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DEtools[canoni] - look for a pair of canonical coordinates for a given Lie group of symmetries
Calling Sequence
canoni([xi(x, y), eta(x, y)], y(x), s(r))
Parameters
[xi(x, y), eta(x, y)]
-
list of the coefficients of the infinitesimal symmetry generator (infinitesimals)
y(x)
original dependent variable
s(r)
canonical dependent variable
ode
first order ODE
Description
The canoni command tries to find a set of transformations from the original coordinates to the canonical coordinates by knowing the coefficients of the symmetry generator (infinitesimals) of a one-parameter Lie group.
If there is more than one derivative in the ODE, canoni requires an extra argument (anywhere in the calling sequence), say y(x), specifying the dependent variable.
This function is part of the DEtools package, and so it can be used in the form canoni(..) only after executing the command with(DEtools). However, it can always be accessed through the long form of the command by using DEtools[canoni](..).
Examples
An ODE with an arbitrary function F
A pair of infinitesimals for it
The canonical coordinates
The inverse transformation
The change of variables, using the canonical coordinates, reducing eq to a quadrature (see dchange)
See Also
dchange, DEtools, dsolve, equinv, odeadvisor, odetest, PDEtools, symgen, symtest
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