ChangeSymmetry(TR, S, ITR, DepVars, NewVars, 'options'='value')

Consider a PDE problem with two independent variables and one dependent variable, u(x, t), and consider the list of infinitesimals of a symmetry group

In the input above you can also pass the symmetry as without infinitesimals' labels, as in . The corresponding infinitesimal generator is

Consider now the following transformation to be applied to the infinitesimals S

A direct application of this transformation to each component of  is incorrect because these infinitesimals are coefficients of differentiation operators in the infinitesimal generator  above. That fact is taken into account by ChangeSymmetry; the syntax it uses is the same as that of PDEtools[dchange] and DEtools[Xchange]

You can change variables directly in the infinitesimal generator differential operator, in which case the output has the same format, is also a differential operator

You can also optionally request the output to be in list or operator format to override returning in the same format of the symmetry.

The transformation used in this example introduces the canonical coordinates of the symmetry group with infinitesimals S. That is why the result above is the normal form of the generator, all infinitesimals equal to 0 but for one equal to 1.

Consider now changing variables in a different symmetry, using the same transformation

Compare with the output in different jetnotation or in function notation (jetnotation = false); we also pass the symmetry without the infinitesimals' labels to save some keystrokes; correspondingly the output also comes without infinitesimals' labels

CanonicalCoordinates, InfinitesimalGenerator, PDEtools