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###

Parametric equations

It may also be interesting to use the pre-processing for parametric
systems, i.e. for systems for which some coefficients will be
described in analytical form in the MAPLE formula file, but which are
not unknowns. An additional argument for the generic analyzer will be
a file, called the
*parameter file*
which will give specific values for the parameter. For example
in the equation:
eq1:=x^2-x*cos(y)-x1:

`x1` may be considered as a parameter. On the first run of the
analyzer the intermediary files described in the previous section will
be generated and at run time the value of `x1` will be substituted
by the value indicated in the parameter file. After this first run and
if you want to analyze the system with another value for `x1` you
may use the pre-processing mechanism described in the previous section
and just change the value of `x1` in the parameter file. See
section 12.4.6.1 for an example of the analysis of parametric system.
Each line of the parameter file indicates a name of a parameter and
its value. Thus

x1 1

is a valid parameter file. To indicate a parameter file to the
analyzer use the `-P` argument followed by the name of the
parameter file.
A special case of parameter may be used to speed up the
computation. Assume that you have a system with large numerical
constants (by "large" we mean that the string representing the
numerical values has a large number of characters). Each evaluation of
your system will require first to read the strings representing the
numerical constants and then to convert it in a float number. It may
therefore be interesting to store once the constants values and to
substitute them in the analytical form of the equations by symbols
which may be attached to these values. This may be done by
substituting the numerical constants by symbols of the form `_IA` where is an integer starting from 0. These parameters have
then to be stored in a parameter file. Thus, for example, consider the
equations:

eq1:=1.12345678901*x1+4.563213456789222:

Using MAPLE you may easily change this equation to:
eq1:=_IA0*x1+_IA1:

and store the values in a parameter file:
_IA0 1.12345678901
_IA1 4.563213456789222

When reading the parameter file the program will store in a special
array the value of the parameters whose name start by the symbol `_IA`. Then, when the parser find a symbol starting with this
symbol it will determine the number following this keyword
(which is the value of
the index in the parameter table) and will just substitute the
corresponding value found in the parameter table. Hence when
evaluating an expression the parser will
have to read less character and avoid unnecessary conversion from a
string to a double. Note that these parameters must be numbered
in sequence, starting from 0.

** Next:** Errors and Debug
** Up:** Pre-processing and dealing with
** Previous:** Pre-processing
** Contents**
Jean-Pierre Merlet
2012-12-20