books/bookvolbib Axiom Citations in the Literature

Goal: Axiom Literate Programming

\index{Rigal, Alain}
\begin{chunk}{axiom.bib}
@Article{Riga99,
  author = "Rigal, Alain",
  title = "High-order compact schemes: Application to bidimensional unsteady
           diffusion-convection problems.",
  journal = "C. R. Acad. Sci.",
  volume = "328",
  number = "6",
  pages = "535-538",
  year = "1999",
  keywords = "axiomref",
  abstract =
    "For unsteady 2D diffusion-convection problems, we present two classes
    of compact difference schemes of order 2 in time and 4 in space. These
    finite difference schemes are essentially derived from 1D schemes,
    extensively analyzed in our previous paper [J. Comput. Phys. 114,
    No. 1, 59-76 (1994; Zbl 0807.65056)]. We propose two approaches:
    construction of 2D schemes as product of 1D schemes and global
    formulation of 2D schemes. Part II by M. Fournié [C. R. Acad. Sci.,
    Paris, Sér. I, Math. 328, No. 6, 539-542 (1999; reviewed below)]
    focuses on the development and analysis of global schemes with the
    assistance of symbolic computation software (AXIOM)."
}

\end{chunk}

\index{Roesner, K. G.}
\begin{chunk}{axiom.bib}
@Article{Roes99,
  author = "Roesner, K. G.",
  title = "Supersonic flow around accelerated and decelerated bodies,
           analysed by analytical methods",
  journal = "Z. Angew. Math. Mech.",
  volume = "79",
  number = "3",
  pages = "815-816",
  year = "1999",
  keywords = "axiomref",
  abstract =
    "By an extensive use of the computer algebra system AXIOM, a power
    series expansion with respect to the radial variable $r$ is used to
    describe the accelerated or decelerated supersonic flow field around
    the tip of slender conical bodies. The set of coupled nonlinear
    differential equations for the coefficient functions, depending on
    $\theta$ and $t$, is derived in closed form, and the first and second
    approximation of the coefficient functions are determined
    numerically."
}

\end{chunk}

\index{Stroeker, Roelof J.}
\index{Kaashoek, Johan F.}
\begin{chunk}{axiom.bib}
@book{Stro99,
  author = "Stroeker, Roelof J. and Kaashoek, Johan F.",
  title = "Discovering mathematics with Maple. An interactive exploration for
           mathematicians, engineers and econometricians",
  year = "1999",
  publisher = "Birkhauser",
  keywords = "axiomref",
  abstract =
    "During the past decade, the mathematical computer software packages
    such as Mathematica, Maple, MATLAB (Axiom, Derive, Macsyma, MuPad are
    some further examples of such software) [see Macsyma 2.3. Lite – the
    student edition (1998; Zbl 0911.68089); B. W. Char, K. O. Geddes,
    G. H. Gonnet, B. L. Leong, M. B. Monagan, and S. M. Watt, Maple V
    Library reference manual (1991; Zbl 0763.68046); J. L. Zachary,
    Introduction to scientific programming. Computational problem solving
    using Mathematica and C (1997; Zbl 0891.68053); The student edition of
    MATLAB. Student user guide. The problem-solving tool for engineers,
    mathematicians, and scientists (1992; Zbl 0782.65001); H. Benker,
    Ingenieurmathematik mit Computeralgebra-Systemen. AXIOM, DERIVE,
    MACSYMA, MAPLE, MATHCAD, MATHEMATICA, MATLAB und MuPAD in der
    Anwendung (1998; Zbl 0909.68109); W. Koepf, Hohere Analysis mit DERIVE
    (1994; Zbl 0819.26003)] have greatly faciliated mathematical
    experiments and have thus become popular tools for the modern
    mathematician. It is a pity that most of these packages are quite
    expensive, and that the frequently upgraded versions are not free for
    the owners of the earlier versions (fortunately, there are inexpensive
    student versions of some of these packages). There is a constant
    demand of instructional textbooks by users of these packages. This
    demand is reflected in the growing number of such textbooks. Many of
    these books provide software support (diskette, CD-ROM, access by
    ftp). Such a textbook should meet, in my opinion, the following
    criteria: (1) The size should be small, not bulky like the complete
    technical descriptions of the software. (2) There should be a lot of
    examples of the use of the software covering a wide range of
    mathematical topics. Electronic versions of these examples should be
    made available for free to the users of the textbook
    (e.g. diskette/CD-ROM, access by ftp). (3) There should be a good
    supply of exercises covering the basic mathematical applications. (4)
    The book should be visually pleasing, easy to read, have good indexes
    and provide pointers to other books and electronic sources of
    information. The book under review provides, in addition to the actual
    text, an interactive exploratorium of its topics, based on the
    mechanism of Maple worksheets. These worksheets can be ``opened'' by
    the Maple program and they form a mixture of usual text, hypertext,
    and Maple commands and have a nice style appearance. They also can be
    ``exported'' in a file and included in a file for further treatment.
    The book meets all the aforementioned criteria (1)-(4) with elegance.
    There are many exercises which cover all the usual mathematical topics
    from linear algebra to differential equations and statistics. A
    valuable feature is an appendix with hints and answers for all
    exercises.  One of the highlights of the book is the examination of
    Riemann's non-differentiable function
    \[x \mapsto \sum_{k=1}^\infty{k^{-2}} sin(\pi kx)\]
    which is differentiable only at the rational points $p/q$ with $p$
    and $q$ odd and relatively prime, where its derivative is $-1/2$.

    The book is intended for students of mathematics, engineering
    sciences, and econometry. This book is an ideal guide for this purpose
    and it could probably be used along, without the bulky technical
    documentation of the Maple language. Note that Maple has a
    comprehensive on-line help program, which contains large parts of the
    original documentation."
}

\end{chunk}

\index{Wester, Michael J.}
\begin{chunk}{axiom.bib}
@book{West99,
  author = "Wester, Michael J.",
  title = "Computer Algebra Systems. A practical guide",
  year = "1999",
  publisher = "Wiley",
  keywords = "axiomref",
  abstract =
    "In this book some of the most popular general purpose computer
    algebra systems (CAS), such as Mathematica, Maple, Derive, Axiom,
    MuPAD, and Macsyma, are examined. The strengths and weaknesses of
    these programs are compared and contrasted, and tutorial information
    for using these systems in various ways is given. The different
    packages are quantitatively compared using standard test suites,
    giving the possibility to asses the most appropriate for a particular
    user or application. The origins of these systems are revealed and
    many of their behaviors analyzed. This furnishes a feel for where the
    current computer algebra system state of the art stays and what can be
    expected for existing and future systems. The book is organized in
    several chapters written by different authors. Chapters 1,2, and 3 are
    organized as reviews, comparisons, and critiques of CAS
    capabilities. Then more technical issues are discussed considering
    different approaches taken by different CAS: simplifying square roots
    of square roots by denesting (chapter 4), complex number calculation
    (chapter 5), efficiently computing Chebyshev polynomials (chapter 6),
    solving single equations and systems of polynomial equations (chapters
    7, 8), computing limits (chapter 9), multiple integration (chapter
    10), solving ordinary differential equation (chapter 11), integration
    of nonlinear evolution equations (chapter 12), code generation
    (chapter 13), evaluation of expressions and programs in the embedded
    computer algebra programming language (chapter 14), and computer
    algebra in education (chapter 15). Chapter 16 covers the origin of CA,
    and, finally chapter 17 gives a list of most CAS available today."
}

\end{chunk}

\index{Benker, Hans}
\begin{chunk}{axiom.bib}
@book{Benk98,
  author = "Benker, Hans",
  title = "Engineering mathematics with computer algebra systems",
  year = "1998",
  keywords = "axiomref",
  comment = "german"
}

\end{chunk}

\index{Breuer, Thomas}
\index{Linton, Steve}
\begin{chunk}{axiom.bib}
@InProceedings{Breu98,
  author = "Breuer, Thomas and Linton, Steve",
  title = "The GAP 4 type system organising algebraic algorithms",
  booktitle = "Proc. ISSAC 98",
  series = "ISSAC 98",
  year = "1998",
  publisher = "ACM Press",
  location = "Rostock, Germany",
  pages = "13-15",
  keywords = "axiomref",
  paper = "Breu98.pdf",
  url = "http://www.gap-system.org/Doc/Talks/paper.ps",
  abstract =
    "Version 4 of the GAP (Groups, Algorithms, Programming) system for
    computational discrete mathematics has a number of novel features. In
    this paper, we describe the type system, and the way in which it is
    used for method selection. This system is central to the organization
    of the library which is the main part of the GAP system. Unlike
    simpler object-oriented systems, GAP allows method selection based on
    the types of all arguments and on certain aspects of the relationship
    between the arguments. In addition, the type of an object can change,
    in a controlled way, during its life. This reflects information about
    the object which has been computed and stored. Individual methods can
    be written and installed independently. Furthermore, most checking of
    the arguments is done in a uniform way by the method selection system,
    making individual methods simpler and less prone to error. The methods
    are combined automatically to produce a powerful and usable system for
    interactive use or programming."
}

\end{chunk}

\index{Linton, Stephen}
\begin{chunk}{axiom.bib}
@misc{Lint98,
  author = "Linton, Stephen",
  title = "The GAP 4 Type System Organising Algebraic Algorithms",
  paper = "Lint98.pdf",
  url = "http://www.gap-system.org/Doc/Talks/kobe.ps",
  keywords = "axiomref"
}

\end{chunk}

\index{Diaz, Angel}
\index{Kaltofen, Erich}
\begin{chunk}{axiom.bib}
@InProceedings{Diaz98,
  author = "Diaz, A. and Kaltofen, E.",
  title = "{FoxBox}, a System for Manipulating Symbolic Objects in Black Box
           Representation",
  booktitle = "Proc. 1998 Internat. Symp. Symbolic Algebraic Comput.",
  crossref = "ISSAC98",
  publisher = "ACM Press",
  year = "1998",
  pages = "30--37",
  url = "http://www.math.ncsu.edu/~kaltofen/bibliography/98/DiKa98.pdf",
  paper = "Diaz98.pdf",
  abstract =
    "The FOXBOX system puts in practice the black box representation of
    symbolic objects and provides algorithms for performing the symbolic
    calculus with such representations. Black box objects are stored as
    functions. For instance: a black box polynomial is a procedure that
    takes values for the variables as input and evaluates the polynomial
    at that given point. FOXBOX can compute the greatest common divisor
    and factorize polynomials in black box representation, producing as
    output new black boxes. It also can compute the standard sparse
    distributed representation of a black box polynomial, for example, one
    which was computed for an irreducible factor. We establish that the
    black box representation of objects can push the size of symbolic
    expressions far beyond what standard data structures could handle
    before.

    Furthermore, FOXBOX demonstrates the generic program design
    methodology. The FOXBOX system is written in C++. C++ template
    arguments provide for abstract domain types. Currently, FOXBOX can be
    compiled with SACLIB 1.1, Gnu-MP 1.0, and NTL 2.0 as its underlying
    field and polynomial arithmetic. Multiple arithmetic plugins can be
    used in the same computation. FOXBOX provides an MPI compliant
    distribution mechanism that allows for parallel and distributed
    execution of FOXBOX programs. Finally, FOXBOX plugs into a
    server/client-style Maple application interface."
}

\end{chunk}

\index{Dooley, Samuel S.}
\begin{chunk}{axiom.bib}
@InProceedings{Dool98,
  author = "Dooley, Samuel S.",
  title = "Coordinating mathematical content and presentation markup in
           interactive mathematical documents",
  booktitle = "Proc. ISSAC 1998",
  series = "ISSAC 98",
  year = "1998",
  publisher = "ACM Press",
  location = "Rostock, Germany",
  pages = "13-15",
  keywords = "axiomref",
  abstract =
    "This paper presents a method for representing mathematical content
    and presentation markup in interactive mathematical documents that
    treats each view of the information on a separate and equal
    footing. By providing extensible, overridable, default mappings from
    content to presentation in a way that supports efficient mappings back
    from the presentation to the underlying content, a user interface for
    an interactive textbook has been implemented where the user interacts
    with high-quality presentation markup that supports user operations
    defined in terms of the mathematical content. In addition, the user
    interface can be insulated from content-specific information, while
    still being enabled to transfer that information to other programs for
    computation. This method has been employed to embed interactive
    mathematical content into the IBM techexplorer Interactive Textbook
    for Linear Algebra. The issues involved in the implementation of the
    interactive textbook also shed some light on the problems faced by the
    MathML working group in representing both presentation and content for
    mathematics for interactive web documents."
}

\end{chunk}

\index{Dunstan, Martin}
\index{Kelsey, Tom}
\index{Linton, Steve A.}
\index{Martin, Ursula}
\begin{chunk}{axiom.bib}
@InProceedings{Duns98,
  author = "Dunstan, Martin and Kelsey, Tom and Linton, Steve and
            Martin, Ursula",
  title = "Lightweight Formal Methods For Computer Algebra Systems",
  publisher = "ACM Press",
  booktitle = "Proc. ISSAC 1998",
  year = "1998",
  location = "Rostock, Germany",
  pages = "80-87",
  url = "http://www.cs.st-andrews.ac.uk/~tom/pub/issac98.pdf",
  paper = "Duns98.pdf",
  keywords = "axiomref",
  abstract =
    "Demonstrates the use of formal methods tools to provide a semantics
    for the type hierarchy of the Axiom computer algebra system, and a
    methodology for Aldor program analysis and verification. There are
    examples of abstract specifications of Axiom primitives."
}

\end{chunk}

\index{Harrison, J.}
\index{Thery, L.}
\begin{chunk}{axiom.bib}
@Article{Harr98,
  author = "Harrison, J. and Thery, L.",
  title = "A Skeptic's approach to combining HOL and Maple",
  journal = "J. Autom. Reasoning",
  volume = "21",
  number = "3",
  pages = "279-294",
  year = "1998",
  keywords = "axiomref",
  paper = "Harr98.pdf",
  url = "http://www.cl.cam.ac.uk/~jrh13/papers/cas.ps.gz",
  abstract =
    "We contrast theorem provers and computer algebra systems, pointing
    out the advantages and disadvantages of each, and suggest a simple way
    to achieve a synthesis of some of the best features of both. Our
    method is based on the systematic separation of search for a solution
    and checking the solution, using a physical connection between
    systems. We describe the separation of proof search and checking in
    some detail, relating it to proof planning and to the complexity class
    NP, and discuss different ways of exploiting a physical link between
    systems. Finally, the method is illustrated by some concrete examples
    of computer algebra results proved formally in the HOL theorem prover
    with the aid of Maple."
}

\end{chunk}

\index{Kerber, Manfred}
\index{Kohlhase, Michael}
\index{Volker, Sorge}
\begin{chunk}{axiom.bib}
@Article{Kerb98,
  author = "Kerber, Manfred and Kohlhase, Michael and Volker, Sorge",
  title = "Integrating computer algebra into proof planning",
  journal = "J. Autom. Reasoning",
  volume = "21",
  number = "3",
  pages = "327-355",
  keywords = "axiomref",
  paper = "Kerb98.pdf",
  url =
"http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.40.3914&rep=rep1&type=pdf",
  abstract =
    "Mechanized reasoning systems and computer algebra systems have
    different objectives. Their integration is highly desirable, since
    formal proofs often involve both of the two different tasks proving
    and calculating. Even more important, proof and computation are often
    interwoven and not easily separable.

    In this article, we advocate an integration of computer algebra into
    mechanized reasoning systems at the proof plan level. This approach
    allows us to view the computer algebra algorithms as methods, that is,
    declarative representations of the problem-solving knowledge specific
    to a certain mathematical domain. Automation can be achieved in many
    cases by searching for a hierarchic proof plan at the method level by
    using suitable domain-specific control knowledge about the
    mathematical algorithms. In other words, the uniform framework of
    proof planning allows us to solve a large class of problems that are
    not automatically solvable by separate systems.

    Our approach also gives an answer to the correctness problems inherent
    in such an integration. We advocate an approach where the computer
    algebra system produces high-level protocol information that can be
    processed by an interface to derive proof plans. Such a proof plan in
    turn can be expanded to proofs at different levels of abstraction, so
    the approach is well suited for producing a high-level verbalized
    explication as well as for a low-level, machine-checkable,
    calculus-level proof. We present an implementation of our ideas and
    exemplify them using an automatically solved example."
}

\end{chunk}

\index{Naudin, Patrice}
\index{Quitte, Claude}
\begin{chunk}{axiom.bib}
@Article{Naud98,
  author = "Naudin, Patrice and Quitte, Claude",
  title = "Univariate polynomial factorization over finite fields",
  journal = "Theor. Comput. Sci.",
  volume = "191",
  number = "1-2",
  pages = "1-36",
  year = "1998",
  paper = "Naud98.pdf",
  abstract =
    "This paper is a tutorial introduction to univariate polynomial
    factorization over finite fields. The authors recall the classical
    methods that induced most factorization algorithms (Berlekamp’s and
    the Cantor-Zassenhaus ones) and some refinements which can be applied
    to these methods. Explicit algorithms are presented in a form suitable
    for almost immediate implementation. They give a detailed description
    of an efficient implementation of the Cantor-Zassenhaus algorithm used
    in the release 2 of the Axiom computer algebra system."
}

\end{chunk}