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<H2><A NAME="SECTION00515000000000000000">
Temporary Functions</A>
</H2>
<P>
In order to improve evaluation efficiency, it is often useful
to define temporary variables to be used in the definition of
vector fields or auxiliary functions. This can be done by
defining a function <EM>before</EM> defining the dynamical system.
Here is an example where temporary variables are used
in both the vector field definition and in the auxiliary functions
definition.
<P>
<PRE>
# A D4 symmetric system (d4symm.def)
xsq = x x # xsq and zsq are temporary functions
zsq = z z
x' = y
y' = x (mu - (xsq+zsq)) + delta x zsq +
epsilon ((xsq+zsq) y + nu y + Axzw x (x y + z w) + Ayz2 y zsq
z' = w
w' = z (mu - (xsq+zsq)) + delta z xsq +
epsilon ((xsq+zsq) w + nu w + Axzw z (x y + z w) + Ayz2 w xsq
Energy = 0.5 (y y + w w - mu (xsq + zsq) + 0.5 (xsq + zsq) (xsq + zsq) -
delta xsq zsq)
AngMom = y z - x w
INITIAL mu 2 delta 0.95 epsilon 0 nu -3.52 Axzw 1 Ayz2 0
RANGE x -5 5 y -5 5 z -5 5 w -5 5
</PRE>
<P>
<BR><HR>
<ADDRESS>
<I>John Lapeyre</I>
<BR><I>1998-09-04</I>
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