BibTeX entries

[1]

Pierre Lairez, Marc Mezzarobba, and Mohab Safey El Din. Computing the volume of compact semi-algebraic sets. In Proceedings of the 2019 on International Symposium on Symbolic and Algebraic Computation, page 259–266, New York, NY, USA, 2019. ACM.

@inproceedings{LairezMezzarobbaSafeyElDin2019,
  address = {New York, NY, USA},
  author = {Pierre Lairez and Marc Mezzarobba and Mohab {Safey El Din}},
  booktitle = {Proceedings of the 2019 on International Symposium on Symbolic and Algebraic Computation},
  doi = {10.1145/3326229.3326262},
  isbn = {978-1-4503-6084-5},
  pages = {259–266},
  publisher = {{ACM}},
  title = {Computing the Volume of Compact Semi-Algebraic Sets},
  url = {http://arxiv.org/abs/1904.11705},
  year = {2019}
}

[2]

Marc Mezzarobba. Truncation bounds for differentially finite series. Annales Henri Lebesgue, 2:99–148, 2019.

@article{Mezzarobba2019,
  author = {Marc Mezzarobba},
  doi = {10.5802/ahl.17},
  journal = {Annales Henri Lebesgue},
  pages = {99–148},
  publisher = {ÉNS Rennes},
  title = {Truncation Bounds for Differentially Finite Series},
  volume = {2},
  year = {2019}
}

[3]

Alexandre Benoit, Mioara Joldeș, and Marc Mezzarobba. Rigorous uniform approximation of D-finite functions using Chebyshev expansions. Mathematics of Computation, 86(305):1303–1341, 2017.

@article{BenoitJoldesMezzarobba2017,
  author = {Alexandre Benoit and Mioara Joldeș and Marc Mezzarobba},
  doi = {10.1090/mcom/3135},
  journal = {Mathematics of Computation},
  number = {305},
  pages = {1303–1341},
  publisher = {American Mathematical Society},
  title = {Rigorous Uniform Approximation of {D}-finite Functions Using {C}hebyshev Expansions},
  url = {http://hal.archives-ouvertes.fr/hal-01022420/},
  volume = {86},
  year = {2017}
}

[4]

Nicolas Brisebarre, Christoph Lauter, Marc Mezzarobba, and Jean-Michel Muller. Comparison between binary and decimal floating-point numbers. IEEE Transactions on Computers, 65(7):2032–2044, 2016.

@article{BrisebarreLauterMezzarobbaMuller2016,
  author = {Nicolas Brisebarre and Christoph Lauter and Marc Mezzarobba and Jean-Michel Muller},
  journal = {IEEE Transactions on Computers},
  number = {7},
  pages = {2032–2044},
  title = {Comparison between binary and decimal floating-point numbers},
  url = {http://hal.archives-ouvertes.fr/hal-01021928/},
  volume = {65},
  year = {2016}
}

[5]

Alexandre Benoit, Frédéric Chyzak, Alexis Darrasse, Stefan Gerhold, Marc Mezzarobba, and Bruno Salvy. The dynamic dictionary of mathematical functions (DDMF). In Fukuda et al. [27], page 35–41.

@inproceedings{BenoitChyzakDarrasseGerholdMezzarobbaSalvy2010,
  author = {Alexandre Benoit and Frédéric Chyzak and Alexis Darrasse and Stefan Gerhold and Marc Mezzarobba and Bruno Salvy},
  crossref = {ICMS2010},
  pages = {35–41},
  title = {The Dynamic Dictionary of Mathematical Functions ({DDMF})},
  url = {http://marc.mezzarobba.net/papers/BenoitEtAl_DDMF_2010.pdf},
  year = {2010}
}

@proceedings{ICMS2010,
  booktitle = {Mathematical Software — ICMS 2010},
  editor = {Komei Fukuda and Joris van der Hoeven and Michael Joswig and Nobuki Takayama},
  publisher = {Springer},
  series = {Lecture Notes in Computer Science},
  title = {Mathematical Software – {ICMS} 2010},
  volume = {6327},
  year = {2010}
}

[6]

Nicolas Brisebarre, Christoph Lauter, Marc Mezzarobba, and Jean-Michel Muller. Comparison between binary64 and decimal64 floating-point numbers. In Nannarelli et al. [29], page 145–152.

@inproceedings{BrisebarreLauterMezzarobbaMuller2013,
  author = {Nicolas Brisebarre and Christoph Lauter and Marc Mezzarobba and Jean-Michel Muller},
  crossref = {ARITH2013},
  pages = {145–152},
  title = {Comparison between binary64 and decimal64 floating-point numbers},
  url = {http://hal.archives-ouvertes.fr/ensl-00737881},
  year = {2013}
}

@proceedings{ARITH2013,
  address = {Austin, Texas, USA},
  booktitle = {ARITH~21},
  editor = {Alberto Nannarelli and Peter-Michael Seidel and Ping Tak Peter Tang},
  publisher = {IEEE},
  title = {Proceedings of the 21st {IEEE} Symposium on Computer Arithmetic},
  year = {2013}
}

[7]

Sylvain Chevillard and Marc Mezzarobba. Multiple precision evaluation of the Airy Ai function with reduced cancellation. In Nannarelli et al. [29], page 175–182.

@inproceedings{ChevillardMezzarobba2013,
  author = {Sylvain Chevillard and Marc Mezzarobba},
  crossref = {ARITH2013},
  pages = {175–182},
  title = {Multiple precision evaluation of the {A}iry {Ai} function with reduced cancellation},
  url = {http://arxiv.org/abs/1212.4731},
  year = {2013}
}

@proceedings{ARITH2013,
  address = {Austin, Texas, USA},
  booktitle = {ARITH~21},
  editor = {Alberto Nannarelli and Peter-Michael Seidel and Ping Tak Peter Tang},
  publisher = {IEEE},
  title = {Proceedings of the 21st {IEEE} Symposium on Computer Arithmetic},
  year = {2013}
}

[8]

Marc Mezzarobba. A note on the space complexity of fast D-finite function evaluation. In Gerdt et al. [28], page 212–223.

@inproceedings{Mezzarobba2012,
  author = {Marc Mezzarobba},
  crossref = {CASC2012},
  pages = {212–223},
  title = {A Note on the Space Complexity of Fast {D}-Finite Function Evaluation},
  url = {http://arxiv.org/abs/1209.5097},
  year = {2012}
}

@proceedings{CASC2012,
  booktitle = {CASC 2012},
  editor = {V. P. Gerdt and W. Koepf and E. W. Mayr and E. V. Vorozhtsov},
  number = {7442},
  publisher = {Springer},
  series = {Lecture Notes in Computer Science},
  title = {Computer Algebra in Scientific Computing},
  year = {2012}
}

[9]

Marc Mezzarobba. NumGfun: a package for numerical and analytic computation with D-finite functions. In Watt [30], page 139–146.

@inproceedings{Mezzarobba2010,
  author = {Marc Mezzarobba},
  crossref = {ISSAC2010},
  doi = {10.1145/1837934.1837965},
  hal = {inria-00456983},
  pages = {139–146},
  title = {{NumGfun}: a Package for Numerical and Analytic Computation with {D}-finite Functions},
  url = {http://arxiv.org/abs/1002.3077},
  year = {2010}
}

@proceedings{ISSAC2010,
  booktitle = {{ISSAC} '10},
  editor = {Stephen M. Watt},
  isbn = {978-1-4503-0150-3},
  location = {Munich, Germany},
  publisher = {ACM},
  title = {{ISSAC} '10: Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation},
  year = {2010}
}

[10]

Alexandre Casamayou, Nathann Cohen, Guillaume Connan, Thierry Dumont, Laurent Fousse, François Maltey, Matthias Meulien, Marc Mezzarobba, Clément Pernet, Nicolas M. Thiéry, and Paul Zimmermann. Calcul mathématique avec Sage. Createspace, 2013.

@book{sagebook,
  author = {Alexandre Casamayou and Nathann Cohen and Guillaume Connan and Thierry Dumont and Laurent Fousse and François Maltey and Matthias Meulien and Marc Mezzarobba and Clément Pernet and Nicolas M. Thiéry and Paul Zimmermann},
  isbn = {1481191047},
  publisher = {Createspace},
  title = {Calcul mathématique avec {S}age},
  url = {http://sagebook.gforge.inria.fr/},
  year = {2013}
}

[11]

Fredrik Johansson, Manuel Kauers, and Marc Mezzarobba. Finding hyperexponential solutions of linear ODEs by numerical evaluation. In ISSAC '13 [26].

@inproceedings{JohanssonKauersMezzarobba2013,
  author = {Fredrik Johansson and Manuel Kauers and Marc Mezzarobba},
  crossref = {ISSAC2013},
  title = {Finding Hyperexponential Solutions of Linear {ODE}s by Numerical Evaluation},
  url = {http://arxiv.org/abs/1301.2486}
}

@proceedings{ISSAC2013,
  booktitle = {{ISSAC} '13},
  location = {Boston, MA, USA},
  publisher = {ACM},
  title = {{ISSAC} 2013: Proceedings of the 38th international symposium on Symbolic and algebraic computation},
  year = {2013}
}

[12]

Marc Mezzarobba. Autour de l'évaluation numérique des fonctions D-finies. Thèse de doctorat, École polytechnique, November 2011.

@phdthesis{Mezzarobba2011,
  author = {Marc Mezzarobba},
  month = nov,
  school = {École polytechnique},
  title = {Autour de l'évaluation numérique des fonctions {D}-finies},
  type = {Thèse de doctorat},
  url = {http://tel.archives-ouvertes.fr/pastel-00663017/},
  year = {2011}
}

[13]

Marc Mezzarobba. NumGfun User Manual, 2014.

@manual{NumGfunManual,
  author = {Marc Mezzarobba},
  title = {{NumGfun} User Manual},
  url = {http://marc.mezzarobba.net/papers/NumGfun_User_Manual.pdf},
  year = {2014}
}

[14]

Marc Mezzarobba. Génération automatique de procédures numériques pour les fonctions D-finies. Rapport de stage, Master parisien de recherche en informatique, October 2007. Version 1.2.

@mastersthesis{Mezzarobba2007,
  author = {Marc Mezzarobba},
  month = oct,
  note = {Version 1.2},
  school = {Master parisien de recherche en informatique},
  title = {Génération automatique de procédures numériques pour les fonctions {D}-finies},
  type = {Rapport de stage},
  url = {http://marc.mezzarobba.net/m2/Mezzarobba_MScThesisMPRI2007-1.2.pdf},
  year = {2007}
}

[15]

Marc Mezzarobba and Mohab Safey El Din. Computing roadmaps in smooth real algebraic sets. In Jean-Guillaume Dumas, editor, Proceedings of Transgressive Computing 2006, page 327–338, 2006.

@inproceedings{MezzarobbaSafey2006,
  author = {Marc Mezzarobba and Mohab {Safey El Din}},
  booktitle = {Proceedings of Transgressive Computing 2006},
  editor = {Jean-Guillaume Dumas},
  pages = {327–338},
  title = {Computing roadmaps in smooth real algebraic sets},
  url = {http://marc.mezzarobba.net/papers/MezzarobbaSafey_Roadmaps_v2_2006.pdf},
  year = {2006}
}

[16]

Marc Mezzarobba and Bruno Salvy. Effective bounds for P-recursive sequences. Journal of Symbolic Computation, 45(10):1075–1096, 2010.

@article{MezzarobbaSalvy2010,
  author = {Marc Mezzarobba and Bruno Salvy},
  doi = {10.1016/j.jsc.2010.06.024},
  journal = {Journal of Symbolic Computation},
  number = {10},
  pages = {1075–1096},
  title = {Effective Bounds for {P}-recursive sequences},
  url = {http://arxiv.org/abs/0904.2452},
  volume = {45},
  year = {2010}
}

[17]

Christoph Lauter and Marc Mezzarobba. Semi-automatic floating-point implementation of special functions. In Muller et al. [25].

@inproceedings{LauterMezzarobba2015,
  author = {Christoph Lauter and Marc Mezzarobba},
  crossref = {ARITH2015},
  title = {Semi-Automatic Floating-Point Implementation of Special Functions},
  url = {https://hal.archives-ouvertes.fr/hal-01137953},
  year = {2015}
}

@proceedings{ARITH2015,
  address = {Lyon, France},
  booktitle = {ARITH~22},
  editor = {Jean-Michel Muller and Arnaud Tisserand and Julio Villalba},
  publisher = {IEEE},
  title = {Proceedings of the 22nd {IEEE} Symposium on Computer Arithmetic},
  year = {2015}
}

[18]

Frédéric Chyzak, Thomas Dreyfus, Philippe Dumas, and Marc Mezzarobba. Computing solutions of linear Mahler equations. Mathematics of Computation, 87(314):2977–3021, 2018.

@article{ChyzakDreyfusDumasMezzarobba2018,
  author = {Frédéric Chyzak and Thomas Dreyfus and Philippe Dumas and Marc Mezzarobba},
  doi = {10.1090/mcom/3359},
  journal = {Mathematics of Computation},
  number = {314},
  pages = {2977–3021},
  title = {Computing solutions of linear {M}ahler equations},
  url = {https://arxiv.org/abs/1612.05518},
  volume = {87},
  year = {2018}
}

[19]

Marc Mezzarobba. Rigorous multiple-precision evaluation of D-finite functions in SageMath. Technical Report 1607.01967, arXiv, 2016. Extended abstract of a talk at the 5th International Congress on Mathematical Software.

@techreport{Mezzarobba2016,
  author = {Marc Mezzarobba},
  institution = {arXiv},
  note = {Extended abstract of a talk at the 5th International Congress on Mathematical Software},
  number = {1607.01967},
  title = {Rigorous Multiple-Precision Evaluation of {D}-Finite Functions in {S}age{M}ath},
  url = {http://arxiv.org/abs/1607.01967},
  year = {2016}
}

[20]

Fredrik Johansson and Marc Mezzarobba. Fast and rigorous arbitrary-precision computation of Gauss–Legendre quadrature nodes and weights. SIAM Journal on Scientific Computing, 40(6):C726–C747, 2018.

@article{JohanssonMezzarobba2018,
  author = {Fredrik Johansson and Marc Mezzarobba},
  doi = {10.1137/18M1170133},
  journal = {SIAM Journal on Scientific Computing},
  number = {6},
  pages = {C726–C747},
  title = {Fast and Rigorous Arbitrary-Precision Computation of {G}auss–{L}egendre Quadrature Nodes and Weights},
  url = {https://arxiv.org/abs/1802.03948},
  volume = {40},
  year = {2018}
}

[21]

Paul Zimmermann, Alexandre Casamayou, Nathann Cohen, Guillaume Connan, Thierry Dumont, Laurent Fousse, François Maltey, Matthias Meulien, Marc Mezzarobba, Clément Pernet, Nicolas M. Thiéry, Erik Bray, John Cremona, Marcelo Forets, Alexandru Ghitza, and Hugh Thomas. Computational Mathematics with SageMath. SIAM, 2018.

@book{sagebook-en,
  author = {Paul Zimmermann and Alexandre Casamayou and Nathann Cohen and Guillaume Connan and Thierry Dumont and Laurent Fousse and François Maltey and Matthias Meulien and Marc Mezzarobba and Clément Pernet and Nicolas M. Thiéry and Erik Bray and John Cremona and Marcelo Forets and Alexandru Ghitza and Hugh Thomas},
  isbn = {9781611975451},
  publisher = {SIAM},
  title = {Computational Mathematics with SageMath},
  url = {http://sagebook.gforge.inria.fr/english.html},
  year = {2018}
}

[22]

Horatio Boedihardjo, Joscha Diehl, Marc Mezzarobba, and Hao Ni. The expected signature of brownian motion stopped on the boundary of a circle has finite radius of convergence. Bulletin of the London Mathematical Society, 53(1):285–299, 2021.

@article{BoedihardjoDiehlMezzarobbaNi2021,
  author = {Horatio Boedihardjo and Joscha Diehl and Marc Mezzarobba and Hao Ni},
  journal = {Bulletin of the London Mathematical Society},
  number = {1},
  pages = {285–299},
  title = {The expected signature of Brownian motion stopped on the boundary of a circle has finite radius of convergence},
  url = {https://arxiv.org/abs/1905.13034},
  volume = {53},
  year = {2021}
}

[23]

Manuel Kauers and Marc Mezzarobba. Multivariate Ore polynomials in SageMath. ACM Communications in Computer Algebra, 53(2):57–60, 2019. ISSAC 2019 software presentations.

@article{KauersMezzarobba2019,
  author = {Manuel Kauers and Marc Mezzarobba},
  doi = {10.1145/3371991.3371998},
  institution = {HAL},
  journal = {{ACM} Communications in Computer Algebra},
  note = {{ISSAC} 2019 software presentations},
  number = {2},
  pages = {57–60},
  title = {Multivariate {O}re Polynomials in {S}age{M}ath},
  url = {https://hal.archives-ouvertes.fr/hal-02145876},
  volume = {53},
  year = {2019}
}

[24]

Marc Mezzarobba. Error analysis of linear recurrences using generating series. Technical Report hal-02984459, 2020.

@techreport{Mezzarobba2020,
  author = {Marc Mezzarobba},
  number = {hal-02984459},
  organization = {HAL},
  title = {Error Analysis of Linear Recurrences Using Generating Series},
  url = {https://hal.archives-ouvertes.fr/hal-02984459},
  year = {2020}
}

[25]

Jean-Michel Muller, Arnaud Tisserand, and Julio Villalba, editors. Proceedings of the 22nd IEEE Symposium on Computer Arithmetic, Lyon, France, 2015. IEEE.

@proceedings{ARITH2015,
  address = {Lyon, France},
  booktitle = {ARITH~22},
  editor = {Jean-Michel Muller and Arnaud Tisserand and Julio Villalba},
  publisher = {IEEE},
  title = {Proceedings of the 22nd {IEEE} Symposium on Computer Arithmetic},
  year = {2015}
}

[26]

ISSAC 2013: Proceedings of the 38th international symposium on Symbolic and algebraic computation. ACM, 2013.

@proceedings{ISSAC2013,
  booktitle = {{ISSAC} '13},
  location = {Boston, MA, USA},
  publisher = {ACM},
  title = {{ISSAC} 2013: Proceedings of the 38th international symposium on Symbolic and algebraic computation},
  year = {2013}
}

[27]

Komei Fukuda, Joris van der Hoeven, Michael Joswig, and Nobuki Takayama, editors. Mathematical Software – ICMS 2010, volume 6327 of Lecture Notes in Computer Science. Springer, 2010.

@proceedings{ICMS2010,
  booktitle = {Mathematical Software — ICMS 2010},
  editor = {Komei Fukuda and Joris van der Hoeven and Michael Joswig and Nobuki Takayama},
  publisher = {Springer},
  series = {Lecture Notes in Computer Science},
  title = {Mathematical Software – {ICMS} 2010},
  volume = {6327},
  year = {2010}
}

[28]

V. P. Gerdt, W. Koepf, E. W. Mayr, and E. V. Vorozhtsov, editors. Computer Algebra in Scientific Computing, number 7442 in Lecture Notes in Computer Science. Springer, 2012.

@proceedings{CASC2012,
  booktitle = {CASC 2012},
  editor = {V. P. Gerdt and W. Koepf and E. W. Mayr and E. V. Vorozhtsov},
  number = {7442},
  publisher = {Springer},
  series = {Lecture Notes in Computer Science},
  title = {Computer Algebra in Scientific Computing},
  year = {2012}
}

[29]

Alberto Nannarelli, Peter-Michael Seidel, and Ping Tak Peter Tang, editors. Proceedings of the 21st IEEE Symposium on Computer Arithmetic, Austin, Texas, USA, 2013. IEEE.

@proceedings{ARITH2013,
  address = {Austin, Texas, USA},
  booktitle = {ARITH~21},
  editor = {Alberto Nannarelli and Peter-Michael Seidel and Ping Tak Peter Tang},
  publisher = {IEEE},
  title = {Proceedings of the 21st {IEEE} Symposium on Computer Arithmetic},
  year = {2013}
}

[30]

Stephen M. Watt, editor. ISSAC '10: Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation. ACM, 2010.

@proceedings{ISSAC2010,
  booktitle = {{ISSAC} '10},
  editor = {Stephen M. Watt},
  isbn = {978-1-4503-0150-3},
  location = {Munich, Germany},
  publisher = {ACM},
  title = {{ISSAC} '10: Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation},
  year = {2010}
}