Systems of Computer Algebra: A New Software Toolbox for
noosphere_academy@yahoo.com, academy60@hotmail.com
Computer Algebra (also known as Symbolic Computation or Computational Algebra) has found application in many fields of science such as mathematics,
physics, chemistry, computer science, engineering, education, technology, computational
biology, etc. The computer algebra
systems (CAS) such as Maple, Reduce, MuPAD, Axiom, Macsyma, Mathematica, Derive, Magma, and others are becoming more and more popular in teaching, research and
industry. The area of symbolic and algebraic computation aims at automation of
mathematical computations of all sorts. The resulting computer systems, both
experimental and commercial, are powerful tools for scientists, engineers, and
educators. This research combines mathematics with advanced computing
techniques. CAS is an interdisciplinary area between Mathematics and Computer Science. Its research focuses on the development of
algorithms for performing symbolic manipulations with
algebraic objects on computers, and design of programming languages and
environments for implementing these algorithms.
In a series [1-45] of our books and papers, such packages as Maple, Reduce,
MathCAD and Mathematica have been considered. Our experience in the detailed
testing and practical use of different mathematical and physical applications of
four mathematical packages (Reduce, Maple, MathCAD
and Mathematica) enables us to consider the packages Maple and Mathematica as
undoubted leaders (on the basis of a generalized index) among all listed modern
tools of computer algebra. Meanwhile, we give preference to the package Maple due to a number of strong reasons described in the above
books enough in detail.
Computer
algebra becomes a
rather powerful and useful tool for scientists and experts from various fields.
However, manifold applications demand that the essential significant numerical
calculations be combined with algebraic ones. With each new release, the
package Maple
meets more and more requirements. The Maple package has been widely used not
only as a tool of solving mathematical problems. The package allows us to
revise approaches to teaching subjects related to mathematics in universities
by defining in many cases the methods for a teaching of subjects with the use
of PCs to solve mathematical problems
for various purposes [6-35,38,39,40,41-45].
Researchers use well-known Maple package as an essential tool when
solving problems related to their investigation. The package is ideal for
formulating, solving, and exploring different mathematical models. Its symbolic
manipulation facilities extend greatly over a range of problems that can be
solved with its help. Educators in high schools, colleges, and universities
have revitalized traditional curricula by introducing problems and exercises,
which use Maple's interactive mathematics and
physics. Students can concentrate on the more fundamental concepts rather than
on tedious algebraic manipulations. Finally, engineers and experts in
industries use Maple as an efficient tool replacing
many traditional resources such as reference books, calculators, spreadsheets
and programming languages. These users easily solve mathematical problems,
creating projects and consolidating their computations into professional
reports.
Maple products
embody advanced technologies such as symbolic computation, infinite precision
numeric, innovative Web components, extensible
user-interface technology, and an unrivalled suite of mathematical algorithms
for intelligent management of complex mathematics. Over 5 million users benefit from
advanced Maple
technology. Virtually, all major universities and research institutes in the
world, including such as MIT,
Oxford, Stanford
and Waterloo, has adopted Maple products to enhance their education
and research activities. Waterloo Maple's industrial customers
base includes Boeing,
Bosch, Canon, NASA,
etc.
Meanwhile, our operational
experience in the period of 1997
- 2006
with Maple
of releases 4 - 10 enabled us not only to estimate
its advantages compared with other similar mathematical packages, but has also
revealed a number of faults and shortcomings which were eliminated by us.
Furthermore, Maple does not support a number of
important procedures of information processing, symbolic and numeric computing, including the tools of
access to datafiles. By operating Maple we have developed rather
effective tools (procedures and program
modules), largely
extending the possibilities of the package. This software has been organized as
a Library
that is structurally similar to the main Maple library, and is provided with a
rather detailed Help system analogous to Maple Help system.
In particular, Maple does not provide sufficient
compatibility of releases 6 - 10.
This fact and the incompatibility of the package found out by us at a level of
base platforms - Windows 98SE and lower, on the one hand, and Windows
ME/2000/XP
and above, on the other hand, the decision of a compatibility problem for the Library means have demanded.
The tools represented in the Library 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) extension of capabilities of a series of standard
tools, and (3) replenishment
of the package by new means which increase the capabilities of its program
environment, including the facilities improving the 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 of the package of releases 4 - 8 which by some parameters
considerably extend the capabilities of the package making the work with it
much easier; a considerable attention is also devoted to the tools providing
package compatibility of releases 6 - 10. The experience in using the
above software for various applications has confirmed its valuable operational
characteristics.
It should be noted that a series
of books on Maple [6-35,38,39,40,41-45], representing tools developed by
the authors and containing suggestions on further development of the package
encouraged the development of such applications as package modules FileTools, LibraryTools,
ListTools and StringTools. However, the means suggested by
us essentially extend the capabilities of the package, which in many cases
exceed those of the specified modules.
The above
software has been organized into the user Library, whose a current version contains
tools (more than 575 procedures and program modules)
which are oriented to a wide area 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 in the PC with Windows platform of the installed Maple package of releases 6, 7, 8, 9/9.5 or 10.
The package incompatibility found by us as at the level of its
releases, and at the level of underlying platforms - Windows
98SE and
lower, on the one hand, and Windows ME/2000/XP and above, on the other hand,
shows need for solving a compatibility problem of for the Library tools. A current Library version contains means (more
than 740 procedures and program modules), oriented onto the following
basic kinds of processing and calculations:
1. General purpose software
2. Software for operation with
procedural and modular objects of Maple
3. Software for operation with
numeric expressions
4. Software for operation with
strings and symbolic expressions
5. Software for operation with sets,
tables and lists
6. Software to support data
structures of a special type
7. Software to support bit-by-bit
processing of symbolic information
8. Tools extending graphic
possibilities of Maple of releases 6 – 9/9.5
9. Tools that extend and improve the
standard tools of Maple
10. Software for working with Maple datafiles and documents
10.1. General purpose software
10.2. Software for operation with TEXT datafiles
10.3. Software for operation with BINARY datafiles
10.4. Software for operation with Maple files
10.5. Some special tools for operation with datafiles
11. Software for solving problems of mathematical analysis
12. Software for solving problems of
linear algebra
12.1. General purpose software
12.2. Software for operation with rtable-objects
13. Software to support simple statistics problems
13.1. Software for solving problems of descriptive statistics
13.2. Software for solving problems of regression analysis
13.3. Software for testing of statistical hypotheses
13.4. Elements for simple analysis of time (dynamic) and variation series
14. Software for operation with the user libraries
The basic innovations of our Library with respect of the listed sections that thematically classify the Library tools can be briefly characterized as follows (in brackets, quantity of corresponding procedures is given):
1. General purpose software:
- increasing
compatibility of Maple of releases 6 - 10 concerning its
standard functions {'assign', 'close', 'fclose', 'fremove'};
- definition of full
paths to the basic subdirectories of the package Maple;
- definition of
installed releases of the package Maple on your computer;
- definition of the
current release of the package Maple;
- definition of the
current version of underlying operational system of a computer, etc.
2. Software for operation with procedural and modular objects of Maple:
- output of source code
of a program module or package and variables exported by them;
- a simple method of
procedures debugging based on the basis of a method of checkpoints;
- checking the
availability in datafiles of the specified procedures and program modules;
- checking the
datafiles for presence of incorrect program modules;
- checking the type of
a module table;
- dynamic call of the
variables exported by a program module;
- checking the
availability in a current Maple session of the
specified procedures, modules or variables;
- definition of formal
arguments of a procedure, a program module or package;
- checking onto
compatibility of files of type {".m", ".lib"} with the current release of Maple;
- merging of datafiles
created by the standard Maple function 'save';
- converting of a
program module into equivalent procedure;
- converting of program
modules of the second type into equivalent
modules of the first type;
- extraction of
procedures and program modules from text datafiles;
- converting of files
of the input Maple language format into
the internal Maple format, and vice
versa;
- converting of any Maple-object into the program module, etc.
3. Software for operation with numeric expressions:
- converting of the
floating-point numbers into the stylized standard format;
- an useful special
converting of integers into the list, and vice versa;
- converting of the
numbers presented in a symbolical or string format, into numerical values, etc.
4. Software for operation with strings and symbolic expressions:
- extraction of Maple expressions from their symbolical or string representations;
- a special converting
of strings or symbolical expressions containing blanks, for an opportunity of
their subsequent correct use by the standard Maple functions {'system', 'ssystem'};
- a set of tools to
remove strings and symbolic expressions of their components;
- a set of tools for an
analysis of contents of strings and symbolic expressions;
- the expanded set of
tools for converting of strings and symbolical expressions into lists, vectors
and numerical values, and vice versa;
- the expanded search
for the patterns containing wildcard-symbols;
- special insertions of
symbols into strings and symbolic expressions;
- definition of
multiple entries into strings, symbolic expressions and lists;
- special methods of
searching for strings and symbolic expressions;
- reducing to the
specified multiplicity of entries of symbols or substrings into a string;
- extraction from
strings and symbolical expressions of substrings limited to the specified
delimiters;
- the extended set of
tools for substitutions into strings and symbolical expressions;
- the extended set of
searching tools to in strings and symbolical expressions;
- the extended set of
tools for sorting the elements of strings, symbolic expressions and lists;
- simple tools for coding / decoding of text information, etc.
5. Software for operation with sets, tables and lists:
- support of a special
algebra with lists and scalars;
- support of the
set-theory operations with lists;
- special conversions
of lists into sets, and vice versa;
- tools for expansion
of sets and lists, and subsequent elements rearrangements;
- the extended means
for substitutions into lists and sets;
- a set of special
facilities for operation with lists and sets;
- the extended means of
analysis of multiple entries of elements into lists;
- special conversions
of lists into vectors;
- definition of indices
of a table by its entry, and the analysis of multiplicity of its entries;
- removing elements
from tables, and providing the output of a table graph with numerical entries;
- a representation of
special kinds of tables;
- extension of the
standard function 'map' onto lists, tables and sets;
- tools for sorting
ordinary and nested lists;
- dynamic assignment of
expressions to elements of a list or set;
- a converting of
tables into lists, and vice versa;
- reduction of entries
into a list of multiple elements, etc.
6. Software to support data structures of a special type:
- support of a new data
structure of dirax-type of direct access;
- an extension of the
standard function `type` by a new dirax-type, and conversion
of its algorithm of check onto heap-type;
- tools for
reorganization of data structures of various types {stack, queue, heap};
- the extended check of
a Maple object onto type {dirax, list, table, heap, stack, queue}, etc.
7. Software to support bit-by-bit processing of symbolic information:
- the above tools are not
available in all current releases of the package Maple, therefore these means
of the Library are both rather pertinent, and applicable for a wide range of
applications. A number of useful procedures created on their basis are
represented.
8. Tools extending graphic possibilities of Maple of releases 6 - 10:
- a dynamic coloring of
frames of the animated 2D-graphs. For support of the dynamics the method of "disk transits", a rather useful in the advanced programming in the Maple environment is used;
- an extension of the
standard functions 'animate' and 'animate3d' onto any quantity of parameters of animation. For maintenance of
dynamics the method of "disk transits", rather useful in
conditions of advanced programming in Maple is used. The given
method has been developed by us and successfully used for computers of 3rd generation (IBM/360, IBM/370, etc.) and appeared
especially effective with appearance of the personal computers whose
development is characterized (including) by enough quick decreasing of time of access to external memory on
hard disks;
- an extension of the
standard functions 'smartplot' and 'smartplot3d', etc.
9. Tools that extend and improve the standard tools of Maple:
- checking the type of
expressions, active in a current Maple session;
- essential extensions
of the standard functions 'map', 'map2', 'op', 'read', 'save', 'seq', 'curry' and 'rcurry';
- an essential
extension of the standard function 'assign' with elimination of its incompatibility concerning
releases 6 - 10 of the package Maple;
- an expansion of the
standard operators 'and', 'or' and 'xor' onto any quantity of operands;
- converting the
expressions sequence into string, and checking an expression onto type 'expressions sequence';
- an extension of the standard
function 'type' onto such types as 'binary', 'nestlist', 'boolproc', 'dir', 'file', 'path', 'byte', 'digit', 'letter', 'ssign', 'mod1', 'package', 'sequent', 'setset', 'realnum', 'upper', 'Upper', 'lower', 'Lower';
- an expansion of the
standard function 'member' for checking if an expression belongs to a set, range, string,
symbolical expression, list, module, table, procedure, array and rtable-object;
- an useful extension
of the standard function 'convert';
- checking Maple expressions onto emptiness;
- elimination of
certain defects of the standard function 'evalf';
- means of increasing
the compatibility of releases 6 - 10 of the package Maple, etc.
10. Software for working with Maple datafiles and documents
10.1. General purpose software:
- deletion of datafiles
having an any set of attributes;
- testing of datafiles,
logic input/output channels and input/output devices;
- dynamic increase of
quantity of accessible logic input/output channels;
- the extended means of
closing of all open datafiles and logic input/output channels of a current Maple session;
- definition of
components composing a filename or full path to it;
- a standardization of
path to a datafile or directory that allows to correctly use them by the
standard functions {'system', 'ssystem'};
- opening of the same
datafile on the different logic input/output channels;
- searching for
datafiles with Maple documents containing
the specified context;
- checking of datafiles
and directories onto emptiness, copying of one
catalogue into another;
- renaming of
directories and datafiles with retention of their attributes;
- the extended checking
of properties of directories and datafiles;
- checking of datafiles
types concerning extensions of their names and logical organization {TEXT, BINARY};
- an extension of the
standard function 'type' onto a new rlb-type of datafiles;
- an extension of the
standard function 'convert' providing conversion of an arbitrary datafile into a datafile of type {rlb, TEXT};
- definition and
redefinition of attributes of datafiles and directories;
- checking datafiles
onto a mode of their opening;
- checking of a logic
input/output channel for the specified open datafile; opening of a datafile on
the specified logic input/output channel;
- essential extensions
of the standard functions 'currentdir', 'fopen', 'open', 'mkdir' and 'rmdir';
- creation of a chain
of directories of any nesting level or an empty closed datafile, path to which has
been specified by a chain of subdirectories of any nesting level;
- creation of an
accessible empty target datafile, etc.
10.2. Software for operation with TEXT datafiles:
- an essential
extension of the standard functions 'writedata' and 'readdata';
- tools of providing of
direct access to datafiles of the TEXT-type;
- tools of extended
processing of datafiles of the TEXT-type providing a
number of mass operations with text datafiles, etc.
10.3. Software for operation with BINARY datafiles:
- an effective
processing of a situation «the end of a datafile»;
- tools for extended
processing of datafiles of the BINARY-type providing a
number of mass operations with binary datafiles, etc.
10.4. Software for operation with Maple files:
- a special
re-structuring of a text datafile created by the standard function 'save';
- checking the
availability of a datafile for reading by the standard function 'read';
- providing of
compatibility of a datafile of the internal Maple format with the current
Maple release;
- checking the types of
all datafiles of the specified directory;
- removal of all
results of calculations from the specified mws-file;
- calculation of the
attribute determining name length of a Maple object in files of the
internal Maple format;
- definition of
presence in mws-files of links and
their types, etc.
10.5. Some special tools for operation with datafiles:
- selection of correct email-addresses out of datafiles of the ASCII-format;
- a coding / decoding of datafiles
of the ASCII-format;
- selection out of a
datafile of words satisfying to the specified conditions;
- providing of support
of the mechanism of "disk transits";
- a specific
statistical analysis of text datafiles and strings, etc.
11. Software for solving problems of mathematical analysis:
- extension of the shift-operator onto any
quantity of leading variables;
- calculation of values
of the tabulated functions;
- calculation of
partial derivatives in the specified points;
- full integration of
algebraic expressions;
- a polynomial data
interpolation;
- a dynamic generation
of linear constraints for optimization problems;
- calculation of
independent variables of algebraic expressions;
- an analysis of
algebraic expressions or functions from one independent variable;
- searching for a
minimax of algebraic expressions, etc.
12. Software for solving problems of linear algebra
12.1. General purpose software:
- an interactive
creation of numerical rectangular matrixes;
- full factorization of
a polynomial from one leading variable;
- an useful special
sorting of matrixes of types Maple and NAG;
- a dynamic generation
of cyclic constructions "for_do" and "seq" of any nesting level;
- an extension of the
standard function 'type' onto check of types of indices and entries of tables, etc.
12.2. Software for operation with rtable-objects:
- the extended
converting of Maple-objects into NAG-objects, and vice versa;
- checking rtable-objects, active in a current Maple session;
- checking
identification numbers of the active rtable-objects;
- checking the saving
of the active rtable-objects in a current Maple session;
- checking the
availability of rtable-objects in mws-files with Maple documents;
- converting of the mws-files containing rtable-objects;
- restoration of a work
history with rtable-objects in the
previous Maple sessions, etc.
13. Software to support simple statistics problems:
- checking of a view of
distribution generated by the built-in generator 'rand' of pseudo-random integers;
- a statistical
analysis of text datafiles;
- operations with the
weighed statistical data;
- creation of
single-factor linear and nonlinear models of regression for the specified
resultant and factor variables with calculation of the correlation relation and
of correlation coefficient, and with graphic representation of both the initial
data, and the model of regress on the same 2D-graph;
- parametric (Fisher and Student) and nonparametric (Van der Waerden and Mann-Whitney) criteria of checking of
the null-hypothesis of equality of populations variances;
- elements of the
simple analysis of time and variation series, etc.
14. Software for operation with the user libraries:
- checking of a Maple object to be a library similar to the main library of the package;
- selective call of
procedures, modules and variables from the specified libraries;
- maintenance of the
simple user libraries structurally distinct from the main Maple library;
- the extended means of
maintenance of the libraries similar to the main Maple library;
- an effective method
of a saving of procedures and program modules in libraries;
- facilities for
operation with the damaged libraries similar to the main Maple library;
- the extended
gathering of statistics on use of library tools, etc.
Taking into account our long-term experience in operation with the Maple package of releases 4 - 9 and experience of our colleagues from universities and the academic
institutes of Lithuania, Latvia, Belarus, Estonia and Russia, it is should be noted, that many of tools (or their analogues) of our Library are worth to be included into standard deliveries of
subsequent Maple releases. At present,
they are accessible to the Maple users as the offered Library supporting releases 6 - 10 and functioning on platforms Windows
3.1x and later. Library tools in many cases allow us to facilitate programming
of various applied problems in the Maple environment of
releases 6 - 10.
It is possible to state, that a series of our books on
the Maple problems [6-37,40,41-45] that represent the means developed by us and contain useful tips on
the further development of the package, has encouraged the development of
package modules FileTools, LibraryTools, ListTools and StringTools. However in this respect tools represented by us essentially extend
capabilities of the package, exceeding those of the specified package modules
in many cases.
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, 8, 9/9.5 or 10 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 provides more opportunities of Maple of releases 6 - 10, simplifying the programming of various
practical problems in its environment. This Library will be of special interest above
all to those who use Maple not only as a highly intellectual
calculator but also as environment for programming of different problems in
their professional activities. The Library has been rewarded by "Smart Award" from Smart DownLoads Network.
Furthermore, the presence in the Library delivery of the text datafile “ProcUser.txt” with source codes of the Library software and mws-files with help-pages composing Help database of the Library allows us to adapt it to other
underlying platforms different from Windows.
Finally, the CD with the Library contains the electronic library
of source texts of our twenty-one books on Computer
Science (including Computer
Algebra Systems),
General Statistics and Cellular Automata that have been published in English and Russian in
In conclusion of the given preamble we shall rather briefly state, addressing to our numerous readers both hereby, and the future ones, the personal opinion on a comparative rating of packages Maple and Mathematica. Both one and another package have numerous mistakes (in many cases inadmissible ones for systems of a similar sort) to elimination of which developers both Waterloo Maple and Wolfram Research pays rather small attention. Of commercial reasons unreasonably often are issued the new releases saving former mistakes and containing in a series of cases various exotic luxuries. However, if Maple developers in a form of open dialogue with users in any measure try to solve the given problem, the Wolfram Research an enough painfully perceives any criticism (in overwhelming majority a well-founded) about own product.
On the other hand, Wolfram Research conducts rather aggressive marketing politics completely inadequate to quality of its products. That, first of all, explains its temporary quantitative advantages that quickly enough decrease. Comparing responses of users of Maple and Mathematica, it is possible to ascertain quite unequivocally, that the second ones at use of the package have essentially more problems. If Waterloo Maple can improve the marketing politics, it can change essentially a situation on the market of systems of computer algebra and will play a positive role for the given field of modern computer science in view of the more perspective Maple technology. In this respect, certain contribution to affair of popularization of the Maple was brought also by a series [6-35,40,41-45] of our books and papers in Russian and English against five books on Mathematica [1-5]. Whereas our above-mentioned Library allows to expand first of all basic tools of the package Maple of releases since the sixth one. Furthermore, very expediently a series of tools out of the Library to include in a set of standard basic tools of Maple, above all, tools such as for operation with file system of a computer, for support of new data types, for operation with program modules, for increase of compatibility level of the releases of Maple, etc. Many of the Library tools have shown oneself as effective enough means at problems solving in the various fields, by providing in a series of cases a simplification of programming in Maple.
The experience gained by the
authors in operating and testing of both packages shows that the Maple is essentially a more friendly
and open system which uses built-in Ñ-like
language simplifying employment of the package by the user improving his skills
in programming. Whereas Mathematica has a little bit archaic and not
so graceful language which in many respects is distinct from popular
programming languages. Finally, the Maple
has the more advanced tools (for
example, for solving differential equations with partial derivatives, for
developing algorithms for solving the problems, etc.), providing a wide spectrum of
applications in many fields.
Summing up (in more details a comparative analysis of both packages can be found in our previous books and papers [6-39,40,41-45]), we can recommend to the beginner user of systems of computer algebra, the Maple package as the most perspective tool in this area of computer science. This is essentially caused also by creative alliance Waterloo Maple with the world famous developer of mathematical software - NAG Ltd. Moreover, the given package constantly wins back positions of Mathematica and starts to dominate in education what is rather essential with orientation toward future prospect.
At the same time, modern development of the Maple package causes a number of serious fears which in general can be defined as follows. Quality of the software is being defined by a lot of characteristics among which it is possible to note such as: compatibility upwards, stability of operation concerning operational platforms, along with qualitative support and maintenance, etc. By these parameters the last Maple versions, starting with 7-th, leaves much to be desired, namely. Rather essential bugs (many of them were repeatedly reflected both in our books and articles, and in many other sources, including numerous forums on Maple ) are passed from a release to a release. There is no compatibility of Maple releases from below upwards. About incompatibility of Maple versions we repeatedly marked in the books and articles. Something for improvement of compatibility by us has been made (in particular, by means of our library represented in the article), however not all. Meanwhile, for release 9 the incompatibility already among its clones has been found out also. As is known, Maple 9 supports two operating modes - classical (kernel 'cwmaple9.exe') and standard (kernel 'maplew9.exe'). It turn out, that these clones are incompatible even at a level of the built-in functions. In particular, if in the classical mode the function 'system' is carried out correctly, then in standard mode, giving return code 0, it incorrectly carries out some commands (programs) of MS DOS. For this reason, the procedures which use this function and which have been debugged in releases 8 and are lower, and also in classical Maple 9, in standard Maple 9 are carried out incorrectly, often provoking unpredictable erroneous situations. Naturally, similar infringements of requirements to the qualitative software are not allowable for software of similar type and can lead to consequences undesirable for Maple. As it seems to us, their action already starts to become apparent.
The book [40], attached to the Library,
is a fully revised edition of our book [30] whose
pressrun was completely sold out. The book presents the Library for Maple of releases 6 - 10 or
higher, expanding its basic tools. Source codes of the Library tools introduce the reader into
both effective and non-standard programming technique in Maple. You can download demo of the Library here.
R
e f e r e n c e s
1.
Aladjev V.Z., Hunt U.J., Shishakov M.L. Basics of
Computer Science.-
Gomel: Salcombe Eesti Publisher, 1997, 396 p., ISBN 5-14-064254-5 (in
Russian with extended English summary)
2.
Aladjev V.Z., Hunt U.J., Shishakov M.L. Basics of Computer Science: Textbook.- Moscow: Filin Press,
1998, 496 p., ISBN 5-89568-068-2 (in Russian
with extended English summary)
3.
Aladjev V.Z., Hunt U.J., Shishakov M.L. Basics of Computer Science. 2nd
edition.- Moscow: Filin Press, 1999, 520 p., ISBN 5-89568-068-6 (in
Russian with extended English summary)
4.
Aladjev V.Z., Hunt U.J., Shishakov M.L. Mathematics on Personal Computer.- Gomel: FORT Press, 1996, 498 p.,
ISBN 3-420-614023-3 (in Russian with extended English
summary)
5.
Aladjev V.Z., Shishakov M.L.
Introduction into Environment of Package
Mathematica 2.2.- Moscow: Filin Press, 1997, 362 p., ISBN 5-89568-004-6 (in Russian with extended English summary)
6.
Aladjev V.Z., Vaganov V.A., Hunt U.J., Shishakov M.L. Introduction
into Environment of Mathematical Package Maple
V.- Minsk:
IAN Press, 1998, 452 p., ISBN 14-064256-98 (in Russian
with extended English summary)
7.
Aladjev V.Z., Vaganov V.A., Shishakov M.L., Hunt U.J. Programming
in Environment of Mathematical Package Maple
V.- Gomel:
TRG & Salcombe & VASCO, 1999, 470 p, ISBN 4-10-121298-2 (in
Russian with extended English summary)
8.
Aladjev V.Z., Vaganov V.A., Shishakov M.L., Hunt U.J. Workstation
for Mathematicians.-
Gomel-Tallinn-Moscow: International Academy of Noosphere, the
Baltic Branch,
1999, 605 p., ISBN 3-42061-402-3 (in Russian
with extended English summary)
9.
Aladjev V.Z., Bogdevicius M.A.
Solution of Physical, Technical and Mathematical Problems with
Package Maple V.- Vilnius: Technics Press, 1999,
686 p., ISBN 9986-05-398-6 (in Russian with extended English
summary).
10.
Aladjev V.Z., Shishakov M.L.
Workstation for Mathematicians.- Moscow: Laboratory of Basic Knowledge, 2000, 751 p. + CD, ISBN
5-93208-052-3 (in Russian with extended English
summary)
11.
Aladjev V.Z., Bogdevicius M.A.
Maple 6: Solution
of Mathematical, Statistical, Engineering and Physical Problems.- Moscow: Laboratory of Basic
Knowledge, 2001, 850 p., CD, ISBN 5-93308-085-X (in
Russian with extended English summary)
12.
Aladjev V.Z., Bogdevicius M.A.
Interactive Maple: Solution
of Mathematical, Statistical, Engineering and Physical Problems.- Tallinn-Vilnius, International
Academy of Noosphere, the Baltic Branch, 2001-2002, CD, ISBN 9985-9277-1-0
13.
Aladjev V.Z., Bogdevicius M.A.
Use of package Maple V for solution of physical and
engineering problems // Intern. Conf. TRANSBALTICA-99,
Technics Press, April 1999,
14.
Aladjev V.Z., Hunt U.J.
Workstation for mathematicians // Intern. Conf. TRANSBALTICA-99,
Technics Press, April 1999,
15.
Aladjev V.Z., Hunt U.J.
Workstation for mathematicians // Intern. Conf. "Perfection of Mechanisms of
Management",
Institute of Modern Knowledge, April 1999,
16.
Aladjev V.Z., Shishakov M.L.
Programming in Package Maple V // 2nd Intern.
Conf. “Computer
Algebra in Fundamental and Applied Researches and Education”.-
17.
Aladjev V.Z., Shishakov M.L.
A Workstation for mathematicians // 2nd Intern.
Conf. “Computer
Algebra in Fundamental and Applied Researches and Education”.-
18.
Aladjev V.Z., Shishakov M.L., Trokhova T.A. Educational computer laboratory of the engineer // Proc. 8th Byelorussian Mathemat. Conf., vol. 3,
19.
Aladjev V.Z., Shishakov M.L., Trokhova T.A. Modelling in program environment of mathematical package Maple
V // Proc.
Intern. Conf. on Mathematical Modelling ÌÊÌÌ-2000.-
20.
Aladjev V.Z., Shishakov M.L., Trokhova T.A. A workstation for solution of systems of differential equations
// 3rd Intern. Conf. “Differential Equations and
Applications”.-
Saint-Petersburg, 2000
21.
Aladjev V.Z., Shishakov M.L., Trokhova T.A. Computer laboratory for engineering researches // Intern. Conf. ACA-2000.– Saint-Petersburg,
22.
Aladjev V.Z., Bogdevicius M.A., Hunt U.J. A Workstation for mathematicians // Lithuanian Ñonference TRANSPORT-2000.- Vilnius: Technics Press, April
2000,
23.
Aladjev V.Z. Computer
algebra // Alpha, ¹ 1, 2001,
24.
Aladjev V.Z. Modern computer
algebra for modelling of the transport systems // Proc. Intern. Conference TRANSBALTICA-2001.-
25.
Aladjev V.Z., Shishakov M.L., Trokhova T.A. Workstation for the engineer-mathematician // Proceedings of the
GSTU, ¹ 3, 2000, pp. 42-47,
26.
Aladjev V.Z., Bogdevicius M.A.
Special Questions of Operation in Environment of the Mathematical
Maple Package.- Tallinn-Vilnius: International
Academy of Noosphere, the Baltic Branch & Vilnius Gediminas Technical
University, 2001, 215 p., ISBN 9985-9277-2-9 (in Russian
with extended English summary)
27.
Aladjev V.Z., Vaganov V.A., Grishin E.P. Additional Functional Tools of
Mathematical Package Maple
6/7.- Tallinn:
28.
Aladjev V.Z. Effective
Work in Maple
6/7.- Moscow:
Laboratory of Basic Knowledge, 2002, 334 p. + CD, ISBN 5-93208-118-Õ (in
Russian with extended English summary)
29.
Aladjev V.Z., Liopo V.A., Nikitin A.V. Mathematical Package Maple
in Physical Modelling.-
Grodno: Grodno State University, 2002, 416 p., ISBN 3-093-31831-3 (in
Russian with extended English summary)
30.
Aladjev V.Z., Vaganov V.A. Computer Algebra System Maple:
A New Software Library.- Tallinn:
31.
Aladjev V.Z., Bogdevicius M.A., Prentkovskis O.V. A New
Software for Mathematical Package Maple
of Releases 6,
7 and 8.- Vilnius:
32.
Aladjev V.Z. Interactive
Course of General Theory of Statistics.- Tallinn:
33.
Aladjev V. Z., Bogdevicius M.A.
Computer algebra system Maple: A new
software toolbox
// Intern. Conf. TRANSBALTICA-03, Technics Press, May 2003,
34.
Aladjev V.Z., Vaganov V.A.
Systems of Computer Algebra: A
New Software Toolbox for Maple.- Tallinn:
35.
Aladjev V.Z., Gershgorn N.A.
Computing Problems on Personal Computer.- Kiev: Technics Press, 1991, 248
p. (in Russian with extended English summary)
36.
Aladjev V.Z., Tupalo V.G. Algebraic Calculations on Computer.- Moscow: Mintopenergo Press,
1993, 251p., ISBN 5-942-00456-8 (in Russian
with extended English summary)
37.
Aladjev
V.Z., Bogdevicius M.A., Vaganov V.A. Systems of Computer Algebra: A New
Software Toolbox for
Maple.
Second edition.- Tallinn:
38.
Aladjev
V., Bogdevicius M., Vaganov V.
Systems of Computer Algebra: New Software Toolbox for Maple // The 2004 Intern. Conf. on Software
Engineering Research and Practice, SERP'04,
2004,
39.
Aladjev
V. Computer
Algebra System Maple: A New
Software Library
// Intern. Conf. on Comp. Sci., ICCS-2003,
40. Aladjev
V. Computer
Algebra Systems: A New Software Toolbox for Maple.- Palo Alto: Fultus Corporation,
2004, 575 p., ISBN
1-59682-000-4.
41. Aladjev V.Z., Bogdevicius M.A. Maple: Programming, Physical and Engineering Problems. CA: Palo
Alto, Fultus Corp., 2006, 404 p., ISBN 1-59682-080-2, Adobe Acrobat eBook (pdf), ISBN 1-59682-081-0.
42. Aladjev V.Z., Haritonov V.N. General Theory of Statistics.- CA: Palo Alto, Fultus
Corp., 2006, 256 p., ISBN 1-59682-086-1, Adobe Acrobat eBook (pdf), ISBN 1-59682-081-0 (in Russian with extended English summary).
43. Aladjev V.Z. Computer
Algebra Systems. Maple: Art of Programming.- Moscow: BINOM Press, 2006, 792 p.,
ISBN 5-93208-189-9 (in Russian with extended English summary).
44. Aladjev V.Z. Foundations
of Programming
in Maple:
Textbook.- Tallinn: International Academy of Noosphere, 2006, 300 p., (pdf),
ISBN 9985-9508-1-X, 978-9985-9508-1-4, http://www.aladjev-maple.narod.ru
(in Russian)
45. Aladjev V.Z., Boiko V.K., Rovba E.A. Programming and Applications Elaboration in Maple:
Monograph.- Grodno: Grsu, Tallinn: International Academy of Noosphere, 2007,
456 p., ISBN 978-985-417-891-2, ISBN 978-9985-9508-2-1, http://www.aladjev-maple-book.narod.ru
(in Russian)
