I have moved to NCSU.

## Research interests

I am a PhD student codirected by Frédéric Chyzak (INRIA, France) and Ziming Li (AMSS, China). Since the first time my Chinese supervisor introduced me the book “Symbolic integration I” by M. Bronstein, symbolic integration has always been my research interest. When I arrived at the last chapter of the book, I met my French supervisor and learnt about Zeilberger's method of creative telescoping from him. From then on, I started my PhD thesis with the motivation of developing fast algorithms for creative telescoping by incorporating techniques from symbolic integration.

## Current work

Creative telecoping via Hermite reduction.

## Publications list

2011
• @phdthesis{Chen2011,
author      = {Chen, Shaoshi},
title       = {Quelques applications de l'algèbre différentielle et aux
différences pour le télescopage créatif},
year        = {2011},
month       = {February},
school      = {École polytechnique (Palaiseau, France)},
note        = {Defended on February 16, 2011},
abstract    = {Since the 1990's, Zeilberger's method of creative
telescoping has played an important role in the automatic verification of
special-function identities. The long-term goal initiated in this work is to
obtain fast algorithms and implementations for definite integration and
summation in the framework of this method. Our contributions include new
practical algorithms, complexity analyses of algorithms, and theoretical
criteria for the termination of existing algorithms. On the practical side,
we present a new algorithm for computing minimal telescopers for bivariate
rational functions. This algorithm is based on Hermite reduction. We also
improve the classical Almkvist and Zeilberger's algorithm for
rational-function inputs. The Hermite-reduction based algorithm and improved
Almkvist and Zeilberger's algorithm are analyzed in terms of field
operations. Both complexity analysis and experimental results show that our
algorithms are superior to other known ones for rational-function inputs. On
the theoretic side, we present a structure theorem for multivariate
hyperexponential-hypergeometric functions. This theorem is based on
(multivariate) Christoper's theorem for hyperexponential functions, the
Ore-Sato theorem for hypergeometric terms, and our generalization of a recent
result by Feng, Singer, and Wu on compatible bivariate continuous-discrete
rational functions. The structure theorem allows us to decomposes a
hyperexponential-hypergeometric function as a product of a rational function,
several exponential and power functions, and factorial terms. Furthermore, we
derive two criteria for the existence of telescopers for bivariate
hyperexponential-hypergeometric functions: one is with respect to the
continuous variable, and the other with respect to the discrete one. The two
criteria solve the termination problems of the continuous-discrete analogue
of Zeilberger's algorithms.},
}

Shaoshi Chen
. — Quelques applications de l'algèbre différentielle et aux différences pour le télescopage créatif. — PhD thesis, École polytechnique (Palaiseau, France), February 2011. — Defended on February 16, 2011.
Since the 1990's, Zeilberger's method of creative telescoping has played an important role in the automatic verification of special-function identities. The long-term goal initiated in this work is to obtain fast algorithms and implementations for definite integration and summation in the framework of this method. Our contributions include new practical algorithms, complexity analyses of algorithms, and theoretical criteria for the termination of existing algorithms. On the practical side, we present a new algorithm for computing minimal telescopers for bivariate rational functions. This algorithm is based on Hermite reduction. We also improve the classical Almkvist and Zeilberger's algorithm for rational-function inputs. The Hermite-reduction based algorithm and improved Almkvist and Zeilberger's algorithm are analyzed in terms of field operations. Both complexity analysis and experimental results show that our algorithms are superior to other known ones for rational-function inputs. On the theoretic side, we present a structure theorem for multivariate hyperexponential-hypergeometric functions. This theorem is based on (multivariate) Christoper's theorem for hyperexponential functions, the Ore-Sato theorem for hypergeometric terms, and our generalization of a recent result by Feng, Singer, and Wu on compatible bivariate continuous-discrete rational functions. The structure theorem allows us to decomposes a hyperexponential-hypergeometric function as a product of a rational function, several exponential and power functions, and factorial terms. Furthermore, we derive two criteria for the existence of telescopers for bivariate hyperexponential-hypergeometric functions: one is with respect to the continuous variable, and the other with respect to the discrete one. The two criteria solve the termination problems of the continuous-discrete analogue of Zeilberger's algorithms.
2010
• @inproceedings{BoChChLi10,
author      = {Bostan, Alin and Chen, Shaoshi and Chyzak, Fr\'{e}d\'{e}ric
and Li, Ziming},
title       = {Complexity of creative telescoping for bivariate rational
functions},
booktitle   = {ISSAC'10: Proceedings of the 2010 International Symposium
on Symbolic and Algebraic Computation},
year        = {2010},
publisher   = {ACM},
address     = {New York, NY, USA},
pages       = {203--210},
doi         = {http://doi.acm.org/10.1145/1837934.1837975},
abstract    = {The long-term goal initiated in this work is to obtain fast
algorithms and implementations for definite integration in Almkvist and
Zeilberger's framework of (differential) creative telescoping. Our
complexity-driven approach is to obtain tight degree bounds on the various
expressions involved in the method. To make the problem more tractable, we
restrict to \emph{bivariate rational\/} functions. By considering this
constrained class of inputs, we are able to blend the general method of
creative telescoping with the well-known Hermite reduction. We then use our
new method to compute diagonals of rational power series arising from
combinatorics.},
}

Alin Bostan, Shaoshi Chen, Frédéric Chyzak, and Ziming Li
. — Complexity of creative telescoping for bivariate rational functions. — In ISSAC'10: Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation, pages 203–210, New York, NY, USA, 2010. ACM. (doi:10.1145/1837934.1837975)
The long-term goal initiated in this work is to obtain fast algorithms and implementations for definite integration in Almkvist and Zeilberger's framework of (differential) creative telescoping. Our complexity-driven approach is to obtain tight degree bounds on the various expressions involved in the method. To make the problem more tractable, we restrict to bivariate rational functions. By considering this constrained class of inputs, we are able to blend the general method of creative telescoping with the well-known Hermite reduction. We then use our new method to compute diagonals of rational power series arising from combinatorics.
2009
• @misc{BoChChLi09,
author      = {Bostan, Alin and Chyzak, Frédéric and Chen, Shaoshi
and Li, Ziming},
title       = {Rational-functions telescopers: Blending creative
telescoping with Hermite reduction},
year        = {2009},
howpublished= {Poster at the conference ISSAC'09 (Seoul, South Korea)},
url         = {http://issac2009.kias.re.kr/program_page.html#posters},
}

Alin Bostan, Frédéric Chyzak, Shaoshi Chen, and Ziming Li
. — Rational-functions telescopers: Blending creative telescoping with Hermite reduction. — Poster at the conference ISSAC'09 (Seoul, South Korea), 2009.
• @misc{ChLi90,
author      = {Chen, Shaoshi and Li, Ziming},
title       = {A speed-up of the Hermite reduction for rational
functions},
year        = {2009},
howpublished= {Poster at the conference ICMM'09 (Beijing, China)},
url         = {http://mmrc.iss.ac.cn/wu90/},
}

Shaoshi Chen and Ziming Li
. — A speed-up of the Hermite reduction for rational functions. — Poster at the conference ICMM'09 (Beijing, China), 2009.

## Slides of talks

Shaoshi Chen
Projet Algo
INRIA Rocquencourt
B. P. 105
78153 Le Chesnay Cedex
France

Tel: +33 1 39 63 50 43
Fax: +33 1 39 63 55 96
E-mail: shaoshi. chen! inria. fr (replace bang with at, remove spaces)