Discovering How to Write Semantic Math with new Symbols

The ActiveMath learning environment is based on semantic math-ematical formulæ encoded using OpenMath1. This gives it a chance to render formulæ on a variety of platforms, using cultural-dependent adap-tations, and with added-value services that may help the learners in read-ing the formulæ. The price to pay at authoring, however, is high since it requires encod-ing the meaning and not only the graphical presentation of the formulæ. Examples of challenges include the input of K[x1,..., xn] which is well known to represent the ring of polynomials on n variables but which does not enjoy, yet, the support of official Content Dictionaries for the symbols. In this paper, we explain methods we propose to discover the symbols needed to encode expressions, the typical expressions, and the ways to input this within the ActiveMath learning environment with jEditO-QMath and to have it rendered. En passant, we describe requirements on the browsing and search methods for the presentations of OpenMath Content Dictionaries. symbol: from Latin symbolum token, sign, symbol, from Greek sym-bolon, literally, token of identity verified by comparing its other half, from symballein to throw together, compare, from syn- + ballein: to throw Merriam-Webster dictionary One of the foundations of the manipulations of formulæ in the ActiveMath learning environment is that they are expressed semantically in OpenMath; that is their representation encodes their meaning. This is a strong requirement compared to the long tradition of encoding mathematical formulæ to obtain their typeset form. It brings along several features (such as a mathematical search, a rendering which may help the learner, or the facility to copy-and-paste