Publications by Joris van der Hoeven
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My research interests mainly concern the automation of asymptotic calculus using transseries and effective complex analysis.

My PhD. thesis and my book Transseries and Real Differential Algebra are devoted to the theory of transseries. My joint book Asymptotic Differential Algebra and Model Theory of Transseries with M. Aschenbrenner and L. van den Dries also studies the corresponding model theory. The main results concern the asymptotic resolution of differential equations, several closure theorems, embedding theorems into Hardy fields, and quantifier elimination for asymptotic differential algebra.

Another main research topic of mine is the automation of complex analysis and computations with special functions or more general solutions to differential equations. On the one hand, this leads to interesting theoretical questions about computability, zero-testing, singularities, etc. On the other hand, this requires the development and implementation of fast, certified and numerically stable algorithms for multi-precision computations.

The development of fast algorithms for basic mathematical operations has evolved into one of my research topics on its own. In collaboration with D. Harvey and G. Lecerf, we improved the best known complexity bounds for integer multiplication and polynomial multiplication over finite fields. Continued work with David Harvey culminated in our O(n log n) bound for integer multiplication. 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

2023

Maximal Hardy Fields

Authors: M. Aschenbrenner, L. van den Dries, J. van der Hoeven

2020

The Jolly Writer

Your Guide to GNU TeXmacs

Scypress, Chevreuse, France

2017

Asymptotic Differential Algebra and Model Theory of Transseries

Authors: M. Aschenbrenner, L. van den Dries, J. van der Hoeven

Annals of Mathematics Studies, Princeton University Press

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

*

J. van der Hoeven, G. Lecerf. Univariate polynomial factorization over large finite fields. Technical Report, HAL 03019847, 2020. Accepted for publication in AAECC.

J. van der Hoeven. Fuchsian holonomic sequences Prepublication, HAL 03291372, 2021. Accepted for publication in AAECC.

J. van der Hoeven, G. Lecerf. Sparse polynomial interpolation: faster strategies over finite fields. Prepublication, HAL 02382117, 2019. Accepted for publication in AAECC.

V. Bagayoko, J. van der Hoeven. Surreal substructures. Prepublication, HAL 02151377, 2019. Accepted for publication in Fundamenta Mathematicae.

2024

J. van der Hoeven, F. Johansson. Fast multiple precision with precomputations. Proc. ARITH '24, pages 80–87, Malaga, France, June 2024.

M. Aschenbrenner, L. van den Dries, J. van der Hoeven. Maximal Hardy fields. ArXiv 2304.10846, 2024.

M. Aschenbrenner, L. van den Dries, J. van der Hoeven. Constructing -free Hardy fields. ArXiv 2404.03695, 2024.

M. Aschenbrenner, L. van den Dries, J. van der Hoeven. A normalization theorem in asymptotic differential algebra. ArXiv 2403.19732, 2024.

2023

J. van der Hoeven, G. Lecerf. Amortized multi-point evaluation of multivariate polynomials. Journal of Complexity, 74, Article 101693, 2023.

J. van der Hoeven, G. Lecerf. Fast interpolation of sparse multivariate polynomials. Prepublication, HAL 04366836, 2023.

A. Demin, J. van der Hoeven. Factoring sparse polynomials fast. Prepublication, HAL 04366390, 2023.

M. Aschenbrenner, L. van den Dries, J. van der Hoeven. Filling gaps in Hardy fields. ArXiv 2308.02446, 2023.

2022

M. Aschenbrenner, L. van den Dries, J. van der Hoeven. Revisiting closed asymptotic couples. Proc. of the Edinburgh Math. Soc. 65(2):530—555, 2022.

M. Aschenbrenner, L. van den Dries, J. van der Hoeven. On a differential intermediate value property. Revista de la Unión Matemática Argentina, 64(1):1–10, 2022.

D. Harvey, J. van der Hoeven. Polynomial multiplication over finite fields in time O(n log n). J. ACM, 69(2):1–40, 2022. Article No.: 12.

J. van der Hoeven. On the complexity of symbolic computation. Proc. ISSAC '22, pages 3–12, July 2022.

V. Bagayoko, J. van der Hoeven. Surreal numbers as hyperseries. Prepublication, HAL 03681007, 2022.

J. van der Hoeven, G. Lecerf. Approximate contact factorization of germs of plane curves. Prepublication, HAL 03745581, 2022.

J. van der Hoeven. Optimizing the half-gcd algorithm Prepublication, HAL 03912084, 2022.

2021

D. Harvey, J. van der Hoeven. Integer multiplication in time O(n log n). Annals of Math. 193(2):563–617, 2021.

J. van der Hoeven, G. Lecerf. On the complexity exponent of polynomial system solving. Foundations of Comp. Math., 21:1–57, 2021.

J. van der Hoeven. Multiplier des entiers en temps . La gazette du GDR-IM, 2:10–18, 2021.

J. van der Hoeven, M. Monagan. Computing one billion roots using the tangent Graeffe method. ACM SIGSAM Communications in Computer Algebra 54(3):65–85, 2021.

J. van der Hoeven, G. Lecerf. On sparse interpolation of rational functions and gcds. ACM SIGSAM Communications in Computer Algebra 55(1):1–12, 2021.

J. van der Hoeven. Constructing reductions for creative telescoping. AAECC, 32:575–602, 2021.

J. van der Hoeven, G. Lecerf. Fast computation of generic bivariate resultants. Journal of Complexity, 62, Article 101499, 2021.

J. van der Hoeven, Grégoire Lecerf. Fast amortized multi-point evaluation. Journal of Complexity, 67, Article 101574, 2021.

J. van der Hoeven, G. Lecerf. Amortized bivariate multi-point evaluation. Proc. ISSAC '21, pages 479–185, July 2021.

J. van der Hoeven, G. Pogudin. A zero test for -algebraic power series. Proc. ISSAC '21, pages 187–192, July 2021.

V. Bagayoko, J. van der Hoeven, E. Kaplan. Hyperserial fields. Prepublication, HAL 03196388, 2021.

V. Bagayoko, J. van der Hoeven. The hyperserial field of surreal numbers. Prepublication, HAL 03232836, 2021.

2020

J. van der Hoeven. Getallen vermenigvuldigen in stappen. Nieuw Archief voor Wiskunde. Vijfde serie, 21(1):55–60, 2020.

J. van der Hoeven, G. Lecerf. Ultimate complexity for numerical algorithms. ACM SIGSAM Communications in Computer Algebra 54(1):1–13, 2020.

C. Grunspan, J. van der Hoeven. Effective asymptotic analysis for finance. Intern. J. of Th. and Appl. Finance 23(2):2050013, 2020.

J. van der Hoeven, G. Lecerf. Fast multivariate multi-point evaluation revisited. Journal of Complexity, 56, Article 101405, 2020.

J. van der Hoeven, G. Lecerf. Directed evaluation. Journal of Complexity, 60, Article 101498, 2020.

J. van der Hoeven, M. Monagan. Implementing the tangent Graeffe root finding method. In Mathematical Software — Proc. ICMS 2020, pages 482–492. Springer International Publishing. Cham. 2020.

J. van der Hoeven. Probably faster multiplication of sparse polynomials. Prepublication, HAL 02473830, 2020.

V. Bagayoko, J. van der Hoeven, V. Mantova. Defining a surreal hyperexponential. Prepublication, HAL 02861485, 2020.

2019

D. Harvey, J. van der Hoeven. Faster integer multiplication using plain vanilla FFT primes. Math. Comp., 88(315):501–514, 2019.

J. van der Hoeven. Computing with D-algebraic power series. AAECC, 30(1):17–49, 2019.

J. van der Hoeven, R. Larrieu. Fast Gröbner basis computation and polynomial reduction for generic bivariate ideals. AAECC, 30(6):509–539, 2019.

M. Aschenbrenner, L. van den Dries, J. van der Hoeven. The surreal numbers as a universal -field. J. Eur. Math. Soc., 21(4):1179–1199, 2019.

L. van den Dries, J. van der Hoeven, E. Kaplan. Logarithmic hyperseries. Trans. of the AMS, 372(7):5199–5241, 2019.

J. van der Hoeven. From implicit to recursive equations. AAECC, 30(3):243–262, 2019.

J. van der Hoeven. Effective power series computations. Foundations of Comp. Math., 19(3): 623–651, 2019.

J. van der Hoeven and R. Larrieu. Fast Gröbner basis computation and polynomial reduction for generic bivariate ideals. ACM SIGSAM Communications in Computer Algebra 52(3):55–58, 2019.

D. Harvey, J. van der Hoeven. Faster polynomial multiplication over finite fields using cyclotomic coefficient rings. Journal of Complexity, 54, Article 101404, 2019.

J. van der Hoeven, G. Lecerf. Accelerated tower arithmetic. Journal of Complexity, 55, Article 101402, 2019.

D. Harvey, J. van der Hoeven. Faster integer multiplication using short lattice vectors. In R. Scheidler and J. Sorenson, editors, Proc. of the 13-th Algorithmic Number Theory Symposium, Open Book Series 2, pages 293–310. Mathematical Sciences Publishes, Berkeley, 2019.

J.-G. Dumas, J. van der Hoeven, C. Pernet, D. S. Roche. LU factorization with errors. In Proc. ISSAC '19, pages 131–138. New York, NY, USA, 2019. ACM.

M. Aschenbrenner, L. van den Dries, J. van der Hoeven. Hardy fields, the intermediate value property, and -freeness. In Structures algébriques ordonnées, séminaire 2017–18, Delon, F., Dickmann, M., Gondard, D., and Servi, T., Eds., vol. 93 of Prépublications de l'équipe de logique mathématique de l'Université Paris Diderot. 2019.

2018

D. Harvey, J. van der Hoeven. On the complexity of integer matrix multiplication. JSC, 89:1–8, 2018.

J. van der Hoeven, G. Lecerf. Modular composition via factorization. Journal of Complexity, 48:36–68, 2018.

M. Aschenbrenner, L. van den Dries, J. van der Hoeven. Maximal immediate extensions of valued differential fields. Proc. of the London Math. Soc., 117(2):376–406, 2018.

M. Aschenbrenner, L. van den Dries, J. van der Hoeven. On Numbers, Germs, and Transseries. In Proc. Int. Cong. of Math., volume 1, pages 1–24. Rio de Janeiro, Brasil, 2018.

J. van der Hoeven, R. Larrieu. Fast reduction of bivariate polynomials with respect to sufficiently regular Gröbner bases. Proc. ISSAC '18, pages 199–206, New York, USA, July 2018.

J. van der Hoeven. Creative telescoping using reductions. Prepublication, HAL 01773137, 2018.

J. van der Hoeven. On high precision integration of stiff differential equations. Prepublication, HAL 01889324, 2018.

J. van der Hoeven, J.-C. Yakoubsohn. Certified Singular Value Decomposition. Prepublication, HAL 01941987, 2018.

2017

D. Harvey, J. van der Hoeven, G. Lecerf. Faster polynomial multiplication over finite fields. JACM, 63(6), Article 52, 2017.

M. Aschenbrenner, L. van den Dries, J. van der Hoeven. Dimension in the realm of transseries. In Fabrizio Broglia, Françoise Delon, Max Dickmann, Danielle Gondard-Cozette, and Victoria Ann Powers, editors, Proc. International conference on Ordered Algebraic Structures and Related Topics, volume 697 of Contemporary Mathematics, pages 23–40. AMS, 2017.

J. van der Hoeven. Multiple precision floating point arithmetic on SIMD processors. Proc. ARITH '17, pages 2–9, London, UK, July 2017.

J. van der Hoeven, R. Larrieu. The Frobenius FFT. Proc. ISSAC '17, pages 437–444, Kaiserslautern, Germany, July 2017.

J. van der Hoeven, G. Lecerf. Composition modulo powers of polynomials. Proc. ISSAC '17, pages 445–452, Kaiserslautern, Germany, July 2017.

J. van der Hoeven, B. Mourrain. Efficient certification of numeric solutions to eigenproblems. Proc. MACIS '17, pages 81–94, Vienna, Austria, November 2017.

J. van der Hoeven, R. Larrieu, G. Lecerf. Implementing fast carryless multiplication. Proc. MACIS '17, pages 121–136, Vienna, Austria, November 2017.

J. van der Hoeven. Fast Chinese remaindering in practice. Proc. MACIS '17, pages 95–106, Vienna, Austria, November 2017.

2016

D. Harvey, J. van der Hoeven, G. Lecerf. Even faster integer multiplication. Journal of Complexity, 36:1–30, 2016.

J. van der Hoeven. On the complexity of skew arithmetic. AAECC, 27(2):105–122, 2016.

B. Grenet, J. van der Hoeven, G. Lecerf. Deterministic root finding over finite fields using Graeffe transforms. AAECC, 27(3):237–257, 2016.

J. van der Hoeven, G. Lecerf, and G. Quintin. Modular SIMD arithmetic in Mathemagix. ACM Trans. Math. Softw., 43(1), 5:1–5:37, 2016.

D. Harvey, J. van der Hoeven, G. Lecerf. Fast Polynomial Multiplication over . Proc. ISSAC '16, pages 255–262, Waterloo, Canada, July 2016.

J. van der Hoeven. Mathematical Font Art. Proc. ICMS '16, pages 522–529, Berlin, Germany, July 2016.

J. van der Hoeven, G. Lecerf. Evaluating straight-line programs over balls. Proc. ARITH '16, pages 142–149, Silicon Valley, USA, July 2016.

J. van der Hoeven. Uniformly fast evaluation of holonomic functions. Prepublication, HAL 01374898, 2016.

J. van der Hoeven. Faster Chinese remaindering. Prepublication, HAL 01403810, 2016.

2015

J. van der Hoeven and G. Lecerf. Sparse polynomial interpolation in practice. ACM SIGSAM Communications in Computer Algebra 48(3/4):187–191, 2015.

J. van der Hoeven. Towards semantic mathematical editing. JSC, 71:1–46, 2015.

J. van der Hoeven and G. Lecerf. Faster FFTs in medium precision. Proc. ARITH '15, pages 75–82, Lyon, France, June 2015.

B. Grenet, J. van der Hoeven, G. Lecerf. Randomized root finding over finite fields using tangent Graeffe transforms. Proc. ISSAC '15, pages 197–204, Bath, United Kingdom, July 2015.

J. van der Hoeven. Certifying trajectories of dynamical systems. Proc. MACIS '15, pages 520–532, Berlin, Germany, November 2015.

J. van der Hoeven, G. Lecerf, D. Raux. Preserving syntactic correctness while editing mathematical formulas. Proc. ACA '15, pages 447–458, Kalamata, Greece, July 2015.

J. van der Hoeven. On the complexity of polynomial reduction. Proc. ACA '15, pages 459–471, Kalamata, Greece, July 2015.

2014

J. van der Hoeven. Faster relaxed multiplication. Proc. ISSAC '14, pages 405–412, Kobe, Japan, July 2014.

Massimiliano Gubinelli, Joris van der Hoeven, François Poulain, Denis Raux. GNU TeXmacs: towards a scientific office suite. Proc. ICMS '14, pages 562–569, Seoul, South Korea, August 2014.

J. van der Hoeven and F. Poulain. Conservative conversion between LaTeX and TeXmacs. Prepublication, HAL 00952926, 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, 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, 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, R. Lebreton, 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, 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, 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.

A. Benoit, A. Bostan, 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, 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.

2011

J. Berthomieu, J. van der Hoeven, 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, 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.

T. DeVries, J. van der Hoeven, R. Pemantle. Automatic asymptotics for coefficients of smooth, bivariate rational functions. Online Journal of Analytic Combinatorics, Issue 6, 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. Efficient root counting for analytic functions on a disk. Prepublication, HAL 00569351, 2011.

J. van der Hoeven. Reliable homotopy continuation. Prepublication, 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. Prepublication, 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, 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. 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. Prepublication, 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. Prepublication 2008-09, Université Paris-Sud, Orsay, France, 2008.

J. van der Hoeven. Making fast multiplication of polynomials numerically stable. Prepublication 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. Prepublication 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, 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, J. van der Hoeven. Differentially algebraic gaps. Selecta Mathematica, 11(2):247–280, 2005.

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

J. van der Hoeven. Notes on the Truncated Fourier Transform. Prepublication 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. Prepublication 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. Prepublication 2001-62, Prépublications d'Orsay, 2001.

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

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

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

2000

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

J. van der Hoeven. A differential intermediate value theorem. Prepublication 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, 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, 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, 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. Prepublication 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. Prepublication LIX/RR/95/06, LIX, École polytechnique, France, 1995.

1994

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

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

J. van der Hoeven. Outils effectifs en asymptotique et applications. Prepublication 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.