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To load the package, you must set the directory to where the file is located, \
say c:\\myDirectory, and load the package as follows:\
\>", "Text"],

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 "The companion paper by Baldwin and Hereman, entitled ``Symbolic Software \
for the Painleve Test of Nonlinear Ordinary and Partial Differential \
Equations\" has been published in the Journal of Nonlinear Mathematical \
Physics, vol. 13, number 1, Februrary 2006, pages 90-110. ",
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Painleve test of a single nonlinear ordinary differential equation. \
\\nPainleveTest[eqn, u[x1, x2, ... ], {x1, x2, ... }, opts] performs the \
standard Painleve test of a single nonlinear partial differential equation. \
\\nPainleveTest[{eqn1, eqn2, ... }, {u1[x], u2[x], ... }, x, opts] performs \
the standard Painleve test of a system of nonlinear ordinary differential \
equations. \\nPainleveTest[{eqn1, eqn2, ... }, {u1[x,t], u2[x,t], ... }, \
{x,t}, opts] performs the standard Painleve test of a system of nonlinear \
partial differential equations. \\nPainleveTest has a number of \
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algorithm;\\nKruskalSimplification -> x2 will use g[x1, x2, ... ] = x2 - \
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incremented in integer steps from -3 up to i, where i is an Integer given by \
the user (the default is -1);\\nDominantBehaviorMin -> k specifies that if a \
minimum value for the free dominant exponent, say \!\(\[Alpha]\_1\), cannot \
be determined, then \!\(\[Alpha]\_1\) will be incremented by integer steps \
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dominant exponents and the user-specified value of i, which must be \
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steps of the computation in increasing detail as j is increased (j = 0, 1, 2 \
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As a first example, we consider the equation due to Korteweg and de Vries \
(the KdV equation) :\
\>", "Text"],

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The output of the Painleve Test is in the form {{Dominant Behavior, \
Resonances, {Constants of Integration, Constraints}, ...}.  In this example, \
the dominant behavior implies that the singularity manifold given by \
\>", "Text"],

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is a double pole and the solutions has a Laurent series expansion of the form\
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neighborhood of the singularity manifold.  Furthermore, since the \
compatibility conditions were trivially satisfied, the solution lacks \
logarithmic branch-points in the neighborhood of the singularity manifold. \
Indeed, at resonance levels r = 4 and r = 6, there were arbitrary \
coefficients  in the series and at all other levels the coefficients (also \
called integration constants) were unambigiously and uniquely determined. \n\n\
Detail can be seen for each of the three main steps of the algorithm by \
setting DominantBehaviorVerbose, ResonancesVerbose, and \
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numbers give incrementally more detail). \nWe run the same example to see a \
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Let us now turn to our second example: a system of nonlinearly coupled \
Korteweg-de Vries equations (due to Hirota and Satsuma). This example will \
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So, be patient!\
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Here, we see that the system has a parameter, aa.  Note that (i) there are \
two choices for the dominant behavior of the solution, and (ii) the \
combatibility condition implies that aa = 1/2. 

Below, the Verbose option is set to True in order for the user to see a \
detailed trace of the computations.  A greater level of  detail can be see \
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Lorenz Model of a Dissipative System with lim_{epsilon\[Rule]0}\
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Equation (2) in \"A note on the Painlev\.b4e property
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Example 1 is a coupled system of KdV - mKdV equations taken from  \
Integrability of Kersten - Krasilshchik coupled KdV - mKdV equations : \
singularity analysis and Lax pair  by  Kalkani, Sakovich, and Yurdusen. J. \
Math. Phys. 44 (4) 2003, pp. 1703 - 1708. \
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We first run the test without specifiction of DominantBehaviorMax (which by \
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 The software misses two non - generic branches : alpha1 = -2 with alpha2 = \
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