| Project/Area Number |
03640233
|
|---|
| Research Category |
Grant-in-Aid for General Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
|
|---|
| Research Institution | Hosei University |
|---|
Principal Investigator |
NAGASAKA Kenji Hosei University, College of Eng., Professor, 工学部, 教授 (40000187)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
FUSE Mitso Hosei University, College of Eng., Lecturer, 工学部, 講師 (00120832)
HIRAMATSU Toyokazu Hosei University, College of Eng., Professor, 工学部, 教授 (40029674)
ANDO Shiro Hosei University, College of Eng., Professor, 工学部, 教授 (60061016)
TANAKA Hisao Hosei University, College of Eng., Professor, 工学部, 教授 (70061025)
平野 鉄太郎 法政大学, 工学部, 教授 (60060993)
|
|---|
| Project Period (FY) |
1991 – 1993
|
| Project Status |
Completed (Fiscal Year 1993)
|
| Budget Amount *help |
¥1,900,000 (Direct Cost: ¥1,900,000)
Fiscal Year 1993: ¥400,000 (Direct Cost: ¥400,000)
Fiscal Year 1992: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 1991: ¥1,000,000 (Direct Cost: ¥1,000,000)
|
|---|
| Keywords | Chinese remainder theorem / Finite field / Multiplicative function / Error-free computation / Computational complexity / Oracle / Pascal's triangle / Goppa code / 多項式環 / 基本変形 / クリーネの階層 / ゴツパ符号 / パスカル三角形 / 有限1本 / ユークリッド環 / 数式処理 / 計算量の理論 / オラクルテューリングマシン / クリーネのハイアラーキー / 中国剥余定理 / ユ-クリッド環 / 記述集合論 / オラクルテュ-リングマシン / 数論的関数の特徴付け |
|---|
| Research Abstract |
We propose newly developed fast algorithm of the Chinese remainder theorem, which is one of most important and basic computing algorithms and examined numerically the efficiency of our algorithm in comparison with the usual method and confirm the effectiveness of our method. This fast algorithm is proved to be valid on polynomial rings over finite fields.
Under the regularity conditions, or the difference conditions, we show that multiplicative arithmetical functions are constant multiple of power functions with some exponent.
We also obtain that integral row operations of matrices admit the one-to-one mapping between Farey-N-fractions and subsets of finite precision in quadratic rationals. This result allows us to solve integral linear equations (congruences) and hence leads to an error-free computation method.(Nagasaka and Fuse)
As for computational complexity theory, we consider it from the scope of relitivisation. Then we give the solution of Bennet-Gill's problem in the classification of Kleene's hierarchy under the existence of oracles and determine the levels of certain classes. Some results on BPP are also obtained.(Tanaka)
We investigate the configuration of generalized binomial and multinomial coefficients and get remarks on the proof of GCD and LCM equalities and also another generalization of David's theorem. These results are generalized in more general set up and give necessary and sufficient conditions on a certain configuration.(Ando)
Goppa code is a fundamental tool in coding theory and we mention the link between Goppa code and number theory then summarize unsolved problems, some of which are partially solved.(Hiramatsu)
|
