| Project/Area Number |
24700014
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Fundamental theory of informatics
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| Research Institution | Kyushu University |
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Principal Investigator |
DAHAN Xavier 九州大学, システム情報科学研究科(研究院, 研究員 (50567518)
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| Project Period (FY) |
2012-04-01 – 2014-03-31
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| Project Status |
Completed (Fiscal Year 2013)
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| Budget Amount *help |
¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | グレブナー基底 / 補間式 / ビット長の見積もり / 多変数多項式 / 三角形方 / ビット長の上界 / 国際情報交換 |
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| Research Abstract |
Systems of multivariate polynomial equations allow to describe a variety of physical phenomenon and solving them efficiently is thus a fundamental problem. Lexicographic Groebner bases (later on "lex Gb") are the mainstream tool to achieve this task. The particular lexicographic order is unfortunately the most difficult order to compute Groebner bases. The aim of this project was to grasp furthermore the structure of these lex Gb and to open the way to new improvements for their computation. After having set up new interpolation formulas, we could easily deduce the structure and obtain the first upper bounds on the bit-size of their coefficients.
Then, from the structure we have understood how to set up a new efficient decomposition algorithm of lex Gb, in order to get smaller and thus easier to solve polynomial systems. Moreover, with Prof. Yokoyama (Rikkyo University) we found out how to derive a new efficient algorithm to remove multiple solutions.
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