No 1001 (00016) Family name : Aladjev Given name : Victor .Z. Affiliation : International Academy of Noosphere Abbreviation : E-mail address : aladjev@lenta.ru Title : Systems of Computer Algebra: New Software ToolBox for Maple Authors : Victor Aladjev Abstract : This paper is based on our previous monograph whose pressrun was completely sold out. The paper presents a Library for the moder computer algebra system Maple of releases 6 - 9, expanding its basic tools. Source codes of the Library tools introduce the reader into both effective and non-standard programming technique in Maple. The reader should have a background in Maple of any release. The tools represented in the paper increase the range and efficiency of use of the package on the Windows platform owing to the innovations in three basic directions: (1) elimination of a series of basic defects and shortcomings, (2) expansion of capabilities of a series of standard tools and (3) replenishment of the package by new means which increase capabilities of its program environment, including the means which improve the level of compatibility of releases 6, 7, 8 and 9. The basic attention is devoted to additional tools created in the process of practical use and testing the packages of releases 4-8 which by some parameters expand essentially the opportunities of the package and facilitate the work with it. The considerable attention is also devoted to the means providing packages compatibility of releases 6, 7, 8 and 9. The experience in the use of given software was confirmed its high operational characteristics at use of Maple in numerous appendices. The above software had been organized into the user Library whose a current version contains tools (more than 400 procedures and program modules) which are oriented upon wide enough sphere of computing and information processing. The Library is structurally similar to the main Maple library and is supplied with the advanced Help system about the tools located in it. In addition, it is logically connected with the main Maple library, providing access to the tools contained in it similarly to the package tools. The simple guide describes the installation of the Library at presence on PC with Windows platform of installed Maple package of releases 6, 7 or 8. The Library is designed for a wide audience of experts, teachers, post-graduates and students of natural-science professions who use Maple of releases 6, 7 and 8 on Windows platform in their own professional work. The Library contains well-designed software (a set of procedures and program modules), which supplements well the already available Maple software with the orientation towards the widest circle of the Maple users, greatly enhancing its usability and effectiveness. Our experience reveals that the use of Library creates more opportunities of Maple of releases 6, 7 and 8, simplifying the programming of various practical problems in its environment. This Library will present special interest above all for those who use Maple not only as a highly intellectual calculator but also as environment for programming of different problems in one's own professional activity. The paper will be interesting for scientists, researchers, candidates for doctor's or master's degree in the field of computer algebra systems, and experts and researchers in other areas of physics and mathematics who use computer algebra systems in own professional activity.