MathML constants

In MathML, constants are defined as being any of the following: e, i, pi, gamma, infinity, true, false or not a number (NaN). They appear within <cn> tags when the attribute type is set to constant. For instance $\pi$ would be represented in MathML as:

        <cn type="constant">pi</cn>

In OpenMath, these constants all appear as different symbols and from different CDs. Hence, we face a similar problem as we did with MathML attributes. The <cn> tag with the attribute set to constant can map to different OpenMath symbols.

It is important that the translator detects the use of the constant attribute value and maps the constant expressed to the correct OpenMath symbol.

MathML also allows to define Cartesian complex numbers and polar complex numbers. A complex number is of the form two real point numbers separated by the <sep/> tag. For instance  3+4i is represented as:

        <cn type="cartesian_complex"> 3 <sep/> 4 </cn>

OpenMath is more flexible in its definition of complex numbers. The real and imaginary parts, or the magnitude and argument of a complex number do not have to be only real numbers. They may be variables. This allows OpenMath to represent numbers such as x+iy or $re^{i\theta}$ which cannot be done in MathML.

So how should one map such an OpenMath expression to MathML? Because there is no specific construct for such complex numbers, the easiest way is to generate a MathML representation using simple operators. The two expressions in figure 3.3 are equivalent and illustrate how a translator should perform:

Figure 3.3: How to translate complex numbers

The problem is the same when representing rationals, since OpenMath allows variables to be used as elements of a rational number, whereas MathML only allows real numbers.