## University of Western Ontario: (2010)

### BibTeX

@MISC{Retired10universityof,

author = {Keith Geddes (waterloo Retired and Peter Borwein Mathematics and Petr Lisonek Mathematics and Marnie Mishna Mathematics and Michael Monagan Mathematics and George Labahn and Computing Science and Eric Schost and Computer Science and Vahid Dabbaghian and Ilias Kotsirias and Wilfred Laurier},

title = {University of Western Ontario:},

year = {2010}

}

### OpenURL

### Abstract

Project website:

### Citations

239 |
Probabilistic algorithms for sparse polynomials
- Zippel
- 1979
(Show Context)
Citation Context ... (or rational function) with t non-zero terms modulo a prime p. One way to compare algorithms is to count the number of evaluations, called “probes”, of f. For polynomials, Zippel’s 1979 algorithm in =-=[44]-=- does O(ndt) probes. Since it works one variable at a time, it has limited parallelism. The best result is that of Kaltofen, Lee and Lobo ([23]) in 2000 which does O(nt) probes. However their approach... |

24 | Computing cylindrical algebraic decomposition via triangular decomposition
- Chen, Maza, et al.
(Show Context)
Citation Context ...tware tools for computing geometric and topological information for the real components of the solution sets of polynomial systems. We shall draw on recent work on cylindrical algebraic decomposition =-=[9, 5]-=- and the RealTriangularize Algorithm [8]. We will enhance the RegularChains Maple library with new functionality such as set-theoretical operations on semi-algebraic sets, computation of the real dime... |

20 | Two non-holonomic lattice walks in the quarter plane
- Mishna, Rechnitzer
- 2009
(Show Context)
Citation Context ...ng symbolic techniques and manipulations to make the closure properties of D-finite functions effective. A key family of objects under consideration is lattice paths with restricted steps. The papers =-=[3, 31, 32]-=- constitute an algorithmic approach to their exact enumeration using a technique called the kernel method. This has led to strongly supported conjectures on the nature of functional equations, arising... |

16 | Computations modulo regular chains
- Li, Maza, et al.
- 2009
(Show Context)
Citation Context ...lynomial arithmetic based on Fast Fourier Transforms (FFTs) and Straight-Line Programs. The code consists of 36,000 lines of C code and 3,000 lines of Maple code. The experimental results reported in =-=[27, 28]-=- demonstrate that this library is competitive and often outperforms the available packages with similar functionality. The modpn library was integrated in Maple 13. For this work, each of the PhD stud... |

14 | Triangular decomposition of semi-algebraic systems
- Chen, Davenport, et al.
(Show Context)
Citation Context ... can incorporate the transposition principle as an operation (in the same way that FFT is used). Project 3.2 : Polynomial Algebra and Solvers Subproject 3.2.1. Triangular decomposition and solvers In =-=[8]-=- Chen, Davenport, May, Moreno Maza, Xia and Xiao present a new algorithm, called RealTriangularize, for solving any systems of polynomial equations, inequations and inequalities. Under genericity assu... |

14 | Distance-based classification of handwritten symbols
- Golubitsky, Watt
(Show Context)
Citation Context ...ntegration of special functions in Maple. Subproject 3.4.4. Application of the geometry of curves to handwriting analysis We have developed a new geometric theory for recognizing mathematical symbols =-=[18]-=-. Characters are represented as parametric curves approximated by truncated orthogonal series, mapping symbols to low-dimensional vector space of series coefficients. Euclidean distance in this space ... |

14 | Early termination in Ben-Or/Tiwari sparse interpolation and a hybrid of Zippel’s algorithm
- Kaltofen, Lee, et al.
(Show Context)
Citation Context ...obes”, of f. For polynomials, Zippel’s 1979 algorithm in [44] does O(ndt) probes. Since it works one variable at a time, it has limited parallelism. The best result is that of Kaltofen, Lee and Lobo (=-=[23]-=-) in 2000 which does O(nt) probes. However their approach is incremental which results in a completely sequential algorithm. In 2010 Monagan and Javadi [21]) found a new method which also does O(nt) p... |

14 | Classifying lattice walks restricted to the quarter plane
- Mishna
- 2009
(Show Context)
Citation Context ...systems of linear differential equations with polynomial coefficients, known as D-finite classes. Combinatorially, we try to predict which classes of objects have D-finite generating functions, as in =-=[32]-=-. Analytically, the emphasis is on finding symbolic techniques and manipulations to make the closure properties of D-finite functions effective. A key family of objects under consideration is lattice ... |

12 | S.M.: Online Computation of Similarity between Handwritten Characters
- Golubitsky, Watt
- 2009
(Show Context)
Citation Context ...of linear SVMs. The distance to separating planes provides a reliable confidence measure for classifications [17]. The series coefficients can be computed in real-time, as the symbol is being written =-=[15]-=- and orientationindependent recognition is achieved [16]. We are currently investigating how orthogonal series representations may be used to compress ink traces in a form that may allow recognition w... |

9 | Interpolation of shifted-lacunary polynomials
- Giesbrecht, Roche
- 2010
(Show Context)
Citation Context ...linear for these operations, without any overhead exponential in the number of variables.Labahn and Monagan 5 Subproject 3.2.3. Lacunary and space-efficient polynomial algebra In the papers [12] and =-=[13]-=-, Giesbrecht and Roche describe arithmetic with lacunary (or supersparse) polynomials. A C++/NTL implementation of the first work is available on Giesbrecht’s website. Roche [41] examines the tradeoff... |

9 | Parallel Sparse Polynomial Multiplication Using Heaps
- Monagan, Pearce
(Show Context)
Citation Context ...s with integer coefficients. The goal of Subproject 3.1.1 was to try to design and implement fast parallel algorithms. We can report that this goal was essentially reached. In 2009 Monagan and Pearce =-=[33]-=- parallelized sparse polynomial multiplication and in 2010 [34] they succeeded in parallelizing sparse division which is much more difficult. The algorithms were implemented in C using P-threads. Rema... |

8 | S.M.: Orientation-independent recognition of handwritten characters with integral invariants
- Golubitsky, Mazalov, et al.
- 2009
(Show Context)
Citation Context ...es a reliable confidence measure for classifications [17]. The series coefficients can be computed in real-time, as the symbol is being written [15] and orientationindependent recognition is achieved =-=[16]-=-. We are currently investigating how orthogonal series representations may be used to compress ink traces in a form that may allow recognition without decompression of the database. Preliminary work o... |

8 | Sparse Polynomial Division Using a Heap
- Monagan, Pearce
- 2008
(Show Context)
Citation Context ...o try to design and implement fast parallel algorithms. We can report that this goal was essentially reached. In 2009 Monagan and Pearce [33] parallelized sparse polynomial multiplication and in 2010 =-=[34]-=- they succeeded in parallelizing sparse division which is much more difficult. The algorithms were implemented in C using P-threads. Remarkably, a super-linear speedup was achieved, typically a factor... |

7 | Average-Case Analysis of Perfect Sorting by Reversals
- Bouvel, Chauve, et al.
- 2011
(Show Context)
Citation Context ...search is to create tools for enumerative combinatorics using algebraic and symbolic computation methods, and mine the analytic nature of generating functions for additional combinatorial information =-=[4]-=-. The focus is on classes of objects whose generating functions satisfy systems of linear differential equations with polynomial coefficients, known as D-finite classes. Combinatorially, we try to pre... |

5 | Parallel Computation of the Minimal Elements of a Poset - Leiserson, Li, et al. - 2010 |

5 | Balanced dense polynomial multiplication on multicores
- Maza, Xie
- 2009
(Show Context)
Citation Context ...se division which is much more difficult. The algorithms were implemented in C using P-threads. Remarkably, a super-linear speedup was achieved, typically a factor of 5 on a 4 core desktop. modpn: In =-=[38]-=- Moreno Maza and Xie present efficient implementation strategies for dense polynomial multiplication targeting multi-cores. They show that balanced input data can maximize parallel speedup and minimiz... |

5 | Integer Matrix Rank Certification
- Storjohann
- 2009
(Show Context)
Citation Context ...the input matrix. However, for problems on input matrices that are singular of unknown rank, a main roadblock to obtaining certified algorithms has been the lack of a certified algorithm for rank. In =-=[43]-=-, Storjohann finally rectifies this situation by giving the first reduction to matrix multiplication for the integer rank certification problem. Rank certification is required to obtain fast certified... |

4 | Efficient Evaluation of Large Polynomials - Leiserson, Li, et al. - 2010 |

3 | Detecting lacunary perfect powers and computing their roots. Computing Research Repository abs/0901.1848
- Giesbrecht, Roche
- 2009
(Show Context)
Citation Context ...e almost linear for these operations, without any overhead exponential in the number of variables.Labahn and Monagan 5 Subproject 3.2.3. Lacunary and space-efficient polynomial algebra In the papers =-=[12]-=- and [13], Giesbrecht and Roche describe arithmetic with lacunary (or supersparse) polynomials. A C++/NTL implementation of the first work is available on Giesbrecht’s website. Roche [41] examines the... |

3 |
An in-place truncated fourier transform and applications to polynomial multiplication
- Harvey, Roche
(Show Context)
Citation Context ...ense polynomial arithmetic, and through an amortized analysis demonstrates a hybrid algorithm providing a smooth gradient between the best algorithms in the two circumstances. The results in [40] and =-=[20]-=- demonstrate lowspace and in-place asymptotically fast algorithms for polynomial arithmetic. These are effective for large sizes and when space is at a premium, such as hardware implementations for cr... |

3 | Parallel Sparse Polynomial Interpolation over Finite Fields
- Javadi, Monagan
- 2010
(Show Context)
Citation Context ...t result is that of Kaltofen, Lee and Lobo ([23]) in 2000 which does O(nt) probes. However their approach is incremental which results in a completely sequential algorithm. In 2010 Monagan and Javadi =-=[21]-=-) found a new method which also does O(nt) probes but which allows one to interpolate the degrees of each term in each variable in parallel – a breakthrough. Their parallel implementation in Cilk gave... |

3 | On Factorization of Multivariate Polynomials over Algebraic Number and Function Fields - Javadi, Monagan - 2009 |

3 |
Raqeeb Rasheed, and Éric Schost. The modpn library: Bringing fast polynomial arithmetic into
- Li, Maza
- 2011
(Show Context)
Citation Context ...nivariate) multiplication to balanced bivariate multiplication. Their implementation in Cilk++ demonstrates good speedup (often super-linear) on multi-cores. At the heart of their software, the modpn =-=[27]-=- library relies on Fast Fourier Transforms which are now taking advantage of the auto-tuning techniques from the SPIRAL group [30]. Subproject 3.1.3. Transposition techniques De Feo and Schost [11] ha... |

3 |
Efficient computation of order bases
- Zhou, Labahn
- 2009
(Show Context)
Citation Context ... algorithms for more complicated problems such as computing the null-space and Smith normal form, both of which reveal the rank of an input matrix. Subproject 3.3.5. Vector rational reconstruction In =-=[45]-=-, Zhou and Labahn give a new algorithm for the effective computation of order bases. Order bases represent all possible solutions to matrix rational approximation problems (including for example vecto... |

2 | Sparse polynomial multiplication and division in Maple 14
- Monagan, Pearce
- 2009
(Show Context)
Citation Context ...) 391.44s 17.15s 15.59s 117.53s 164.49s Timings in CPU seconds for f = (1 + x + y + z) 30 + 1 on an Intel Core i7 Additional benchmarks and details about the integration into Maple 14 can be found in =-=[35]-=- on our project website. Currently we are integrating our parallel division from [34] into Maple. Integration of the modpn library. This library is dedicated to fast polynomial arithmetic based on Fas... |

2 |
time-efficient polynomial multiplication
- Space-
- 2009
(Show Context)
Citation Context ...rse and dense polynomial arithmetic, and through an amortized analysis demonstrates a hybrid algorithm providing a smooth gradient between the best algorithms in the two circumstances. The results in =-=[40]-=- and [20] demonstrate lowspace and in-place asymptotically fast algorithms for polynomial arithmetic. These are effective for large sizes and when space is at a premium, such as hardware implementatio... |

2 |
Chunky and Equal-Spaced Polynomial Multiplication (PDF). Submitted to
- Roche
- 2008
(Show Context)
Citation Context ...n the papers [12] and [13], Giesbrecht and Roche describe arithmetic with lacunary (or supersparse) polynomials. A C++/NTL implementation of the first work is available on Giesbrecht’s website. Roche =-=[41]-=- examines the tradeoff between sparse and dense polynomial arithmetic, and through an amortized analysis demonstrates a hybrid algorithm providing a smooth gradient between the best algorithms in the ... |

1 |
Fraction-Free Computation of Simultaneous Pade Approximants
- Beckermann, Labahn
- 2009
(Show Context)
Citation Context ...mal complexity for the class of problems where coefficient growth is not an issue. In the case where coefficient growth is an issue, a second, completely different, algorithm by Beckermann and Labahn =-=[2]-=- was developed. The new method reduces the bit-complexity cost of computing simultaneous Padé approximants for a vector of power series by a factor of m3 , where m is the size of the vector. Project 3... |

1 |
with small steps in the quarter plane, Algorithmic Probability and Combinatorics (special volume of the Contemporary Mathematics series of the Amer
- Bousquet-Melou, Mishna, et al.
(Show Context)
Citation Context ...ng symbolic techniques and manipulations to make the closure properties of D-finite functions effective. A key family of objects under consideration is lattice paths with restricted steps. The papers =-=[3, 31, 32]-=- constitute an algorithmic approach to their exact enumeration using a technique called the kernel method. This has led to strongly supported conjectures on the nature of functional equations, arising... |

1 |
François Lemaire and Marc Moreno Maza, Real Root Isolation of Regular Chains
- Boulier, Chen
(Show Context)
Citation Context ...tware tools for computing geometric and topological information for the real components of the solution sets of polynomial systems. We shall draw on recent work on cylindrical algebraic decomposition =-=[9, 5]-=- and the RealTriangularize Algorithm [8]. We will enhance the RegularChains Maple library with new functionality such as set-theoretical operations on semi-algebraic sets, computation of the real dime... |

1 | François Lemaire and Marc Moreno Maza, Computing differential characteristic sets by change of ordering - Boulier |

1 |
Poteaux and Éric Schost, Almost-linear time operations with triangular sets, Poster at ISSAC’10
- Dahan, Maza, et al.
- 2010
(Show Context)
Citation Context ...mark that RealTriangularize is currently being integrated into the RegularChains library in Maple with the assistance of J.P. May and J. Gerhard from Maplesoft. Dahan, Moreno Maza, Poteaux and Schost =-=[10]-=- have generalized Kedlaya and Umans’ modular composition algorithm to the multivariate case. As an application, they have obtained fast algorithms for operations modulo triangular sets (over a finite ... |

1 |
Feo and Éric Schost, Transalpyne: a language for automatic transposition
- De
- 2010
(Show Context)
Citation Context ...pn [27] library relies on Fast Fourier Transforms which are now taking advantage of the auto-tuning techniques from the SPIRAL group [30]. Subproject 3.1.3. Transposition techniques De Feo and Schost =-=[11]-=- have designed transalpyne, a small scripting language, that is specifically conceived for automatic transposition of linear functions. Its type system is able to automatically infer all the possible ... |

1 | On computing the Hermite form of a matrix of differential polynomials
- Giesbrecht, Kim
(Show Context)
Citation Context ...rototype implementation in Maple has been produced and an investigation is now underway to achieve a more complete and general implementation. Subproject 3.3.3. Matrix normal forms of Ore matrices In =-=[14]-=- Giesbrecht and Kim give the first polynomial-time algorithm for the computation of the Hermite form of a matrix of differential polynomials. The approach reduces the problem to one of linear solving ... |

1 | Cache friendly sparse matrixvector multiplication - Haque, Hossain, et al. - 2010 |

1 | Wei Pan and Yuzhen Xie. When does (T) equal Sat(T - Lemaire, Maza - 2010 |

1 |
Franz Franchetti and Yuzhen Xie. Spiral-generated modular FFT algorithms
- Meng, Voronenko, et al.
- 2010
(Show Context)
Citation Context ...per-linear) on multi-cores. At the heart of their software, the modpn [27] library relies on Fast Fourier Transforms which are now taking advantage of the auto-tuning techniques from the SPIRAL group =-=[30]-=-. Subproject 3.1.3. Transposition techniques De Feo and Schost [11] have designed transalpyne, a small scripting language, that is specifically conceived for automatic transposition of linear function... |

1 |
Fast polynomial multiplication on a GPU. Submitted to the post-conference proceedings of High-Performance Computing Symposium 2010
- Maza, Pan
(Show Context)
Citation Context ...Technology Transfer Award. Recently, the modpn library has been enhanced with GPU code (3,000 lines of CUDA code) in order to accelerate computations of FFTs and polynomial GCDs modulo regular chains =-=[36]-=-. This is also being integrated into Maple.Labahn and Monagan 10 Mitacs Internships Our mitacs project was awarded an internship cluster. All internships involve a significant amount of technology tr... |

1 |
Symbolic Integration of Convolution Integrals, MMath
- Peasgood
- 2009
(Show Context)
Citation Context ...te integration, particularly improper definite integrals. In these cases the result often depends on the type of parameter values present in the integrands. We plan on continuing the work of Peasgood =-=[39]-=- in extending the Salvy approach to solving definite integrals of convolution type. Such integrals are prominent in many applications. For example all well known integral transforms can be represented... |

1 |
Computing with Abstract Matrix
- Sexton, Sorge, et al.
(Show Context)
Citation Context ... symbols to describe their internal structure. While working with such classes of matrices is everyday mathematical practice, it has little support in computer algebra systems. Sexton, Sorge and Watt =-=[42]-=- describe an algebraic encoding of such matrices in terms of support functions and define the corresponding addition and multiplication algorithms. The encoding of these abstract matrices has the impo... |