Structure and interpretation of computer programs

Poised to become the leading reference in the field, the Handbook of Finite Fields is exclusively devoted to the theory and applications of finite fields. More than 80 international contributors compile state-of-the-art research in this definitive handbook. Edited by two renowned researchers, the book uses a uniform style and format throughout and each chapter is self contained and peer reviewed. The first part of the book traces the history of finite fields through the eighteenth and nineteenth centuries. The second part presents theoretical properties of finite fields, covering polynomials, special functions, sequences, algorithms, curves, and related computational aspects. The final part describes various mathematical and practical applications of finite fields in combinatorics, algebraic coding theory, cryptographic systems, biology, quantum information theory, engineering, and other areas. The book provides a comprehensive index and easy access to over 3,000 references, enabling you to quickly locate up-to-date facts and results regarding finite fields.

Handbook of Finite Fields

A web application development environment and method employs an extensible user interface (XUI) Framework for creating GUI-managing components written in a declarative format for handling GUI components in a web application. The GUI-managing components are coordinated in a view presentation layer by a Controller in an Extended-Model-View-Controller (XMVC) pattern in conjunction with the business logic layer. The Controller is invoked by a user request for a web page and in turn invokes the GUI-managing components to parse information contained in a corresponding web application file for the requested web page in order to determine the templates and sub-templates to be invoked for handling the GUI components. Each template has a mode value which is set by mode information contained in the web application file for the requested web page. The XUI Framework has the ability to handle a rich set of GUI components without having to implement web applications development technologies. Instead, the declarative-formatted GUI components can be created and processed using lightweight technologies for client-side and server-side processing. The XUI Framework allows for the efficient authoring and processing of GUI components for a wide range of web applications.

Extensible user interface (xui) framework and development environment

Data in a document are displayed according to a transformation stylesheet, and the transformation stylesheet is automatically updated in response to a document modification made using a graphical editor. Mapping between the transformation stylesheet and the document is automated, so that user modifications to the document or to the transformation stylesheet are automatically incorporated in both. The transformation stylesheet is automatically annotated to create the mapping, and the data are transformed according to the annotated transformation stylesheet. Annotations are carried over to the resulting document. The annotations map nodes within the document to corresponding nodes in the transformation stylesheet. Annotations affected by modifications to the document are translated and replace corresponding nodes in the transformation stylesheet. The updated transformation stylesheet is re-annotated and the data are again transformed. Differences between the updated document and the original document are merged into the original document to maintain user selection information.

Transformation stylesheet editor

A user interface (UI) in the form of a single navigable window enables a user to navigate to and between multiple different functionalities that are provided by a single application program. Novel use is made of navigation model that manages the user's navigation activites to and between the different functionalities. Navigation instrumentalities enable the user to navigate among the different functionalities and include links to each of the different functionalities as well as browser-like navigation buttons. Context-sensitive command sets can also be provided along with the single navigable window. The context sensitive command sets include commands that automatically change as the user's computing context changes, e.g. as the user moves from functionality to functionality. The single application can be defined as a software platform that is extensible to receive and incorporate different functionalities. The functionalities can be provided as software modules that can be sent over a network such as the Internet. The extensible software platform provides a basis to offer a subscriber or fee-based service where different subscribers can, for a fee, access different functionalities via a network such as the Internet.

Single window navigation methods and systems

A method (and structure) for enacting changes to a document containing a template-based program that transforms tree-structured data from a first tree-structured data into a second tree-structured data, including providing an interface to permit selection of a document containing the template-based program, constructing a model of the template-based program in the selected document by parsing elements of the template-based program into a corresponding logical construct having a match condition and at least one generator, where the match condition determines whether an element in the first tree-structure data is to be processed by one or more of the at least one generator, and displaying a representation of the model to the user.

Method and system for stylesheet-centric editing

The dreaded phenomenon of expression swell in symbolic computation can be palliated by adopting implicit representations for symbolic objects, such as straight-line programs or so-called black box representations. In the latter, each expression is a symbolic object, more specifically, a computer program with a set of statically initialized data, which takes as input a value for each variable and then produces the value of the symbolic object it represents at the specified point.
In this thesis we introduce F sc OXB sc OX, a software package that puts in practice the black box representation of symbolic objects and provides algorithms for performing the symbolic calculus with such representations. Improved versions of the algorithms found in Kaltofen and Trager (Journal of Symbolic Computing, vol. 9, nr. 3, p. 311 (1990)) and Kaltofen and Diaz (International Symposium on Symbolic and Algebraic Computation '95,) p. 232) are discussed. Also we describe an interpolation scheme based on a Zippel's algorithm (Journal of Symbolic Computing, vol. 9, nr. 3, p. 375 (1990)) that optimizes the number of required black box evaluations.
The design of F sc OXB sc OX is intended to demonstrate how plug-in software components can be employed for generally used symbolic systems. Our implementation incorporates data types parameterized by arbitrary coefficient domains and generic algorithms. By providing a mechanism for interfacing to general purpose computer algebra systems, we broaden F sc OXB scOX's applicability. Furthermore we provide a distribution mechanism that allows for parallel and distributed execution of F sc OXB sc OX programs independent of the underlying parallel architecture.
Finally, we present the results of several challenge problems which exercise our F sc OXB sc OX library and represent the first symbolic solutions of such problems.

FOXBOX: a system for manipulating symbolic objects in black box representation

A method (and structure) for displaying mapping relationships defined by a plurality of instruction elements, each instruction element providing a relation between zero or more source elements and zero or more result elements, where each source element includes one of a plurality of source elements and each result element includes one of a plurality of result elements, including providing a user a representation including a portion of the mapping relationships and including one or more of the plurality of source elements, the plurality of instruction elements, and the plurality of result elements. The user is provided a method to select one of the elements in the representation. The selected element is highlighted in the representation and the highlighting can be propagated to any other elements related by the mapping that are displayed in the representation.

Method and system for stylesheet execution interactive feedback

The proliferation of general purpose mathematical software and specialized mathematical libraries has provided a wealth of computing resources for students, scientists, and engineers. The challenge remains to harness the power of these independent software tools within a single framework. OpenMath will provide formats and a protocol for the exchange of mathematical expressions and objects, thus enabling a unification from a user's point of view. This work will also allow the inclusion of mathematical objects in a universal format within databases and electronically published scientific and technical documents.This report will detail the steps taken to date by the OpenMath Consortium to achieve the aforementioned goals. In particular, §2 provides an overview of OpenMath. Emphasis is placed on OpenMath's design goals, initial target applications, and Consortium structure. In §3, an exposition of the levels of the OpenMath model which maps mathematical concepts to their respective concrete representations is provided. Some issues that arise when a mathematical object is transcribed between its visual form and internal representation are presented in §4. Finally, §5 and §6 communicate the current state of the OpenMath prototyping efforts and concomitantly detail the future directions of the OpenMath consortium.

A report on OpenMath: a protocol for the exchange of mathematical information

DSC is a general purpose tool that allows the distribution of a computation over a network of Unix workstations. Its control mechanisms automatically start up daemon processes on the participating workstations in order to communicate data by the standard IP/TCP/UDP protocols. The user's program distributes either remote procedure calls or source code of programs and their corresponding input data files by calling a DSC library function. DSC then automatically finds a suitable workstation and sends the information necessary to execute the given subtask. If source code, which may be written in either ANSI C or Common Lisp, is distributed, this includes compilation on the remote workstation to first make an executable object module. In this mode, a Unix workstation of any architecture type or without prior preparation of problem specific object modules on its file system can be involved. A call to another library function synchronizes the user's program execution by selectively waiting for the completion of a specific or all distributed subtasks. DSC also has an interactive monitor facility that lets a user watch the progress of a distributed computation. We have tested DSC with a primality test for large integers and with a factorization algorithm for polynomials over large finite fields and observed significant speed-ups over executing the best-known methods on a single workstation computation. These experiments have been carried out not only on our local area network but also on off-site workstations at the University of Delaware.

Angel Díaz

Papers

Method and system for stylesheet-centric editing

FOXBOX: a system for manipulating symbolic objects in black box representation

Method and system for stylesheet execution interactive feedback

A report on OpenMath: a protocol for the exchange of mathematical information

DSC: a system for distributed symbolic computation