William W. Adams, Philippe Loustaunau, An Introduction to Gröbner Bases, American Mathematical Society, 1994.

Karim Adiprasito, June Huh, Eric Katz, Hodge theory for combinatorial geometries, Ann. of Math. (2), 188(2), 381–452, 2018.

Ivan V. Arzhantsev, Sergei A. Gaǐfullin, Cox rings, semigroups, and automorphisms of affine varieties, Mat. Sb., 201(1), 3–24, 2010.

Spencer Backman, Christopher Eur, Connor Simpson, Simplicial generation of Chow rings of matroids, 2019.

Matthew Baker, Serguei Norine, Riemann-Roch and Abel-Jacobi theory on a finite graph, Adv. Math., 215(2), 766–788, 2007.

David J. Benson, Polynomial invariants of finite groups, Cambridge University Press, Cambridge, 1993.

Neil Berry, Artūras Dubickas, Noam D. Elkies, Bjorn Poonen, Chris Smyth, The conjugate dimension of algebraic numbers, Q. J. Math., 55(3), 237–252, 2004.

Jérémy Berthomieu, Christian Eder, Mohab 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, 51-–58, New York, NY, USA, 2021. Association for Computing Machinery.

Martin Bies, Cohomologies of coherent sheaves and massless spectra in F-theory, PhD thesis, Heidelberg U., 2018.

Louis J. Billera, Carl W. Lee, A proof of the sufficiency of McMullen's conditions for {$f$}-vectors of simplicial convex polytopes, J. Combin. Theory Ser. A, 31(3), 237–255, 1981.

Ralph Blumenhagen, Benjamin Jurke, Thorsten Rahn, Helmut Roschy, Cohomology of line bundles: A computational algorithm, Journal of Mathematical Physics, 51(10), 103525, 2010.

Ralph Blumenhagen, Benjamin Jurke, Thorsten Rahn, Helmut Roschy, cohomCalg package, 2010, High-performance line bundle cohomology computation based on BJRR10.

Ralph Blumenhagen, Benjamin Jurke, Thorsten Rahn, Helmut Roschy, Cohomology of line bundles: Applications, Journal of Mathematical Physics, 53(1), 012302, 2012.

Tom Braden, June Huh, Jacob P. Matherne, Nicholas Proudfoot, Botong Wang, A semi-small decomposition of the Chow ring of a matroid, 2020.

Winfried Bruns, Jürgen Herzog, Cohen-Macaulay rings, Cambridge University Press, Cambridge, 2009.

José Bueso, José Gómez-Torrecillas, Alain Verschoren, Algorithmic methods in non-commutative algebra. Applications to quantum groups., Dordrecht: Kluwer Academic Publishers, 2003.

Janko Böhm, Parametrisierung rationaler Kurven, Master's thesis, Universität Bayreuth, 1999.

Janko Böhm, Wolfram Decker, Santiago Laplagne, Gerhard Pfister, Local to global algorithms for the Gorenstein adjoint ideal of a curve, In Algorithmic and experimental methods in algebra, geometry, and number theory, editors, 51–96. Springer, Cham, 2017.

Janko Böhm, Wolfram Decker, Santiago Laplagne, Gerhard Pfister, Computing integral bases via localization and Hensel lifting, In MEGA 2019 - International Conference on Effective Methods in Algebraic Geometry, Madrid, Spain, 2019.

Janko Böhm, Wolfram Decker, Santiago Laplagne, Gerhard Pfister, Andreas Steenpaß, Stefan Steidel, Parallel algorithms for normalization, Journal of Symbolic Computation, 51, 99-114, 2013.

Janko Böhm, Simon Keicher, Yue Ren, Computing GIT-fans with symmetry and the Mori chamber decomposition of $\overline M_{0,6}$, Math. Comp., 89(326), 3003–3021, 2020.

Peter J. Cameron, Permutation groups, Cambridge University Press, Cambridge, 1999.

Ignacio Ojeda Martínez de Castilla, Ramón Peidra Sánchez, Cellular binomial ideals. Primary decomposition of binomial ideals, J. Symbolic Comput., 30(4), 383–400, 2000.

Jan Arthur 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), editors, 81–92. Springer, Berlin, 1991.

Jose Luis Cisneros Molina, Dung Trang Le, Jose Seade, Handbook of Geometry and Topology of Singularities I, Springer-Verlag, Cham, 2020.

Jose Luis Cisneros Molina, Dung Trang Le, Jose Seade, Handbook of Geometry and Topology of Singularities II, Springer-Verlag, Cham, 2021.

Henri Cohen, A course in computational algebraic number theory, Springer-Verlag, Berlin, 1993.

Henri Cohen, Advanced topics in computational number theory, Springer-Verlag, New York, 2000.

J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker, R. A. Wilson, Atlas of finite groups, Oxford University Press, Eynsham, 1985.

J. H. Conway, N. J. A. Sloane, Sphere packings, lattices and groups, Springer-Verlag, New York, 1999.

John H. Conway, Alexander Hulpke, John McKay, On transitive permutation groups, LMS J. Comput. Math., 1, 1–8, 1998.

D. Corey, Initial degenerations of Grassmannians, Sel. Math. New Ser., 27(57), 2021.

David A. Cox, John B. Little, Henry K. Schenck, Toric varieties, Providence, RI: American Mathematical Society (AMS), 2011.

G. De Franceschi, Centralizers and conjugacy classes in finite classical groups, 2020.

Jesús A. De Loera, Jörg Rambau, Francisco Santos, Triangulations. Structures for algorithms and applications, Springer-Verlag, Berlin, 2010.

Wolfram Decker, Lawrence Ein, Frank-Olaf Schreyer, Construction of surfaces in ${\mathbb P}_4$, J. Algebr. Geom., 2(2), 185–237, 1993.

Wolfram Decker, Gert-Martin Greuel, Gerhard Pfister, Primary decomposition: algorithms and comparisons, In Algorithmic algebra and number theory. Selected papers from a conference, Heidelberg, Germany, October 1997, editors, 187–220. Springer, Berlin, 1999.

Wolfram Decker, Agnes Eileen Heydtmann, Frank-Olaf Schreyer, Generating a Noetherian normalization of the invariant ring of a finite group, J. Symbolic Comput., 25(6), 727–731, 1998.

Wolfram Decker, Theo 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, editors, 61–89. Cambridge Univ. Press, Cambridge, 1998.

Wolfram Decker, Christoph Lossen, Computing in algebraic geometry. A quick start using SINGULAR, Springer-Verlag, Berlin; Hindustan Book Agency, New Delhi, 2006.

Wolfram Decker, Gerhard Pfister, A first course in computational algebraic geometry, Cambridge University Press, Cambridge, 2013.

Wolfram Decker, Frank-Olaf Schreyer, Non-general type surfaces in ${\mathbb P}^4$: Some remarks on bounds and constructions, J. Symb. Comput., 29(4-5), 545–582, 2000.

Harm Derksen, Computation of invariants for reductive groups, Adv. Math., 141(2), 366–384, 1999.

Harm Derksen, Gregor 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, Springer, Heidelberg, 2015.

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

Mátyás Domokos, Pál Hegedűs, Noether's bound for polynomial invariants of finite groups, Arch. Math. (Basel), 74(3), 161–167, 2000.

Maria Donten-Bury, Simon Keicher, Computing resolutions of quotient singularities, J. Algebra, 472, 546–572, 2017.

David Eisenbud, Commutative algebra. With a view toward algebraic geometry, Berlin: Springer-Verlag, 1995.

David Eisenbud, Craig Huneke, Bernd Ulrich, What is the Rees algebra of a module?, Proc. Am. Math. Soc., 131(3), 701–708, 2003.

David Eisenbud, Craig Huneke, Wolmer Vasconcelos, Direct methods for primary decomposition, Invent. Math., 110(2), 207–235, 1992.

David Eisenbud, Bernd Sturmfels, Binomial ideals, Duke Math. J., 84(1), 1–45, 1996.

Zekiye Sahin Eser, Laura Felicia Matusevich, Decompositions of cellular binomial ideals, J. Lond. Math. Soc. (2), 94(2), 409–426, 2016.

Zekiye Sahin Eser, Laura Felicia Matusevich, Corrigendum: Decompositions of cellular binomial ideals: (J. Lond. Math. Soc. 94 (2016) 409–426), J. Lond. Math. Soc. (2), 100(2), 717–719, 2019.

Huijun Fan, Tyler Jarvis, Yongbin Ruan, A mathematical theory of the gauged linear sigma model, Geometry & Topology, 22(1), 235–303, 2017.

J.C. Faugère, P. Gianni, D. Lazard, T. Mora, Efficient Computation of Zero-dimensional Gröbner Bases by Change of Ordering, Journal of Symbolic Computation, 16(4), 329-344, 1993.

Jean-Charles Faugère, A new efficient algorithm for computing Gröbner bases (F4), Journal of Pure and Applied Algebra, 139(1–3), 61–88, 1999.

Eva Maria Feichtner, Sergey Yuzvinsky, Chow rings of toric varieties defined by atomic lattices, Inventiones Mathematicae, 155(3), 515–536, 2004.

William Fulton, Algebraic curves. An introduction to algebraic geometry, W. A. Benjamin, Inc., New York-Amsterdam, 1969.

William Fulton, Young tableaux, Cambridge University Press, Cambridge, 1997.

Karin Gatermann, Semi-invariants, equivariants and algorithms, Appl. Algebra Engrg. Comm. Comput., 7(2), 105–124, 1996.

Andreas Gathmann, Class notes „Plane Algebraic Curves” (SS 2018), 2018.

Ewgenij Gawrilow, Simon Hampe, Michael Joswig, The polymake XML File Format, In Mathematical Software – ICMS 2016, 403–410, Cham, 2016. Springer International Publishing.

Ewgenij Gawrilow, Michael Joswig, polymake: a Framework for Analyzing Convex Polytopes, In Polytopes — Combinatorics and Computation, editors, Gil Kalai, Günter M. Ziegler, 43–74. Birkhäuser, 2000.

Ewgenij Gawrilow, Michael Joswig, Thilo Rörig, Nikolaus Witte, Drawing polytopal graphs with polymake, Comput. Vis. Sci., 13(2), 99–110, 2010.

Patrizia Gianni, Barry Trager, Gail Zacharias, Gröbner bases and primary decomposition of polynomial ideals, In Computational aspects of commutative algebra, editors, 149–167. Elsevier Ltd, Oxford, 1988.

G.-M. Greuel, C. Lossen, E. Shustin, Introduction to Singularities and Deformations, Springer-Verlag, Berlin, 2007.

Gert-Martin Greuel, Santiago Laplagne, Frank Seelisch, Normalization of rings, J. Symbolic Comput., 45(9), 887–901, 2010.

Gert-Martin Greuel, Gerhard Pfister, A Singular introduction to commutative algebra. With contributions by Olaf Bachmann, Christoph Lossen and Hans Schönemann. 2nd extended ed., Springer, Berlin, 2008.

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

Robin Hartshorne, Algebraic Geometry, Springer-Verlag, New York, 1977.

Derek F. Holt, Bettina Eick, Eamonn A. O'Brien, Handbook of computational group theory, Chapman & Hall/CRC, Boca Raton, FL, 2005.

Derek F. Holt, W. Plesken, Perfect groups, The Clarendon Press, Oxford University Press, New York, 1989.

B. Huppert, Endliche Gruppen. I, Springer-Verlag, Berlin-New York, 1967.

Daniel Huybrechts, Lectures on K3 surfaces, Cambridge University Press, Cambridge, 2016.

OEIS Foundation Inc., The On-Line Encyclopedia of Integer Sequences, 2023, Published electronically at \url{http://oeis.org}.

Yukari Ito, Miles Reid, The McKay correspondence for finite subgroups of ${\rm SL}(3,\mathbb C)$, In Higher-dimensional complex varieties (Trento, 1994), editors, 221-240. de Gruyter, 1996.

C. Jansen, K. Lux, R. Parker, R. Wilson, An atlas of Brauer characters, The Clarendon Press Oxford University Press, New York, 1995.

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

Theo de Jong, Gerhard Pfister, Local Analytic Geometry, Vieweg+Teubner Verlag, 2000.

Michael Joswig, Essentials of tropical combinatorics, American Mathematical Society, Providence, RI, 2021.

Michael Joswig, Thorsten Theobald, Polyhedral and algebraic methods in computational geometry, Springer, London, 2013.

Shin-Yao Jow, Cohomology of toric line bundles via simplicial Alexander duality, Journal of Mathematical Physics, 52(3), 033506, 2011.

Thomas Kahle, Decompositions of binomial ideals, Ann. Inst. Statist. Math., 62(4), 727–745, 2010.

Marek Kaluba, Benjamin Lorenz, Sascha Timme, Polymake.jl: A New Interface to polymake, In Mathematical Software – ICMS 2020, 377–385, Cham, 2020. Springer International Publishing.

Sheldon Katz, David R. Morrison, Sakura Schafer-Nameki, James Sully, Tate's algorithm and F-theory, arXiv:1106.3854 [hep-th].

J. Kelleher, B. O'Sullivan, Generating All Partitions: A Comparison Of Two Encodings, 2014.

Gregor Kemper, An algorithm to calculate optimal homogeneous systems of parameters, J. Symbolic Comput., 27(2), 171–184, 1999.

Gregor Kemper, The calculation of radical ideals in positive characteristic, J. Symbolic Comput., 34(3), 229–238, 2002.

Gregor Kemper, Allan Steel, Some algorithms in invariant theory of finite groups, In Computational methods for representations of groups and algebras (Essen, 1997), editors, 267–285. Birkhäuser, Basel, 1999.

Simon King, Fast computation of secondary invariants, arXiv:math/0701270, 2007.

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

Donald E. Knuth, The art of computer programming. Vol. 4A. Combinatorial algorithms. Part 1, Addison-Wesley, Upper Saddle River, NJ, 2011.

János Kollár, Singularities of the minimal model program, Cambridge University Press, 2013.

Dmitry Kozlov, Combinatorial algebraic topology, Springer, Berlin, 2008.

Martin Kreuzer, Lorenzo Robbiano, Computational commutative algebra. II, Berlin: Springer, 2005.

Teresa Krick, Alessandro 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), editors, 195–205. Springer, Berlin, 1991.

Viktor Levandovskyy, Non-commutative Computer Algebra for polynomial algebras: Gröbner bases, applications and implementation, PhD thesis, Technische Universität Kaiserslautern, 2005.

Viktor Levandovskyy, Hans 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., editors, 176–183. New York, NY: ACM Press, 2003.

Rudolf Lidl, Harald Niederreiter, Finite fields, Cambridge University Press, Cambridge, 1997.

Eduard Looijenga, Isolated Singular Points on Complete Intersections, Cambridge University Press, Cambridge, 1984.

Diane Maclagan, Bernd Sturmfels, Introduction to tropical geometry, Providence, RI: American Mathematical Society (AMS), 2015.

Daniel A. Marcus, Number fields, Springer, Cham, 2018.

M Merca, Fast algorithm for generating ascending compositions, J. Math. Model. Algorithms, 11(1), 89–104, 2012.

Ezra Miller, Bernd Sturmfels, Combinatorial commutative algebra, New York, NY: Springer, 2005.

V. V. Nikulin, Integer symmetric bilinear forms and some of their geometric applications, Izv. Akad. Nauk SSSR Ser. Mat., 43(1), 111–177, 238, 1979.

James Oxley, Matroid theory, Oxford University Press, Oxford, 2011.

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

Christoph Pegel, Chow Rings of Toric Varieties, Master's thesis, University of Bremen, Faculty of Mathematics, 2014.

Gerhard Pfister, Afshan Sadiq, Stefan Steidel, An algorithm for primary decomposition in polynomial rings over the integers, Cent. Eur. J. Math., 9(4), 897–904, 2011.

M. Pohst, H. Zassenhaus, Algorithmic algebraic number theory, Cambridge University Press, Cambridge, 1997.

Sorin Popescu, On smooth surfaces of degree $\geq 11$ in the projective fourspace, PhD thesis, Universität des Saarlandes, Saarbrücken, 1993.

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

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

Helmut Roschy, Thorsten Rahn, Cohomology of line bundles: Proof of the algorithm, Journal of Mathematical Physics, 51(10), 103520, 2010.

Johannes Schmitt, {On $\mathbb Q$-factorial terminalizations of symplectic linear quotient singularities}, PhD thesis, RPTU Kaiserslautern-Landau, 2023.

Ákos Seress, Permutation group algorithms, Cambridge University Press, Cambridge, 2003.

Müfit Sezer, Sharpening the generalized Noether bound in the invariant theory of finite groups, J. Algebra, 254(2), 252–263, 2002.

Ichiro Shimada, An algorithm to compute automorphism groups of $K3$ surfaces and an application to singular $K3$ surfaces, Int. Math. Res. Not. IMRN, (22), 11961–12014, 2015.

Ichiro Shimada, Connected Components of the Moduli of Elliptic $K3$ Surfaces, Michigan Mathematical Journal, 67(3), 511 – 559, 2018.

Takeshi Shimoyama, Kazuhiro Yokoyama, Localization and primary decomposition of polynomial ideals, J. Symbolic Comput., 22(3), 247–277, 1996.

Richard P. Stanley, Invariants of finite groups and their applications to combinatorics, Bull. Amer. Math. Soc. (N.S.), 1(3), 475–511, 1979.

Jan Stevens, On the versal deformation of cyclic quotient singularities, In Singularity theory and its applications, Part I (Coventry, 1988/1989), editors, 302–319. Springer, Berlin, 1991.

Bernd Sturmfels, Algorithms in invariant theory, Springer-Verlag, Vienna, 1993.

Peter Symonds, On the Castelnuovo-Mumford regularity of rings of polynomial invariants, Ann. of Math. (2), 174(1), 499–517, 2011.

D. E. Taylor, Pairs of Generators for Matrix Groups. I, The Cayley Bulletin, 3, 76–85, 1987.

Lawrence C. Washington, Elliptic curves, Chapman & Hall/CRC, Boca Raton, FL, 2008.

Timo Weigand, TASI Lectures on F-theory, arXiv:1806.01854 [hep-th].

Timo Weigand, Lectures on F-theory compactifications and model building, arXiv:1009.3497 [hep-th].

James B. Wilson, Optimal algorithms of Gram-Schmidt type, Linear Algebra Appl., 438(12), 4573–4583, 2013.

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

Edward Witten, Topological Sigma Models, Commun. Math. Phys., 118, 411, 1988.

Ryo Yamagishi, On smoothness of minimal models of quotient singularities by finite subgroups of ${\rm SL}_n(\mathbb C)$, Glasg. Math. J., 60(3), 603–634, 2018.

Günter M. Ziegler, Lectures on polytopes, Springer-Verlag, New York, 1995.

A. Zoghbi, I. Stojmenovic, Fast algorithms for generating integer partitions, Int. J. Comput. Math., 70(2), 319–332, 1998.