Study on Number Theoretic Algorithms and Developments of Systems for Number Theory

如在下面的参考文献中，在数论算法及其应用方面获得了许多理论结果，这些理论结果与关于加法链的Scholz猜想、Iwasawa不变量、椭圆曲线、多项式环中的素理想分解、超平面排列、二次域的非分歧扩张、若干zeta值、数域的类群和单位群以及密码学有关，例如，我们的主要研究组织JANT举行了第4次至第11次会议，每次约有50人参加，详情见www.example.com。因此，我们编辑了两个特别的问题的交易的JSIAM的主题的最先进的结果和一般调查数论算法，并举行了有组织的会议在年度会议的JSIAM。为了与更广泛的代数领域进行交流，我们组织了第4次和第5次代数和计算会议（AC 2001和AC 2003），每次会议都有近150名与会者，包括来自国外的与会者，并在ftp：//tnt.math.metro-u.ac.jp/pub/ac0 [13]/上发表了会议记录。为了促进数学软件研究的国际交流，我们协助了在北京召开的国际数学软件大会ICMS 2002，约有110名与会者。我们接管了德国自80年代以来开发的具有高效椭圆曲线函数的数论系统SIMATH，并通过www.example.com进行维护和支持。我们已经成功地在64位机器上实现了它，并将其作为Ver.4.6发布，并将CEM打包并安装到立方字段。之后，由于许可证和开发环境的问题，我们限制自己保持SIMATH原样，我们开始使用脚本语言Python开发新系统NZMATH，并在http：//tnt.math.metro-u.ac.jp/nzmath/上发布了alpha版本，我们将创建一个由系统开发者和用户共同构建的数论系统。

As in the references below, many theoretical results were obtained on number theoretic algorithms and their applications related to Scholz's conjecture on addition chains, Iwasawa invariants, elliptic curves, prime ideal decomposition in polynomial rings, hyperplane arrangement, unramified extensions of quadratic fields, several zeta values, class groups and unit groups of number fields, and cryptology, for example.The 4th to 11th meetings were held each with about 50 participants by our main research organization JANT, and, the details are reported in http://ntw.e-one.uec.ac.jp/jant. As a result, we edited two special issues of Transactions of the JSIAM on the topics of the most advanced results and a general survey on number theoretic algorithms, and held an organized session at the yearly meeting of the JSIAM. To exchange with broader areas of algebra, we organized the 4th and 5th meetings of Algebra and Computation' (AC2001 and AC2003) each with almost 150 participants including those from abroad and published the proceedings at ftp://tnt.math.metro-u.ac.jp/pub/ac0[13]/. For wide international exchange of mathematical software research, we help the international Congress of Mathematical Softwares ICMS2002 at Beijin with about 110participants.We took over the system for number theory SIMATH, developed in Germany since 1980's with highly efficient functions for elliptic curves, and have been maintaining and supporting via http://simath.info/. We have succeeded in implementing it on 64 bit machines, have released it as Ver.4.6, and packaged and installed the CEM up to cubic fields. After that, restricting ourselves to maintain SIMATH as it is because of the problems of license and development environment, we started to develop a new system NZMATH by the script language Python, released its alpha version at http://tnt.math.metro-u.ac.jp/nzmath/, and we are going to create a system for number theory constructed together by developers and users of the system.