

Auxiliary FunctionsThe auxiliary functions are exported to provide help for the developers of further packages. They will not be very useful for a casual user.
MultipleSolutionTestThe function MultipleSolutionTest produces a warning if the given equations have multiple solutions.Example: In[31]:= MultipleSolutionTest[ {{x1 > Sqrt[y1], x1 >  Sqrt[y1]}, {x2 > 4 y2}},{x1,x2}]
Solve::multi: Multiple solution for [x1] encountered
Out[31]= {Null, Null}
SeparateEquationsSeparateEquations separates a list of differential equations into the list of equations and a list of boundary and initial conditions.Examples: In[32]:= SeparateEquations[ {x''[t] == 0,x'[a] == f[t],x[c] == 0},{x[t]}]
Out[32]= {{x''[t] == 0}, {x[c] == 0, x'[a] == f[t]}} In[33]:= SeparateEquations[ { D[phi[x2,x3],{x2,2}]+D[phi[x2,x3],{x3,2}] == 2G J', phi[x2,b/2] == 0, phi[x2,b/2] == 0, phi[a/2,x3] == 0, phi[a/2,x3] == 0 }, {phi[x2,x3]}]
Out[33]= (0,2) (2,0) {{phi [x2, x3] + phi [x2, x3] == 2 G J'}, a a b b {phi[, x3] == 0, phi[, x3] == 0, phi[x2, ] == 0, phi[x2, ] == 0}} 2 2 2 2
FindGaugeFunctionFindGaugeFunction returns a list of gauge functions found in differential equations.Example: In[34]:= FindGaugeFunction[ Sqrt[eps] x + Sin[eps] x + eps x + 5 ==3, eps]
Searching gauge functions...
Out[34]= {1, Sqrt[eps], eps, Sin[eps]}
SortGaugeFunctionsSortGaugeFunctions sorts a list of gauge functions in increasing order. Functions of the same order are combined into sublists.Examples: In[35]:= SortGaugeFunctions[ {1,1/eps, eps, eps^2,eps Log[1/eps], Sin[7 eps], Cos[eps], Sin[eps], Sin[eps^2], Coth[eps], (1  Cos[eps])}, eps]
Out[35]= 1 1 {{Coth[eps], }, {Cos[eps], 1}, {eps Log[]}, eps eps 2 2 {Sin[eps], Sin[7 eps], eps}, {1  Cos[eps], Sin[eps ], eps }} In[36]:= SortGaugeFunctions[{1, 1/eps, eps, eps^2, eps^3}, eps]
Out[36]= 1 2 3 {{}, {1}, {eps}, {eps }, {eps }} eps
FindEquationFindEquation combines the equations of the same order after the substitution of an asymptotic expansion into equations.The list of gauge functions must be of level two, i.e., the functions of the same order must be combined into a sublist, even if there is only one for each order. Example: In[37]:= FindEquation[ {u[0]''[t] + u[0][t] + eps u[1]''[t] + eps u[1][t] == eps u[0][t]^3, u[0][0] + eps u[1][0] == a, u[0]'[0] + eps u[1]'[0] == 0}, eps, {{1},{eps}}]
Out[37]= {{u[0][t] + (u[0])''[t] == 0, a + u[0][0] == 0, (u[0])'[0] == 0}, 3 {u[0][t] + u[1][t] + (u[1])''[t] == 0, u[1][0] == 0, (u[1])'[0] == 0}}
TransformInCondTransformInCond is used by the function Transform to transform initial conditions.Because it uses arguments which are calculated by Transform, it is not suited to be used separately. Use Transform to do the same.
SubstituteSubstitute is also an auxiliary function used by Transform. It performs the actual transformation, after the necessary arguments have been determined by Transform.Up to PerturbationPDE 
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