Wave Propagation in Linear Media | re-examined

7.3 Implementation of OscInt and related functions
OscInt
PartInt PartitionTable
OscIntControlled
PartitionPoints PartitionOffs
Figure 7.1: The package structure of OscInt
Auxiliary
Functions
PartitionOffs computes an index o set value for the list of partition points. This
o set is then used in PartitionPoints.
PartitionPoints returns a list of subdivision points with given length and the possibility
to specify a starting index. The index o set obtained from PartitionOffs adjusts
the numbering such that the point with index zero always is the lowest possible partition
point, with both the lower integration limit a or a manually set rst partition point a0
taken into account. Therefore, x (0) > maxfa; a0g or x0 > maxfa; a0g, depending on
the function being used to compute the subdivision points.
The aforementioned functions are also directly accessible from outside the package. Their
syntax and implementation details are dealt with in the next section. Apart from these
functions that constitute the building blocks for the quadrature routine, a few auxiliary
function are also included in the package. They have nothing to do with the quadrature
itself, but are useful for several special applications. The names and dependencies of these
functions are summarised in g. 7.2.
7.3 Implementation of OscInt and related functions
This section discusses the submodules of the quadrature routine and provides information on
the actual implementation. However, as we only want to outline the principles of operation,
we shall concentrate on the most important details and avoid boring source code listings.
Also, we shall not concern ourselves with the formal way of de ning a Mathematica package,
as this is covered extensively in books like those by Wolfram [140] and Maeder [146] or in
tutorial works like the book by Shaw and Tigg [147].
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