Doctoral Program “Computational Mathematics” [DK W1214]

@article{RISC5831,
author = {Jiménez-Pastor Antonio and Pillwein Veronika},
title = {{A Computable Extension for Holonomic Functions: DD-Finite Functions}},
language = {english},
abstract = {Differentiably finite (D-finite) formal power series form a large class of useful functions for which a variety of symbolic algorithms exists. Among these methods are several closure properties that can be carried out automatically. We introduce a natural extension of these functions to a larger class of computable objects for which we prove closure properties. These are again algorithmic. This extension can be iterated constructively preserving the closure properties},
journal = {Journal of Symbolic Computation},
volume = {94},
pages = {90--104},
isbn_issn = {ISSN 0747-7171},
year = {2019},
month = {September-October},
refereed = {yes},
length = {15},
url = {https://doi.org/10.1016/j.jsc.2018.07.002}
}

@article{RISC5700,
author = {Jose Capco and Matteo Gallet and Georg Grasegger and Christoph Koutschan and Niels Lubbes and Josef Schicho},
title = {{The Number of Realizations of a Laman Graph}},
language = {english},
journal = {SIAM Journal on Applied Algebra and Geometry},
volume = {2},
number = {1},
pages = {94--125},
isbn_issn = {2470-6566},
year = {2018},
refereed = {yes},
length = {32},
url = {https://doi.org/10.1137/17M1118312}
}

@article{RISC5535,
author = {A. Lin and M. Makhul and H. N. Mojarrad and J. Schicho and K. Swanepoel and F. de Zeeuw},
title = {{On sets defining few ordinary circles}},
language = {english},
journal = {Discrete and Computational Geometry},
volume = {59},
pages = {59--87},
isbn_issn = {0179-5376},
year = {2018},
refereed = {yes},
length = {29}
}

@article{RISC5586,
author = {Bruno Buchberger},
title = {{Gröbner Bases Computation by Triangularizing Macaulay Matrices}},
language = {english},
journal = {Advanced Studies in Pure Mathematics (The 50th Anniversary of Gröbner Bases)},
volume = {75},
pages = {1--9},
publisher = {Mathematical Society of Japan},
isbn_issn = {0},
year = {2017},
refereed = {no},
length = {9}
}

@article{RISC5587,
author = { Abraham Erika and Abbott John and Becker Bernd and Bigatti Anna Maria and Brain Martin and Buchberger Bruno and Cimatti Alessandro and Davenport James and England Matthew and Fontaine Pascal and Forrest Stephen and Griggio Alberto and Kröning Daniel and Seiler Werner M. and Sturm },
title = {{Satisfiability Checking and Symbolic Computation}},
language = {english},
journal = {ACM Communications in Computer Algebra},
volume = {50},
number = {4},
pages = {145--147},
isbn_issn = {0},
year = {2017},
refereed = {no},
length = {3}
}

@article{RISC5410,
author = {M. Gallet and C. Koutschan and Z. Li and G. Regensburger and J. Schicho and N. Villamizar},
title = {{Planar linkages following a prescribed motion}},
language = {english},
journal = {Math. Comp.},
volume = {87},
pages = {473--506},
isbn_issn = {ISSN: 1088-6842},
year = {2017},
refereed = {yes},
length = {34},
url = {http://www.ams.org/journals/mcom/2017-86-303/S0025-5718-2016-03120-8/}
}

@article{RISC5411,
author = {M. Gallet and G. Nawratil and J. Schicho and J. Selig},
title = {{Mobile Icosapods}},
language = {english},
journal = {Adv. Appl. Math.},
volume = {88},
pages = {1--25},
isbn_issn = {ISSN: 0196-8858},
year = {2017},
refereed = {yes},
length = {25},
url = {http://dx.doi.org/10.1016/j.aam.2016.12.002}
}

@article{RISC5414,
author = {M. Gallet and G. Nawratil and J. Schicho},
title = {{Liaison linkages}},
language = {english},
journal = {J. Symb. Comp.},
volume = {79},
pages = {65--98},
isbn_issn = {ISSN: 0747-7171},
year = {2017},
refereed = {yes},
length = {34},
url = {http://dx.doi.org/10.1016/j.jsc.2016.08.006}
}

@article{RISC5243,
author = {Bruno Buchberger and Tudor Jebelean and Temur Kutsia and Alexander Maletzky and Wolfgang Windsteiger},
title = {{Theorema 2.0: Computer-Assisted Natural-Style Mathematics}},
language = {english},
abstract = {The Theorema project aims at the development of a computer assistant for the working mathematician. Support should be given throughout all phases of mathematical activity, from introducing new mathematical concepts by definitions or axioms, through first (computational) experiments, the formulation of theorems, their justification by an exact proof, the application of a theorem as an algorithm, until to the dissemination of the results in form of a mathematical publication, the build up of bigger libraries of certified mathematical content and the like. This ambitious project is exactly along the lines of the QED manifesto issued in 1994 (see e.g. http://www.cs.ru.nl/~freek/qed/qed.html) and it was initiated in the mid-1990s by Bruno Buchberger. The Theorema system is a computer implementation of the ideas behind the Theorema project. One focus lies on the natural style of system input (in form of definitions, theorems, algorithms, etc.), system output (mainly in form of mathematical proofs) and user interaction. Another focus is theory exploration, i.e. the development of large consistent mathematical theories in a formal frame, in contrast to just proving single isolated theorems. When using the Theorema system, a user should not have to follow a certain style of mathematics enforced by the system (e.g. basing all of mathematics on set theory or certain variants of type theory), rather should the system support the user in her preferred flavour of doing math. The new implementation of the system, which we refer to as Theorema 2.0, is open-source and available through GitHub.},
journal = {JFR},
volume = {9},
number = {1},
pages = {149--185},
isbn_issn = {ISSN 1972-5787},
year = {2016},
refereed = {yes},
keywords = {Mathematical assistant systems, Theorema, automated reasoning, theory exploration, unification},
length = {37},
url = {http://dx.doi.org/10.6092/issn.1972-5787/4568}
}

@article{RISC5408,
author = {Zijia Li and and J. Schicho and Hans-Peter Schröcker},
title = {{The rational motion of minimal dual quaternion degree with prescribed trajectory}},
language = {english},
journal = {Comp. Aided Geom. Des.},
volume = {41},
pages = {1--9},
isbn_issn = {ISSN: 0167-8396},
year = {2016},
refereed = {yes},
length = {9},
url = {http://dx.doi.org/10.1016/j.cagd.2015.10.002}
}

@article{RISC5409,
author = {Zijia Li and Josef Schicho and Hans-Peter Schröcker},
title = {{A survey on the theory of bonds}},
language = {english},
journal = {IMA Journal of Mathematical Control and Information},
pages = {--},
isbn_issn = {ISSN: 1471-6887},
year = {2016},
note = {online},
refereed = {yes},
length = {20},
url = {https://doi.org/10.1093/imamci/dnw048}
}