Christoph Schwarzweller: Papers
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Separable Polynomials and Separable Extensions
in: Journal of Formalized Mathematics, vol. 32(1), pp. 33-46, 2024.
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Extensions of Orderings
in: Journal of Formalized Mathematics, vol. 31(1), pp. 341-352, 2023.
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Simple Extensions
(with A. Rowińska-Schwarzweller)
in: Journal of Formalized Mathematics, vol. 31(1), pp. 287-298, 2023.
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Developing Field Theory in Mizar
in: M. Ganzha, L. Maciaszek, M. Paprzycki, D. Ślęzak (eds.),
Proceedings of the 18th Conference on Computer Science and Information Systems, ACSIS, vol. 35, pp. 303-308, 2023.
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Normal Extensions
in: Journal of Formalized Mathematics, vol. 31(1), pp. 121-130, 2023.
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Existence and Uniqueness of Algebraic Closures
in: Journal of Formalized Mathematics, vol. 30(4), pp. 281-294, 2022.
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Artin’s Theorem Towards the Existence of Algebraic Closures
in: Journal of Formalized Mathematics, vol. 30(3), pp. 199-207, 2022.
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Splitting Fields for the Rational Polynomials X^2-2, X^2+X+1, X^3-1, and X^3-2
(with S. Burgoa)
in: Journal of Formalized Mathematics, vol. 30(1), pp. 23-30, 2022.
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Quadratic Extensions
(with A. Rowińska-Schwarzweller)
in: Journal of Formalized Mathematics, vol. 29(4), pp. 229-240, 2021.
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Splitting Fields
in: Journal of Formalized Mathematics, vol. 29(3), pp. 129-139, 2021.
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Algebraic Extensions
(with A. Rowińska-Schwarzweller)
in: Journal of Formalized Mathematics, vol. 29(1), pp. 39-47, 2021.
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Ring and Field Adjunctions, Algebraic Elements and Minimal Polynomials
in: Journal of Formalized Mathematics, vol. 28(3), pp. 251-261, 2020.
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Refining Algebraic Hierarchy in Mathematical Repository Mizar
(with A. Korniłowicz and A. Grabowski)
in: A. Grabowski, R. Loukanova, Ch. Schwarzweller (eds.),
AI Aspects in Reasoning, Languages, and Computation
Stud. Comp. Intelligence vol. 889, Springer, pp. 49-75, 2020.
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Renamings and a Condition-free Formalization of Kronecker's Construction
in: Journal of Formalized Mathematics, vol. 28(2), pp. 129-135, 2020.
- Field
Extensions and Kronecker's Construction
in: Journal of Formalized Mathematics, vol. 27(3), pp. 229-235, 2019.
- On
the Intersection of Fields F with F[X]
in: Journal of Formalized Mathematics, vol. 27(3), pp. 223-228, 2019.
- On
Monomorphims and Subfields
in: Journal of Formalized Mathematics, vol. 27(2), pp. 133-137, 2019.
- On Roots of
Polynomials over F[X]/‹p›
in: Journal of Formalized Mathematics, vol. 27(2), pp. 93-100, 2019.
- Representation Matters: An Unexpected Property of Polynomial Rings
and its Consequences for Formalizing Abstract Field Theory
in: M. Ganzha, L. Maciaszek, M. Paprzycki (eds.),
Proceedings of the 2018 Federated Conference on Computer Science and Information Systems, ACSIS, vol. 15, pp. 67-72, 2018.
- Formally Real Fields
in: Journal of Formalized Mathematics, vol. 25(4), pp. 249-259, 2017.
- On Roots of
Polynomials and Algebraically Closed Fields
in: Journal of Formalized Mathematics, vol. 25(3), pp. 185-195, 2017.
- Ordered Rings and Fields
in: Journal of Formalized Mathematics, vol. 25(1), pp. 63-72, 2017.
- Some Algebraic Properties of Polynomial Rings
(with A. Korniłowicz and A. Rowińska-Schwarzweller)
in: Journal of Formalized Mathematics, vol. 24(3), pp. 227-237, 2016.
- On Algebraic Hierarchies in Mathematial Repository of Mizar
(with A. Grabowski and Artur Korniłowicz)
in: M. Ganzha, L. Maciaszek, M. Paprzycki (eds.),
Proceedings of the 2016 Federated Conference on Computer Science and Information Systems, ACSIS, vol. 8, pp. 363-371, 2016.
- Characteristic of Rings and Prime Fields
(with A. Korniłowicz)
in: Journal of Formalized Mathematics, vol. 23(4), pp. 333-349, 2015.
- Equality in Computer Proof-Assistants
(with A. Grabowski and A. Korniłowicz)
in: M. Ganzha, L. Maciaszek, M. Paprzycki (eds.),
Proceedings of the 2015 Federated Conference on Computer Science and Information Systems, ACSIS, vol. 5, pp. 45-54, 2015.
- The
First Isomorphism Theorem and Other Properties of Rings
(with A. Korniłowicz)
in: Journal of Formalized Mathematics, vol. 22(4), pp. 291-301, 2014.
- Towards Standard Environments for Formalizing Mathematics
(with A. Grabowski)
in: Proceedings of the 6th Podlasie Conference on Mathematics, Białystok, Poland, 2014.
- Proth Numbers
in: Journal of Formalized Mathematics, vol. 22(2), pp. 111-118, 2014.
- A Test for the Stability of Networks
(with A. Rowińska-Schwarzweller)
in: Journal of Formalized Mathematics, vol. 21(1), pp. 47-53, 2013.
- Towards Automatically Categorizing Mathematical Knowledge
(with A. Grabowski)
in: M. Ganzha, L. Maciaszek, M. Paprzycki (eds.),
Proceedings of the 7th International Symposium on Advances in Artificial Intelligence and Applications, pp.63-68, 2012.
- Introduction to Rational Functions
in: Journal of Formalized Mathematics, vol. 20(2), pp. 181-191, 2012.
- On Duplication in Mathematical Repositories
(with A. Grabowski)
in: S. Autexier, J. Calmet et.al. (eds.), Intelligent Computer Mathematics,
Lecture Notes in Computer Science 6167, pp. 300-314, 2010. © Springer-Verlag
- On Building a Knowledge Base for Stability Theory
(with A. Rowińska-Schwarzweller)
in: S. Autexier, J. Calmet et.al. (eds.), Intelligent Computer Mathematics,
Lecture Notes in Computer Science 6167, pp. 427-439, 2010. © Springer-Verlag
- The Chinese Remainder Theorem, its Proofs and its Generalizations in Mathematical Repositories
in: Studies in Logic, Grammar and Rhetoric 18(31), p. 103-119, 2009.
- Improving Representation of Knowledge within the Mizar Library
(with A. Grabowski)
in: Studies in Logic, Grammar and Rhetoric 18(31), p. 35-50, 2009.
- Modular Integer Arithmetic
in: Journal of Formalized Mathematics, vol. 16(3), pp. 253-258, 2008.
- Towards Mathematical Knowledge Management for Electrical Engineering
(with A. Rowińska-Schwarzweller)
in: M. Kauers, M. Kerber, R. Miner, W. Windsteiger (eds.), Towards Mechanized Mathematical Assistants,
Lecture Notes in Artificial Intelligence 4573, pp. 371-380, 2007. © Springer-Verlag
- Revisions as an Essential Tool to Maintain Mathematical Repositories
(with A. Grabowski)
in: M. Kauers, M. Kerber, R. Miner, W. Windsteiger (eds.), Towards Mechanized Mathematical Assistants,
Lecture Notes in Artificial Intelligence 4573, pp. 235-249, 2007. © Springer-Verlag
- Mizar Attributes: A Technique to Encode Mathematical Knowledge into Type Systems
in: Studies in Logic, Grammar and Rhetoric, vol. 10(23), pp. 387-400, 2007.
- Schur's Theorem on the Stability of Networks
(with A. Rowińska-Schwarzweller)
in: Journal of Formalized Mathematics, vol. 14(4), pp. 135-142, 2006.
- Multiplication of Polynomials using Discrete Fourier Transformation
(with K. Treyderowski)
in: Journal of Formalized Mathematics, vol. 14(4), pp. 121-128, 2006.
- Translating Mathematical Vernacular into Knowledge Repositories
(with A. Grabowski)
in: M. Kohlhase (ed.), Proceedings of the 4th International Conference on Mathematical Knowledge Management,
Lecture Notes in Artificial Intelligence 3863, pp. 49-64, 2006. © Springer-Verlag
- Gröbner Bases --- Theory Refinement in the Mizar System
in: M. Kohlhase (ed.), Proceedings of the 4th International Conference on Mathematical Knowledge Management,
Lecture Notes in Artificial Intelligence 3863, pp. 299-314, 2006. © Springer-Verlag
- Computers and Algorithms in the Mizar System
(with A. Korniłowicz)
in: Mechanized Mathematics and its Applications, vol. 4(1), pp. 43-50, 2005.
- Construction of Gröbner Bases: Buchberger's First Criterium
in: Journal of Formalized Mathematics, vol. 13(1), pp. 147-156, 2005.
- Rough Concept Analysis --- Theory Development in the Mizar System
(with A. Grabowski)
in: A. Asperti, G. Bancerek, A. Trybulec (eds.), Proceedings of the 3rd International Conference on Mathematical Knowledge Management,
Lecture Notes in Computer Science 3119, pp. 130-144, 2004. © Springer-Verlag
- Computers and Algorithms in the Mizar System
(with A. Korniłowicz)
in: G. Bancerek, A. Grabowski (eds.), Proceedings of the International Workshop
''30 Years of Mizar", Białowieża, Poland, September 2004.
- Towards Formal Support for Generic Programming
Habilitation thesis, Wilhelm-Schickard-Institute for Computer Science, University of
Tübingen, 2003.
- Checking Semantic Requirements of Generic Algorithms
(with H. Gast)
unpublished manuscript, 2003.
- Construction of Gröbner bases.
S-Polynomials and Standard Representations
in: Journal of Formalized Mathematics, vol. 11(3-4), pp. 313-322, 2003.
- Characterization and Existence of
Gröbner Bases
in: Journal of Formalized Mathematics, vol. 11(3-4), pp. 303-312, 2003.
- Designing Mathematical Libraries based
on Requirements for Theorems
in: Annals of Mathematics and Artificial Intelligence, vol. 38(1-3), p. 193-209, 2003. © Kluwer Academic Publishers
- Polynomial Reduction
in: Journal of Formalized Mathematics, vol. 11(1-2), pp. 113-124, 2003.
- Term Orders
in: Journal of Formalized Mathematics, vol. 11(1-2), pp. 105-112, 2003.
- Symbolic Deduction in Mathematical Databases
based on Properties
in: S. Colton, V. Sorge (eds.), Proceedings of the 2nd International Workshop on the Role of
Automated Deduction in Mathematics
(RADM2002),
Kopenhagen, Denmark, July 2002.
- Algebraic Requirements for
the Construction of Polynomial Rings
(with Robert Milewski)
in: Mechanized Mathematics and its Applications, vol. 2(1), pp. 1-8, 2002.
- Defining Gröbner Bases
in the Concept Description Language Tecton
unpublished manuscript, 2001.
- More on Multivariate Polynomials:
Monomials and Constant Polynomials
in: Journal of Formalized Mathematics, vol.9(4). pp. 849-856, 2001.
- Designing Mathematical Libraries based on
Minimal Requirements for Theorems
in: B. Buchberger, O. Caprotti (eds.), Proceedings of the 1st International Workshop on
Mathematical Knowledge Management
(MKM2001), Linz, Austria, September 2001.
- Commutative Algebra in the Mizar System
(with Piotr Rudnicki and Andrzej Trybulec)
in: Journal of Symbolic Computation, vol. 32(1/2), pp. 143-169, 2001. © Elsevier
- Ring Ideals
(with Jonathan Backer and Piotr Rudnicki)
in: Journal of Formalized Mathematics, vol.9(3), pp. 565-583, 2000.
- The Binomial Theorem for Algebraic Structures
in: Journal of Formalized Mathematics, vol.9(3), pp. 559-564, 2000.
- Defining Power Series and Polynomials in Mizar
(with Piotr Rudnicki and Andrzej Trybulec)
in: M. Kerber, M. Kohlhase (eds.), Symbolic Computation and Automated Reasoning: The Calculemus-2000
Symposium,
pp. 191-204, 2000. © A K Peters
- Mizar Formalization of Concept Lattices
in: Mechanized Mathematics and its Applications, vol. 1(1), pp. 1-10, 2000.
- The Evaluation of Multivariate Polynomials
(with Andrzej Trybulec)
in: Journal of Formalized Mathematics, vol.9(2), pp. 331-338, 2000.
- Mizar Correctness Proofs of Generic Fraction Field Artihmetic
in: M. Jazayeri, R. Loos, D. Musser (eds.), Generic Programming --- International Seminar on
Generic Programming,
Dagstuhl Castle, Germany,
Lecture Notes in Computer Science 1766, pp. 178-191, 2000. © Springer-Verlag
- A Characterization of Concept
Lattices; Dual Concept Lattices
in: Journal of Formalized Mathematics, vol.9(1), pp. 55-60, 1999.
- Noetherian Lattices
in: Journal of Formalized Mathematics, vol.8(1), pp. 169-174, 1999.
- The Tecton Concept Library
(with Rüdiger Loos, David Musser and Sybille Schupp)
Technical Report WSI-99-02, Faculty for Computer Science, University of Tübingen, 1999.
- The Ring of Integers, Euclidean Rings and Modulo Integers
in: Journal of Formalized Mathematics, vol.8(1), pp. 29-34, 1999.
- Introduction to Concept
Lattices
in: Journal of Formalized Mathematics, vol.7(2), pp. 233-242, 1998.
- The Field of Quotients over an
Integral Domain
in: Journal of Formalized Mathematics, vol.7(1), pp. 69-80, 1998.
- Mizar Verification of Generic Algebraic Algorithms
PhD thesis, Wilhelm-Schickard-Institute for Computer Science, University of
Tübingen, 1997.
- The Correctness of the Generic
Algorithms of Brown and Henrici Concerning Addition and Multiplication in Fraction Fields
in: Journal of Formalized Mathematics, vol.6(3), pp. 381-388, 1997.
- Using Mizar to Prove Generic Algebraic Algorithms Correct
unpublished manuscript, 1997.
- On the Complexity of Computing Gröbner Bases in
Monoid and Group Rings (in German)
Diploma Thesis, University of
Kaiserslautern, 1995.
- On Convergent Representations of Monoids and Groups (in German)
Minor Thesis, University of Kaiserslautern, 1993.
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