OMDoc documents are made of mathematical items which can contain mathematical formulas; the latter may be presented to the screen or print media. The ActiveMath presentation system uses XSLT and Velocity to convert the OMDoc fragments to rendered HTML, XHTML, or PDF. For the mathematical formula to be presented well, an amount of notations are defined which produce XSLT templates.
This handbook page explains by examples how notations are conceived, authored, and used in ActiveMath.
Notations are, traditionally, rules to encode graphically a conceptual construction.
ActiveMath notations are similar, they are made of:
These prototypes are enough for ActiveMath to generate a stylesheet that will render any expression to HTML, MathML, and TeX.
In ActiveMath, notations are provided by any collection that is loaded. To see the notations defined in your current ActiveMath, invoke Tools > Symbol Presentations.
This tool allows you to test the rendering of an OpenMath expression or to get a list of all the notations defined.
Try this on the ActiveMath demo as user eva.
The fact that any collection can contain notations may lead to conflicts... currently, these are not reported but the resulting notation is the "concatenation of the two notations", quite a visible effect!
Let us construct a basic example for the symbol free-group:
<symbolpresentation id="pres-free-group1" xref="free-group">
<notation>
<OMOBJ>
<OMA>
<OMS cd="free-groups" name="free-group"/>
<OMV name="alphabet"/>
</OMA>
</OMOBJ>
<math>
<mrow>
<mo>F(</mo>
<mi>A</mi>
<mo>)</mo>
</mrow>
</math>
</notation>
</symbolpresentation>
This first example will render expressions such as this prototype. Let us try, with the notations of the jEditOQMath tutorial, to render $Fn(S)$. You should obtain something similar to F(S).
If not using SluMBase, ActiveMath needs to be restarted everytime the notations have been changed. Alternatively, one can use the symbol-presentation-tool.
Note the variable names: the OpenMath expression has a variable, named A, which is the same as the content of the MathML's mi element: all variables are replaced this way.
Having the OpenMath in mind is a good idea here since authoring notations involves fine-grained OpenMath matching. But nothing prevents you to use a QMath expression instead of the OpenMath, yielding instead:
<symbolpresentation id="pres-free-group1" xref="free-group">
<notation>$Fn(A)$
<math>
<mrow>
<mo>F(</mo>
<mi>A</mi>
<mo>)</mo>
</mrow>
</math>
</notation>
</symbolpresentation>
Now, what about the formula written down as F(a,b), the free group on two generators?
If you try to input $Fn(a,b)$, you will get a non-presented-symbol free-group(a,b) which is not what one wishes. Actually, this formula does not use the same notation, it has been shortened once more by the removal of the bracket. One needs to add a notation for this:
<symbolpresentation id="pres-free-group2" xref="free-group">
<notation>
<OMOBJ>
<OMA>
<OMS cd="free-groups" name="free-group"/>
<OMA>
<OMS cd="set1" name="set"/>
<OMV name="a"/><OMV name="b"/>
</OMA>
</OMA>
</OMOBJ>
<math>
<mrow>
<mo>F(</mo>
<mi>a</mi>
<mo>,</mo>
<mi>b</mi>
<mo>)</mo>
</mrow>
</math>
</notation>
</symbolpresentation>
The scary bit here is that we would need to introduce a notation for each possible size of the generating set... instead we need n-arity for which a special symbol in the ompe content-dictionary has been defined and a special element in MathML has been allowed:
<symbolpresentation id="pres-free-group2" xref="free-group">
<notation>
<OMOBJ>
<OMA>
<OMS cd="free-groups" name="free-group"/>
<OMA>
<OMS cd="set1" name="set"/>
<OMA><OMS cd="ompe" name="nary"/>
<OMV name="x"/>
</OMA>
</OMA>
<OMV name="alphabet"/>
</OMA>
</OMOBJ>
<math>
<mrow>
<mo>F(</mo>
<nary>
<mi>x</mi>
<mo>,</mo>
</nary>
<mo>)</mo>
</mrow>
</math>
</notation>
</symbolpresentation>
To be continued, about: