Let   be a -dimensional Lie algebra of vector fields, defined on a manifold Let be an infinite dimensional Lie algebra of vector fields on , whose general element depends upon a certain number of arbitrary functions and suppose   Then the normalizer of in  is

 With the calling sequence InfinitesimalPseudoGroupNormalizer(Gamma), the normalizer of   in the full infinitesimal pseudo-group of all vector fields on   is computed.  With output = "general" (the default value),  a  single vector field, depending upon arbitrary constants and functions, is returned.  If the output depends only on constants (that is,  Nor( is a finite-dimensional algebra) and  output = "list", then a list of vectors is returned.  In this case the vector fields in the center of are removed. With  output = "general", the determining differential equations for the normalizer are returned.

With the keyword argument ansatz = Z,  the procedure InfinitesimalPseudoGroupNormalizer calculates Nor(, where   is the infinitesimal pseudo-group defined by the vector field Z. With this keyword option, the unknown functions in Z must be explicitly listed using the keyword argument unknowns = U.  Additional algebraic and differential constraints on the unknown functions in Z may be specified with the keyword argument auxiliaryequations = E. Note that the full system of differential equations for Z is likely to be inconsistent if the vector fields in do not satisfy the differential constraints defined by E.  

 If the abstract Lie algebra determined by has been calculated and initialized (see LieAlgebraData, DGsetup), then this information can be passed to InfinitesimalPseudoGroupNormalizer with the  keyword argument liealgebra  = name.

 The keyword argument parameters = P will invoke the case-splitting capabilities of  pdsolve . In this case, the output of  InfinitesimalPseudoGroupNormalizer will be a sequence of normalizers for both the generic and special values of the parameters.

The command InfinitesimalPseudoGroupNormalizer is part of the DifferentialGeometry:-GroupActions package.  It can be used in the form InfinitesimalPseudoGroupNormalizer(...) only after executing the commands with(DifferentialGeometry) and with(GroupActions), but can always be used by executing DifferentialGeometry:-GroupActions:-InfinitesimalPseudoGroupNormalizer(...).