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DCAR2010 Program
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DateSessionBeginning timeEnding timeDuration (h:m)AuthorsTitle of talk
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2010/07/07Opening13:3013:350:05
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Session 113:4014:200:40Masaru Sanuki (University of Tsukuba)Computing Approximate Polynomial GCD over Z via Various Matrices
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14:2014:500:30Hiroshi Kai (Ehime University)A Secret Sharing Scheme Using Rational Approximation
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14:5015:200:30Akira Terui (University of Tsukuba)GPGCD, an Iterative Method for Calculating Approximate GCD, for Multiple Univariate Polynomials
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We present an extension of our GPGCD method, an iterative method for calculating approximate greatest common divisor (GCD) of univariate polynomials, to multiple polynomial inputs. For a given pair of polynomials and a degree, our algorithm finds a pair of polynomials which has a GCD of the given degree and whose coefficients are perturbed from those in the original inputs, making the perturbations as small as possible, along with the GCD. In our GPGCD method, the problem of approximate GCD is transfered to a constrained minimization problem, then solved with a so-called modified Newton method, which is a generalization of the gradient-projection method, by searching the solution iteratively. In this paper, we extend our method to accept more than two polynomials with the real coefficients as an input.
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Session 215:4016:401:00Eric Schost (University of Western Ontario, ORCCA lab)
Abdulilah Kadri (University of Western Ontario)
Xavier Dahan (Kyushu University)		What for, why and how to get bit-size estimates for polynomial systems over Q: a few answers
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Computing with exact rational numbers implies often the notorious phenomenon of the growth of the data. This already appears at the most fundamental cores of Computer Algebra algorithms: during the Euclidean algorithm and when inverting a matrix. It is hence even worse for multivariate polynomial systems. To "solve" a polynomial system, different methods have emerged besides the famous Grobner bases: the RUR and triangular decompositions are two important ones. How large can the coefficients become when computing such systems ? An answer is to get bit-sizes estimates, that are upper bounds on the number of digits of any number appearing among the coefficients of the output system. It is a very general problem to find such estimates. We will survey the methods that have permitted to obtain some new estimates in this direction (especially a recent result in dimension). A key tool is the "height theory" coming from Diophantine geometry, and especially "arithmetic Bezout theorem".
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2010/07/08Session 39:3010:100:40Hiromasa Nakayama (Kobe University, JST CREST)
Kenta Nishiyama (Kobe University, JST CREST)		An algorithm of computing inhomogeneous differential equations for definite integrals
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10:1010:500:40Issei Yoshida (IBM Research - Tokyo, IBM Japan Ltd.)On the number of slack variables used in representation of semi-algebraic sets
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Session 411:1011:500:40Kinji Kimura (Kyoto University)About a parallel implementation of the polynomial interpolation method
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11:5012:200:30Tatsuyoshi Hamada (Fukuoka University / JST CREST)On USB bootable KNOPPIX/Math/2010
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Tutorial 113:4014:401:00Daisuke Ikegami (National Institute of Advanced Industrial Science and Technology (AIST))Towards a reliable computer algebraic system: dependability, usability, concurrent and parallel computation
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Computer algebraic systems have a long history of being used for computation. One aspect of the systems which makes them powerful as a mathematical language is that it mixes efficient algorithms with computation. Other is graphical user interfaces, literally.
This talk is concerned another topics; dependability, usability concurrent and parallel computations for the computer algebra systems. To describe these features, I will introduce a modern programming language Haskell, and show what the language enables briefly.
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Tutorial 215:0016:001:00Kosaku Nagasaka (Kobe University)Holding International Scientific Meetings - A Case of CASC 2009 -
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Communication16:0016:300:30Communication on information of international conferences, etc.
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2010/07/09Session 59:3010:000:30Satoshi Yoshida (National Defense Academy)
Masayo Fujimura (National Defense Academy)
Yasuhiro Gotoh (National Defense Academy)		On the construction of Böttcher functions and visualization of Julia sets
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10:0010:400:40Takeshi Osoekawa (Rikkyo University)
Yuji Mochizuki (Rikkyo University)
Kazuhiro Yokoyama (Rikkyo University)		Toward a Computer Algebra System for Electron Correlation Theory
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10:4011:100:30Maki Iwami (Osaka University of Economics and Law)An improvement of Voloch's rational point attack on improved algebraic surface cryptosystem
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Session 611:3012:000:30Kosaku Nagasaka (Kobe University)Homomorphic Encryption and Approximate GCDs of Integers and Polynomials over Integers
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12:0012:300:30Takuya Kitamoto (Yamaguchi University)On the boundary polynomial
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