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Cell[TextData[StyleBox["In this example we use the package IntroToSymmetry.m \
to work out the point group of the nonlinear heat equation, \n\n\
Ut-(k(U))xUx-k(U)Uxx=0.\n\nfor two choices of k(U). Reference: Ibragimov, N. \
CRC Handbook Volume 1, page 110.",
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This next command turns off spurious spelling error warnings.\
\>", "Text"],

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Cell[TextData[{
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Cell[TextData[StyleBox["The function u[x,t] is a solution of the equation and \
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Cell[TextData[StyleBox["The maximum derivative order that the infinitesimals \
are assumed to depend on is specified by the input parameter r. This \
parameter is only nonzero when the user is looking for Lie contact groups or \
Lie-Backlund groups. For the usual case where one is searching for point \
groups set r=0.",
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Cell[TextData[StyleBox["When searching for Lie-Backlund groups (r=1 or \
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untransformed. The corresponding infinitesimals (the xse's) are set to zero \
by setting xseon=0. If one is searching for point groups then set xseon=1. \
The choice xseon=1 is also an option when looking for Lie-Backlund groups and \
this can be useful when looking for contact symmetries.",
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Cell[TextData[StyleBox["When searching for Lie-Backlund groups it is \
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independent variables producing derivatives of order p+r. These higher order \
differential consequences are appended to the set of rules applied to the \
invariance condition. This process is carried out automatically when \
internalrules=1. For point groups the equation or equation system is the only \
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Cell[TextData[StyleBox["Now work out the determining equations of the Lie \
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The invariance condition has been created with all rules applied. The final \
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result is the table infinitesimaltablesums corresponding to matching \
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z-variables. Rules for converting between z-variables and conventional \
variables are contained in the table ztableofrules. To view the determining \
equations in terms of conventional variables use the command \
ToExpression[zdeterminingequations]/.ztableofrules. There are two other items \
the user may wish to look at; the equation converted to generic \
(x1,x2,...,y1,y2,...) variables is designated equationgenericvariables and \
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condition can be viewed in the table invarconditiontable. Rules for \
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Now solve the determining equations in terms of multivariable polynomials of \
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