| Project/Area Number |
03558008
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| Research Category |
Grant-in-Aid for Developmental Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Informatics
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| Research Institution | University of Tsukuba |
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Principal Investigator |
SASAKI Tateaki Univ.Tsukuba, Inst.Math., Prof., 数学系, 教授 (80087436)
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| Co-Investigator(Kenkyū-buntansha) |
MARITSUGU Shuuichi Univ.Lib.Inf.Sci., Assistant, 図書館情報学部, 助手 (50220075)
SUZUKI Masayuki Iwate Univ., Fac.Eng., Assoc.Prof., 工学部, 助教授 (20143365)
KAKO Fujio Nara Women's Univ., Fac.Sci., Prof., 理学部, 教授 (90152610)
NODA Matu-tarou Univ.Ehime, Fac.Eng., Prof., 工学部, 教授 (10036402)
KITAMOTO Takuya Univ.Tsukuba, Inst.Math., Assistant, 数学系, 助手 (30241780)
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| Project Period (FY) |
1991 – 1993
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| Project Status |
Completed (Fiscal Year 1993)
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| Budget Amount *help |
¥6,500,000 (Direct Cost: ¥6,500,000)
Fiscal Year 1993: ¥2,000,000 (Direct Cost: ¥2,000,000)
Fiscal Year 1992: ¥2,200,000 (Direct Cost: ¥2,200,000)
Fiscal Year 1991: ¥2,300,000 (Direct Cost: ¥2,300,000)
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| Keywords | approximate algebra / application of approximate algebra / formula manipulation / formula manipulation system / numeric-algebraic hybrid computation / numeric-algebraic hybrid system / 数式処理システム / 近似多項式 / 数値数式融合算法 / ピュイズー級数展開 / 解析接続 / 有理関数近似 / 近似GCD / 近似Grobner基底 / 多項式因数分解 / 近似因数分解 |
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| Research Abstract |
In this research, we aimed at 1) bringing Japanese computer algebra system GAL up to practically usable level, 2) providing a numeric-algebraic hybrid computation facility to GAL, 3) studyng approximate algebraic algorithms, and 4) finding various applications of approximate algebra. As 1), GAL is now usable as a resesarch tool but it still lacks many facilities for general use ; as for 2), we reformed NSL (Nara Standard-Lisp), the host Lisp system for GAL, so that it can link Lisp and C, enabling us to perform numeric-algebraic hybrid computation now ; was for 3), we developed several important algorithms such as "an approximate Puiseux series expansion algorithm of algebraic functions" and "a hybrid algorithm for determining Riemann surface and performing analytic continuation of algebraic functions" ; as for 4), several interesting applications were found such as "application of approximate GCD to rational function approximation" and "sumoothing of data using the rational function approximation".
Summarizing our research, we have the following conclusions.
1. Approximate algebra can fuse numeric and algebraic conputation in algorithm level, and it has a very good possibility of innovating scientific computation.
2. However, development of approximate algebraic algorithm is not so easy at it looks, requesting us to make many years of efforts. In particular, we must construct mathematical theory of approximate algebra urgently.
3. As for computation system of approximate algebra, we must develop a floating-point computation system with facility of monitoring cancellation of numbers.
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