> <\body> By default, the semantic editing mode \Punderstands\Q most classical mathematical notations. This is achieved through the use of a carefully designed grammar for mainstream mathematics. Obviously, the use of a fixed grammar may cause the following problems: <\itemize> Mathematical formulas frequently contain notations. For instance, the formulas might contain some text or meaningful whitespace. Another example of an notation is the sign sequence . In such cases, the user should the appropriate parts of the formula in order to make them semantically meaningful. The grammar used for the interpretation of mathematical formulas may be incomplete or inadequate for certain situations. It is possible to customize or extend the grammar using the standard macro mechanism. Notations for specific areas may be grouped together in dedicated style packages. Besides these intrinsically hard to avoid problems, the following common and \Peasy-to-make\Q mistakes are a further source of trouble for associating semantics to mathematical formulas: <\itemize> Since is a wysiwyg editor, some of the structure of the document is invisible for the user. For instance, the presence of a mathematical formula is indicated through the use of an italic slant and special spacing. However, in the formula > it is easy to type the closing bracket outside the formula, with no visual difference. Various mathematical notations are visually ambiguous. For instance, > would usually be understood as >, whereas > rather corresponds to a function application. In the semantic editing mode, the user is expected to resolve this ambiguity by hand by entering multiplications using and spaces using . The multiply/apply ambiguity is one of the main sources of syntax errors, since many users do not pay attention to invisible differences. Similarly, the > glyph could be the \Plogical and\Q or the \Pwedge product\Q. This \Phomoglyph\Q issue will be addressed in more detail in the section on the .\ It could be that a text was originally written in or an old version of . In that case, the document contains no special indication on matching brackets or the scopes of big operators. For instance, in the formula >, should we interpret the second bracket as a closing bracket? This is indeed the standard french notation for an interval with an open right end. More generally, all problems that we have mentioned so far tend to be present simultaneously when trying to associate semantics to existing documents. After activation of the semantic editing mode, you may check whether a formula is correct by positioning your cursor inside it and looking at the color of the bounding box of the : agreen color corresponds to a correct formula and ared color indicates an error in the formula. Alternatively, assuming that the focus is on a mathematical formula, you may select , in which all incorrect formulas are highlighted inside red boxes. For the second kind of \Peasy-to-make\Q errors, includes an automatic syntax corrector. Assuming that your cursor is inside a formula, you may use for the correction of all formulas in your document, or the correction of the current selection. If the versioning tool is activated, then you may use to show the differences between the original and the corrected versions. You may then use the versioning tool to go through these differences and select the preferred versions. The precise algorithms which are used for the correction may be enabled or disabled from : <\description> >This algorithm is used in order to remove any superfluous function applications or multiplications. For instance, users who are accustomed to editing ASCII files often type spaces around binary infixes such as addition. Such \Pfunction applications\Q will be removed by this algorithm. >In , multiplications and function applications are never entered explicitly. When importing a document, it is therefore important to detect and insert missing multiplications and function applications. >This algorithm may perform some other useful substitutions of symbols by visually similar, but semantically distinct symbols. For instance, the backslash symbol is replaced by the binary set differences infix (as in Y>), whenever appropriate. From the , you may also select those corrections algorithms which should be applied automatically whenever you open a file. The various corrections are always carried out when importing a file. After syntax correction, the remaining errors indicate genuine typos at worst or non standard or non supported notations at best. We also notice that \Pcorrect\Q formulas do not necessarily have the intended meaning. In order to check whether the operators indeed apply to the intended arguments, you should keep an eye on the current focus while typing your formulas.\ >