe647b-3220-5bb0-a1ea-a7954cac585d"

README.md

@@ -37,8 +37,7 @@ julia> using Oscar
  / _ \ / ___| / ___|  / \  |  _ \   |  Combining ANTIC, GAP, Polymake, Singular
 | | | |\___ \| |     / _ \ | |_) |  |  Type "?Oscar" for more information
 | |_| | ___) | |___ / ___ \|  _ <   |  Manual: https://docs.oscar-system.org
- \___/ |____/ \____/_/   \_\_| \_\  |  Version 1.1.0-DEV
-
+ \___/ |____/ \____/_/   \_\_| \_\  |  Version 1.1.0
 julia> k, a = quadratic_field(-5)
 (Imaginary quadratic field defined by x^2 + 5, sqrt(-5))
 
@@ -120,7 +119,7 @@ pm::Array<topaz::HomologyGroup<pm::Integer> >
 If you have used OSCAR in the preparation of a paper please cite it as described below:
 
     [OSCAR]
-        OSCAR -- Open Source Computer Algebra Research system, Version 1.0.0,
+        OSCAR -- Open Source Computer Algebra Research system, Version 1.1.0,
         The OSCAR Team, 2024. (https://www.oscar-system.org)
     [OSCAR-book]
         Wolfram Decker, Christian Eder, Claus Fieker, Max Horn, Michael Joswig, eds.
@@ -133,7 +132,7 @@ If you are using BibTeX, you can use the following BibTeX entries:
       key          = {OSCAR},
       organization = {The OSCAR Team},
       title        = {OSCAR -- Open Source Computer Algebra Research system,
-                      Version 1.0.0},
+                      Version 1.1.0},
       year         = {2024},
       url          = {https://www.oscar-system.org},
       }

docs/oscar_references.bib

@@ -89,6 +89,21 @@ @Article{BBS02
   doi           = {10.1007/s00454-001-0051-x}
 }
 
+@Article{BCL21,
+  author        = {Bies, Martin and Cveti\v{c}, Mirjam and Liu, Muyang},
+  title         = {Statistics of limit root bundles relevant for exact matter spectra of F-theory MSSMs},
+  journal       = {Phys. Rev. D},
+  volume        = {104},
+  publisher     = {American Physical Society},
+  pages         = {L061903},
+  year          = {2021},
+  month         = {Sep},
+  doi           = {10.1103/PhysRevD.104.L061903},
+  url           = {https://link.aps.org/doi/10.1103/PhysRevD.104.L061903},
+  issue         = {6},
+  numpages      = {8}
+}
+
 @Article{BDEPS04,
   author        = {Berry, Neil and Dubickas, Artūras and Elkies, Noam D. and Poonen, Bjorn and Smyth, Chris},
   title         = {The conjugate dimension of algebraic numbers},
@@ -346,6 +361,19 @@ @PhDThesis{Bie18
   school        = {Heidelberg U.}
 }
 
+@Article{Bie24,
+  author        = {Bies, Martin},
+  title         = {{Root bundles: Applications to F-theory Standard Models}},
+  journal       = {Proc. Symp. Pure Math.},
+  volume        = {107},
+  pages         = {17--44},
+  year          = {2024},
+  doi           = {10.1090/pspum/107},
+  eprint        = {2303.08144},
+  archiveprefix = {arXiv},
+  primaryclass  = {hep-th}
+}
+
 @Article{Bis96,
   author        = {Bisztriczky, T.},
   title         = {On a class of generalized simplices},
@@ -388,6 +416,21 @@ @Book{CCNPW85
   year          = {1985}
 }
 
+@Article{CHLLT19,
+  author        = {Cveti\v{c}, Mirjam and Halverson, James and Lin, Ling and Liu, Muyang and Tian, Jiahua},
+  title         = {{Quadrillion $F$-Theory Compactifications with the Exact Chiral Spectrum of the Standard Model}},
+  journal       = {Phys. Rev. Lett.},
+  volume        = {123},
+  number        = {10},
+  pages         = {101601},
+  year          = {2019},
+  doi           = {10.1103/PhysRevLett.123.101601},
+  eprint        = {1903.00009},
+  archiveprefix = {arXiv},
+  primaryclass  = {hep-th},
+  reportnumber  = {UPR-1297-T}
+}
+
 @Article{CHM98,
   author        = {Conway, John H. and Hulpke, Alexander and McKay, John},
   title         = {On transitive permutation groups},
@@ -1109,6 +1152,20 @@ @Misc{HRR23
   url           = {https://gap-packages.github.io/primgrp/}
 }
 
+@Article{HT17,
+  author        = {Halverson, James and Tian, Jiahua},
+  title         = {{Cost of seven-brane gauge symmetry in a quadrillion F-theory compactifications}},
+  journal       = {Phys. Rev. D},
+  volume        = {95},
+  number        = {2},
+  pages         = {026005},
+  year          = {2017},
+  doi           = {10.1103/PhysRevD.95.026005},
+  eprint        = {1610.08864},
+  archiveprefix = {arXiv},
+  primaryclass  = {hep-th}
+}
+
 @Book{Har77,
   author        = {Hartshorne, Robin},
   title         = {Algebraic Geometry},

docs/src/Combinatorics/EnumerativeCombinatorics/schur_polynomials.md

@@ -1,6 +1,6 @@
 # Schur polynomials
 
-Given a partition $\lambda$ of $n$, the **Schur polynomial** is defined to be
+Given a partition $\lambda$ with $n$ parts, the **Schur polynomial** is defined to be
 the polynomial
 
 $$s_\lambda := \sum x_1^{m_1}\dots x_n^{m_n}$$

examples/Idel.jl → examples/Idele.jl

@@ -1,8 +1,8 @@
-module Idel
+module Idele
 
 using Oscar
 
-mutable struct IdelParent
+mutable struct IdeleParent
   k::AbsSimpleNumField
   mG::Map # AutGrp -> Automorohisms
   S::Vector{AbsNumFieldOrderIdeal} # for each prime number ONE ideal above
@@ -20,35 +20,35 @@ mutable struct IdelParent
   mU::Map #S-unit group map
   M::FinGenAbGroup  # the big module
 
-  function IdelParent()
+  function IdeleParent()
     return new()
   end
 end
 
-mutable struct Idel
-  parent::IdelParent
+mutable struct Idele
+  parent::IdeleParent
   m::FinGenAbGroupElem #in parent.M
 end
 
-function support(a::Idel)
+function support(a::Idele)
   #the full galois orbit of parent.S
 end
 
-function getindex(a::Idel, P::AbsNumFieldOrderIdeal)
+function getindex(a::Idele, P::AbsNumFieldOrderIdeal)
   #element at place P as an element in the completion
   #needs to find the "correct" P in parent.S, the (index) of the coset
   #and return the component of the induced module
 end
 
-function getindex(a::Idel, p) #real embedding
+function getindex(a::Idele, p) #real embedding
   # the unit representing this: find the correct component...
 end
 
-function getindex(a::Idel, p) #complex embedding
+function getindex(a::Idele, p) #complex embedding
   # the unit representing this + a vector with the lambda exponents
 end
 
-function disc_exp(a::Idel)
+function disc_exp(a::Idele)
   # a dict mapping primes/places to s.th. in the number field?
 end
 

experimental/FTheoryTools/docs/src/generalities.md

@@ -57,6 +57,8 @@ explicit_model_sections(m::AbstractFTheoryModel)
 defining_section_parametrization(m::AbstractFTheoryModel)
 classes_of_model_sections(m::AbstractFTheoryModel)
 defining_classes(m::AbstractFTheoryModel)
+gauge_algebra(m::AbstractFTheoryModel)
+global_gauge_quotients(m::AbstractFTheoryModel)
 ```
 
 

experimental/FTheoryTools/docs/src/literature.md

@@ -98,7 +98,9 @@ following methods:
 * `has_weighted_resolutions(m::AbstractFTheoryModel)`,
 * `has_weighted_resolution_generating_sections(m::AbstractFTheoryModel)`,
 * `has_weighted_resolution_zero_sections(m::AbstractFTheoryModel)`,
-* `has_zero_section(m::AbstractFTheoryModel)`.
+* `has_zero_section(m::AbstractFTheoryModel)`,
+* `has_gauge_algebra(m::AbstractFTheoryModel)`,
+* `has_global_gauge_quotients(m::AbstractFTheoryModel)`.
 
 
 ## Methods
@@ -118,3 +120,80 @@ Provided that a resolution for a model is known, we can (attempt to) resolve the
 ```@docs
 resolve(m::AbstractFTheoryModel, index::Int)
 ```
+
+
+## The Quadrillion F-Theory Standard Models
+
+A yet more special instance of literature models are the Quadrillion F-theory Standard Models
+(F-theory QSMs) [CHLLT19](@cite). Those hypersurface models come in 708 different families.
+
+The base geometry of an F-theory QSM is obtained from triangulating one of 708 reflexive 3-dimensional
+polytopes. The models, whose bases are obtained from triangulations of the same polytope form a family.
+The following information on the polytope in question and its triangulations is available within our database:
+```@docs
+vertices(m::AbstractFTheoryModel)
+polytope_index(m::AbstractFTheoryModel)
+has_quick_triangulation(m::AbstractFTheoryModel)
+max_lattice_pts_in_facet(m::AbstractFTheoryModel)
+estimated_number_of_triangulations(m::AbstractFTheoryModel)
+```
+
+Beyond the polytope and its triangulations, a number of other integers are of key importance. The following
+are supported in our database.
+```@docs
+kbar3(m::AbstractFTheoryModel)
+hodge_h11(m::AbstractFTheoryModel)
+hodge_h12(m::AbstractFTheoryModel)
+hodge_h13(m::AbstractFTheoryModel)
+hodge_h22(m::AbstractFTheoryModel)
+```
+
+More recently, a research program estimated the exact massless spectra of the F-theory QSMs
+(cf. [Bie24](@cite)). These studies require yet more information about the F-theory QSM geometries,
+which are supported by our database.
+
+First, recall that (currently), the base of an F-theory QSM is a 3-dimensional toric variety B3.
+Let s in H^0(B3, Kbar_B3), then V(s) is a K3-surface. Moreover, let xi be the coordinates
+of the Cox ring of B3. Then V(xi) is a divisor in B3. Consequently, Ci = V(xi) cap V(s)
+is a divisor in the K3-surface V(s). For the root bundle counting program, these curves Ci are
+of ample importance (cf. [Bie24](@cite)). We support the following information on these curves:
+```@docs
+genera_of_ci_curves(m::AbstractFTheoryModel)
+degrees_of_kbar_restrictions_to_ci_curves(m::AbstractFTheoryModel)
+topological_intersection_numbers_among_ci_curves(m::AbstractFTheoryModel)
+indices_of_trivial_ci_curves(m::AbstractFTheoryModel)
+topological_intersection_numbers_among_nontrivial_ci_curves(m::AbstractFTheoryModel)
+```
+
+The collection of the Ci-curves form a nodal curve. To every nodal curve one can associate a
+(dual) graph. In this graph, every irreducible component of the nodal curve becomes a node/vertex
+of the dual graph, and every nodal singularity of the nodal curve turns into an edge of the dual
+graph. In the case at hand, this is rather simple.
+
+The Ci-curves turn into the irreducible components of the nodel curve. Certainly, we only need
+to focus on the non-trivial Ci-curves. A non-trivial Ci-curve can split into multiple irreducible
+components. This is taken into acccount when the nodes/vertices of the dual graph are constructed.
+
+The topological intersection numbers among the Ci-curves (or rather, their irreducible components)
+tells us how many nodal singularities link the Ci-curves (or rather, their irreducible components)
+in question. Hence, if the topological intersection numbers is zero, there is no edge between the
+corresponding nodes. Otherwise, if the topological intersection number is positive - say n -, then
+there are exactly n edges between the nodes in question.
+
+The following functions access/create the so-obtained dual graph:
+```@docs
+dual_graph(m::AbstractFTheoryModel)
+components_of_dual_graph(m::AbstractFTheoryModel)
+degrees_of_kbar_restrictions_to_components_of_dual_graph(m::AbstractFTheoryModel)
+genera_of_components_of_dual_graph(m::AbstractFTheoryModel)
+```
+
+The dual graph is essential in counting root bundles (cf. [BCL21](@cite)). It turns out, that one
+can simplify this graph so that the computations at hand can be conducted on a simpler graph
+instead. The following functionality exists to access this simplified dual graph.
+```@docs
+simplified_dual_graph(m::AbstractFTheoryModel)
+components_of_simplified_dual_graph(m::AbstractFTheoryModel)
+degrees_of_kbar_restrictions_to_components_of_simplified_dual_graph(m::AbstractFTheoryModel)
+genera_of_components_of_simplified_dual_graph(m::AbstractFTheoryModel)
+```