eMath 3.0: building blocks for a social and semantic Web for online mathematics & elearning

In this paper we present recent developments in content markup for mathematics, and a corresponding software stack that functions as an enabling technology for a social and semantic web for the STEM disciplines. We show the potential of this technology in two eMath 3.0 applications: PlanetMathRedux, a re-implementation of the mathematical encyclopedia PlanetMath.org, and PantaRheiRedux, a community reader for course materials. These applications indicate both present and potential uses for this software as a basis for eLearning applications in Science, Technology, Engineering and Mathematics through the addition of suitable pedagogies

Extracting mathematical semantics from LaTeX documents

We report on a project to use SGLR parsing and term rewriting with ELAN4 to extract the semantics of mathematical formulas from a LaTeX document and representing them in MathML. The LaTeX document we used is part of the Digital Library of Mathematical Functions (DLMF) project of the US National Institute of Standards and Technology (NIST) and obeys project-specific conventions, which contains macros for mathematical constructions, among them 200 predefined macros for special functions, the subject matter of the project. The SGLR parser can parse general context-free languages, which suffices to extract the structure of mathematical formulas from calculus that are written in the usual mathematical style, with most parentheses and multiplication signs omitted. The parse tree is then rewritten into a more concise and uniform internal syntax that is used as the base for extracting MathML or other semantical information

Extracting mathematical semantics from LaTeX documents

We report on a project to use SGLR parsing and term rewriting with ELAN4 to extract the semantics of mathematical formulas from a LaTeX document and representing them in MathML. The LaTeX document we used is part of the Digital Library of Mathematical Functions (DLMF) project of the US National Institute of Standards and Technology (NIST) and obeys project-specific conventions, which contains macros for mathematical constructions, among them 200 predefined macros for special functions, the subject matter of the project. The SGLR parser can parse general context-free languages, which suffices to extract the structure of mathematical formulas from calculus that are written in the usual mathematical style, with most parentheses and multiplication signs omitted. The parse tree is then rewritten into a more concise and uniform internal syntax that is used as the base for extracting MathML or other semantical information

XSLT 2.0 vs. XSLT 1.0

International audienceThis article focuses on the new features introduced by Version 2.0 of XSLT, the language of transformations used for XML texts. We show why these new features---groups of XML subtrees, functions, interface with schemas---ease the development of some applications. Some examples, related to bibliography management, will be demonstrated

An Example of Clifford Algebras Calculations with GiNaC

This example of Clifford algebras calculations uses GiNaC (http://www.ginac.de/) library, which includes a support for generic Clifford algebra starting from version~1.3.0. Both symbolic and numeric calculation are possible and can be blended with other functions of GiNaC. This calculations was made for the paper math.CV/0410399. Described features of GiNaC are already available at PyGiNaC (http://sourceforge.net/projects/pyginac/) and due to course should propagate into other software like GNU Octave (http://www.octave.org/), gTybalt (http://www.fis.unipr.it/~stefanw/gtybalt.html), which use GiNaC library as their back-end.Comment: 20 pages, LaTeX2e, 12 PS graphics in one figure; v3 code improvements; v4 small code correction for new libraries; v5 comments are redesined to be more readabl

Search Interfaces for Mathematicians

Access to mathematical knowledge has changed dramatically in recent years, therefore changing mathematical search practices. Our aim with this study is to scrutinize professional mathematicians' search behavior. With this understanding we want to be able to reason why mathematicians use which tool for what search problem in what phase of the search process. To gain these insights we conducted 24 repertory grid interviews with mathematically inclined people (ranging from senior professional mathematicians to non-mathematicians). From the interview data we elicited patterns for the user group "mathematicians" that can be applied when understanding design issues or creating new designs for mathematical search interfaces.Comment: conference article "CICM'14: International Conference on Computer Mathematics 2014", DML-Track: Digital Math Libraries 17 page

Accelerating Computation of the Nonlinear Mass by an Order of Magnitude

The nonlinear mass is a characteristic scale in halo formation that has wide-ranging applications across cosmology. Naively, computing it requires repeated numerical integration to calculate the variance of the power spectrum on different scales and determine which scales exceed the threshold for nonlinear collapse. We accelerate this calculation by working in configuration space and approximating the correlation function as a polynomial at r <= 5 $h^{-1}$ Mpc. This enables an analytic rather than numerical solution, accurate across a variety of cosmologies to 0.1$-$1% (depending on redshift) and 10$-$20 times faster than the naive numerical method. We also present a further acceleration (40$-$80 times faster than the naive method) in which we determine the polynomial coefficients using a Taylor expansion in the cosmological parameters rather than re-fitting a polynomial to the correlation function. Our acceleration greatly reduces the cost of repeated calculation of the nonlinear mass. This will be useful for MCMC analyses to constrain cosmological parameters from the highly nonlinear regime, e.g. with data from upcoming surveys