X. Allamigeon, P. Benchimol, S. Gaubert and M. Joswig. Log-barrier interior point methods are not strongly polynomial. SIAM Journal on Applied Algebra and Geometry 2, 140–178 (2018).

D. Avis, D. Bremner and R. Seidel. How good are convex hull algorithms? Comput. Geom. 7, 265–301 (1997). 11th ACM Symposium on Computational Geometry (Vancouver, BC, 1995).

I. V. Arzhantsev and S. A. Gaĭfullin. Cox rings, semigroups, and automorphisms of affine varieties. Mat. Sb. 201, 3–24 (2010).

B. Amrhein, O. Gloor and W. Küchlin. Walking faster. In: Design and Implementation of Symbolic Computation Systems, DISCO 1996 (Springer Berlin, Heidelberg, Heidelberg, Germany, 1996); pp. 150–161.

B. Amrhein, O. Gloor and W. Küchlin. On the walk. Theoretical Computer Science 187, 179–202 (1997).

K. Adiprasito, J. Huh and E. Katz. Hodge theory for combinatorial geometries. Ann. of Math. (2) 188, 381–452 (2018).

W. W. Adams and P. Loustaunau. An Introduction to Gröbner Bases. Graduate studies in mathematics (American Mathematical Society, 1994).

R. A. Wilson, P. Walsh, J. Tripp, I. Suleiman, R. A. Parker, S. P. Norton, S. Nickerson, S. Linton, J. Bray and R. Abbott. ATLAS of Finite Group Representations. Published electronically.

N. Amenta and G. M. Ziegler. Deformed products and maximal shadows of polytopes. Contemporary Mathematics 223, 57–90 (1999).

M. Bayer, A. Bruening and J. Stewart. A Combinatorial Study of Multiplexes and Ordinary Polytopes. Discrete & Computational Geometry 27, 49–63 (2002).

M. Bies, M. Cvetič and M. Liu. Statistics of limit root bundles relevant for exact matter spectra of F-theory MSSMs. Phys. Rev. D 104, L061903 (2021).

N. Berry, A. Dubickas, N. D. Elkies, B. Poonen and C. Smyth. The conjugate dimension of algebraic numbers. Q. J. Math. 55, 237–252 (2004).

J. Böhm, W. Decker, S. Laplagne and G. Pfister. Local to global algorithms for the Gorenstein adjoint ideal of a curve. In: Algorithmic and experimental methods in algebra, geometry, and number theory (Springer, Cham, 2017); pp. 51–96.

J. Böhm, W. Decker, S. Laplagne and G. Pfister. Computing integral bases via localization and Hensel lifting. In: MEGA 2019 - International Conference on Effective Methods in Algebraic Geometry (Madrid, Spain, 2019). HAL:hal-02912148.

J. Böhm, W. Decker, S. Laplagne, G. Pfister, A. Steenpaß and S. Steidel. Parallel algorithms for normalization. Journal of Symbolic Computation 51, 99–114 (2013). Effective Methods in Algebraic Geometry.

S. Brandhorst and N. D. Elkies. Equations for a K3 Lehmer map. J. Algebraic Geom. 32, 641–675 (2023).

H. U. Besche, B. Eick and E. O'Brien. SmallGrp, The GAP Small Groups Library, Version 1.5.3 (May 2023). GAP package.

J. Berthomieu, C. Eder and M. Safey El Din. Msolve: A Library for Solving Polynomial Systems. In: Proceedings of the 2021 on International Symposium on Symbolic and Algebraic Computation, ISSAC '21 (Association for Computing Machinery, New York, NY, USA, 2021); pp. 51–58.

S. Backman, C. Eur and C. Simpson. Simplicial generation of Chow rings of matroids. JEMS 26, 4491–4535 (2023).

J. L. Bueso, J. Gómez-Torrecillas and A. Verschoren. Algorithmic methods in non-commutative algebra. Applications to quantum groups. Vol. 17 of Math. Model.: Theory Appl. (Dordrecht: Kluwer Academic Publishers, 2003).

W. Bruns and J. Herzog. Cohen-Macaulay rings. Vol. 39 of Cambridge Studies in Advanced Mathematics (Cambridge University Press, Cambridge, 2009). 2nd edition.

S. Brandhorst and T. Hofmann. Finite subgroups of automorphisms of K3 surfaces. Forum of Mathematics, Sigma 11, e54 1–57 (2023).

T. Braden, J. Huh, J. P. Matherne, N. Proudfoot and B. Wang. A semi-small decomposition of the Chow ring of a matroid. Advances in Mathematics 409, 108646 (2022).

W. P. Barth, K. Hulek, C. A. Peters and A. Van de Ven. Compact complex surfaces. 2nd enlarged ed. Edition, Vol. 4 of Ergeb. Math. Grenzgeb., 3. Folge (Berlin: Springer, 2004).

R. Blumenhagen, B. Jurke, T. Rahn and H. Roschy. Cohomology of line bundles: A computational algorithm. Journal of Mathematical Physics 51, 103525 (2010).

R. Blumenhagen, B. Jurke, T. Rahn and H. Roschy, cohomCalg package. Published electronically on GitHub (2010). High-performance line bundle cohomology computation based on BJRR10.

R. Blumenhagen, B. Jurke, T. Rahn and H. Roschy. Cohomology of line bundles: Applications. Journal of Mathematical Physics 53, 012302 (2012).

T. Bogart, A. N. Jensen, D. Speyer, B. Sturmfels and R. R. Thomas. Computing tropical varieties. J. Symb. Comput. 42, 54–73 (2007).

J. Böhm, S. Keicher and Y. Ren. Computing GIT-fans with symmetry and the Mori chamber decomposition of $\overline M_{0,6}$. Math. Comp. 89, 3003–3021 (2020).

L. J. Billera and C. W. Lee. A proof of the sufficiency of McMullen's conditions for $f$-vectors of simplicial convex polytopes. J. Combin. Theory Ser. A 31, 237–255 (1981).

M. Baker and S. Norine. Riemann-Roch and Abel-Jacobi theory on a finite graph. Adv. Math. 215, 766–788 (2007).

T. Banica and R. Speicher. Liberation of orthogonal Lie groups. Advances in Mathematics 222, 1461–1501 (2009).

S. Brandhorst and M. Zach. Elliptic fibrations on Vinberg's most algebraic K3 surface (2023), arXiv:2311.11766 [math.AG].

D. J. Benson. Polynomial invariants of finite groups. Vol. 190 of London Mathematical Society Lecture Note Series (Cambridge University Press, Cambridge, 1993).

J. Böhm. Parametrisierung rationaler Kurven. Diploma Thesis, Universität Bayreuth (1999).

M. Bies. Cohomologies of coherent sheaves and massless spectra in F-theory. Ph.D. Thesis, Heidelberg U. (Feb 2018).

M. Bies. Root bundles: Applications to F-theory Standard Models. Proc. Symp. Pure Math. 107, 17–44 (2024), arXiv:2303.08144 [hep-th].

T. Bisztriczky. On a class of generalized simplices. Mathematika 43, 274–285 (1996).

W. Burnside. Theory of groups of finite order (Dover Publications, Inc., New York, 1911); p. xxiv+512. 2d ed.

J. L. Cisneros Molina, D. T. Le and J. Seade. Handbook of Geometry and Topology of Singularities I (Springer-Verlag, Cham, 2020); p. xviii+601.

J. L. Cisneros Molina, D. T. Le and J. Seade. Handbook of Geometry and Topology of Singularities II (Springer-Verlag, Cham, 2021); p. xii+578.

J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker and R. A. Wilson. Atlas of finite groups (Oxford University Press, Eynsham, 1985); p. xxxiv+252. Maximal subgroups and ordinary characters for simple groups, With computational assistance from J. G. Thackray.

M. Cvetič, J. Halverson, L. Lin, M. Liu and J. Tian. Quadrillion $F$-Theory Compactifications with the Exact Chiral Spectrum of the Standard Model. Phys. Rev. Lett. 123, 101601 (2019), arXiv:1903.00009 [hep-th].

J. H. Conway, A. Hulpke and J. McKay. On transitive permutation groups. LMS J. Comput. Math. 1, 1–8 (1998).

S. Collart, M. Kalkbrener and D. Mall. Converting Bases with the Gröbner Walk. Journal of Symbolic Computation 24, 465–469 (1997).

D. A. Cox, J. Little and D. O'Shea. Using Algebraic Geometry. Vol. 185 of Graduate Texts in Mathematics (Springer-Verlag, 2005).

D. A. Cox, J. B. Little and H. K. Schenck. Toric varieties. Vol. 124 of Graduate Studies in Mathematics (Providence, RI: American Mathematical Society (AMS), 2011); p. xxiv+841.

B. Collins, J. A. Mingo, P. Śniady and R. Speicher. Second order freeness and fluctuations of random matrices. III: Higher order freeness and free cumulants. Documenta Mathematica 12, 1–70 (2007).

A. M. Cohen, S. H. Murray and D. E. Taylor. Computing in groups of Lie type. Math. Comp. 73, 1477–1498 (2004).

J. H. Conway and N. J. Sloane. Sphere packings, lattices and groups. Third Edition, Vol. 290 of Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences] (Springer-Verlag, New York, 1999); p. lxxiv+703. 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.

C. Ceballos, F. Santos and G. M. Ziegler. Many non-equivalent realizations of the associahedron. Combinatorica 35, 513–551 (2015).

G. Cébron and M. Weber. Quantum groups based on spatial partitions (2016), arXiv:1609.02321 [math.QA].

P. J. Cameron. Permutation groups. Vol. 45 of London Mathematical Society Student Texts (Cambridge University Press, Cambridge, 1999); p. x+220.

J. A. Christophersen. On the components and discriminant of the versal base space of cyclic quotient singularities. In: Singularity theory and its applications, Part I (Coventry, 1988/1989), Vol. 1462 of Lecture Notes in Math. (Springer, Berlin, 1991); pp. 81–92.

H. Cohen. Advanced topics in computational number theory. Vol. 193 of Graduate Texts in Mathematics (Springer-Verlag, New York, 2000); p. xvi+578.

H. Cohen. A course in computational algebraic number theory. Vol. 138 of Graduate Texts in Mathematics (Springer-Verlag, Berlin, 1993); p. xii+534.

D. Corey. Initial degenerations of Grassmannians. Sel. Math. New Ser. 27 (2021).

S. D. Cutkosky. Resolution of singularities. Vol. 63 of Graduate Studies in Mathematics (American Mathematical Society, Providence, RI, 2004); p. viii+186.

W. Decker and D. Eisenbud. Sheaf algorithms using the exterior algebra. In: Computations in algebraic geometry with Macaulay 2 (Berlin: Springer, 2002); pp. 215–249.

W. Decker, L. Ein and F.-O. Schreyer. Construction of surfaces in ${\mathbb P}^4$. J. Algebr. Geom. 2, 185–237 (1993).

G. De Franceschi. Centralizers and conjugacy classes in finite classical groups (2020), arXiv:2008.12651 [math.GR].

A. S. Detinko, D. L. Flannery and E. A. O'Brien. Recognizing finite matrix groups over infinite fields. J. Symbolic Comput. 50, 100–109 (2013).

W. Decker, G.-M. Greuel and G. Pfister. Primary decomposition: algorithms and comparisons. In: Algorithmic algebra and number theory. Selected papers from a conference, Heidelberg, Germany, October 1997 (Springer, Berlin, 1999); pp. 187–220.

M. Domokos and P. Hegedűs. Noether's bound for polynomial invariants of finite groups. Arch. Math. (Basel) 74, 161–167 (2000).

W. Decker, A. E. Heydtmann and F.-O. Schreyer. Generating a Noetherian normalization of the invariant ring of a finite group. J. Symbolic Comput. 25, 727–731 (1998).

W. Decker and T. de Jong. Gröbner bases and invariant theory. In: 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, Vol. 251 of London Math. Soc. Lecture Note Ser. (Cambridge Univ. Press, Cambridge, 1998); pp. 61–89.

H. Derksen and G. Kemper. 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, enlarged Edition, Vol. 130 of Encyclopaedia of Mathematical Sciences (Springer, Heidelberg, 2015); p. xxii+366.

M. Donten-Bury and S. Keicher. Computing resolutions of quotient singularities. J. Algebra 472, 546–572 (2017).

W. Decker and C. Lossen. Computing in algebraic geometry. A quick start using SINGULAR. Vol. 16 of Algorithms and Computation in Mathematics (Springer-Verlag, Berlin; Hindustan Book Agency, New Delhi, 2006); p. xvi+327.

J. A. De Loera, J. Rambau and F. Santos. Triangulations. Structures for algorithms and applications. Vol. 25 of Algorithms and Computation in Mathematics (Springer-Verlag, Berlin, 2010); p. xiv+535.

W. Decker and G. Pfister. A first course in computational algebraic geometry. African Institute of Mathematics (AIMS) Library Series (Cambridge University Press, Cambridge, 2013); p. viii+118.

W. Decker and F.-O. Schreyer. Non-general type surfaces in ${\mathbb P}^4$: Some remarks on bounds and constructions. J. Symb. Comput. 29, 545–582 (2000).

M. Drton, B. Sturmfels and S. Sullivant. Lectures on algebraic statistics. Vol. 39 of Oberwolfach Semin. (Basel: Birkhäuser, 2009).

H. Derksen. Computation of invariants for reductive groups. Adv. Math. 141, 366–384 (1999).

D. Eisenbud, G. Fløystad and F.-O. Schreyer. Sheaf cohomology and free resolutions over exterior algebras. Trans. Am. Math. Soc. 355, 4397–4426 (2003).

D. Eisenbud and J. Harris. 3264 and all that. A second course in algebraic geometry (Cambridge: Cambridge University Press, 2016).

D. Eisenbud, C. Huneke and B. Ulrich. What is the Rees algebra of a module? Proc. Am. Math. Soc. 131, 701–708 (2003).

D. Eisenbud, C. Huneke and W. Vasconcelos. Direct methods for primary decomposition. Invent. Math. 110, 207–235 (1992).

Z. S. Eser and L. F. Matusevich. Decompositions of cellular binomial ideals. J. Lond. Math. Soc. (2) 94, 409–426 (2016).

Z. S. Eser and L. F. Matusevich. Corrigendum: Decompositions of cellular binomial ideals: (J. Lond. Math. Soc. 94 (2016) 409–426). J. Lond. Math. Soc. (2) 100, 717–719 (2019).

B. Eröcal, O. Motsak, F.-O. Schreyer and A. Steenpaß. Refined algorithms to compute syzygies. J. Symb. Comput. 74, 308–327 (2016).

D. Eisenbud and B. Sturmfels. Binomial ideals. Duke Math. J. 84, 1–45 (1996).

D. Eisenbud. Commutative algebra. With a view toward algebraic geometry. Vol. 150 (Berlin: Springer-Verlag, 1995); p. xvi + 785.

D. Eisenbud. Computing cohomology. A chapter in W. Vasconcelos, Computational methods in commutative algebra and algebraic geometry (Berlin: Springer, 1998); pp. 209–216.

J. Faugère, P. Gianni, D. Lazard and T. Mora. Efficient Computation of Zero-dimensional Gröbner Bases by Change of Ordering. Journal of Symbolic Computation 16, 329–344 (1993).

K. Fukuda, A. N. Jensen, N. Lauritzen and R. Thomas. The generic Gröbner walk. Journal of Symbolic Computation 42, 298–312 (2007).

H. Fan, T. Jarvis and Y. Ruan. A mathematical theory of the gauged linear sigma model. Geometry & Topology 22, 235–303 (2017).

K. Fukuda, A. N. Jensen and R. R. Thomas. Computing Groebner Fans. Math. Comp. 76, 2189–2213 (2007).

W. B. Hart. Fast Library for Number Theory: An Introduction. In: Proceedings of the Third International Congress on Mathematical Software, ICMS'10 (Springer-Verlag, Berlin, Heidelberg, 2010); pp. 88–91, https://flintlib.org.

A. Frühbis-Krüger, L. Ristau and B. Schober. Embedded desingularization for arithmetic surfaces—toward a parallel implementation. Math. Comp. 90, 1957–1997 (2021).

E. M. Feichtner and S. Yuzvinsky. Chow rings of toric varieties defined by atomic lattices. Inventiones Mathematicae 155, 515–536 (2004).

J.-C. Faugère. A new efficient algorithm for computing Gröbner bases (F4). Journal of Pure and Applied Algebra 139, 61–88 (1999). HAL:hal-01148855.

W. Fulton. Algebraic curves. An introduction to algebraic geometry. Mathematics Lecture Note Series (W. A. Benjamin, Inc., New York-Amsterdam, 1969); p. xiii+226. Notes written with the collaboration of Richard Weiss.

W. Fulton. Young tableaux. Vol. 35 of London Mathematical Society Student Texts (Cambridge University Press, Cambridge, 1997); p. x+260. With applications to representation theory and geometry.

W. Fulton. Intersection theory. Second Edition, Vol. 2 of 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] (Springer-Verlag, Berlin, 1998); p. xiv+470.

T. W. Grimm and H. Hayashi. F-theory fluxes, chirality and Chern-Simons theories. Journal of High Energy Physics 2012 (2012).

E. Gawrilow, S. Hampe and M. Joswig. The polymake XML File Format. In: Mathematical Software – ICMS 2016, edited by G.-M. Greuel, T. Koch, P. Paule and A. Sommese (Springer International Publishing, Cham, 2016); pp. 403–410.

W. A. de Graaf, G. Ivanyos and L. Rónyai. Computing Cartan subalgebras of Lie algebras. Appl. Algebra Eng. Commun. Comput. 7, 339–349 (1996).

E. Gawrilow and M. Joswig, polymake: a Framework for Analyzing Convex Polytopes. In: Polytopes — Combinatorics and Computation, edited by G. Kalai and G. M. Ziegler (Birkhäuser, 2000); pp. 43–74, https://polymake.org.

E. Gawrilow, M. Joswig, T. Rörig and N. Witte. Drawing polytopal graphs with polymake. Comput. Vis. Sci. 13, 99–110 (2010), arXiv:0711.2397.

Y. Giannakopoulos and E. Koutsoupias. Duality and optimality of auctions for uniform distributions. In: Proceedings of the fifteenth ACM conference on Economics and computation (Association for Computing Machinery, New York, 2014); pp. 259–276.

G.-M. Greuel, C. Lossen and E. Shustin. Introduction to Singularities and Deformations. Springer Monographs in Mathematics (Springer-Verlag, Berlin, 2007); p. xii+471.

G.-M. Greuel, S. Laplagne and F. Seelisch. Normalization of rings. J. Symbolic Comput. 45, 887–901 (2010).

G.-M. Greuel and G. Pfister. A Singular introduction to commutative algebra. With contributions by Olaf Bachmann, Christoph Lossen and Hans Schönemann. 2nd extended ed. (Springer, Berlin, 2008); p. xx+689. With 1 CD-ROM (Windows, Macintosh and UNIX).

D. Goldfarb and W. Y. Sit. Worst case behavior of the steepest edge simplex method. Discrete Applied Mathematics 1, 277–285 (1979).

D. R. Grayson, A. Seceleanu and M. E. Stillman. Computations in intersection rings of flag bundles (2022), arXiv:1205.4190 [math.AG].

P. Gianni, B. Trager and G. Zacharias. Gröbner bases and primary decomposition of polynomial ideals. In: Computational aspects of commutative algebra, Vol. 6 (Elsevier Ltd, Oxford, 1988); pp. 149–167.

U. Görtz and T. Wedhorn. Algebraic Geometry I: Schemes with Examples and Exercises. 2 Edition (Springer Spektrum, 2020).

A. Gathmann. Class notes „Plane Algebraic Curves” (SS 2018). Published electronically (2018).

K. Gatermann. Semi-invariants, equivariants and algorithms. Appl. Algebra Engrg. Comm. Comput. 7, 105–124 (1996).

W. A. de Graaf. Lie algebras: theory and algorithms. Vol. 56 of North-Holland Mathematical Library (North-Holland Publishing Co., Amsterdam, 2000); p. xii+393.

D. Gromada. Compact matrix quantum groups and their representation categories, doctoralthesis, Universität des Saarlandes (2020).

B. Grünbaum. Convex polytopes. Second Edition, Vol. 221 of Graduate Texts in Mathematics (Springer-Verlag, New York, 2003); p. xvi+468. Prepared and with a preface by Volker Kaibel, Victor Klee and Günter M. Ziegler.

D. F. Holt, B. Eick and E. A. O'Brien. Handbook of computational group theory. Discrete Mathematics and its Applications (Boca Raton) (Chapman & Hall/CRC, Boca Raton, FL, 2005); p. xvi+514.

J. Hausen, E. Herppich and H. Süss. Multigraded factorial rings and Fano varieties with torus action. Doc. Math. 16, 71–109 (2011).

G. Horrocks and D. Mumford. A rank 2 vector bundle on $\text{P}^4$ with 15,000 symmetries. Topology 12, 63–81 (1973).

D. F. Holt and W. Plesken. Perfect groups. Oxford Mathematical Monographs (The Clarendon Press, Oxford University Press, New York, 1989); p. xii+364. With an appendix by W. Hanrath, Oxford Science Publications.

A. Hulpke, C. Roney-Dougal and C. Russell. PrimGrp, GAP Primitive Permutation Groups Library, Version 3.4.4 (Feb 2023). GAP package.

J. Halverson and J. Tian. Cost of seven-brane gauge symmetry in a quadrillion F-theory compactifications. Phys. Rev. D 95, 026005 (2017), arXiv:1610.08864 [hep-th].

R. Hartshorne. Algebraic Geometry. Graduate Texts in Mathematics (Springer-Verlag, New York, 1977); p. xvi+496.

H. Hasse. Noch eine Begründung der Theorie der höheren Differentialquotienten in einem algebraischen Funktionenkörper einer Unbestimmten. (Nach einer brieflichen Mitteilung von F. K. Schmidt in Jena). J. Reine Angew. Math. 177, 215–237 (1937).

M. Hazewinkel. Hasse-Schmidt Derivations and the Hopf Algebra of Non-Commutative Symmetric Functions. Axioms 1, 149–154 (2012).

A. Hulpke. The perfect groups of order up to two million. Math. Comp. 91, 1007–1017 (2022).

A. Hulpke. TransGrp, Transitive Groups Library, Version 3.6.5 (Dec 2023). GAP package.

J. E. Humphreys. Introduction to Lie Algebras and Representation Theory. Vol. 9 of Graduate Texts in Mathematics (Springer-Verlag, New York, 1972); p. xii+169.

B. Huppert. Endliche Gruppen. I. Vol. 134 of Die Grundlehren der mathematischen Wissenschaften (Springer-Verlag, Berlin-New York, 1967); p. xii+793.

D. Huybrechts. Lectures on K3 surfaces. Vol. 158 of Cambridge Studies in Advanced Mathematics (Cambridge University Press, Cambridge, 2016); p. xi+485.

Y. Ito and M. Reid. The McKay correspondence for finite subgroups of $\mathrm{SL}(3,\mathbb C)$. In: Higher-dimensional complex varieties (Trento, 1994) (de Gruyter, 1996); pp. 221–240.

M. Joswig, M. Klimm and S. Spitz. Generalized permutahedra and optimal auctions. SIAM Journal on Applied Algebra and Geometry 6, 711–739 (2022).

M. Joswig, D. Lofano, F. H. Lutz and M. Tsuruga. Frontiers of sphere recognition in practice. J. Appl. Comput. Topol. 6, 503–527 (2022).

C. Jansen, K. Lux, R. Parker and R. Wilson. An atlas of Brauer characters. Vol. 11 of London Mathematical Society Monographs. New Series (The Clarendon Press Oxford University Press, New York, 1995); p. xviii+327. Appendix 2 by T. Breuer and S. Norton, Oxford Science Publications.

T. de Jong and G. Pfister. Local Analytic Geometry. Advanced Lectures in Mathematics (Vieweg+Teubner Verlag, 2000); p. xi+384.

M. Joswig and T. Theobald. Polyhedral and algebraic methods in computational geometry. Universitext (Springer, London, 2013); p. x+250. Revised and updated translation of the 2008 German original.

M. Joswig and G. M. Ziegler. Neighborly Cubical Polytopes. Discrete & Computational Geometry  24, 325–344 (2000).

F. Johansson. Efficient implementation of the Hardy-Ramanujan-Rademacher formula. LMS J. Comput. Math. 15, 341–359 (2012).

M. Joswig. Beneath-and-Beyond Revisited. In: Algebra, Geometry and Software Systems, edited by M. Joswig and N. Takayama (Springer Berlin Heidelberg, Berlin, Heidelberg, 2003); pp. 1–21.

M. Joswig. Polytope propagation on graphs. In: Algebraic statistics for computational biology. (Cambridge: Cambridge University Press, 2005); pp. 181–192.

M. Joswig. Essentials of tropical combinatorics. Vol. 219 of Graduate Studies in Mathematics (American Mathematical Society, Providence, RI, 2021).

S.-Y. Jow. Cohomology of toric line bundles via simplicial Alexander duality. Journal of Mathematical Physics 52, 033506 (2011).

T. Krick and A. Logar. An algorithm for the computation of the radical of an ideal in the ring of polynomials. In: Applied algebra, algebraic algorithms and error-correcting codes (New Orleans, LA, 1991), Vol. 539 of Lecture Notes in Comput. Sci. (Springer, Berlin, 1991); pp. 195–205.

M. Kaluba, B. Lorenz and S. Timme. Polymake.jl: A New Interface to polymake. In: Mathematical Software – ICMS 2020, edited by A. M. Bigatti, J. Carette, J. H. Davenport, M. Joswig and T. de Wolff (Springer International Publishing, Cham, 2020); pp. 377–385.

D. Klevers, D. K. Mayorga Pena, P.-K. Oehlmann, H. Piragua and J. Reuter. F-Theory on all Toric Hypersurface Fibrations and its Higgs Branches. JHEP 01, 142 (2015), arXiv:1408.4808 [hep-th].

S. Katz, D. R. Morrison, S. Schafer-Nameki and J. Sully. Tate's algorithm and F-theory. JHEP 08, 094 (2011), arXiv:1106.3854 [hep-th].

J. Kelleher and B. O'Sullivan. Generating All Partitions: A Comparison Of Two Encodings (2014), arXiv:0909.2331 [cs.DS].

M. Kreuzer and L. Robbiano. Computational commutative algebra. II (Berlin: Springer, 2005); p. x + 586.

G. Kemper and A. Steel. Some algorithms in invariant theory of finite groups. In: Computational methods for representations of groups and algebras (Essen, 1997), Vol. 173 of Progr. Math. (Birkhäuser, Basel, 1999); pp. 267–285.

T. Kahle. Decompositions of binomial ideals. Ann. Inst. Statist. Math. 62, 727–745 (2010).

G. Kemper. The calculation of radical ideals in positive characteristic. J. Symbolic Comput. 34, 229–238 (2002).

G. Kemper. An algorithm to calculate optimal homogeneous systems of parameters. J. Symbolic Comput. 27, 171–184 (1999).

S. King. Fast computation of secondary invariants (2007), arXiv:math/0701270 [math.AC].

S. King. Minimal generating sets of non-modular invariant rings of finite groups. J. Symb. Comput. 48, 101–109 (2013).

D. E. Knuth. The art of computer programming. Vol. 4A. Combinatorial algorithms. Part 1 (Addison-Wesley, Upper Saddle River, NJ, 2011); p. xv+883.

J. Kollár. Singularities of the minimal model program. Vol. 200 of Cambridge Tracts in Mathematics (Cambridge University Press, 2013). With a collaboration of Sándor Kovács.

D. Kozlov. Combinatorial algebraic topology. Vol. 21 of Algorithms and Computation in Mathematics (Springer, Berlin, 2008).

R. Lidl and H. Niederreiter. Finite fields. Second Edition, Vol. 20 of Encyclopedia of Mathematics and its Applications (Cambridge University Press, Cambridge, 1997); p. xiv+755. With a foreword by P. M. Cohn.

V. Levandovskyy and H. Schönemann. Plural – a computer algebra system for noncommutative polynomial algebras. In: Proceedings of the 2003 international symposium on symbolic and algebraic computation, ISSAC 2003, Philadelphia, PA, USA, August 3–6, 2003. (New York, NY: ACM Press, 2003); pp. 176–183.

C. Lawrie and S. Schäfer-Nameki. The Tate Form on Steroids: Resolution and Higher Codimension Fibers. JHEP 04, 061 (2013), arXiv:1212.2949 [hep-th].

V. Levandovskyy. Non-commutative Computer Algebra for polynomial algebras: Gröbner bases, applications and implementation, doctoralthesis, Technische Universität Kaiserslautern (2005).

Q. Liu. Algebraic geometry and arithmetic curves. Transl. by Reinie Erné. Vol. 6 of Oxf. Grad. Texts Math. (Oxford: Oxford University Press, 2006).

E. Looijenga. Isolated Singular Points on Complete Intersections. Vol. 77 of LMS Lecture Note Series (Cambridge University Press, Cambridge, 1984); p. xi+200.

T. Merkwitz, L. Naughton and G. Pfeiffer. TomLib, The GAP Library of Tables of Marks, Version 1.2.11 (Jan 2024). GAP package.

R. V. Moody and J. Patera. Fast recursion formula for weight multiplicities. Bull. Amer. Math. Soc. (N.S.) 7, 237–242 (1982).

T. Markwig and Y. Ren. Computing tropical varieties over fields with valuation. Found. Comput. Math. 20, 783–800 (2020).

E. Miller and B. Sturmfels. Combinatorial commutative algebra. Vol. 227 (New York, NY: Springer, 2005); p. xiv + 417.

D. Maclagan and B. Sturmfels. Introduction to tropical geometry. Vol. 161 (Providence, RI: American Mathematical Society (AMS), 2015); p. xii + 363.

M. Michałek and B. Sturmfels. Invitation to nonlinear algebra. Vol. 211 (Providence, RI: American Mathematical Society (AMS), 2021); p. xiii + 226.

D. A. Marcus. Number fields. Universitext (Springer, Cham, 2018); p. xviii+203. Second edition of [MR0457396], With a foreword by Barry Mazur.

V. V. Nikulin. Integer symmetric bilinear forms and some of their geometric applications. Izv. Akad. Nauk SSSR Ser. Mat. 43, 111–177, 238 (1979).

OEIS Foundation Inc. The On-Line Encyclopedia of Integer Sequences. Published electronically at https://oeis.org (2024).

T. Oda and K. Miyake. Lectures on Torus Embeddings and Applications. Lectures on mathematics and physics (Tata Institute of Fundamental Research, 1978).

I. Ojeda Martínez de Castilla and R. P. Sánchez. Cellular binomial ideals. Primary decomposition of binomial ideals. J. Symbolic Comput. 30, 383–400 (2000).

J. Oxley. Matroid theory. Second Edition, Vol. 21 of Oxford Graduate Texts in Mathematics (Oxford University Press, Oxford, 2011); p. xiv+684.

A. Postnikov and R. P. Stanley. Chains in the Bruhat order. J. Algebraic Combin. 29, 133–174 (2009).

S. Pokutta and A. S. Schulz. Integer-empty polytopes in the 0/1-cube with maximal Gomory–Chvátal rank. Operations research letters 39, 457–460 (2011).

G. Pfister, A. Sadiq and S. Steidel. An algorithm for primary decomposition in polynomial rings over the integers. Cent. Eur. J. Math. 9, 897–904 (2011).

M. Pohst and H. Zassenhaus. Algorithmic algebraic number theory. Vol. 30 of Encyclopedia of Mathematics and its Applications (Cambridge University Press, Cambridge, 1997); p. xiv+499. Revised reprint of the 1989 original.

E. Pan. SOTGrps, Constructing and identifying groups of small order type, Version 1.2 (Jun 2023). GAP package.

C. Pegel. Chow Rings of Toric Varieties. Master's thesis, University of Bremen (Faculty of Mathematics, Sep 2014). Refereed by Prof. Dr. Eva Maria Feichtner and Dr. Emanuele Delucchi.

G. Pólya. On picture-writing. Amer. Math. Monthly 63, 689–697 (1956).

S. Popescu. On smooth surfaces of degree $\geq 11$ in the projective fourspace, doctoralthesis, Universität des Saarlandes, Saarbrücken (1993).

A. Postnikov. Permutohedra, associahedra, and beyond. International Mathematics Research Notices 2009, 1026–1106 (2009).

S. Posur. Linear systems over localizations of rings. Archiv der Mathematik 111, 23–32 (2018).

W. Riha and K. R. James. Algorithm 29 efficient algorithms for doubly and multiply restricted partitions. Computing 16, 163–168 (1976).

H. Roschy and T. Rahn. Cohomology of line bundles: Proof of the algorithm. Journal of Mathematical Physics 51, 103520 (2010).

G. Rote, F. Santos and I. Streinu. Expansive motions and the polytope of pointed pseudo-triangulations. In: Discrete and Computational Geometry (Springer, 2003); pp. 699–736.

F. Rincón. Computing tropical linear spaces. J. Symb. Comput. 51, 86–98 (2013).

C. Semple and M. Steel. Phylogenetics. Vol. 24 of Oxf. Lect. Ser. Math. Appl. (Oxford University Press, 2003).

C. D. Savage and M. J. Schuster. Ehrhart series of lecture hall polytopes and Eulerian polynomials for inversion sequences. Journal of Combinatorial Theory, Series A 119, 850–870 (2012).

M. Schütt and T. Shioda. Mordell-Weil lattices. Vol. 70 of 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] (Springer, Singapore, 2019); p. xvi+431.

A. J. Sommese and A. Van de Ven. On the adjunction mapping. Math. Ann. 278, 593–603 (1987).

T. Shimoyama and K. Yokoyama. Localization and primary decomposition of polynomial ideals. J. Symbolic Comput. 22, 247–277 (1996).

J. Schmitt. On $\mathbb Q$-factorial terminalizations of symplectic linear quotient singularities. Ph.D. Thesis, RPTU Kaiserslautern-Landau (2023).

P. Schuchert. Matroid-Polytope und Einbettungen kombinatorischer Mannigfaltigkeiten. Ph.D. Thesis, TU Darmstadt (1995).

Á. Seress. Permutation group algorithms. Vol. 152 of Cambridge Tracts in Mathematics (Cambridge University Press, Cambridge, 2003); p. x+264.

M. Sezer. Sharpening the generalized Noether bound in the invariant theory of finite groups. J. Algebra 254, 252–263 (2002).

I. Shimada. An algorithm to compute automorphism groups of $K3$ surfaces and an application to singular $K3$ surfaces. Int. Math. Res. Not. IMRN, 11961–12014 (2015).

I. Shimada. Connected Components of the Moduli of Elliptic $K3$ Surfaces. Michigan Mathematical Journal 67, 511–559 (2018).

R. P. Stanley. Invariants of finite groups and their applications to combinatorics. Bull. Amer. Math. Soc. (N.S.) 1, 475–511 (1979).

The Stacks Project Authors. Stacks Project. Published electronically.

J. R. Stembridge. Computational aspects of root systems, Coxeter groups, and Weyl characters. In: Interaction of combinatorics and representation theory, Vol. 11 of MSJ Memoirs (The Mathematical Society of Japan, 2001); pp. 1–38.

J. Stevens. On the versal deformation of cyclic quotient singularities. In: Singularity theory and its applications, Part I (Coventry, 1988/1989), Vol. 1462 of Lecture Notes in Math. (Springer, Berlin, 1991); pp. 302–319.

B. Sturmfels. Algorithms in invariant theory. Texts and Monographs in Symbolic Computation (Springer-Verlag, Vienna, 1993); p. vi+197.

S. Sullivant. Algebraic statistics. Vol. 194 of Grad. Stud. Math. (Providence, RI: American Mathematical Society (AMS), 2018).

P. Symonds. On the Castelnuovo-Mumford regularity of rings of polynomial invariants. Ann. of Math. (2) 174, 499–517 (2011).

P. Tarrago and M. Weber. The classification of tensor categories of two-colored noncrossing partitions. Journal of Combinatorial Theory, Series A 154, 464–506 (2018).

D. E. Taylor. Pairs of Generators for Matrix Groups. I. The Cayley Bulletin 3, 76–85 (1987), arXiv:2201.09155 [math.GR].

Q.-N. Tran. A Fast Algorithm for Gröbner Basis Conversion and its Applications. Journal of Symbolic Computation 30, 451–467 (2000).

Q.-N. Tran. Efficient Groebner walk conversion for implicitization of geometric objects. Computer Aided Geometric Design 21, 837–857 (2004).

I. Turkalj. Reflective Lorentzian lattices of signature (5, 1). Journal of Algebra 513, 516–544 (2018).

M. Vaughan-Lee and B. Eick. SglPPow, Database of groups of prime-power order for some prime-powers, Version 2.3 (Nov 2022). GAP package.

E. B. Vinberg. Some arithmetical discrete groups in Lobacevsky spaces. In: Discrete subgroups of Lie groups and applications to moduli (Internat. Colloq., Bombay, 1973), No. 7 of Tata Inst. Fundam. Res. Stud. Math. (Published for the Tata Institute of Fundamental Research, Bombay by Oxford University Press, Bombay, 1975); pp. 323–348.

S. Volz. Design and implementation of efficient algorithms for operations on partitions of sets. Bachelor's Thesis, Universität des Saarlandes (2023).

L. C. Washington. Elliptic curves. Second Edition, Discrete Mathematics and its Applications (Boca Raton) (Chapman & Hall/CRC, Boca Raton, FL, 2008); p. xviii+513. Number theory and cryptography.

T. Weigand. Lectures on F-theory compactifications and model building. Class. Quant. Grav. 27, 214004 (2010), arXiv:1009.3497 [hep-th].

T. Weigand. TASI Lectures on F-theory. PoS TASI2017, 016 (2018), arXiv:1806.01854 [hep-th].

J. B. Wilson. Optimal algorithms of Gram-Schmidt type. Linear Algebra Appl. 438, 4573–4583 (2013).

E. Witten. Topological Sigma Models. Commun. Math. Phys. 118, 411 (1988).

E. Witten. On flux quantization in M theory and the effective action. J. Geom. Phys. 22, 1–13 (1997), arXiv:hep-th/9609122.

R. Yamagishi. On smoothness of minimal models of quotient singularities by finite subgroups of $\mathrm{SL}_n(\mathbb C)$. Glasg. Math. J. 60, 603–634 (2018).

A. Zoghbi and I. Stojmenovic. Fast algorithms for generating integer partitions. Int. J. Comput. Math. 70, 319–332 (1998).

G. M. Ziegler. Lectures on polytopes. Vol. 152 of Graduate Texts in Mathematics (Springer-Verlag, New York, 1995); p. x+370.