Publications by Joris van der Hoeven
[ Homepage | Publications | TeXmacs | Mathemagix ]

My research interests mainly concern the automation of asymptotic calculus using transseries and effective complex analysis. My PhD. thesis and the book Transseries and Real Differential Algebra are devoted to the theory of transseries. The main results concern the asymptotic resolution of differential equations, several closure theorems and embedding theorems into Hardy fields. Currently, I am more and more interested in the automation of complex analysis. This leads to interesting theoretical questions about computability, zero-testing, singularities, etc. Another important aspect is the development and implementation of fast, certified and numerically stable algorithms for multi-precision computations. Many special functions fall in, or are related to the class of holonomic functions. I contributed to the development of some particularly efficient algorithms for such functions.

Books

2012

Proceedings of ISSAC 2012

37th International Symposium on Symbolic and Algebraic Computation

22–25 July, Grenoble, France

Editors: J. van der Hoeven, M. van Hoeij

2010

Proceedings of ICMS 2010

Third International Congress on Mathematical Software

Editors: K. Fukuda, J. van der Hoeven, M. Joswig, N. Takayama

Lecture Notes in Computer Science 6327, Springer-Verlag

2006

Transseries and Real Differential Algebra

Lecture Notes in Mathematics 1888, Springer-Verlag

2001

Corps de transséries

PhD. thesis of my former student Michael Schmeling

1997

Automatic asymptotics

PhD. thesis, École polytechnique, Palaiseau, France

Papers

2014

J. van der Hoeven and G. Lecerf. Sparse polynomial interpolation in practice Technical Report, HAL 00980366, 2014. Accepted for publication in ACM SIGSAM Communications in Computer Algebra.

J. van der Hoeven. Towards semantic mathematical editing. Technical Report, HAL 00569351, 2011. Accepted for publication in JSC.

J. van der Hoeven. Faster relaxed multiplication. Technical Report, HAL 00687479, 2012. Accepted for ISSAC 2014.

J. van der Hoeven. Computing with D-algebraic power series. Technical Report, HAL 00979367, 2014.

J. van der Hoeven. Effective power series computations. Technical Report, HAL 00979357, 2014.

J. van der Hoeven and F. Poulain. Conservative conversion between LaTeX and TeXmacs. Technical Report, HAL 00952926, 2014.

J. van der Hoeven, G. Lecerf, and G. Quintin. Modular SIMD arithmetic in Mathemagix. Technical Report, ArXiv:1407.3383, 2014.

D. Harvey, J. van der Hoeven, and G. Lecerf. Even faster integer multiplication. Technical Report, arXiv:1407.3360, 2014.

D. Harvey, J. van der Hoeven, and G. Lecerf. Faster polynomial multiplication over finite fields. Technical Report, arXiv:1407.3361, 2014.

2013

J. van der Hoeven and G. Lecerf. On the bit-complexity of sparse polynomial multiplication. JSC, 50:227–254, 2013.

J. van der Hoeven, A. Grozin, M. Gubinelli, G. Lecerf, F. Poulain and D. Raux. GNU TeXmacs: a scientific editing platform. ACM SIGSAM Communications in Computer Algebra 47(1/2):59–61, 2013.

J. van der Hoeven and É. Schost. Multi-point evaluation in higher dimensions. AAECC, 24(1):37–52, 2013.

J. van der Hoeven. Guessing singular dependencies. JSC, 59:54–80, 2013.

M. Aschenbrenner, L. van den Dries, and J. van der Hoeven. Towards a model theory for transseries. Notre Dame Journal of Formal Logic, 54(3-4):279–310, 2013.

J. van der Hoeven and R. Lebreton and É. Schost. Structured FFT and TFT: symmetric and lattice polynomials. HAL 00780431, 2013. Proc. ISSAC '13, pages 355–362, Boston, USA, June 2013.

J. van der Hoeven and G. Lecerf. Interfacing Mathemagix with C++. HAL 00771214, 2013. Proc. ISSAC '13, pages 363–370, Boston, USA, June 2013.

2012

J. van der Hoeven, G. Lecerf, B. Mourrain, P. Trébuchet, J. Berthomieu, D. Diatta and A. Manzaflaris. Mathemagix, the quest of modularity and efficiency for symbolic and certified numeric computation, ACM SIGSAM Communications in Computer Algebra 45(3/4):186–188, 2012.

T. DeVries, J. van der Hoeven, and R. Pemantle. Automatic asymptotics for coefficients of smooth, bivariate rational functions. Technical Report, Arxiv, 2011. Accepted for publication in the Online Journal of Analytic Combinatorics.

A. Benoit, A. Bostan and J. van der Hoeven. Quasi-optimal multiplication of linear differential operators. Proc. FOCS '12, pages 524–530, New Brunswick, USA, October 2012.

J. van der Hoeven and G. Lecerf. On the complexity of blockwise polynomial multiplication. HAL 00660454, 2012. In J. van der Hoeven, M. van Hoeij, editors, Proc. ISSAC '12, pages 211–218, Grenoble, France, July 2012.

J. van der Hoeven. Overview of the Mathemagix type system. Electronic Proc. ASCM '12, Beijing, China, October 2012. Preprint version: HAL 00702634.

J. van der Hoeven. On the complexity of polynomial reduction. Technical Report, HAL 00658704, 2012.

2011

J. Berthomieu, J. van der Hoeven, and G. Lecerf. Relaxed algorithms for -adic numbers. Journal de Théorie des Nombres de Bordeaux, 23(3):541–577, 2011.

A. Bostan, M. Chowdhury, J. van der Hoeven, and É. Schost. Homotopy methods for multiplication modulo triangular sets. JSC, 46(12):1378–1402, 2011.

J. van der Hoeven. Meta-expansion of transseries. JSC, 46(4):339–359, 2011.

J. van der Hoeven. Calcul analytique. Les cours du CIRM, 2 no. 1, Journées Nationales de Calcul Formel 2011, Exp. No. 4, 2011.

J. van der Hoeven. On the complexity of skew arithmetic. Technical Report, HAL 00557750, 2011.

J. van der Hoeven. From implicit to recursive equations. Technical Report, HAL 00583125, 2011.

J. van der Hoeven. Efficient root counting for analytic functions on a disk. Technical Report, HAL 00569351, 2011.

J. van der Hoeven. Reliable homotopy continuation. Technical Report, HAL 00589948, 2011.

2010

J. van der Hoeven. Newton's method and FFT trading. JSC, 45(8):857–878, 2010.

J. van der Hoeven. Uniformization of multivariate power series. Technical Report, HAL 00466469, 2010.

2009

J. van der Hoeven. On asymptotic extrapolation. JSC, 44(8):1000–1016, 2009.

X.-S. Gao, J. van der Hoeven, C. Yuan, and G. Zhang. Characteristic set method for differential-difference polynomial systems. JSC, 44(9):1137–1163, 2009.

J. van der Hoeven. Transserial Hardy fields. In Felipe Cano, Frank Loray, Juan José Moralez-Ruiz, Paulo Sad, and Mark Spivakovsky, editors, Differential Equations and Singularities. 60 years of J. M. Aroca, volume 323 of Astérisque, pages 453–487. SMF, 2009.

J. van der Hoeven. Ball arithmetic. Technical Report, HAL 00432152, 2009. Also in the informal proceedings of the conference Logical approaches to Barriers in Computing and Complexity, pages 179–208, Greifswald, Germany. Editors: Arnold Beckmann and Christine Gaßner and Bededikt Löwe.

J. van der Hoeven. Relaxed resolution of implicit equations. Technical Report, HAL 00441977, 2009.

2008

J. van der Hoeven. Meta-expansion of transseries. In Y. Boudabbous and N. Zaguia, editors, ROGICS '08: Relations Orders and Graphs, Interaction with Computer Science, pages 390–398, Mahdia, Tunesia, May 2008.

J. van der Hoeven. Fast composition of numeric power series. Technical Report 2008-09, Université Paris-Sud, Orsay, France, 2008.

J. van der Hoeven. Making fast multiplication of polynomials numerically stable. Technical Report 2008-02, Université Paris-Sud, Orsay, France, 2008.

2007

J. van der Hoeven. On effective analytic continuation. MCS, 1(1):111–175, 2007.

J. van der Hoeven. Efficient accelero-summation of holonomic functions. JSC, 42(4):389–428, 2007.

J. van der Hoeven. Around the numeric-symbolic computation of differential Galois groups. JSC, 42:236–264, 2007.

J. van der Hoeven. Generalized power series solutions to linear partial differential equations. JSC, 42(8):771–791, 2007.

J. van der Hoeven. New algorithms for relaxed multiplication. JSC, 42(8):792–802, 2007.

J. van der Hoeven. A zero-test for series defined in terms of solutions to partial differential equations. Technical Report 2007-15, Université Paris-Sud, Orsay, France

J. van der Hoeven. Transséries et analyse complexe effective. PhD thesis, Univ. d'Orsay, 2007. Mémoire d'habilitation.

2006

J. van der Hoeven. Computations with effective real numbers. TCS, 351:52–60, 2006.

J. van der Hoeven. Counterexamples to witness conjectures. JSC, 41:959–963, 2006.

J. van der Hoeven and J.R. Shackell. Complexity bounds for zero-test algorithms. JSC, 41:1004–1020, 2006.

J. van der Hoeven. Effective real numbers in Mmxlib. In D. Saunders, editor, Proc. ISSAC '06, Genova, Italy, July 2006.

J. van der Hoeven. GNU TeXmacs. In W. Decker, M. Dewar, E. Kaltofen, and S. Watt, editors, Challenges in Symbolic Computation Software, number 06271 in Dagstuhl Seminar Proceedings, Dagstuhl, Germany, 2006.

2005

J. van der Hoeven. Effective complex analysis. JSC, 39:433–449, 2005.

M. Aschenbrenner, L. van den Dries, and J. van der Hoeven. Differentially algebraic gaps. Selecta Mathematica, 11(2):247–280, 2005.

J. van der Hoeven. Integral transseries. Technical Report 2005-15, Université Paris-Sud, Orsay, France, 2005.

J. van der Hoeven. Notes on the Truncated Fourier Transform. Technical Report 2005-5, Université Paris-Sud, Orsay, France, 2005.

2004

J. van der Hoeven. The truncated Fourier transform and applications. In J. Gutierrez, editor, Proc. ISSAC 2004, pages 290–296, Univ. of Cantabria, Santander, Spain, July 4–7 2004.

2003

J. van der Hoeven. Relaxed multiplication using the middle product. In Manuel Bronstein, editor, Proc. ISSAC '03, pages 143–147, Philadelphia, USA, August 2003.

J. van der Hoeven. Majorants for formal power series. Technical Report 2003-15, Université Paris-Sud, Orsay, France, 2003.

2002

J. van der Hoeven. FFT-like multiplication of linear differential operators. JSC, 33(1):123–127, 2002.

J. van der Hoeven. Relax, but don't be too lazy. JSC, 34:479–542, 2002.

J. van der Hoeven. A differential intermediate value theorem. In B. L. J. Braaksma, G. K. Immink, M. van der Put, and J. Top, editors, Differential equations and the Stokes phenomenon, pages 147–170. World Scientific, 2002.

J. van der Hoeven. A new zero-test for formal power series. In Teo Mora, editor, Proc. ISSAC '02, pages 117–122, Lille, France, July 2002.

2001

J. van der Hoeven. Fast evaluation of holonomic functions near and in singularities. JSC, 31:717–743, 2001.

J. van der Hoeven. Operators on generalized power series. Journal of the Univ. of Illinois, 45(4):1161–1190, 2001.

J. van der Hoeven. GNU TeXmacs: A free, structured, wysiwyg and technical text editor. In Daniel Filipo, editor, Le document au XXI-ième siècle, volume 39–40, pages 39–50, Metz, 14–17 mai 2001. Actes du congrès GUTenberg.

J. van der Hoeven. Zero-testing, witness conjectures and differential diophantine approximation. Technical Report 2001-62, Prépublications d'Orsay, 2001.

J. van der Hoeven. D-algebraic power series. Technical Report 2001-61, Prépublications d'Orsay, 2001.

J. van der Hoeven. Formal asymptotics of solutions to certain linear differential equations involving oscillation. Technical Report 2001-60, Prépublications d'Orsay, 2001.

J. van der Hoeven. Complex transseries solutions to algebraic differential equations. Technical Report 2001-34, Univ. d'Orsay, 2001.

2000

H. N. Minh, M. Petitot, and J. van der Hoeven. Shuffle algebra and polylogarithms. Discrete Maths, 225:217–230, 2000.

J. van der Hoeven. A differential intermediate value theorem. Technical Report 2000-50, Univ. d'Orsay, 2000.

1999

J. van der Hoeven. Fast evaluation of holonomic functions. TCS, 210:199–215, 1999.

H. N. Minh, M. Petitot, and J. van der Hoeven. L'algèbre des polylogarithmes par les séries génératrices. In Proc. of FPSAC'99, 11-th international Conference on Formal Power Series and Algebraic Combinatorics, Barcelona, June 1999.

1998

J. van der Hoeven. Generic asymptotic expansions. AAECC, 9(1):25–44, 1998.

H. N. Minh, M. Petitot, and J. van der Hoeven. Monodromy of generalized polylogarithms. In O. Gloor, editor, Proc. ISSAC '98, pages 276–283, Rostock, Germany, August 1998.

1997

J. van der Hoeven. Lazy multiplication of formal power series. In W. W. Küchlin, editor, Proc. ISSAC '97, pages 17–20, Maui, Hawaii, July 1997.

1996

J. van der Hoeven. On the computation of limsups. Journal of Pure and Applied Algebra, 117/118:381–394, 1996.

D. Richardson, B. Salvy, J. Shackell, and J. van der Hoeven. Expansions of exp-log functions. In Y.N. Lakhsman, editor, Proc. ISSAC '96, pages 309–313, Zürich, Switzerland, July 1996.

J. van der Hoeven. Generic asymptotic expansions. In A. Carrière and L.R. Oudin, editors, Proc. of the fifth Rhine workshop on computer algebra, pages 17.1–17.17, 1996.

J. van der Hoeven. Differential and mixed differential-difference equations from the effective viewpoint. Technical Report LIX/RR/96/11, LIX, École polytechnique, France, 1996.

1995

J. van der Hoeven. Automatic numerical expansions. In J.-C. Bajard, D. Michelucci, J.-M. Moreau, and J.-M. Müller, editors, Proc. of the conference "Real numbers and computers", Saint-Étienne, France, pages 261–274, 1995.

J. van der Hoeven. Sur certains produits infinis. Technical Report LIX/RR/95/06, LIX, École polytechnique, France, 1995.

1994

J. van der Hoeven. General algorithms in asymptotics II: Common operations. Technical Report LIX/RR/94/10, LIX, École polytechnique, France, 1994.

J. van der Hoeven. General algorithms in asymptotics I: Gonnet and Gruntz' algorithm. Technical Report LIX/RR/94/10, LIX, École polytechnique, France, 1994.

J. van der Hoeven. Outils effectifs en asymptotique et applications. Technical Report LIX/RR/94/09, LIX, École polytechnique, France, 1994.

1993

J. van der Hoeven. Théorie des bases standard et séries Mahleriennes généralisées. Unpublished D.E.A. report, École polytechnique, France, 1993.