# Doctoral Program “Computational Mathematics” [DK W1214]

### Project Lead

### Project Duration

01/10/2008 - 30/09/2011### Project URL

Go to Website## Partners

### The Austrian Science Fund (FWF)

## Publications

### 2018

### Algorithmic Arithmetics with DD-Finite Functions

#### Jiménez-Pastor Antonio, Pillwein Veronika

In: Proceedings of the 2018 ACM on International Symposium on Symbolic and Algebraic Computation, Arreche Carlos (ed.), ISSAC '18 , pp. 231-237. 2018. ACM, New York, NY, USA, ISBN 978-1-4503-5550-6. [url]@

author = {Jiménez-Pastor Antonio and Pillwein Veronika},

title = {{Algorithmic Arithmetics with DD-Finite Functions}},

booktitle = {{Proceedings of the 2018 ACM on International Symposium on Symbolic and Algebraic Computation}},

language = {english},

series = {ISSAC '18},

pages = {231--237},

publisher = {ACM},

address = {New York, NY, USA},

isbn_issn = {ISBN 978-1-4503-5550-6},

year = {2018},

editor = {Arreche Carlos},

refereed = {yes},

keywords = {algorithms, closure properties, holonomic functions},

length = {7},

url = {http://doi.acm.org/10.1145/3208976.3209009}

}

**inproceedings**{RISC5730,author = {Jiménez-Pastor Antonio and Pillwein Veronika},

title = {{Algorithmic Arithmetics with DD-Finite Functions}},

booktitle = {{Proceedings of the 2018 ACM on International Symposium on Symbolic and Algebraic Computation}},

language = {english},

series = {ISSAC '18},

pages = {231--237},

publisher = {ACM},

address = {New York, NY, USA},

isbn_issn = {ISBN 978-1-4503-5550-6},

year = {2018},

editor = {Arreche Carlos},

refereed = {yes},

keywords = {algorithms, closure properties, holonomic functions},

length = {7},

url = {http://doi.acm.org/10.1145/3208976.3209009}

}

### A Computable Extension for Holonomic Functions: DD-Finite Functions

#### Jiménez-Pastor Antonio, Pillwein Veronika

Journal of Symbolic Computation, pp. -. 2018. ISSN 0747-7171. In Press. [url]@

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},

pages = {--},

isbn_issn = {ISSN 0747-7171},

year = {2018},

note = {In Press},

refereed = {yes},

length = {15},

url = {https://doi.org/10.1016/j.jsc.2018.07.002}

}

**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},

pages = {--},

isbn_issn = {ISSN 0747-7171},

year = {2018},

note = {In Press},

refereed = {yes},

length = {15},

url = {https://doi.org/10.1016/j.jsc.2018.07.002}

}

### The Number of Realizations of a Laman Graph

#### Jose Capco, Matteo Gallet, Georg Grasegger, Christoph Koutschan, Niels Lubbes, Josef Schicho

SIAM Journal on Applied Algebra and Geometry 2(1), pp. 94-125. 2018. 2470-6566. [url]@

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**{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}

}

### Positivity of the Gillis-Reznick-Zeilberger rational function

#### V. Pillwein

Technical report no. 18-05 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Schloss Hagenberg, 4232 Hagenberg, Austria. 2018. [pdf]@

author = {V. Pillwein},

title = {{Positivity of the Gillis-Reznick-Zeilberger rational function}},

language = {english},

number = {18-05},

year = {2018},

length = {12},

type = {RISC Report Series},

institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},

address = {Schloss Hagenberg, 4232 Hagenberg, Austria}

}

**techreport**{RISC5612,author = {V. Pillwein},

title = {{Positivity of the Gillis-Reznick-Zeilberger rational function}},

language = {english},

number = {18-05},

year = {2018},

length = {12},

type = {RISC Report Series},

institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},

address = {Schloss Hagenberg, 4232 Hagenberg, Austria}

}

### On sets defining few ordinary circles

#### A. Lin, M. Makhul, H. N. Mojarrad, J. Schicho, K. Swanepoel, F. de Zeeuw

Discrete and Computational Geometry 59, pp. 59-87. 2018. 0179-5376.@

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**{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}

}

### 2017

### Gröbner Bases Computation by Triangularizing Macaulay Matrices

#### Bruno Buchberger

Advanced Studies in Pure Mathematics (The 50th Anniversary of Gröbner Bases) 75, pp. 1-9. 2017. Mathematical Society of Japan, 0.@

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**{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}

}

### Satisfiability Checking and Symbolic Computation

#### Abraham Erika , Abbott John , Becker Bernd , Bigatti Anna Maria , Brain Martin , Buchberger Bruno , Cimatti Alessandro , Davenport James , England Matthew , Fontaine Pascal , Forrest Stephen , Griggio Alberto , Kröning Daniel , Seiler Werner M. , Sturm

ACM Communications in Computer Algebra 50(4), pp. 145-147. 2017. 0.@

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**{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}

}

### Planar linkages following a prescribed motion

#### M. Gallet, C. Koutschan, Z. Li, G. Regensburger, J. Schicho, N. Villamizar

Math. Comp. 87, pp. 473-506. 2017. ISSN: 1088-6842. [url]@

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**{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/}

}

### The number of realizations of a Laman graph

#### Jose Capco, Georg Grasegger, Matteo Gallet, Christoph Koutschan, Niels Lubbes, Josef Schicho

Research Institute for Symbolic Computation (RISC/JKU). Technical report, 2017. [url] [pdf]@

author = {Jose Capco and Georg Grasegger and Matteo Gallet and Christoph Koutschan and Niels Lubbes and Josef Schicho},

title = {{The number of realizations of a Laman graph}},

language = {english},

abstract = {Laman graphs model planar frameworks that are rigid for a general choice of distances between the vertices. There are finitely many ways, up to isometries, to realize a Laman graph in the plane. Such realizations can be seen as solutions of systems of quadratic equations prescribing the distances between pairs of points. Using ideas from algebraic and tropical geometry, we provide a recursion formula for the number of complex solutions of such systems. },

year = {2017},

institution = {Research Institute for Symbolic Computation (RISC/JKU)},

length = {42},

url = {http://www.koutschan.de/data/laman/}

}

**techreport**{RISC5418,author = {Jose Capco and Georg Grasegger and Matteo Gallet and Christoph Koutschan and Niels Lubbes and Josef Schicho},

title = {{The number of realizations of a Laman graph}},

language = {english},

abstract = {Laman graphs model planar frameworks that are rigid for a general choice of distances between the vertices. There are finitely many ways, up to isometries, to realize a Laman graph in the plane. Such realizations can be seen as solutions of systems of quadratic equations prescribing the distances between pairs of points. Using ideas from algebraic and tropical geometry, we provide a recursion formula for the number of complex solutions of such systems. },

year = {2017},

institution = {Research Institute for Symbolic Computation (RISC/JKU)},

length = {42},

url = {http://www.koutschan.de/data/laman/}

}

### Computing the number of realizations of a Laman graph

#### Jose Capco, Georg Grasegger, Matteo Gallet, Christoph Koutschan, Niels Lubbes, Josef Schicho

In: Electronic Notes in Discrete Mathematics (Proceedings of Eurocomb 2017), Vadim Lozin (ed.), Proceedings of The European Conference on Combinatorics, Graph Theory and Applications (EUROCOMB'17)61, pp. 207-213. 2017. ISSN 1571-0653. [url]@

author = {Jose Capco and Georg Grasegger and Matteo Gallet and Christoph Koutschan and Niels Lubbes and Josef Schicho},

title = {{Computing the number of realizations of a Laman graph}},

booktitle = {{Electronic Notes in Discrete Mathematics (Proceedings of Eurocomb 2017)}},

language = {english},

abstract = {Laman graphs model planar frameworks which are rigid for a general choice of distances between the vertices. There are finitely many ways, up to isometries, to realize a Laman graph in the plane. In a recent paper we provide a recursion formula for this number of realizations using ideas from algebraic and tropical geometry. Here, we present a concise summary of this result focusing on the main ideas and the combinatorial point of view.},

volume = {61},

pages = {207--213},

isbn_issn = {ISSN 1571-0653},

year = {2017},

editor = {Vadim Lozin},

refereed = {yes},

keywords = {Laman graph; minimally rigid graph; tropical geometry; euclidean embedding; graph realization},

length = {7},

conferencename = {The European Conference on Combinatorics, Graph Theory and Applications (EUROCOMB'17)},

url = {http://www.koutschan.de/data/laman/}

}

**inproceedings**{RISC5478,author = {Jose Capco and Georg Grasegger and Matteo Gallet and Christoph Koutschan and Niels Lubbes and Josef Schicho},

title = {{Computing the number of realizations of a Laman graph}},

booktitle = {{Electronic Notes in Discrete Mathematics (Proceedings of Eurocomb 2017)}},

language = {english},

abstract = {Laman graphs model planar frameworks which are rigid for a general choice of distances between the vertices. There are finitely many ways, up to isometries, to realize a Laman graph in the plane. In a recent paper we provide a recursion formula for this number of realizations using ideas from algebraic and tropical geometry. Here, we present a concise summary of this result focusing on the main ideas and the combinatorial point of view.},

volume = {61},

pages = {207--213},

isbn_issn = {ISSN 1571-0653},

year = {2017},

editor = {Vadim Lozin},

refereed = {yes},

keywords = {Laman graph; minimally rigid graph; tropical geometry; euclidean embedding; graph realization},

length = {7},

conferencename = {The European Conference on Combinatorics, Graph Theory and Applications (EUROCOMB'17)},

url = {http://www.koutschan.de/data/laman/}

}

### Iterative and Iterative-Noniterative Integral Solutions in 3-Loop Massive QCD Calculations

#### J. Ablinger, A. Behring, J. Blümlein, A. De Freitas, E. Imamoglu, M. van Hoeij A. von Manteuffel, C.G. Raab, C.-S. Radu, C. Schneider

In: Proc. of the 13th International Symposium on Radiative Corrections (Applications of Quantum Field Theory to Phenomenology), A. Hoang, C. Schneider (ed.)PoS (RADCOR2017) 069, pp. 1-13. 2017. ISSN 1824-8039. arXiv:1711.09742 [hep-ph]. [url]@

author = {J. Ablinger and A. Behring and J. Blümlein and A. De Freitas and E. Imamoglu and M. van Hoeij A. von Manteuffel and C.G. Raab and C.-S. Radu and C. Schneider},

title = {{Iterative and Iterative-Noniterative Integral Solutions in 3-Loop Massive QCD Calculations}},

booktitle = {{Proc. of the 13th International Symposium on Radiative Corrections (Applications of Quantum Field Theory to Phenomenology)}},

language = {english},

volume = {PoS (RADCOR2017) 069},

pages = {1--13},

isbn_issn = {ISSN 1824-8039},

year = {2017},

note = {arXiv:1711.09742 [hep-ph]},

editor = {A. Hoang and C. Schneider},

refereed = {no},

length = {13},

url = {https://pos.sissa.it/290/069/pdf}

}

**inproceedings**{RISC5350,author = {J. Ablinger and A. Behring and J. Blümlein and A. De Freitas and E. Imamoglu and M. van Hoeij A. von Manteuffel and C.G. Raab and C.-S. Radu and C. Schneider},

title = {{Iterative and Iterative-Noniterative Integral Solutions in 3-Loop Massive QCD Calculations}},

booktitle = {{Proc. of the 13th International Symposium on Radiative Corrections (Applications of Quantum Field Theory to Phenomenology)}},

language = {english},

volume = {PoS (RADCOR2017) 069},

pages = {1--13},

isbn_issn = {ISSN 1824-8039},

year = {2017},

note = {arXiv:1711.09742 [hep-ph]},

editor = {A. Hoang and C. Schneider},

refereed = {no},

length = {13},

url = {https://pos.sissa.it/290/069/pdf}

}

### Mobile Icosapods

#### M. Gallet, G. Nawratil, J. Schicho, J. Selig

Adv. Appl. Math. 88, pp. 1-25. 2017. ISSN: 0196-8858. [url]@

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**{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}

}

### Liaison linkages

#### M. Gallet, G. Nawratil, J. Schicho

J. Symb. Comp. 79, pp. 65-98. 2017. ISSN: 0747-7171. [url]@

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**{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}

}

### 2016

### Theorema 2.0: Computer-Assisted Natural-Style Mathematics

#### Bruno Buchberger, Tudor Jebelean, Temur Kutsia, Alexander Maletzky, Wolfgang Windsteiger

JFR 9(1), pp. 149-185. 2016. ISSN 1972-5787. [url]@

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**{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}

}

### The rational motion of minimal dual quaternion degree with prescribed trajectory

#### Zijia Li, , J. Schicho, Hans-Peter Schröcker

Comp. Aided Geom. Des. 41, pp. 1-9. 2016. ISSN: 0167-8396. [url]@

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**{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}

}

### A survey on the theory of bonds

#### Zijia Li , Josef Schicho, Hans-Peter Schröcker

IMA Journal of Mathematical Control and Information, pp. -. 2016. ISSN: 1471-6887. online. [url]@

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}

}

**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}

}

### 2015

### 3-loop heavy flavor Wilson coefficients in deep-inelastic scattering

#### J. Ablinger, A. Behring, J. Blümlein, A. De Freitas, A. Hasselhuhn, A. von Manteuffel, C. Raab, M. Round, S. Schneider, F. Wißbrock

In: 17th International Conference in Quantum Chromodynamics (QCD 14), Stephan Narison (ed.), Nucl. Phys. B (Proc. Suppl.) 258-259, pp. 41-44. 2015. ISSN 0550-3213. arXiv:1409.1804 [hep-ph]. [url]@

author = {J. Ablinger and A. Behring and J. Blümlein and A. De Freitas and A. Hasselhuhn and A. von Manteuffel and C. Raab and M. Round and S. Schneider and F. Wißbrock},

title = {{3-loop heavy flavor Wilson coefficients in deep-inelastic scattering}},

booktitle = {{17th International Conference in Quantum Chromodynamics (QCD 14)}},

language = {english},

series = {Nucl. Phys. B (Proc. Suppl.)},

volume = {258-259},

pages = {41--44},

isbn_issn = {ISSN 0550-3213},

year = {2015},

note = { arXiv:1409.1804 [hep-ph]},

editor = {Stephan Narison},

refereed = {yes},

length = {4},

url = {http://arxiv.org/abs/arXiv:1409.1804}

}

**inproceedings**{RISC5060,author = {J. Ablinger and A. Behring and J. Blümlein and A. De Freitas and A. Hasselhuhn and A. von Manteuffel and C. Raab and M. Round and S. Schneider and F. Wißbrock},

title = {{3-loop heavy flavor Wilson coefficients in deep-inelastic scattering}},

booktitle = {{17th International Conference in Quantum Chromodynamics (QCD 14)}},

language = {english},

series = {Nucl. Phys. B (Proc. Suppl.)},

volume = {258-259},

pages = {41--44},

isbn_issn = {ISSN 0550-3213},

year = {2015},

note = { arXiv:1409.1804 [hep-ph]},

editor = {Stephan Narison},

refereed = {yes},

length = {4},

url = {http://arxiv.org/abs/arXiv:1409.1804}

}

### 3-Loop Corrections to the Heavy Flavor Wilson Coefficients in Deep-Inelastic Scattering

#### J. Ablinger, A. Behring, J. Blümlein, A. De Freitas, A. Hasselhuhn, A. von Manteuffel, C.G. Raab, M. Round, C. Schneider, F. Wißbrock

In: Proceedings of the European Physical Society Conference on High Energy Physics (EPS-HEP), PoS(EPS-HEP2015)504, pp. 1-13. 2015. ISSN 1824-8039. arXiv:1602.00583 [hep-ph]. [url]@

author = {J. Ablinger and A. Behring and J. Blümlein and A. De Freitas and A. Hasselhuhn and A. von Manteuffel and C.G. Raab and M. Round and C. Schneider and F. Wißbrock},

title = {{3-Loop Corrections to the Heavy Flavor Wilson Coefficients in Deep-Inelastic Scattering}},

booktitle = {{Proceedings of the European Physical Society Conference on High Energy Physics (EPS-HEP)}},

language = {english},

volume = {PoS(EPS-HEP2015)504},

pages = {1--13},

isbn_issn = {ISSN 1824-8039},

year = {2015},

note = {arXiv:1602.00583 [hep-ph]},

editor = {?},

refereed = {yes},

length = {13},

url = {http://pos.sissa.it/archive/conferences/234/504/EPS-HEP2015_504.pdf}

}

**inproceedings**{RISC5247,author = {J. Ablinger and A. Behring and J. Blümlein and A. De Freitas and A. Hasselhuhn and A. von Manteuffel and C.G. Raab and M. Round and C. Schneider and F. Wißbrock},

title = {{3-Loop Corrections to the Heavy Flavor Wilson Coefficients in Deep-Inelastic Scattering}},

booktitle = {{Proceedings of the European Physical Society Conference on High Energy Physics (EPS-HEP)}},

language = {english},

volume = {PoS(EPS-HEP2015)504},

pages = {1--13},

isbn_issn = {ISSN 1824-8039},

year = {2015},

note = {arXiv:1602.00583 [hep-ph]},

editor = {?},

refereed = {yes},

length = {13},

url = {http://pos.sissa.it/archive/conferences/234/504/EPS-HEP2015_504.pdf}

}

### Symbolic Computation and Finite Element Methods.

#### V. Pillwein

In: CASC 2015, V.P. Gerdt, W. Koepf, W.M. Seiler, and E.V. Vorozhtsov (ed.), LNCS 9301, pp. 374-388. 2015. Springer-Verlag Berlin Heidelberg, 0302-9743. [pdf]@

author = {V. Pillwein},

title = {{Symbolic Computation and Finite Element Methods.}},

booktitle = {{CASC 2015}},

language = {english},

series = {LNCS},

volume = {9301},

pages = {374--388},

publisher = {Springer-Verlag Berlin Heidelberg},

isbn_issn = {0302-9743},

year = {2015},

editor = {V.P. Gerdt and W. Koepf and W.M. Seiler and and E.V. Vorozhtsov},

refereed = {no},

length = {15}

}

**inproceedings**{RISC5182,author = {V. Pillwein},

title = {{Symbolic Computation and Finite Element Methods.}},

booktitle = {{CASC 2015}},

language = {english},

series = {LNCS},

volume = {9301},

pages = {374--388},

publisher = {Springer-Verlag Berlin Heidelberg},

isbn_issn = {0302-9743},

year = {2015},

editor = {V.P. Gerdt and W. Koepf and W.M. Seiler and and E.V. Vorozhtsov},

refereed = {no},

length = {15}

}

### Efficient Computation of Multiplicity and Directional Multiplicity of an Isolated Point

#### Angelos Mantzaflaris, Hamid Rahkooy, Zafeirakis Zafeirakopoulos

Technical report no. 15-08 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Schloss Hagenberg, 4232 Hagenberg, Austria. 2015. [pdf]@

author = { Angelos Mantzaflaris and Hamid Rahkooy and Zafeirakis Zafeirakopoulos},

title = {{Efficient Computation of Multiplicity and Directional Multiplicity of an Isolated Point}},

language = {english},

number = {15-08},

year = {2015},

length = {25},

type = {RISC Report Series},

institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},

address = {Schloss Hagenberg, 4232 Hagenberg, Austria}

}

**techreport**{RISC5152,author = { Angelos Mantzaflaris and Hamid Rahkooy and Zafeirakis Zafeirakopoulos},

title = {{Efficient Computation of Multiplicity and Directional Multiplicity of an Isolated Point}},

language = {english},

number = {15-08},

year = {2015},

length = {25},

type = {RISC Report Series},

institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},

address = {Schloss Hagenberg, 4232 Hagenberg, Austria}

}