Software application root embedding

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If an author is primarily presentation-oriented, interspersing some content markup will often produce more accessible, more re-usable results. For example, an author writing about linear algebra might write:. On account of the linear algebra context, a visually impaired reader may have directed his or her voice synthesis software to render superscripts as vector components.

By explicitly encoding the power, the content markup yields a much better voice rendering than would likely happen by default. If an author is primarily content-oriented, there are two reasons to intersperse presentation markup. First, using presentation markup provides a way of modifying or refining how a content expression is rendered.

For example, one might write:. In this case, the use of embedded presentation markup allows the author to specify that v should be rendered in boldface. In the same way, it is sometimes the case that a completely different notation is desired for a content expression. This content expression would render using the given notation as: A second reason to use presentation within content markup is that there is a continually growing list of areas of discourse that do not have pre-defined content elements for encoding their objects and operators.

As a consequence, any system of content markup inevitably requires an extension mechanism that combines notation with semantics in some way. MathML content markup specifies several ways of attaching an external semantic definitions to content objects.

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It is necessary, however, to use MathML presentation markup to specify how such user-defined semantic extensions should be rendered. For example, the "rank" operator from linear algebra is not included as a pre-defined MathML content element. The main consideration when presentation markup and content markup are mixed together in a single expression is that the result should still make sense. When both kinds of markup are contained in a presentation expression, this means it should be possible to render the resulting mixed expressions simply and sensibly.

Conversely, when mixed markup appears in a content expression, it should be possible to simply and sensibly assign a semantic interpretation to the expression as a whole. These requirements place a few natural constraints on how presentation and content markup can be mixed in a single expression, in order to avoid ambiguous or otherwise problematic expressions. Two examples illustrate the kinds of problems that must be avoided in mixed markup.

In this example, the content element bvar has been indiscriminately embedded in a presentation expression. Since bvar requires an enclosing context for its meaning, this expression is unclear. Here, the mo element is problematic. Should a renderer infer that the usual arithmetic operator is intended, and act as if the prefix content element plus had been used? These questions do not have particularly compelling answers, so this kind of mixing of content and presentation markup is also prohibited.

The use of presentation markup within content markup is limited to situations that do not effect the ability of content markup to unambiguously encode mathematical meaning. Specifically, presentation markup may only appear in content markup in three ways:. Any other presentation markup occurring within a content markup is a MathML error.

More detailed discussion of these three cases follows:. Contiguous blocks of MathML characters in ci and cn elements are rendered as if they were wrapped in mi and mn elements respectively.

Software application root embedding - Root application delete

If a token element contains both MathML characters and presentation elements, contiguous blocks of MathML characters if any are treated as if wrapped in mi or mn elements as appropriate, and the resulting collection of presentation elements are rendered as if wrapped in an mrow element. The csymbol element may contain either MathML characters interspersed with presentation markup, or content elements of the container type. It is a MathML error for a csymbol element to contain both presentation and content elements. When the csymbol element contains both raw data and presentation markup, the same rendering rules that apply to content elements of the token type should be used.

One of the main purposes of the semantics element is to provide a mechanism for incorporating arbitrary MathML expressions into content markup in a semantically meaningful way.

In particular, any valid presentation expression can be embedded in a content expression by placing it as the first child of a semantics element. The meaning of this wrapped expression should be indicated by one or more annotation elements also contained in the semantics element. The guiding principle for embedding content markup within presentation expressions is that the resulting expression should still have an unambiguous rendering. In general, this means that embedded content expressions must be semantically meaningful, since rendering of content markup depends on its meaning.

Certain content elements derive part of their semantic meaning from the surrounding context, such as whether a bvar element is qualifying an integral, logical quantifier or lambda expression. Another example would be whether a degree element occurs in a root or partialdiff element. Thus, in a presentation context, elements such as these do not have a clearly defined meaning, and hence there is no obvious choice for a rendering. Consequently, they are not allowed. Note that interval may be used either as a general container, or as a qualifier.

Outside these categories, certain elements deserve specific comment: Finally, the element semantics carries with it sufficient information to be permitted in presentation. The complete list of content elements that cannot appear as a child in a presentation element is: Note that within presentation markup, content expressions may only appear in locations where it is valid for any MathML expression to appear.

In particular, content expressions may not appear within presentation token elements. In this regard mixing presentation and content are asymmetrical. Note that embedding content markup in presentation will often require applications to render operators outside of an apply context. Some applications are able to make use of both presentation and content information.

For these applications it is desirable to provide both forms of markup for the same mathematical expression. Parallel markup is achieved with the semantics element. Parallel markup for an expression can be used on its own, or can be incorporated as part of a larger content or presentation tree.

In many cases what is desired is to provide presentation markup and content markup for a mathematical expression as a whole. To achieve this, a single semantics element is used pairing two markup trees, with the first branch being the MathML presentation markup, and the second branch being the MathML content markup.

This example is non-trivial in the sense that the content markup could not be easily derived from the presentation markup alone. Top-level pairing of independent presentation and content markup is sufficient for many, but not all, situations. Applications that allow treatment of sub-expressions of mathematical objects require the ability to associate presentation, content or information with the parts of an object with mathematical markup.

Top-level pairing with a semantics element is insufficient in this type of situation; identification of a sub-expression in one branch of a semantics element gives no indication of the corresponding parts in other branches. The ability to identify corresponding sub-expressions is required in applications such as mathematical expression editors.

In this situation, selecting a sub-expression on a visual display can identify a particular portion of a presentation markup tree. The application then needs to determine the corresponding annotations of the sub-expressions; in particular, the application requires the sub-expressions of the annotation-xml tree in MathML content notation.

It is, in principle, possible to provide annotations for each presentation node by incorporating semantics elements recursively. To be complete this example would be much more verbose, wrapping each of the individual leaves mi , mo and mn in a further seven semantics elements. This approach is very general and works for all kinds of annotations including non-MathML annotations and multiple annotations. It leads, however, to O n log n increase in size of the document. This is therefore not a suitable approach for fine-grained parallel markup of large objects. To better accommodate applications that must deal with sub-expressions of large objects, MathML uses cross-references between the branches of a semantics element to identify corresponding sub-structures.

Cross-referencing is achieved using id and xref attributes within the branches of a containing semantics element. These attributes may optionally be placed on MathML elements of any type. An id attribute and a corresponding xref appearing within the same semantics element create a correspondence between sub-expressions. In creating these correspondences by cross-reference, all of the id attributes referenced by any xref must be in the same branch of an enclosing semantics element. This constraint guarantees that these correspondences do not create unintentional cycles.

Note that this restriction does not exclude the use of id attributes within the other branches of the enclosing semantics element. It does, however, exclude references to these other id attributes originating in the same semantics element. There is no restriction on which branch of the semantics element may contain the destination id attributes. It is up to the application to determine which branch to use.

In general, there will not be a one-to-one correspondence between nodes in parallel branches. For example, a presentation tree may contain elements, such as parentheses, that have no correspondents in the content tree. It is therefore often useful to put the id attributes on the branch with the finest-grained node structure.

Then all of the other branches will have xref attributes to some subset of the id attributes. In absence of other criteria, the first branch of the semantics element is a sensible choice to contain the id attributes. Applications that add or remove annotations will then not have to re-assign attributes to the semantics trees.

In general, the use of id and xref attributes allows a full correspondence between sub-expressions to be given in text that is at most a constant factor larger than the original. The direction of the references should not be taken to imply that sub-expression selection is intended to be permitted only on one child of the semantics element. It is equally feasible to select a subtree in any branch and to recover the corresponding subtrees of the other branches.

As an example, the boolean expression of the previous section can be annotated with OpenMath, and cross-linked as follows:. The references from the OpenMath annotation are given by the xlink:

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