polyhedral: more standard constructions

Project.toml

@@ -18,6 +18,7 @@ Preferences = "21216c6a-2e73-6563-6e65-726566657250"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 RandomExtensions = "fb686558-2515-59ef-acaa-46db3789a887"
 RecipesBase = "3cdcf5f2-1ef4-517c-9805-6587b60abb01"
+Revise = "295af30f-e4ad-537b-8983-00126c2a3abe"
 Singular = "bcd08a7b-43d2-5ff7-b6d4-c458787f915c"
 TOPCOM_jll = "36f60fef-b880-50dc-9289-4aaecee93cc3"
 UUIDs = "cf7118a7-6976-5b1a-9a39-7adc72f591a4"

docs/oscar_references.bib

@@ -1,4 +1,29 @@
 
+@Article{ABGJ18,
+  author        = {Allamigeon, Xavier and Benchimol, Pascal and Gaubert, St{\'e}phane and Joswig, Michael},
+  title         = {Log-barrier interior point methods are not strongly polynomial},
+  journal       = {SIAM Journal on Applied Algebra and Geometry},
+  volume        = {2},
+  number        = {1},
+  publisher     = {SIAM},
+  pages         = {140--178},
+  year          = {2018}
+}
+
+@Article{ABS97,
+  author        = {Avis, David and Bremner, David and Seidel, Raimund},
+  title         = {How good are convex hull algorithms?},
+  mrnumber      = {1447243},
+  journal       = {Comput. Geom.},
+  fjournal      = {Computational Geometry. Theory and Applications},
+  volume        = {7},
+  number        = {5-6},
+  note          = {11th ACM Symposium on Computational Geometry (Vancouver, BC, 1995)},
+  pages         = {265--301},
+  year          = {1997},
+  doi           = {10.1016/S0925-7721(96)00023-5}
+}
+
 @Article{AG10,
   author        = {Arzhantsev, Ivan V. and Ga\v{i}fullin, Sergei A.},
   title         = {Cox rings, semigroups, and automorphisms of affine varieties},
@@ -33,13 +58,34 @@ @Book{AL94
   url           = {https://doi.org/10.1090/gsm/003}
 }
 
+@Article{AZ99,
+  author        = {Amenta, Nina and Ziegler, Gunter M},
+  title         = {Deformed products and maximal shadows of polytopes},
+  journal       = {Contemporary Mathematics},
+  volume        = {223},
+  publisher     = {Providence, RI: American Mathematical Society},
+  pages         = {57--90},
+  year          = {1999},
+  pdf           = {https://citeseerx.ist.psu.edu/document?repid=rep1&type=pdf&doi=6eaea4b5c868c84295a0977ed9fce92d7c960a39}
+}
+
 @Misc{Aut00,
   author        = {{A}uthors, {T}he {S}tacks {P}roject},
   title         = {{S}tacks {P}roject},
   year          = {0000},
   url           = {https://stacks.math.columbia.edu/}
 }
 
+@Article{BBS02,
+  author        = {Bayer, M. and Bruening, A. and Stewart, J.},
+  title         = {A Combinatorial Study of Multiplexes and Ordinary Polytopes},
+  journal       = {Discrete & Computational Geometry},
+  volume        = {27},
+  pages         = {49–63},
+  year          = {2002},
+  doi           = {https://doi.org/10.1007/s00454-001-0051-x}
+}
+
 @Article{BDEPS04,
   author        = {Berry, Neil and Dubickas, Art\={u}ras and Elkies, Noam D. and Poonen, Bjorn and Smyth, Chris},
   title         = {The conjugate dimension of algebraic numbers},
@@ -257,6 +303,18 @@ @PhDThesis{Bie18
   school        = {Heidelberg U.}
 }
 
+@Article{Bis96,
+  author        = {Bisztriczky, T.},
+  title         = {On a class of generalized simplices},
+  journal       = {Mathematika},
+  volume        = {43},
+  number        = {2},
+  publisher     = {London Mathematical Society},
+  pages         = {274–285},
+  year          = {1996},
+  doi           = {10.1112/S0025579300011773}
+}
+
 @Book{C-MLS20,
   author        = {Cisneros Molina, Jose Luis and Le, Dung Trang and Seade, Jose},
   title         = {Handbook of Geometry and Topology of Singularities {I}},
@@ -331,6 +389,19 @@ @Book{CS99
   url           = {https://doi.org/10.1007/978-1-4757-6568-7}
 }
 
+@Article{CSZ15,
+  author        = {Ceballos, Cesar and Santos, Francisco and Ziegler, Günter M.},
+  title         = {Many non-equivalent realizations of the associahedron},
+  journal       = {Combinatorica},
+  volume        = {35},
+  number        = {5},
+  publisher     = {Springer},
+  pages         = {513--551},
+  year          = {2015},
+  doi           = {10.1007/s00493-014-2959-9},
+  url           = {https://doi.org/10.1007/s00493-014-2959-9}
+}
+
 @Book{Cam99,
   author        = {Cameron, Peter J.},
   title         = {Permutation groups},
@@ -788,6 +859,15 @@ @Article{GJRW10
   arxiv         = {0711.2397}
 }
 
+@InProceedings{GK14,
+  author        = {Giannakopoulos, Yiannis and Koutsoupias, Elias},
+  title         = {Duality and optimality of auctions for uniform distributions},
+  booktitle     = {Proceedings of the fifteenth ACM conference on Economics and computation},
+  publisher     = {Association for Computing Machinery, New York},
+  pages         = {259--276},
+  year          = {2014}
+}
+
 @Book{GLS07,
   author        = {Greuel, G.-M. and Lossen, C. and Shustin, E.},
   title         = {Introduction to Singularities and Deformations},
@@ -824,6 +904,19 @@ @Book{GP08
   url           = {https://doi.org/10.1007/978-3-540-73542-7}
 }
 
+@Article{GS79,
+  author        = {Goldfarb, Donald and Sit, William Y},
+  title         = {Worst case behavior of the steepest edge simplex method},
+  journal       = {Discrete Applied Mathematics},
+  volume        = {1},
+  number        = {4},
+  publisher     = {Elsevier},
+  pages         = {277--285},
+  year          = {1979},
+  doi           = {10.1016/0166-218X(79)90004-0},
+  url           = {https://doi.org/10.1016/0166-218X(79)90004-0}
+}
+
 @InCollection{GTZ88,
   author        = {Gianni, Patrizia and Trager, Barry and Zacharias, Gail},
   title         = {Gröbner bases and primary decomposition of polynomial ideals},
@@ -952,6 +1045,17 @@ @InCollection{IR96
   location      = {Berlin}
 }
 
+@Article{JKS22,
+  author        = {Joswig, Michael and Klimm, Max and Spitz, Sylvain},
+  title         = {Generalized permutahedra and optimal auctions},
+  journal       = {SIAM Journal on Applied Algebra and Geometry},
+  volume        = {6},
+  number        = {4},
+  publisher     = {SIAM},
+  pages         = {711--739},
+  year          = {2022}
+}
+
 @Book{JLPW95,
   author        = {Jansen, C. and Lux, K. and Parker, R. and Wilson, R.},
   title         = {An atlas of {B}rauer characters},
@@ -988,6 +1092,16 @@ @Book{JT13
   url           = {https://doi.org/10.1007/978-1-4471-4817-3}
 }
 
+@Article{JZ00,
+  author        = {Joswig, Michael and Ziegler, Günter M.},
+  title         = {Neighborly Cubical Polytopes},
+  journal       = {Discrete & Computational Geometry },
+  volume        = {24},
+  pages         = {325–344},
+  year          = {2000},
+  doi           = {https://doi.org/10.1007/s004540010039}
+}
+
 @Article{Joh12,
   author        = {Johansson, Fredrik},
   title         = {Efficient implementation of the {H}ardy-{R}amanujan-{R}ademacher formula},
@@ -1001,6 +1115,32 @@ @Article{Joh12
   url           = {https://doi.org/10.1112/S1461157012001088}
 }
 
+@InProceedings{Jos03,
+  author        = {Joswig, Michael},
+  title         = {Beneath-and-Beyond Revisited},
+  editor        = {Joswig, Michael and Takayama, Nobuki},
+  booktitle     = {Algebra, Geometry and Software Systems},
+  address       = {Berlin, Heidelberg},
+  publisher     = {Springer Berlin Heidelberg},
+  pages         = {1--21},
+  year          = {2003},
+  doi           = {10.1007/978-3-662-05148-1_1},
+  url           = {https://doi.org/10.1007/978-3-662-05148-1_1}
+}
+
+@InCollection{Jos05,
+  author        = {Joswig, Michael},
+  title         = {Polytope propagation on graphs},
+  booktitle     = {Algebraic statistics for computational biology.},
+  zbl           = {1374.60141},
+  publisher     = {Cambridge: Cambridge University Press},
+  pages         = {181--192},
+  year          = {2005},
+  doi           = {10.1017/CBO9780511610684.010},
+  language      = {English},
+  zbmath        = {6811701}
+}
+
 @Book{Jos21,
   author        = {Joswig, Michael},
   title         = {Essentials of tropical combinatorics},
@@ -1359,6 +1499,17 @@ @Article{PS09
   doi           = {10.1007/s10801-008-0125-4}
 }
 
+@Article{PS11,
+  author        = {Pokutta, Sebastian and Schulz, Andreas S},
+  title         = {Integer-empty polytopes in the 0/1-cube with maximal Gomory--Chv{\'a}tal rank},
+  journal       = {Operations research letters},
+  volume        = {39},
+  number        = {6},
+  publisher     = {Elsevier},
+  pages         = {457--460},
+  year          = {2011}
+}
+
 @Article{PSS11,
   author        = {Pfister, Gerhard and Sadiq, Afshan and Steidel, Stefan},
   title         = {An algorithm for primary decomposition in polynomial rings over the integers},
@@ -1415,6 +1566,17 @@ @PhDThesis{Pop93
   school        = {Universität des Saarlandes, Saarbr\"{u}cken}
 }
 
+@Article{Pos09,
+  author        = {Postnikov, Alexander},
+  title         = {Permutohedra, associahedra, and beyond},
+  journal       = {International Mathematics Research Notices},
+  volume        = {2009},
+  number        = {6},
+  publisher     = {OUP},
+  pages         = {1026--1106},
+  year          = {2009}
+}
+
 @Article{Pos18,
   author        = {Posur, Sebastian},
   title         = {Linear systems over localizations of rings},
@@ -1449,6 +1611,28 @@ @Article{RR10
   url           = {https://doi.org/10.1063/1.3501135}
 }
 
+@Article{RSS03,
+  author        = {Rote, Günter and Santos, Francisco and Streinu, Ileana},
+  title         = {Expansive motions and the polytope of pointed pseudo-triangulations},
+  journal       = {Discrete and Computational Geometry: The Goodman-Pollack Festschrift},
+  publisher     = {Springer},
+  pages         = {699--736},
+  year          = {2003}
+}
+
+@Article{SS12,
+  author        = {Savage, Carla D. and Schuster, Michael J.},
+  title         = {Ehrhart series of lecture hall polytopes and Eulerian polynomials for inversion sequences},
+  journal       = {Journal of Combinatorial Theory, Series A},
+  volume        = {119},
+  number        = {4},
+  publisher     = {Elsevier},
+  pages         = {850--870},
+  year          = {2012},
+  doi           = {10.1016/j.jcta.2011.12.005},
+  url           = {https://doi.org/10.1016/j.jcta.2011.12.005}
+}
+
 @Article{SY96,
   author        = {Shimoyama, Takeshi and Yokoyama, Kazuhiro},
   title         = {Localization and primary decomposition of polynomial ideals},
@@ -1469,6 +1653,13 @@ @PhDThesis{Sch23
   school        = {RPTU Kaiserslautern-Landau}
 }
 
+@PhDThesis{Sch95,
+  author        = {Schuchert, Peter},
+  title         = {{Matroid-Polytope und Einbettungen kombinatorischer Mannigfaltigkeiten}},
+  year          = {1995},
+  school        = {TU Darmstadt}
+}
+
 @Book{Ser03,
   author        = {Seress, \'{A}kos},
   title         = {Permutation group algorithms},

docs/src/PolyhedralGeometry/Polyhedra/constructions.md

@@ -136,19 +136,54 @@ regular_600_cell
 ## Other polytope constructions
 
 ```@docs
+SIM_body_polytope
+associahedron
 billera_lee_polytope
+binary_markov_graph_polytope
 birkhoff_polytope
+cyclic_caratheodory_polytope
 cyclic_polytope
 del_pezzo_polytope
+dwarfed_cube
+dwarfed_product_polygons
+explicit_zonotope
 fano_simplex
 fractional_cut_polytope
+fractional_knapsack_polytope
 fractional_matching_polytope
 gelfand_tsetlin_polytope
+goldfarb_cube
+goldfarb_sit_cube
+hypersimplex
+hypertruncated_cube
+k_cyclic_polytope
+klee_minty_cube
+lecture_hall_simplex
+max_GC_rank_polytope
+multiplex_polytope
+n_gon
+neighborly_cubical_polytope
 newton_polytope
 orbit_polytope
-perles_nonrational_8_polytope
+permutahedron
+pile_polytope
+pitman_stanley_polytope
+perles_irrational_8_polytope
+pseudo_del_pezzo_polytope
+rand01_polytope
+rand_box
+rand_cyclic_polytope
+rand_metric
+rand_metric_int
+rand_normal_polytope
 rand_spherical_polytope
 rand_subpolytope
+rss_associahedron
+signed_permutahedron
+stable_set_polytope
+transportation_polytope
+zonotope
+zonotope_vertices_fukuda_matrix
 ```
 
 ## Operations on polyhedra

src/PolyhedralGeometry/PolyhedralComplex/properties.jl

@@ -569,5 +569,5 @@ true
 function is_embedded(PC::PolyhedralComplex)
     pmo = pm_object(PC)
     schedule = Polymake.call_method(pmo,:get_schedule,"VERTICES")
-    return schedule != nothing
+    return !isnothing(schedule)
 end