## Interactive mathematical documents on the web (2003)

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Venue: | In Algebra, Geometry and Software Systems |

Citations: | 14 - 2 self |

### BibTeX

@INPROCEEDINGS{Cohen03interactivemathematical,

author = {A. M. Cohen and H. Cuypers and E. Reinaldo Barreiro and H. Sterk},

title = {Interactive mathematical documents on the web},

booktitle = {In Algebra, Geometry and Software Systems},

year = {2003},

pages = {289--306},

publisher = {Springer-Verlag}

}

### OpenURL

### Abstract

This paper deals with our work on interactive mathematical documents that make use of the World Wide Web. The work is concerned with a computer environment that is able to invoke various specialized mathematical software systems. We are concerned with interactive mathemtical documents taking input from various sources, users and mathematical services. Communication between these three different entities has been realized using OpenMath. But, such communication and the interactivity inside the mathematical document take place in a specific, but dynamic context or state. In this paper we present a solution on how to keep track of this dynamical state and describe our implementation of this. 1

### Citations

65 |
The On-Line Encyclopedia of Integer Sequences, www.research.att.com/̃ njas/sequences
- Sloane
(Show Context)
Citation Context ...ow to handle the state in which a mathematical query takes place. We note that this problem has not been addressed in some of the more successful mathematical services on the internet, such as Sloane =-=[27]-=-, Faugère’s Gröbner basis service [14], Wilson’s Atlas of representations of finite simple groups [32], Brouwer’s coding theory data base [3], and WebMathematica [31]. For example, Webmathematica is a... |

9 |
Electronic communication of mathematics and the interaction of computer algebra systems and proof assistants
- Barendregt, Cohen
(Show Context)
Citation Context ...uter algebra system, the interpretation is often ‘evaluation’ or ‘simplification’: when passed 2 + 3, these applications will return 5. If the application is a proof assistant (e.g., Lego or Coq, cf. =-=[9]-=-), then ‘verifying’ or ‘proving’ is a more likely interpretation of what the application is supposed to do, and, if the application is a browser or printing, the interpretation is to prepare the mathe... |

6 |
Java phrasebooks for Computer Algebra and Automated Deduction, Sigsam Bulletin
- Caprotti, Cohen, et al.
- 2000
(Show Context)
Citation Context ...nto experimental versions of both Axiom and GAP, cf. [2, 15]. We have 3sdeveloped a Java library, called ROML, for building full phrasebooks outside mathematical software packages. It is described in =-=[4]-=- and can be found at [26]. By use of ROML, such external phrasebooks have been implemented for the proof checkers Lego and Coq, for the computer algebra packages Maple, Mathematica and GAP [5, 6]. 2.2... |

6 |
Using OpenMath Servers for Distributing Mathematical Computations
- Caprotti, Cohen, et al.
- 2000
(Show Context)
Citation Context ...nt as input for computations leading to a consultancy. In each of the above scenarios a suitable interactive mathematical document can offer the appropriate mathematical services via the internet. In =-=[12]-=- we have described a way to provide the computing facilities of various mathematical software packages via OpenMath servers to the internet community. However, in the scenarios described above, the ma... |

6 |
JavaMath: an API for internet accessible mathematical services
- Solomon, Struble
- 2001
(Show Context)
Citation Context ...sebook tends to interpret the OpenMath object as an evaluation command, whereas the same expression would just be printed as something like “Factors of X 2 − 1” when sent to a typesetting program. In =-=[31]-=-, a mode of interaction is implemented where the behavior of a computer algebra system can be controlled from within a JSP page (see §4.2 below) by using a set of primitives such as assigning and retr... |

5 |
Connecting proof checkers and computer algebra using OpenMath
- Caprotti, Cohen
- 1999
(Show Context)
Citation Context ...ibed in [4] and can be found at [26]. By use of ROML, such external phrasebooks have been implemented for the proof checkers Lego and Coq, for the computer algebra packages Maple, Mathematica and GAP =-=[5, 6]-=-. 2.2 Mathematical Web Services The OpenMath set up is only the beginning. For mathematical services across the internet, many more issues have to be resolved. In §3.2 of [28], some of these issues ar... |

4 |
How to formally and efficiently prove Prime(2999
- Caprotti, Oostdijk
- 2000
(Show Context)
Citation Context ...ibed in [4] and can be found at [26]. By use of ROML, such external phrasebooks have been implemented for the proof checkers Lego and Coq, for the computer algebra packages Maple, Mathematica and GAP =-=[5, 6]-=-. 2.2 Mathematical Web Services The OpenMath set up is only the beginning. For mathematical services across the internet, many more issues have to be resolved. In §3.2 of [28], some of these issues ar... |

4 |
The ACELA project: Aims and Plans
- Cohen, Meertens
- 1998
(Show Context)
Citation Context ...on how to keep track of this dynamical state and describe our implementation of this. 1 Introduction Although the notion of an interactive mathematical document has been around for several years, cf. =-=[13]-=-, its realization is nowhere near the final stage. Recent web technological progress, for instance, has enabled a much smoother communication of mathematics than ever before. The use of an interactive... |

2 |
Algebra Interactive!, Interactive lecture notes on Algebra (paper book and CD-Rom
- Cohen, Cuypers, et al.
- 1999
(Show Context)
Citation Context ...cuss how we have implemented the architecture presented in §2 within a Java-xml enviroment. Our big motivating example 8sis a forthcoming new edition of the interactive book Algebra Interactive! (see =-=[7]-=-), which is interactive course material for first year undergraduate algebra. We shall use the word MathBook for an interactive mathematical document, as well as for the ensemble of software tools we ... |

2 | OpenMath Technology for Interactive Mathematical Documents
- Caprotti, Cohen, et al.
- 2002
(Show Context)
Citation Context ...ent. The purpose of this paper is to describe an architecture and the latest tools we have developed towards an interactive mathematical document. In this vein, the paper can be viewed as a sequel to =-=[11]-=-. In this paper we describe the type of web service we have in mind, as well as a way in which we have realized such services. Thereby we focus 1son the user end of this window to the world of mathema... |

2 | for dynamically generated Web content, java.sun.com/products/jsp - Pages |

2 |
the computer algebra system
- Maple
(Show Context)
Citation Context ... closes the example. 3.6 Examples We make the picture described above more concrete by considering the following five scenarios. 14s1. An author of a book on mathematical analysis has used both Maple =-=[18]-=- and Mathematica [19] to write algorithms discussed in his/her book. At times, the results of one system are fed into the other. Preferably, the author would like to write the code only once. 2. At a ... |

2 |
the computer algebra system
- Mathematica
(Show Context)
Citation Context ...3.6 Examples We make the picture described above more concrete by considering the following five scenarios. 14s1. An author of a book on mathematical analysis has used both Maple [18] and Mathematica =-=[19]-=- to write algorithms discussed in his/her book. At times, the results of one system are fed into the other. Preferably, the author would like to write the code only once. 2. At a high school, students... |

2 |
a standard for open mathematical documents, www.mathweb.org/omdoc
- OMDoc
(Show Context)
Citation Context ...e, an xml document. As a result, there is an xml based markup language (the MathBook DTD) for the creation of interactive mathematical documents. We have been influenced by both DocBook [8] and OMDoc =-=[22]-=-. The former is a fairly general standard for electronic books, the latter is a very rich, and strongly logic-oriented standard for mathematical documents. We intend to maintain a close link with OMDo... |

1 |
Coding theory server, for bounds on the minimum distance of q-ary linear codes, q
- Brouwer
(Show Context)
Citation Context ...ful mathematical services on the internet, such as Sloane [27], Faugère’s Gröbner basis service [14], Wilson’s Atlas of representations of finite simple groups [32], Brouwer’s coding theory data base =-=[3]-=-, and WebMathematica [31]. For example, Webmathematica is a way to access Mathematica via the Web. Via browser pages users can formulate either full Mathematica commands or input for pre-programmed Ma... |

1 | The OpenMath Standard, www.nag.co.uk/projects/omstd - Caprotti, Cohen, et al. |

1 |
interface to OpenMath
- GAP
(Show Context)
Citation Context ...he interpretation is to prepare the mathematical object for a presentation. Phrasebooks providing interfaces to and from OpenMath have been built into experimental versions of both Axiom and GAP, cf. =-=[2, 15]-=-. We have 3sdeveloped a Java library, called ROML, for building full phrasebooks outside mathematical software packages. It is described in [4] and can be found at [26]. By use of ROML, such external ... |

1 |
Stilo’s editor for rapid generation of mathematical expressions for display and processing
- MathWriter
(Show Context)
Citation Context ...l purpose editors have been developed, no author will need to work with the elaborate xml sources. However, currently there is no alternative at hand. There are two editors for OpenMath objects, viz. =-=[17, 20]-=-, but these do not suffice for the more elaborate source documents described in §3.1. By means of the IDA tag library, we have tried to reduce the difficulties of authoring as far as possible, but som... |

1 | a browser development project, www.mozilla.org - Mozilla |

1 |
Distributed Computing for Mathematical System Integration
- Solomon
- 2001
(Show Context)
Citation Context ...e, Mathematica and GAP [5, 6]. 2.2 Mathematical Web Services The OpenMath set up is only the beginning. For mathematical services across the internet, many more issues have to be resolved. In §3.2 of =-=[28]-=-, some of these issues are listed. In [9], the reliability (quality guarantee) aspects are emphasized. Up till now, complexity, the (estimated) time a computation will take, has been one of the major ... |

1 | servlet container used - Tomcat |

1 |
Atlas of Finite Group Representations, www.mat.bham.ac.uk/atlas
- Wilson
(Show Context)
Citation Context ...en addressed in some of the more successful mathematical services on the internet, such as Sloane [27], Faugère’s Gröbner basis service [14], Wilson’s Atlas of representations of finite simple groups =-=[32]-=-, Brouwer’s coding theory data base [3], and WebMathematica [31]. For example, Webmathematica is a way to access Mathematica via the Web. Via browser pages users can formulate either full Mathematica ... |

1 |
The RIACA OpenMath Library, crystal.win.tue.nl/public/projects
- ROML
(Show Context)
Citation Context ...e been built into Axiom and GAP [2,16]. We have developed a Java library, called ROML, for building full phrasebooks outside mathematical software packages. It is described in [4] and can be found at =-=[28]-=-. By use of ROML, such external phrasebooks have been implemented for the proof checkers Lego and Coq, for the computer algebra packages Maple, Mathematica, and GAP [5,6]. 2.2 Mathematical Web Service... |

1 |
The interactive geometry software (book and CD-Rom
- Cinderella
- 1999
(Show Context)
Citation Context ... 2, by way of example, we display an experimental CD for planar Euclidean geometry, which was recently constructed in joint work with Ulrich Kortenkamp for the purpose of interfacing with Cinderella, =-=[29]-=-. Phrasebooks provide the means to convert OpenMath objects to/from software applications. They parse OpenMath objects into an application-native language (e.g., Mathematica, Maple, GAP), sending the ... |