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@Article{ABGJ18,
  author        = {Allamigeon, Xavier and Benchimol, Pascal and Gaubert, Stéphane 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},
  doi           = {10.1137/17M1142132}
}

@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},
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  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 Gaĭfullin, Sergey A.},
  title         = {Cox rings, semigroups, and automorphisms of affine varieties},
  journal       = {Mat. Sb.},
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  volume        = {201},
  number        = {1},
  pages         = {3--24},
  year          = {2010},
  eprint        = {0810.1148}
}

@InProceedings{AGK96,
  author        = {Amrhein, Beatrice and Gloor, Oliver and Küchlin, Wolfgang},
  title         = {Walking faster},
  booktitle     = {Design and Implementation of Symbolic Computation Systems},
  series        = {DISCO 1996},
  address       = {Heidelberg, Germany},
  publisher     = {Springer Berlin, Heidelberg},
  pages         = {150--161},
  year          = {1996},
  doi           = {10.1007/3-540-61697-7_14},
  location      = {Karlsruhe, Germany}
}

@Article{AGK97,
  author        = {Amrhein, Beatrice and Gloor, Oliver and Küchlin, Wolfgang},
  title         = {On the walk},
  journal       = {Theoretical Computer Science},
  volume        = {187},
  number        = {1},
  pages         = {179--202},
  year          = {1997},
  doi           = {10.1016/s0304-3975(97)00064-9}
}

@Article{AHK18,
  author        = {Adiprasito, Karim and Huh, June and Katz, Eric},
  title         = {Hodge theory for combinatorial geometries},
  mrnumber      = {3862944},
  journal       = {Ann. of Math. (2)},
  fjournal      = {Annals of Mathematics. Second Series},
  volume        = {188},
  number        = {2},
  pages         = {381--452},
  year          = {2018},
  doi           = {10.4007/annals.2018.188.2.1}
}

@Book{AL94,
  author        = {Adams, William W. and Loustaunau, Philippe},
  title         = {An Introduction to Gröbner Bases},
  series        = {Graduate studies in mathematics},
  publisher     = {American Mathematical Society},
  year          = {1994},
  doi           = {10.1090/gsm/003}
}

@Misc{ATLAS,
  bibkey        = {ATLAS},
  author        = {Wilson, R. A. and Walsh, P. and Tripp, J. and Suleiman, I. and Parker, R. A. and Norton, S. P. and
                  Nickerson, S. and Linton, S. and Bray, J. and Abbott, R.},
  title         = {ATLAS of Finite Group Representations},
  howpublished  = {Published electronically},
  url           = {http://atlas.math.rwth-aachen.de/Atlas/v3}
}

@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},
  url           = {https://citeseerx.ist.psu.edu/document?repid=rep1&type=pdf&doi=6eaea4b5c868c84295a0977ed9fce92d7c960a39}
}

@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           = {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},
  journal       = {Q. J. Math.},
  fjournal      = {The Quarterly Journal of Mathematics},
  volume        = {55},
  number        = {3},
  pages         = {237--252},
  year          = {2004},
  doi           = {10.1093/qjmath/55.3.237}
}

@InCollection{BDLP17,
  author        = {Böhm, Janko and Decker, Wolfram and Laplagne, Santiago and Pfister, Gerhard},
  title         = {Local to global algorithms for the Gorenstein adjoint ideal of a curve},
  booktitle     = {Algorithmic and experimental methods in algebra, geometry, and number theory},
  publisher     = {Springer, Cham},
  pages         = {51--96},
  year          = {2017},
  doi           = {10.1007/978-3-319-70566-8_3}
}

@InProceedings{BDLP19,
  author        = {Böhm, Janko and Decker, Wolfram and Laplagne, Santiago and Pfister, Gerhard},
  title         = {Computing integral bases via localization and Hensel lifting},
  booktitle     = {MEGA 2019 - International Conference on Effective Methods in Algebraic Geometry},
  address       = {Madrid, Spain},
  year          = {2019},
  archiveprefix = {HAL},
  eprint        = {hal-02912148}
}

@Article{BDLPSS13,
  author        = {Böhm, Janko and Decker, Wolfram and Laplagne, Santiago and Pfister, Gerhard and Steenpaß, Andreas
                  and Steidel, Stefan},
  title         = {Parallel algorithms for normalization},
  journal       = {Journal of Symbolic Computation},
  volume        = {51},
  note          = {Effective Methods in Algebraic Geometry},
  pages         = {99--114},
  year          = {2013},
  doi           = {10.1016/j.jsc.2012.07.002}
}

@Misc{BEO23,
  author        = {Besche, Hans Ulrich and Eick, Bettina and O'Brien, Eamonn},
  title         = {SmallGrp, The GAP Small Groups Library, Version 1.5.3},
  note          = {GAP package},
  year          = {2023},
  month         = {5},
  url           = {https://gap-packages.github.io/smallgrp/}
}

@InProceedings{BES-E-D21,
  author        = {Berthomieu, Jérémy and Eder, Christian and Safey El Din, Mohab},
  title         = {Msolve: A Library for Solving Polynomial Systems},
  booktitle     = {Proceedings of the 2021 on International Symposium on Symbolic and Algebraic Computation},
  series        = {ISSAC '21},
  address       = {New York, NY, USA},
  publisher     = {Association for Computing Machinery},
  pages         = {51--58},
  year          = {2021},
  doi           = {10.1145/3452143.3465545},
  location      = {Virtual Event, Russian Federation}
}

@Article{BES19,
  author        = {Backman, Spencer and Eur, Christopher and Simpson, Connor},
  title         = {Simplicial generation of Chow rings of matroids},
  journal       = {arXiv:1905.07114},
  year          = {2019},
  doi           = {10.48550/arxiv.1905.07114},
  primaryclass  = {math.CO}
}

@Book{BGV03,
  author        = {Bueso, José Luis and Gómez-Torrecillas, José and Verschoren, Alain},
  title         = {Algorithmic methods in non-commutative algebra. {Applications} to quantum groups.},
  zbl           = {1063.16054},
  series        = {Math. Model.: Theory Appl.},
  volume        = {17},
  publisher     = {Dordrecht: Kluwer Academic Publishers},
  year          = {2003},
  fseries       = {Mathematical Modelling: Theory and Applications},
  language      = {English},
  zbmath        = {1988897}
}

@Book{BH09,
  author        = {Bruns, Winfried and Herzog, Jürgen},
  title         = {Cohen-{M}acaulay rings},
  series        = {Cambridge Studies in Advanced Mathematics},
  volume        = {39},
  note          = {2nd edition},
  publisher     = {Cambridge University Press, Cambridge},
  year          = {2009}
}

@Article{BH23,
  author        = {Brandhorst, Simon and Hofmann, Tommy},
  title         = {Finite subgroups of automorphisms of K3 surfaces},
  journal       = {Forum of Mathematics, Sigma},
  volume        = {11},
  publisher     = {Cambridge University Press, Cambridge},
  pages         = {e54 1--57},
  year          = {2023},
  doi           = {10.1017/fms.2023.50}
}

@Article{BHMPW20,
  author        = {Braden, Tom and Huh, June and Matherne, Jacob P. and Proudfoot, Nicholas and Wang, Botong},
  title         = {A semi-small decomposition of the Chow ring of a matroid},
  journal       = {arXiv:2002.03341},
  year          = {2020},
  doi           = {10.48550/arXiv.2002.03341},
  primaryclass  = {math.AG}
}

@Book{BHPV-D-V04,
  author        = {Barth, Wolf P. and Hulek, Klaus and Peters, Chris A. M. and Van de Ven, Antonius},
  title         = {Compact complex surfaces},
  zbl           = {1036.14016},
  series        = {Ergeb. Math. Grenzgeb., 3. Folge},
  volume        = {4},
  publisher     = {Berlin: Springer},
  edition       = {2nd enlarged ed.},
  year          = {2004},
  fseries       = {Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge},
  language      = {English},
  zbmath        = {2008523}
}

@Article{BJRR10,
  author        = {Blumenhagen, Ralph and Jurke, Benjamin and Rahn, Thorsten and Roschy, Helmut},
  title         = {Cohomology of line bundles: A computational algorithm},
  journal       = {Journal of Mathematical Physics},
  volume        = {51},
  number        = {10},
  publisher     = {AIP Publishing},
  pages         = {103525},
  year          = {2010},
  month         = {Oct},
  doi           = {10.1063/1.3501132}
}

@Misc{BJRR10*1,
  author        = {Blumenhagen, Ralph and Jurke, Benjamin and Rahn, Thorsten and Roschy, Helmut},
  title         = {cohomCalg package},
  note          = {High-performance line bundle cohomology computation based on BJRR10},
  howpublished  = {Published electronically on GitHub},
  year          = {2010},
  url           = {https://github.com/BenjaminJurke/cohomCalg}
}

@Article{BJRR12,
  author        = {Blumenhagen, Ralph and Jurke, Benjamin and Rahn, Thorsten and Roschy, Helmut},
  title         = {Cohomology of line bundles: Applications},
  journal       = {Journal of Mathematical Physics},
  volume        = {53},
  number        = {1},
  publisher     = {AIP Publishing},
  pages         = {012302},
  year          = {2012},
  month         = {Jan},
  doi           = {10.1063/1.3677646}
}

@Article{BJSST07,
  author        = {Bogart, T. and Jensen, A. N. and Speyer, D. and Sturmfels, B. and Thomas, R. R.},
  title         = {Computing tropical varieties},
  zbl           = {1121.14051},
  journal       = {J. Symb. Comput.},
  fjournal      = {Journal of Symbolic Computation},
  volume        = {42},
  number        = {1-2},
  pages         = {54--73},
  year          = {2007},
  doi           = {10.1016/j.jsc.2006.02.004},
  language      = {English},
  zbmath        = {5203512}
}

@Article{BKR20,
  author        = {Böhm, Janko and Keicher, Simon and Ren, Yue},
  title         = {Computing {GIT}-fans with symmetry and the {M}ori chamber decomposition of $\overline M_{0,6}$},
  journal       = {Math. Comp.},
  fjournal      = {Mathematics of Computation},
  volume        = {89},
  number        = {326},
  pages         = {3003--3021},
  year          = {2020},
  doi           = {10.1090/mcom/3546}
}

@Article{BL81,
  author        = {Billera, Louis J. and Lee, Carl W.},
  title         = {A proof of the sufficiency of {M}c{M}ullen's conditions for $f$-vectors of simplicial convex
                  polytopes},
  journal       = {J. Combin. Theory Ser. A},
  volume        = {31},
  number        = {3},
  pages         = {237--255},
  year          = {1981},
  doi           = {10.1016/0097-3165(81)90058-3}
}

@Article{BN07,
  author        = {Baker, Matthew and Norine, Serguei},
  title         = {Riemann-{R}och and {A}bel-{J}acobi theory on a finite graph},
  mrnumber      = {2355607},
  journal       = {Adv. Math.},
  fjournal      = {Advances in Mathematics},
  volume        = {215},
  number        = {2},
  pages         = {766--788},
  year          = {2007},
  doi           = {10.1016/j.aim.2007.04.012}
}

@Article{BS09,
  author        = {Banica, Teodor and Speicher, Roland},
  title         = {Liberation of orthogonal Lie groups},
  journal       = {Advances in Mathematics},
  volume        = {222},
  number        = {4},
  pages         = {1461--1501},
  year          = {2009},
  doi           = {10.1016/j.aim.2009.06.009}
}

@Book{Ben93,
  author        = {Benson, David J.},
  title         = {Polynomial invariants of finite groups},
  series        = {London Mathematical Society Lecture Note Series},
  volume        = {190},
  address       = {Cambridge},
  publisher     = {Cambridge University Press},
  year          = {1993}
}

@MastersThesis{Bhm99,
  author        = {Böhm, Janko},
  title         = {Parametrisierung rationaler Kurven},
  year          = {1999},
  school        = {Universität Bayreuth},
  type          = {Diploma Thesis}
}

@PhDThesis{Bie18,
  author        = {Bies, Martin},
  title         = {Cohomologies of coherent sheaves and massless spectra in {F}-theory},
  year          = {2018},
  month         = {2},
  doi           = {10.11588/heidok.00024045},
  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},
  journal       = {Mathematika},
  volume        = {43},
  number        = {2},
  publisher     = {London Mathematical Society},
  pages         = {274--285},
  year          = {1996},
  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}},
  publisher     = {Springer-Verlag, Cham},
  pages         = {xviii+601},
  year          = {2020},
  doi           = {10.1007/978-3-030-53061-7}
}

@Book{C-MLS21,
  author        = {Cisneros Molina, Jose Luis and Le, Dung Trang and Seade, Jose},
  title         = {Handbook of Geometry and Topology of Singularities II},
  publisher     = {Springer-Verlag, Cham},
  pages         = {xii+578},
  year          = {2021},
  doi           = {10.1007/978-3-030-78024-1}
}

@Book{CCNPW85,
  author        = {Conway, J. H. and Curtis, R. T. and Norton, S. P. and Parker, R. A. and Wilson, R. A.},
  title         = {Atlas of finite groups},
  mrnumber      = {827219 (88g:20025)},
  note          = {Maximal subgroups and ordinary characters for simple groups, With computational assistance from J. G.
                  Thackray},
  address       = {Eynsham},
  publisher     = {Oxford University Press},
  pages         = {xxxiv+252},
  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},
  mrnumber      = {1635715},
  journal       = {LMS J. Comput. Math.},
  fjournal      = {LMS Journal of Computation and Mathematics},
  volume        = {1},
  pages         = {1--8},
  year          = {1998},
  doi           = {10.1112/S1461157000000115}
}

@Article{CKM97,
  author        = {Collart, S. and Kalkbrener, M. and Mall, D.},
  title         = {Converting Bases with the Gröbner Walk},
  journal       = {Journal of Symbolic Computation},
  volume        = {24},
  number        = {3},
  pages         = {465--469},
  year          = {1997},
  doi           = {10.1006/jsco.1996.0145}
}

@Book{CLO05,
  author        = {Cox, David A. and Little, John and O'Shea, Donal},
  title         = {Using Algebraic Geometry},
  series        = {Graduate Texts in Mathematics},
  volume        = {185},
  publisher     = {Springer-Verlag},
  year          = {2005},
  doi           = {10.1007/b138611}
}

@Book{CLS11,
  author        = {Cox, David A. and Little, John B. and Schenck, Henry K.},
  title         = {Toric varieties},
  mrnumber      = {2810322},
  series        = {Graduate Studies in Mathematics},
  volume        = {124},
  publisher     = {Providence, RI: American Mathematical Society (AMS)},
  pages         = {xxiv+841},
  year          = {2011},
  doi           = {10.1090/gsm/124}
}

@Article{CMS07,
  author        = {Collins, Benoît and Mingo, James A. and Śniady, Piotr and Speicher, Roland},
  title         = {Second order freeness and fluctuations of random matrices. III: Higher order freeness and free
                  cumulants},
  journal       = {Documenta Mathematica},
  volume        = {12},
  pages         = {1--70},
  year          = {2007},
  doi           = {10.4171/dm/220}
}

@Article{CMT04,
  author        = {Cohen, Arjeh M. and Murray, Scott H. and Taylor, D. E.},
  title         = {Computing in groups of Lie type},
  mrnumber      = {2047097},
  journal       = {Math. Comp.},
  fjournal      = {Mathematics of Computation},
  volume        = {73},
  number        = {247},
  pages         = {1477--1498},
  year          = {2004},
  doi           = {10.1090/S0025-5718-03-01582-5}
}

@Book{CS99,
  author        = {Conway, J. H. and Sloane, N. J. A.},
  title         = {Sphere packings, lattices and groups},
  mrnumber      = {1662447},
  series        = {Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]},
  volume        = {290},
  note          = {With additional contributions by E. Bannai, R. E. Borcherds, J. Leech, S. P. Norton, A. M. Odlyzko,
                  R. A. Parker, L. Queen and B. B. Venkov},
  publisher     = {Springer-Verlag, New York},
  edition       = {Third},
  pages         = {lxxiv+703},
  year          = {1999},
  doi           = {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}
}

@Article{CW16,
  author        = {Cébron, Guillaume and Weber, Moritz},
  title         = {Quantum groups based on spatial partitions},
  journal       = {arXiv:1609.02321},
  year          = {2016},
  doi           = {10.48550/arXiv.1609.02321},
  primaryclass  = {math.QA}
}

@Book{Cam99,
  author        = {Cameron, Peter J.},
  title         = {Permutation groups},
  series        = {London Mathematical Society Student Texts},
  volume        = {45},
  publisher     = {Cambridge University Press, Cambridge},
  pages         = {x+220},
  year          = {1999},
  doi           = {10.1017/CBO9780511623677}
}

@InCollection{Chr91,
  author        = {Christophersen, Jan Arthur},
  title         = {On the components and discriminant of the versal base space of cyclic quotient singularities},
  booktitle     = {Singularity theory and its applications, Part {I} ({C}oventry, 1988/1989)},
  series        = {Lecture Notes in Math.},
  volume        = {1462},
  publisher     = {Springer, Berlin},
  pages         = {81--92},
  year          = {1991},
  doi           = {10.1007/BFb0086376}
}

@Book{Coh00,
  author        = {Cohen, Henri},
  title         = {Advanced topics in computational number theory},
  series        = {Graduate Texts in Mathematics},
  volume        = {193},
  publisher     = {Springer-Verlag, New York},
  pages         = {xvi+578},
  year          = {2000},
  doi           = {10.1007/978-1-4419-8489-0}
}

@Book{Coh93,
  author        = {Cohen, Henri},
  title         = {A course in computational algebraic number theory},
  series        = {Graduate Texts in Mathematics},
  volume        = {138},
  publisher     = {Springer-Verlag, Berlin},
  pages         = {xii+534},
  year          = {1993},
  doi           = {10.1007/978-3-662-02945-9}
}

@Article{Cor21,
  author        = {Corey, D.},
  title         = {Initial degenerations of {G}rassmannians},
  journal       = {Sel. Math. New Ser.},
  fjournal      = {Selecta Mathematica New Series},
  volume        = {27},
  number        = {57},
  year          = {2021},
  doi           = {10.1007/s00029-021-00679-6}
}

@InCollection{DE02,
  author        = {Decker, Wolfram and Eisenbud, David},
  title         = {Sheaf algorithms using the exterior algebra},
  booktitle     = {Computations in algebraic geometry with Macaulay 2},
  zbl           = {0994.14010},
  publisher     = {Berlin: Springer},
  pages         = {215--249},
  year          = {2002},
  language      = {English},
  zbmath        = {1693054}
}

@Article{DES93,
  author        = {Decker, Wolfram and Ein, Lawrence and Schreyer, Frank-Olaf},
  title         = {Construction of surfaces in ${\mathbb P}^4$},
  zbl           = {0795.14019},
  journal       = {J. Algebr. Geom.},
  fjournal      = {Journal of Algebraic Geometry},
  volume        = {2},
  number        = {2},
  pages         = {185--237},
  year          = {1993},
  language      = {English},
  zbmath        = {404355}
}

@Article{DF20,
  bibkey        = {DF20},
  author        = {De Franceschi, G.},
  title         = {Centralizers and conjugacy classes in finite classical groups},
  journal       = {arXiv:2008.12651},
  year          = {2020},
  doi           = {10.48550/arXiv.2008.12651},
  primaryclass  = {math.GR}
}

@Article{DFO13,
  author        = {Detinko, A. S. and Flannery, D. L. and O'Brien, E. A.},
  title         = {Recognizing finite matrix groups over infinite fields},
  journal       = {J. Symbolic Comput.},
  fjournal      = {Journal of Symbolic Computation},
  volume        = {50},
  pages         = {100--109},
  year          = {2013},
  doi           = {10.1016/j.jsc.2012.04.002}
}

@InCollection{DGP99,
  author        = {Decker, Wolfram and Greuel, Gert-Martin and Pfister, Gerhard},
  title         = {Primary decomposition: algorithms and comparisons},
  booktitle     = {Algorithmic algebra and number theory. Selected papers from a conference, Heidelberg, Germany,
                  October 1997},
  publisher     = {Springer, Berlin},
  pages         = {187--220},
  year          = {1999},
  doi           = {10.1007/978-3-642-59932-3}
}

@Article{DH00,
  author        = {Domokos, Mátyás and Hegedűs, Pál},
  title         = {Noether's bound for polynomial invariants of finite groups},
  mrnumber      = {1739493},
  journal       = {Arch. Math. (Basel)},
  fjournal      = {Archiv der Mathematik},
  volume        = {74},
  number        = {3},
  pages         = {161--167},
  year          = {2000},
  doi           = {10.1007/s000130050426}
}

@Article{DHS98,
  author        = {Decker, Wolfram and Heydtmann, Agnes Eileen and Schreyer, Frank-Olaf},
  title         = {Generating a {N}oetherian normalization of the invariant ring of a finite group},
  journal       = {J. Symbolic Comput.},
  fjournal      = {Journal of Symbolic Computation},
  volume        = {25},
  number        = {6},
  pages         = {727--731},
  year          = {1998},
  doi           = {10.1006/jsco.1997.0196}
}

@InCollection{DJ98,
  author        = {Decker, Wolfram and de Jong, Theo},
  title         = {Gröbner bases and invariant theory},
  booktitle     = {Gröbner bases and applications. Based on a course for young researchers, January 1998, and the
                  conference "33 years of Gröbner bases", Linz, Austria, February 2--4, 1998},
  mrnumber      = {1699814},
  series        = {London Math. Soc. Lecture Note Ser.},
  volume        = {251},
  publisher     = {Cambridge Univ. Press, Cambridge},
  pages         = {61--89},
  year          = {1998},
  doi           = {10.1017/CBO9780511565847.005}
}

@Book{DK15,
  author        = {Derksen, Harm and Kemper, Gregor},
  title         = {Computational invariant theory. With two appendices by Vladimir L. Popov, and an addendum by Norbert
                  A'Campo and Popov, 2nd enlarged edition, Invariant Theory and Algebraic Transformation Groups, VIII},
  series        = {Encyclopaedia of Mathematical Sciences},
  volume        = {130},
  publisher     = {Springer, Heidelberg},
  edition       = {enlarged},
  pages         = {xxii+366},
  year          = {2015},
  doi           = {10.1007/978-3-662-48422-7}
}

@Article{DK17,
  author        = {Donten-Bury, Maria and Keicher, Simon},
  title         = {Computing resolutions of quotient singularities},
  journal       = {J. Algebra},
  fjournal      = {Journal of Algebra},
  volume        = {472},
  pages         = {546--572},
  year          = {2017}
}

@Book{DL06,
  author        = {Decker, Wolfram and Lossen, Christoph},
  title         = {Computing in algebraic geometry. A quick start using SINGULAR},
  series        = {Algorithms and Computation in Mathematics},
  volume        = {16},
  publisher     = {Springer-Verlag, Berlin; Hindustan Book Agency, New Delhi},
  pages         = {xvi+327},
  year          = {2006},
  doi           = {10.1007/3-540-28993-3}
}

@Book{DLRS10,
  bibkey        = {DLRS10},
  author        = {De Loera, Jesús A. and Rambau, Jörg and Santos, Francisco},
  title         = {Triangulations. Structures for algorithms and applications},
  zbl           = {1207.52002},
  series        = {Algorithms and Computation in Mathematics},
  volume        = {25},
  address       = {Berlin},
  publisher     = {Springer-Verlag},
  pages         = {xiv+535},
  year          = {2010},
  doi           = {10.1007/978-3-642-12971-1}
}

@Book{DP13,
  author        = {Decker, Wolfram and Pfister, Gerhard},
  title         = {A first course in computational algebraic geometry},
  series        = {African Institute of Mathematics (AIMS) Library Series},
  publisher     = {Cambridge University Press, Cambridge},
  pages         = {viii+118},
  year          = {2013},
  doi           = {10.1017/CBO9781139565769}
}

@Article{DS00,
  author        = {Decker, Wolfram and Schreyer, Frank-Olaf},
  title         = {Non-general type surfaces in ${\mathbb P}^4$: {Some} remarks on bounds and constructions},
  zbl           = {1012.14014},
  journal       = {J. Symb. Comput.},
  fjournal      = {Journal of Symbolic Computation},
  volume        = {29},
  number        = {4-5},
  pages         = {545--582},
  year          = {2000},
  doi           = {10.1006/jsco.1999.0323},
  language      = {English},
  zbmath        = {1471046}
}

@Book{DSS09,
  author        = {Drton, Mathias and Sturmfels, Bernd and Sullivant, Seth},
  title         = {Lectures on algebraic statistics},
  zbl           = {1166.13001},
  series        = {Oberwolfach Semin.},
  volume        = {39},
  publisher     = {Basel: Birkh{\"a}user},
  year          = {2009},
  fseries       = {Oberwolfach Seminars},
  language      = {English},
  zbmath        = {5303649}
}

@Article{Der99,
  author        = {Derksen, Harm},
  title         = {Computation of invariants for reductive groups},
  journal       = {Adv. Math.},
  fjournal      = {Advances in Mathematics},
  volume        = {141},
  number        = {2},
  pages         = {366--384},
  year          = {1999},
  doi           = {10.1006/aima.1998.1787}
}

@Article{EFS03,
  author        = {Eisenbud, David and Fl{\o}ystad, Gunnar and Schreyer, Frank-Olaf},
  title         = {Sheaf cohomology and free resolutions over exterior algebras},
  zbl           = {1063.14021},
  journal       = {Trans. Am. Math. Soc.},
  fjournal      = {Transactions of the American Mathematical Society},
  volume        = {355},
  number        = {11},
  pages         = {4397--4426},
  year          = {2003},
  doi           = {10.1090/S0002-9947-03-03291-4},
  language      = {English},
  zbmath        = {1963988}
}

@Book{EH16,
  author        = {Eisenbud, David and Harris, Joe},
  title         = {3264 and all that. {A} second course in algebraic geometry},
  zbl           = {1341.14001},
  publisher     = {Cambridge: Cambridge University Press},
  year          = {2016},
  doi           = {10.1017/CBO9781139062046},
  language      = {English},
  zbmath        = {6562439}
}

@Article{EHU03,
  author        = {Eisenbud, David and Huneke, Craig and Ulrich, Bernd},
  title         = {What is the {Rees} algebra of a module?},
  journal       = {Proc. Am. Math. Soc.},
  fjournal      = {Proceedings of the American Mathematical Society},
  volume        = {131},
  number        = {3},
  pages         = {701--708},
  year          = {2003},
  doi           = {10.1090/S0002-9939-02-06575-9},
  language      = {English}
}

@Article{EHV92,
  author        = {Eisenbud, David and Huneke, Craig and Vasconcelos, Wolmer},
  title         = {Direct methods for primary decomposition},
  journal       = {Invent. Math.},
  fjournal      = {Inventiones Mathematicae},
  volume        = {110},
  number        = {2},
  pages         = {207--235},
  year          = {1992},
  doi           = {10.1007/BF01231331}
}

@Article{EM16,
  author        = {Eser, Zekiye Sahin and Matusevich, Laura Felicia},
  title         = {Decompositions of cellular binomial ideals},
  journal       = {J. Lond. Math. Soc. (2)},
  fjournal      = {Journal of the London Mathematical Society. Second Series},
  volume        = {94},
  number        = {2},
  pages         = {409--426},
  year          = {2016},
  doi           = {10.1112/jlms/jdw012}
}

@Article{EM19,
  author        = {Eser, Zekiye Sahin and Matusevich, Laura Felicia},
  title         = {Corrigendum: Decompositions of cellular binomial ideals: (J. Lond. Math. Soc. 94 (2016) 409--426)},
  journal       = {J. Lond. Math. Soc. (2)},
  fjournal      = {Journal of the London Mathematical Society. Second Series},
  volume        = {100},
  number        = {2},
  pages         = {717--719},
  year          = {2019},
  doi           = {10.1112/jlms.12232}
}

@Article{EMSS16,
  author        = {Er{\"o}cal, Bur{\c{c}}in and Motsak, Oleksandr and Schreyer, Frank-Olaf and Steenpa{\ss}, Andreas},
  title         = {Refined algorithms to compute syzygies},
  zbl           = {1405.14138},
  journal       = {J. Symb. Comput.},
  fjournal      = {Journal of Symbolic Computation},
  volume        = {74},
  pages         = {308--327},
  year          = {2016},
  doi           = {10.1016/j.jsc.2015.07.004},
  language      = {English},
  zbmath        = {6517845}
}

@Article{ES96,
  author        = {Eisenbud, David and Sturmfels, Bernd},
  title         = {Binomial ideals},
  journal       = {Duke Math. J.},
  fjournal      = {Duke Mathematical Journal},
  volume        = {84},
  number        = {1},
  pages         = {1--45},
  year          = {1996},
  doi           = {10.1215/S0012-7094-96-08401-X}
}

@Book{Eis95,
  author        = {Eisenbud, David},
  title         = {Commutative algebra. With a view toward algebraic geometry},
  zbl           = {0819.13001},
  journal       = {Grad. Texts Math.},
  fjournal      = {Graduate Texts in Mathematics},
  volume        = {150},
  publisher     = {Berlin: Springer-Verlag},
  pages         = {xvi + 785},
  year          = {1995}
}

@Book{Eis98,
  author        = {Eisenbud, David},
  title         = {Computing cohomology. A chapter in W. Vasconcelos, Computational methods in commutative algebra and
                  algebraic geometry},
  publisher     = {Berlin: Springer},
  pages         = {209--216},
  year          = {1998},
  language      = {English}
}

@Article{FGLM93,
  author        = {Faugère, J.C. and Gianni, P. and Lazard, D. and Mora, T.},
  title         = {Efficient Computation of Zero-dimensional Gröbner Bases by Change of Ordering},
  journal       = {Journal of Symbolic Computation},
  volume        = {16},
  number        = {4},
  pages         = {329--344},
  year          = {1993},
  doi           = {10.1006/jsco.1993.1051}
}

@Article{FJLT07,
  author        = {Fukuda, K. and Jensen, A. N. and Lauritzen, N. and Thomas, R.},
  title         = {The generic Gröbner walk},
  journal       = {Journal of Symbolic Computation},
  volume        = {42},
  number        = {3},
  pages         = {298--312},
  year          = {2007},
  doi           = {10.1016/j.jsc.2006.09.004}
}

@Article{FJR17,
  author        = {Fan, Huijun and Jarvis, Tyler and Ruan, Yongbin},
  title         = {A mathematical theory of the gauged linear sigma model},
  journal       = {Geometry \& Topology},
  volume        = {22},
  number        = {1},
  publisher     = {Mathematical Sciences Publishers},
  pages         = {235--303},
  year          = {2017},
  month         = {Oct},
  doi           = {10.2140/gt.2018.22.235}
}

@Article{FJT07,
  author        = {Fukuda, Komei and Jensen, Anders N. and Thomas, Rekha R.},
  title         = {Computing Groebner Fans},
  journal       = {Math. Comp.},
  fjournal      = {Mathematics of Computation},
  volume        = {76},
  number        = {260},
  pages         = {2189--2213},
  year          = {2007},
  doi           = {10.1090/S0025-5718-07-01986-2}
}

@InProceedings{FLINT,
  bibkey        = {FLINT},
  author        = {W. B. Hart},
  title         = {Fast Library for Number Theory: An Introduction},
  booktitle     = {Proceedings of the Third International Congress on Mathematical Software},
  series        = {ICMS'10},
  note          = {\url{https://flintlib.org}},
  address       = {Berlin, Heidelberg},
  publisher     = {Springer-Verlag},
  pages         = {88--91},
  year          = {2010},
  location      = {Kobe, Japan},
  numpages      = {4}
}

@Article{FY04,
  author        = {Feichtner, Eva Maria and Yuzvinsky, Sergey},
  title         = {Chow rings of toric varieties defined by atomic lattices},
  journal       = {Inventiones Mathematicae},
  volume        = {155},
  number        = {3},
  publisher     = {Springer Science and Business Media {LLC}},
  pages         = {515--536},
  year          = {2004},
  month         = {mar},
  doi           = {10.1007/s00222-003-0327-2}
}

@Article{Fau99,
  author        = {Faugère, Jean-Charles},
  title         = {A new efficient algorithm for computing Gröbner bases (F4)},
  journal       = {Journal of Pure and Applied Algebra},
  volume        = {139},
  number        = {1--3},
  publisher     = {Elsevier},
  pages         = {61--88},
  year          = {1999},
  doi           = {10.1016/S0022-4049(99)00005-5},
  archiveprefix = {HAL},
  eprint        = {hal-01148855}
}

@Book{Ful69,
  author        = {Fulton, William},
  title         = {Algebraic curves. An introduction to algebraic geometry},
  series        = {Mathematics Lecture Note Series},
  note          = {Notes written with the collaboration of Richard Weiss},
  publisher     = {W. A. Benjamin, Inc., New York-Amsterdam},
  pages         = {xiii+226},
  year          = {1969}
}

@Book{Ful97,
  author        = {Fulton, William},
  title         = {Young tableaux},
  series        = {London Mathematical Society Student Texts},
  volume        = {35},
  note          = {With applications to representation theory and geometry},
  publisher     = {Cambridge University Press, Cambridge},
  pages         = {x+260},
  year          = {1997}
}

@Book{Ful98,
  author        = {Fulton, William},
  title         = {Intersection theory},
  mrnumber      = {1644323},
  series        = {Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics
                  [Results in Mathematics and Related Areas. 3rd Series. A Series of Modern Surveys in Mathematics]},
  volume        = {2},
  publisher     = {Springer-Verlag, Berlin},
  edition       = {Second},
  pages         = {xiv+470},
  year          = {1998},
  doi           = {10.1007/978-1-4612-1700-8}
}

@InProceedings{GHJ16,
  author        = {Gawrilow, Ewgenij and Hampe, Simon and Joswig, Michael},
  title         = {The polymake XML File Format},
  editor        = {Greuel, Gert-Martin and Koch, Thorsten and Paule, Peter and Sommese, Andrew},
  booktitle     = {Mathematical Software -- ICMS 2016},
  address       = {Cham},
  publisher     = {Springer International Publishing},
  pages         = {403--410},
  year          = {2016}
}

@InCollection{GJ00,
  author        = {Gawrilow, Ewgenij and Joswig, Michael},
  title         = {polymake: a Framework for Analyzing Convex Polytopes},
  editor        = {Kalai, Gil and Ziegler, Günter M.},
  booktitle     = {Polytopes --- Combinatorics and Computation},
  note          = {https://polymake.org},
  publisher     = {Birkhäuser},
  pages         = {43--74},
  year          = {2000},
  doi           = {10.1007/978-3-0348-8438-9_2}
}

@Article{GJRW10,
  author        = {Gawrilow, Ewgenij and Joswig, Michael and Rörig, Thilo and Witte, Nikolaus},
  title         = {Drawing polytopal graphs with polymake},
  mrnumber      = {2577692 (2011c:68147)},
  journal       = {Comput. Vis. Sci.},
  fjournal      = {Computing and Visualization in Science},
  volume        = {13},
  number        = {2},
  pages         = {99--110},
  year          = {2010},
  doi           = {10.1007/s00791-009-0127-3},
  eprint        = {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},
  mrnumber      = {2290112},
  series        = {Springer Monographs in Mathematics},
  publisher     = {Springer-Verlag, Berlin},
  pages         = {xii+471},
  year          = {2007},
  doi           = {10.1007/3-540-28419-2}
}

@Article{GLS10,
  author        = {Greuel, Gert-Martin and Laplagne, Santiago and Seelisch, Frank},
  title         = {Normalization of rings},
  journal       = {J. Symbolic Comput.},
  fjournal      = {Journal of Symbolic Computation},
  volume        = {45},
  number        = {9},
  pages         = {887--901},
  year          = {2010},
  doi           = {10.1016/j.jsc.2010.04.002}
}

@Book{GP08,
  author        = {Greuel, Gert-Martin and Pfister, Gerhard},
  title         = {A Singular introduction to commutative algebra. With contributions by Olaf Bachmann, Christoph Lossen
                  and Hans Schönemann. 2nd extended ed.},
  note          = {With 1 CD-ROM (Windows, Macintosh and UNIX)},
  publisher     = {Springer, Berlin},
  pages         = {xx+689},
  year          = {2008},
  doi           = {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}
}

@InCollection{GTZ88,
  author        = {Gianni, Patrizia and Trager, Barry and Zacharias, Gail},
  title         = {Gröbner bases and primary decomposition of polynomial ideals},
  booktitle     = {Computational aspects of commutative algebra},
  journal       = {J. Symbolic Comput.},
  fjournal      = {Journal of Symbolic Computation},
  volume        = {6},
  publisher     = {Elsevier Ltd, Oxford},
  pages         = {149--167},
  year          = {1988},
  doi           = {10.1016/S0747-7171(88)80040-3}
}

@Book{GW20,
  author        = {Görtz, Ulrich and Wedhorn, Torsten},
  title         = {Algebraic Geometry I: Schemes with Examples and Exercises},
  publisher     = {Springer Spektrum},
  edition       = {2},
  year          = {2020},
  doi           = {10.1007/978-3-658-30733-2}
}

@Misc{Gat18,
  author        = {Gathmann, Andreas},
  title         = {Class notes „Plane Algebraic Curves” (SS 2018)},
  howpublished  = {Published electronically},
  year          = {2018},
  url           = {https://www.mathematik.uni-kl.de/~gathmann/en/curves.php}
}

@Article{Gat96,
  author        = {Gatermann, Karin},
  title         = {Semi-invariants, equivariants and algorithms},
  journal       = {Appl. Algebra Engrg. Comm. Comput.},
  fjournal      = {Applicable Algebra in Engineering, Communication and Computing},
  volume        = {7},
  number        = {2},
  pages         = {105--124},
  year          = {1996},
  doi           = {10.1007/BF01191379}
}

@PhDThesis{Gro20,
  author        = {Gromada, Daniel},
  title         = {Compact matrix quantum groups and their representation categories},
  year          = {2020},
  doi           = {10.22028/D291-32389},
  type          = {doctoralthesis},
  school        = {Universität des Saarlandes}
}

@Book{Gru03,
  bibkey        = {Gru03},
  author        = {Grünbaum, Branko},
  title         = {Convex polytopes},
  series        = {Graduate Texts in Mathematics},
  volume        = {221},
  note          = {Prepared and with a preface by Volker Kaibel, Victor Klee and Günter M. Ziegler},
  address       = {New York},
  publisher     = {Springer-Verlag},
  edition       = {Second},
  pages         = {xvi+468},
  year          = {2003},
  doi           = {10.1007/978-1-4613-0019-9}
}

@Book{HEO05,
  author        = {Holt, Derek F. and Eick, Bettina and O'Brien, Eamonn A.},
  title         = {Handbook of computational group theory},
  series        = {Discrete Mathematics and its Applications (Boca Raton)},
  publisher     = {Chapman \& Hall/CRC, Boca Raton, FL},
  pages         = {xvi+514},
  year          = {2005},
  doi           = {10.1201/9781420035216}
}

@Article{HHS11,
  author        = {Hausen, Jürgen and Herppich, Elaine and Süss, Hendrik},
  title         = {Multigraded factorial rings and {F}ano varieties with torus action},
  mrnumber      = {2804508},
  journal       = {Doc. Math.},
  fjournal      = {Documenta Mathematica},
  volume        = {16},
  pages         = {71--109},
  year          = {2011}
}

@Article{HM73,
  author        = {Horrocks, G. and Mumford, D.},
  title         = {A rank 2 vector bundle on $\text{P}^4$ with 15,000 symmetries},
  zbl           = {0255.14017},
  journal       = {Topology},
  fjournal      = {Topology},
  volume        = {12},
  pages         = {63--81},
  year          = {1973},
  doi           = {10.1016/0040-9383(73)90022-0},
  language      = {English},
  zbmath        = {3402784}
}

@Book{HP89,
  author        = {Holt, Derek F. and Plesken, W.},
  title         = {Perfect groups},
  mrnumber      = {1025760},
  series        = {Oxford Mathematical Monographs},
  note          = {With an appendix by W. Hanrath, Oxford Science Publications},
  publisher     = {The Clarendon Press, Oxford University Press, New York},
  pages         = {xii+364},
  year          = {1989}
}

@Misc{HRR23,
  author        = {Hulpke, Alexander and Roney-Dougal, Colva and Russell, Christopher},
  title         = {PrimGrp, GAP Primitive Permutation Groups Library, Version 3.4.4},
  note          = {GAP package},
  year          = {2023},
  month         = {2},
  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},
  series        = {Graduate Texts in Mathematics},
  publisher     = {Springer-Verlag, New York},
  pages         = {xvi+496},
  year          = {1977},
  doi           = {10.1007/978-1-4757-3849-0}
}

@Article{Hul22,
  author        = {Hulpke, Alexander},
  title         = {The perfect groups of order up to two million},
  journal       = {Math. Comp.},
  volume        = {91},
  pages         = {1007--1017},
  year          = {2022},
  doi           = {10.1090/mcom/3684}
}

@Misc{Hul23,
  author        = {Hulpke, Alexander},
  title         = {TransGrp, Transitive Groups Library, Version 3.6.5},
  note          = {GAP package},
  year          = {2023},
  month         = {12},
  url           = {https://www.math.colostate.edu/~hulpke/transgrp}
}

@Book{Hum72,
  author        = {Humphreys, James E.},
  title         = {Introduction to Lie Algebras and Representation Theory},
  series        = {Graduate Texts in Mathematics},
  volume        = {9},
  publisher     = {Springer-Verlag, New York},
  pages         = {xii+169},
  year          = {1972},
  doi           = {10.1007/978-1-4612-6398-2}
}

@Book{Hup67,
  author        = {Huppert, B.},
  title         = {Endliche Gruppen. I},
  series        = {Die Grundlehren der mathematischen Wissenschaften},
  volume        = {134},
  publisher     = {Springer-Verlag, Berlin-New York},
  pages         = {xii+793},
  year          = {1967},
  doi           = {10.1007/978-3-642-64981-3}
}

@Book{Huy16,
  author        = {Huybrechts, Daniel},
  title         = {Lectures on {K}3 surfaces},
  mrnumber      = {3586372},
  series        = {Cambridge Studies in Advanced Mathematics},
  volume        = {158},
  publisher     = {Cambridge University Press, Cambridge},
  pages         = {xi+485},
  year          = {2016},
  doi           = {10.1017/CBO9781316594193}
}

@InCollection{IR96,
  author        = {Ito, Yukari and Reid, Miles},
  title         = {The {M}c{K}ay correspondence for finite subgroups of ${\rm SL}(3,\mathbb C)$},
  booktitle     = {Higher-dimensional complex varieties ({T}rento, 1994)},
  publisher     = {de Gruyter},
  pages         = {221--240},
  year          = {1996},
  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}
}

@Article{JLLT22,
  author        = {Joswig, Michael and Lofano, Davide and Lutz, Frank H. and Tsuruga, Mimi},
  title         = {Frontiers of sphere recognition in practice},
  mrnumber      = {4496689},
  journal       = {J. Appl. Comput. Topol.},
  fjournal      = {Journal of Applied and Computational Topology},
  volume        = {6},
  number        = {4},
  pages         = {503--527},
  year          = {2022},
  doi           = {10.1007/s41468-022-00092-8}
}

@Book{JLPW95,
  author        = {Jansen, C. and Lux, K. and Parker, R. and Wilson, R.},
  title         = {An atlas of {B}rauer characters},
  mrnumber      = {1367961 (96k:20016)},
  series        = {London Mathematical Society Monographs. New Series},
  volume        = {11},
  note          = {Appendix 2 by T. Breuer and S. Norton, Oxford Science Publications},
  address       = {New York},
  publisher     = {The Clarendon Press Oxford University Press},
  pages         = {xviii+327},
  year          = {1995}
}

@Book{JP00,
  author        = {de Jong, Theo and Pfister, Gerhard},
  title         = {Local Analytic Geometry},
  series        = {Advanced Lectures in Mathematics},
  publisher     = {Vieweg+Teubner Verlag},
  pages         = {xi+384},
  year          = {2000},
  doi           = {10.1007/978-3-322-90159-0}
}

@Book{JT13,
  author        = {Joswig, Michael and Theobald, Thorsten},
  title         = {Polyhedral and algebraic methods in computational geometry},
  series        = {Universitext},
  note          = {Revised and updated translation of the 2008 German original},
  publisher     = {Springer, London},
  pages         = {x+250},
  year          = {2013},
  doi           = {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           = {10.1007/s004540010039}
}

@Article{Joh12,
  author        = {Johansson, Fredrik},
  title         = {Efficient implementation of the {H}ardy-{R}amanujan-{R}ademacher formula},
  mrnumber      = {2988821},
  journal       = {LMS J. Comput. Math.},
  fjournal      = {LMS Journal of Computation and Mathematics},
  volume        = {15},
  pages         = {341--359},
  year          = {2012},
  doi           = {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}
}

@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},
  series        = {Graduate Studies in Mathematics},
  volume        = {219},
  address       = {Providence, RI},
  publisher     = {American Mathematical Society},
  year          = {2021}
}

@Article{Jow11,
  author        = {Jow, Shin-Yao},
  title         = {Cohomology of toric line bundles via simplicial Alexander duality},
  journal       = {Journal of Mathematical Physics},
  volume        = {52},
  number        = {3},
  publisher     = {AIP Publishing},
  pages         = {033506},
  year          = {2011},
  month         = {Mar},
  doi           = {10.1063/1.3562523}
}

@InCollection{KL91,
  author        = {Krick, Teresa and Logar, Alessandro},
  title         = {An algorithm for the computation of the radical of an ideal in the ring of polynomials},
  booktitle     = {Applied algebra, algebraic algorithms and error-correcting codes (New Orleans, LA, 1991)},
  series        = {Lecture Notes in Comput. Sci.},
  volume        = {539},
  publisher     = {Springer, Berlin},
  pages         = {195--205},
  year          = {1991},
  doi           = {10.1007/3-540-54522-0_108}
}

@InProceedings{KLT20,
  author        = {Kaluba, Marek and Lorenz, Benjamin and Timme, Sascha},
  title         = {Polymake.jl: A New Interface to polymake},
  editor        = {Bigatti, Anna Maria and Carette, Jacques and Davenport, James H. and Joswig, Michael and de Wolff,
                  Timo},
  booktitle     = {Mathematical Software -- ICMS 2020},
  address       = {Cham},
  publisher     = {Springer International Publishing},
  pages         = {377--385},
  year          = {2020},
  doi           = {10.1007/978-3-030-52200-1_37}
}

@Article{KM-POPR15,
  author        = {Klevers, Denis and Mayorga Pena, Damian Kaloni and Oehlmann, Paul-Konstantin and Piragua, Hernan and
                  Reuter, Jonas},
  title         = {F-Theory on all Toric Hypersurface Fibrations and its Higgs Branches},
  journal       = {JHEP},
  volume        = {01},
  pages         = {142},
  year          = {2015},
  doi           = {10.1007/JHEP01(2015)142},
  eprint        = {1408.4808},
  primaryclass  = {hep-th},
  reportnumber  = {UPR-1264-T, CERN-PH-TH-2014-171, Bonn-TH-2014-13}
}

@Article{KMSS11,
  author        = {Katz, Sheldon and Morrison, David R. and Schafer-Nameki, Sakura and Sully, James},
  title         = {Tate's algorithm and F-theory},
  journal       = {JHEP},
  volume        = {08},
  pages         = {094},
  year          = {2011},
  doi           = {10.1007/JHEP08(2011)094},
  eprint        = {1106.3854},
  primaryclass  = {hep-th},
  reportnumber  = {UCSB-MATH-2011-09, IPMU11-0107, NSF-KITP-11-110, KCL-MTH-11-13}
}

@Article{KO14,
  author        = {Kelleher, Jerome and O'Sullivan, Barry},
  title         = {Generating All Partitions: A Comparison Of Two Encodings},
  journal       = {arXiv:0909.2331},
  year          = {2014},
  doi           = {10.48550/arXiv.0909.2331},
  primaryclass  = {cs.DS}
}

@Book{KR05,
  author        = {Kreuzer, Martin and Robbiano, Lorenzo},
  title         = {Computational commutative algebra. II},
  zbl           = {1090.13021},
  publisher     = {Berlin: Springer},
  pages         = {x + 586},
  year          = {2005}
}

@InCollection{KS99,
  author        = {Kemper, Gregor and Steel, Allan},
  title         = {Some algorithms in invariant theory of finite groups},
  booktitle     = {Computational methods for representations of groups and algebras ({E}ssen, 1997)},
  series        = {Progr. Math.},
  volume        = {173},
  publisher     = {Birkhäuser, Basel},
  pages         = {267--285},
  year          = {1999}
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@Article{Kah10,
  author        = {Kahle, Thomas},
  title         = {Decompositions of binomial ideals},
  journal       = {Ann. Inst. Statist. Math.},
  fjournal      = {Annals of the Institute of Statistical Mathematics},
  volume        = {62},
  number        = {4},
  pages         = {727--745},
  year          = {2010},
  doi           = {10.1007/s10463-010-0290-9}
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@Article{Kem02,
  author        = {Kemper, Gregor},
  title         = {The calculation of radical ideals in positive characteristic},
  journal       = {J. Symbolic Comput.},
  fjournal      = {Journal of Symbolic Computation},
  volume        = {34},
  number        = {3},
  pages         = {229--238},
  year          = {2002},
  doi           = {10.1006/jsco.2002.0560}
}

@Article{Kem99,
  author        = {Kemper, Gregor},
  title         = {An algorithm to calculate optimal homogeneous systems of parameters},
  journal       = {J. Symbolic Comput.},
  fjournal      = {Journal of Symbolic Computation},
  volume        = {27},
  number        = {2},
  pages         = {171--184},
  year          = {1999},
  doi           = {10.1006/jsco.1998.0247}
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@Article{Kin07,
  author        = {King, Simon},
  title         = {Fast computation of secondary invariants},
  journal       = {arXiv:math/0701270},
  year          = {2007},
  doi           = {10.48550/arXiv.math/0701270},
  primaryclass  = {math.AC}
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@Article{Kin13,
  author        = {King, Simon},
  title         = {Minimal generating sets of non-modular invariant rings of finite groups},
  journal       = {J. Symb. Comput.},
  fjournal      = {Journal of Symbolic Computation},
  volume        = {48},
  publisher     = {Elsevier (Academic Press), London},
  pages         = {101--109},
  year          = {2013},
  doi           = {10.1016/j.jsc.2012.05.002}
}

@Book{Knu11,
  author        = {Knuth, Donald E.},
  title         = {The art of computer programming. {V}ol. 4{A}. {C}ombinatorial algorithms. {P}art 1},
  publisher     = {Addison-Wesley, Upper Saddle River, NJ},
  pages         = {xv+883},
  year          = {2011}
}

@Book{Kol13,
  author        = {Kollár, János},
  title         = {Singularities of the minimal model program},
  series        = {Cambridge Tracts in Mathematics},
  volume        = {200},
  note          = {With a collaboration of Sándor Kovács},
  publisher     = {Cambridge University Press},
  year          = {2013},
  location      = {Cambridge}
}

@Book{Koz08,
  author        = {Kozlov, Dmitry},
  title         = {Combinatorial algebraic topology},
  series        = {Algorithms and Computation in Mathematics},
  volume        = {21},
  publisher     = {Springer, Berlin},
  year          = {2008},
  doi           = {10.1007/978-3-540-71962-5}
}

@Book{LN97,
  author        = {Lidl, Rudolf and Niederreiter, Harald},
  title         = {Finite fields},
  series        = {Encyclopedia of Mathematics and its Applications},
  volume        = {20},
  note          = {With a foreword by P. M. Cohn},
  publisher     = {Cambridge University Press, Cambridge},
  edition       = {Second},
  pages         = {xiv+755},
  year          = {1997}
}

@InCollection{LS03,
  author        = {Levandovskyy, Viktor and Schönemann, Hans},
  title         = {Plural -- a computer algebra system for noncommutative polynomial algebras},
  booktitle     = {Proceedings of the 2003 international symposium on symbolic and algebraic computation, ISSAC 2003,
                  Philadelphia, PA, USA, August 3--6, 2003.},
  zbl           = {1072.68681},
  publisher     = {New York, NY: ACM Press},
  pages         = {176--183},
  year          = {2003},
  language      = {English},
  zbmath        = {2151198}
}

@Article{LS13,
  author        = {Lawrie, Craig and Sch\"afer-Nameki, Sakura},
  title         = {{The Tate Form on Steroids: Resolution and Higher Codimension Fibers}},
  journal       = {JHEP},
  volume        = {04},
  pages         = {061},
  year          = {2013},
  doi           = {10.1007/JHEP04(2013)061},
  eprint        = {1212.2949},
  archiveprefix = {arXiv},
  primaryclass  = {hep-th},
  reportnumber  = {KCL-MTH-12-14}
}

@PhDThesis{Lev05,
  author        = {Viktor Levandovskyy},
  title         = {Non-commutative Computer Algebra for polynomial algebras: Gröbner bases, applications and
                  implementation},
  year          = {2005},
  url           = {http://nbn-resolving.de/urn:nbn:de:hbz:386-kluedo-18830},
  type          = {doctoralthesis},
  school        = {Technische Universität Kaiserslautern}
}

@Book{Liu06,
  author        = {Liu, Qing},
  title         = {Algebraic geometry and arithmetic curves. Transl. by Reinie Erné},
  zbl           = {1103.14001},
  series        = {Oxf. Grad. Texts Math.},
  volume        = {6},
  publisher     = {Oxford: Oxford University Press},
  year          = {2006},
  fseries       = {Oxford Graduate Texts in Mathematics},
  language      = {English},
  zbmath        = {5048200}
}

@Book{Loo84,
  author        = {Looijenga, Eduard},
  title         = {Isolated Singular Points on Complete Intersections},
  series        = {LMS Lecture Note Series},
  volume        = {77},
  publisher     = {Cambridge University Press, Cambridge},
  pages         = {xi+200},
  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},
  zbl           = {1445.14085},
  journal       = {Found. Comput. Math.},
  fjournal      = {Foundations of Computational Mathematics},
  volume        = {20},
  number        = {4},
  pages         = {783--800},
  year          = {2020},
  doi           = {10.1007/s10208-019-09430-2},
  language      = {English},
  zbmath        = {7244216}
}

@Book{MS05,
  author        = {Miller, Ezra and Sturmfels, Bernd},
  title         = {Combinatorial commutative algebra},
  zbl           = {1066.13001},
  journal       = {Grad. Texts Math.},
  fjournal      = {Graduate Texts in Mathematics},
  volume        = {227},
  publisher     = {New York, NY: Springer},
  pages         = {xiv + 417},
  year          = {2005},
  doi           = {10.1007/b138602}
}

@Book{MS15,
  author        = {Maclagan, Diane and Sturmfels, Bernd},
  title         = {Introduction to tropical geometry},
  journal       = {Grad. Stud. Math.},
  fjournal      = {Graduate Studies in Mathematics},
  volume        = {161},
  publisher     = {Providence, RI: American Mathematical Society (AMS)},
  pages         = {xii + 363},
  year          = {2015}
}

@Book{MS21,
  author        = {Michałek, Mateusz and Sturmfels, Bernd},
  title         = {Invitation to nonlinear algebra},
  journal       = {Grad. Stud. Math.},
  fjournal      = {Graduate Studies in Mathematics},
  volume        = {211},
  publisher     = {Providence, RI: American Mathematical Society (AMS)},
  pages         = {xiii + 226},
  year          = {2021}
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@Book{Mar18,
  author        = {Marcus, Daniel A.},
  title         = {Number fields},
  series        = {Universitext},
  note          = {Second edition of [ MR0457396], With a foreword by Barry Mazur},
  publisher     = {Springer, Cham},
  pages         = {xviii+203},
  year          = {2018},
  doi           = {10.1007/978-3-319-90233-3}
}

@Article{Nik79,
  author        = {Nikulin, V. V.},
  title         = {Integer symmetric bilinear forms and some of their geometric applications},
  mrnumber      = {525944},
  journal       = {Izv. Akad. Nauk SSSR Ser. Mat.},
  fjournal      = {Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya},
  volume        = {43},
  number        = {1},
  pages         = {111--177, 238},
  year          = {1979}
}

@Misc{OEIS,
  bibkey        = {OEIS},
  author        = {{OEIS Foundation Inc.}},
  title         = {The {O}n-{L}ine {E}ncyclopedia of {I}nteger {S}equences},
  howpublished  = {Published electronically at \url{https://oeis.org}},
  year          = {2024},
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@Book{OM78,
  author        = {Oda, T. and Miyake, K.},
  title         = {Lectures on Torus Embeddings and Applications},
  series        = {Lectures on mathematics and physics},
  publisher     = {Tata Institute of Fundamental Research},
  year          = {1978},
  url           = {https://mathweb.tifr.res.in/sites/default/files/publications/ln/tifr58.pdf},
  lccn          = {lc81901205}
}

@Article{OMdCS00,
  bibkey        = {OMdCS00},
  author        = {Ojeda Martínez de Castilla, Ignacio and Sánchez, Ramón Peidra},
  title         = {Cellular binomial ideals. Primary decomposition of binomial ideals},
  journal       = {J. Symbolic Comput.},
  fjournal      = {Journal of Symbolic Computation},
  volume        = {30},
  number        = {4},
  pages         = {383--400},
  year          = {2000},
  doi           = {10.1006/jsco.1999.0413}
}

@Book{Oxl11,
  author        = {Oxley, James},
  title         = {Matroid theory},
  mrnumber      = {2849819},
  series        = {Oxford Graduate Texts in Mathematics},
  volume        = {21},
  publisher     = {Oxford University Press, Oxford},
  edition       = {Second},
  pages         = {xiv+684},
  year          = {2011},
  doi           = {10.1093/acprof:oso/9780198566946.001.0001}
}

@Article{PS09,
  author        = {Postnikov, Alexander and Stanley, Richard P.},
  title         = {Chains in the {B}ruhat order},
  mrnumber      = {2475632},
  journal       = {J. Algebraic Combin.},
  volume        = {29},
  number        = {2},
  pages         = {133--174},
  year          = {2009},
  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--Chvátal rank},
  journal       = {Operations research letters},
  volume        = {39},
  number        = {6},
  publisher     = {Elsevier},
  pages         = {457--460},
  year          = {2011},
  doi           = {10.1016/j.orl.2011.09.004}
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@Article{PSS11,
  author        = {Pfister, Gerhard and Sadiq, Afshan and Steidel, Stefan},
  title         = {An algorithm for primary decomposition in polynomial rings over the integers},
  journal       = {Cent. Eur. J. Math.},
  fjournal      = {Central European Journal of Mathematics},
  volume        = {9},
  number        = {4},
  pages         = {897--904},
  year          = {2011},
  doi           = {10.2478/s11533-011-0037-8}
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@Book{PZ97,
  author        = {Pohst, M. and Zassenhaus, H.},
  title         = {Algorithmic algebraic number theory},
  series        = {Encyclopedia of Mathematics and its Applications},
  volume        = {30},
  note          = {Revised reprint of the 1989 original},
  publisher     = {Cambridge University Press, Cambridge},
  pages         = {xiv+499},
  year          = {1997}
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@Misc{Pan23,
  author        = {Pan, Eileen},
  title         = {SOTGrps, Constructing and identifying groups of small order type, Version 1.2},
  note          = {GAP package},
  year          = {2023},
  month         = {6},
  url           = {https://gap-packages.github.io/sotgrps/}
}

@MastersThesis{Peg14,
  author        = {Pegel, Christoph},
  title         = {Chow Rings of Toric Varieties},
  note          = {Refereed by Prof. Dr. Eva Maria Feichtner and Dr. Emanuele Delucchi},
  address       = {Faculty of Mathematics},
  year          = {2014},
  month         = {9},
  school        = {University of Bremen}
}

@Article{Pol56,
  bibkey        = {Pol56},
  author        = {Pólya, G.},
  title         = {On picture-writing},
  mrnumber      = {81865},
  journal       = {Amer. Math. Monthly},
  fjournal      = {American Mathematical Monthly},
  volume        = {63},
  pages         = {689--697},
  year          = {1956},
  doi           = {10.2307/2309555}
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@PhDThesis{Pop93,
  author        = {Popescu, Sorin},
  title         = {On smooth surfaces of degree $\geq 11$ in the projective fourspace},
  year          = {1993},
  url           = {https://www.math.stonybrook.edu/~sorin/eprints/thesis.pdf},
  type          = {doctoralthesis},
  school        = {Universität des Saarlandes, Saarbrücken}
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@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}
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@Article{Pos18,
  author        = {Posur, Sebastian},
  title         = {Linear systems over localizations of rings},
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  volume        = {111},
  pages         = {23--32},
  year          = {2018},
  doi           = {10.1007/s00013-018-1183-z}
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@Article{RJ76,
  author        = {Riha, W. and James, K. R.},
  title         = {Algorithm 29 efficient algorithms for doubly and multiply restricted partitions},
  journal       = {Computing},
  volume        = {16},
  pages         = {163--168},
  year          = {1976},
  doi           = {10.1007/BF02241987}
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@Article{RR10,
  author        = {Roschy, Helmut and Rahn, Thorsten},
  title         = {Cohomology of line bundles: Proof of the algorithm},
  journal       = {Journal of Mathematical Physics},
  volume        = {51},
  number        = {10},
  publisher     = {AIP Publishing},
  pages         = {103520},
  year          = {2010},
  month         = {Oct},
  doi           = {10.1063/1.3501135}
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@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}
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@Article{Rin13,
  author        = {Rinc{\'o}n, Felipe},
  title         = {Computing tropical linear spaces},
  zbl           = {1319.14060},
  journal       = {J. Symb. Comput.},
  fjournal      = {Journal of Symbolic Computation},
  volume        = {51},
  pages         = {86--98},
  year          = {2013},
  doi           = {10.1016/j.jsc.2012.03.008},
  language      = {English},
  zbmath        = {6143064}
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@Book{SS03,
  author        = {Semple, Charles and Steel, Mike},
  title         = {Phylogenetics},
  series        = {Oxf. Lect. Ser. Math. Appl.},
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