About

The East Coast Computer Algebra Day (ECCAD) is a one-day meeting for those interested in computer algebra and symbolic mathematical computation. It provides opportunities to learn and to share new results and current work in progress. The schedule includes invited speakers along with contributed posters and software demonstrations. Plenty of time is allowed for unstructured interaction among the participants. Researchers, teachers, students, and users of computer algebra are all welcome!

 

Invited Speakers

Marc Moreno Maza, Western University, Canada
Johan S.R. Nielsen, Technical University of Denmark
Marni Mishna, Simon Fraser University, Canada

 

Schedule

8:30 a.m.	Registration and refreshments
9:15	Opening remarks
9:30	Marc Moreno Maza Quantifier Elimination, Polyhedral Computations and their Applications to the Parallelization of Computer Programs
10:30 a.m.	Coffee Break and poster session I
11:30 a.m.	Johan Nielsen Polynomial Approximation Problems in Algebraic Coding Theory
12:30 p.m.	Lunch break
2:30 p.m.	Marni Mishna The art and science of systematic combinatorics: a study in lattice path enumeration and holonomic functions
3:30 p.m.	Coffee Break and poster session II
4:30 p.m.	Closing remarks
4:45 p.m.	Wine and cheese reception

Registration

Online registration has now closed, but registration will be available at the Fields Institute during the workshop. There are no fees to attend East Coast Computer Algebra Day.

Poster and Software Demonstrations

Proposals are invited for poster presentations and software demonstrations on any topic related to computer algebra. Abstracts received by Friday, September 25 will appear in the conference program. Click here to proceed to poster abstract submission.

 

Abstracts

Marc Moreno Maza, Western University, Canada

Quantifier Elimination, Polyhedral Computations and their Applications to the Parallelization of Computer Programs

In the past decade, the introduction of low-level heterogeneous programming models, in particular CUDA, has brought supercomputing to the level of the desktop computer. However, these models bring notable challenges, even to expert programmers. Indeed, fully exploiting the power of hardware accelerators with CUDA-like code often requires significant code optimization effort. While this development can certainly yield high performance, it is desirable for some programmers to avoid the explicit management of device initialization and data transfer between memory levels. To this end, high-level models for accelerator programming, like OpenMP and OpenACC, have become an important research direction. With these models, programmers only need to annotate their C/C++ code to indicate which code portion is to be executed on the device and how data maps between host and device.

We will argue in this talk that the process of generating CUDA-like kernel functions from C/C++ code can greatly benefit from symbolic computation. The core idea is to support the generation of kernel functions that depend on program parameters (like number of threads per thread-block) and machine parameters (like shared memory size). These parameters need not to be known at code-generation-time: machine parameters and program parameters can be respectively determined and optimized when the generated code is installed on the target machine.

This generation of parametric kernel functions leads us to deal with non-linear polynomial expressions during the dependence analysis and tiling phase of the code. To achieve these algebraic calculations, we propose specific operations on polyhedral sets as well as quantifier elimination techniques. Their implementation in the RegularChains and PolyhedraSets libraries endow the MetaFork compilation framework with the necessary algebraic tools for generating parametric kernel functions from annotated C/C++ code. Various examples will illustrate the talk.

 

Marni Mishna, Simon Fraser University, Canada

The art and science of systematic combinatorics: a study in lattice path enumeration and holonomic functions

In recent decades a robust scaffolding has been built which makes combinatorial analysis more systematic, and hence amenable to computer algebra techniques and innovations. We will discuss some of the key features of analytic combinatorics, and illustrate recent developments through the example of the asymptotic enumeration of lattice path walks in restricted domains. In particular, we will see how results on formal power series, recurrences, and integral expressions have been essential to combinatorial insights, and conversely how combinatorial questions have driven progress in these areas.

 

Johan S.R. Nielsen, Technical University of Denmark

Polynomial Approximation Problems in Algebraic Coding Theory

Error-correcting codes are low-dimensional vector spaces embedded in larger-dimensional ones such that vectors, or codewords, are spaced far apart. This enables one to recover codewords by knowing noisy versions of them. Algebraic Coding Theory deals with constructing such spaces using algebraic relations. Recovering a codeword then becomes solving certain structured equations.

Reed-Solomon codes are the most famous, and arguably the simplest, algebraic codes. Since the work of Berlekamp in the 60s, we know how to correct errors by solving a Padé approximation over $GF(q)[x]$. Since a breakthrough result of Guruswami and Sudan in 1999, interest in generalising this method has been reinvigorated. In Power decoding, by Schmidt, Sidorenko and Bossert, 2006, one solves a Simultaneous Padé approximation with the aim of correcting more errors.

In this talk, I will introduce the problem of error-correction, and describe in modern and simple terms how these approximation problem naturally arise for Reed-Solomon codes. I will go on to describe a very recent extension of Power decoding, where one solves a type of Simultaneous Hermite Padé approximation.

 

Registered Participants

Parisa Alvandi, University of Western Ontario
Rob Andrews,
Andrew Arnold, University of Waterloo
Carlos Arreche, North Carolina State University
Reinhold Burger, University of Waterloo
Haowei Chen, Western University
Shaoshi Chen, Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences
Xiaohui Chen, University of Western Ontario
Artem Chikin, IBM Canada
Robert Corless, University of Western Ontario
Matthew DeClerico, Deloitte
Mustafa Elsheikh, University of Waterloo
Jürgen Gerhard, Maplesoft
Mark Giesbrecht, University of Waterloo
Lawrence Guan, Western University
Sonia Gupta, University of Western Ontario
Sardar Haque, Delphax Technologies
Itamar Halevy,
Liqiang He,
Albert Heinle, University of Waterloo
Khodabakhsh Hessami Pilehrood, Fields Institute
Tatiana Hessami Pilehrood, Fields Institute
Jonah Horowitz, Ryerson University
Silvana Ilie, Ryerson University
Erich Kaltofen, North Carolina State University
Abdoul-kader Keita, IBM Canada
Mohamed Khochtali, University of Waterloo
Ilias Kotsireas, WLU
George Labahn, University of Waterloo
Suzy Maddah, Fields Institute
Marni Mishna, Simon Fraser University
Davood Mohajerani, Western University
Michael Monagan, Simon Fraser University
Marc Moreno Maza, Univ. Western Ontario
Simone Naldi, Fields Institute
Vincent Neiger, ENS de Lyon / U. Waterloo
Johan Nielsen, Technical University of Denmark
Roman Pearce, Simon Fraser University
Jeeva Paudel, IBM Canada
Arne Storjohann, University of Waterloo
Steven Thornton, Western University
Cleveland Waddell, North Carolina State University
Stephen Watt, University of Waterloo
Ning Xie, University of Western Ontario
Zhuoran Yu, University of Waterloo

Last Updated October 6

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