#Working with infinitesimals generator#

See also the Library routine CloseSystem. To assure that all the integrability conditions are explicitly present use the option closesystem. Note also that, for a system to be closed, it is not sufficient to have it in reduced involutive or equivalent form produced by the casesplit and rifsimp commands or the DifferentialAlgebra package. Correspondingly, some infinitesimals may not be present in the output of Infinitesimals. Otherwise, the determining system for the symmetries may in rare situations also (correctly) include equations that however may restrict the possible values of the symmetry solutions, and hence some of the symmetries be missed. If, in PDESYS, all the integrability conditions that can be derived from its equations are explicitly present, then the determining system for the symmetries is assured to have for solution all the symmetries of PDESYS. Note that you could construct the determining system for the symmetries of an inconsistent PDESYS, in which case the solution of the determining system and everything else derived from it would be meaningless.īy default Infinitesimals processes PDESYS as given. The default value is false when true, the consistency of PDESYS is checked before proceeding. (optional) list of two names to be used as roots for the ξ n and eta components of the infinitesimals (optional) can be any of pointlike (default), contact, evolutionary, or general, or any of polynomial or functionfield, or And(, ) where kind is any of the first three types mentioned and functionality is any of polynomial or functionfield indicates the type of symmetry to be computed (optional) can be true (default) or false to split or not the list of infinitesimals into cases by specializing the integration constants _Cn (optional) can be true, false (default), or a set of procedures to specialize any arbitrary functions that may appear in the infinitesimals

(optional) indicates the simplifier to be used instead of the default simplify/size (optional) can be jetvariables (default), jetvariableswithbrackets, jetnumbers or jetODE to respectively return or not using the different jet notations available

#Working with infinitesimals generator#

(optional) list with the functional form of the infinitesimals of a symmetry generator (optional) can be true (default) or false to display the functionality on the left-hand side of the _&xi n ⁡. (optional) indicates the dependency of the infinitesimals, as a number (of jet variables), a range of them, a name, or a set of dependencies each of which can be a set or list of variables or numbers (optional) related to the option typeofsymmetry = polynomial, indicates the upper bound degree of the polynomial infinitesimals with respect to all or each of the dependent variables (optional) can be true or false (default) to derive and then include in PDESYS, explicitly, all its integrability conditions, necessary to compute all the infinitesimals of PDESYS (optional) can be true or false (default) to check the consistency of PDESYS before proceeding (optional - may be required) function or list of functions indicating the dependent variables of the problem PDE or a set or list of PDEs it can include ODEs and non-differential equations Infinitesimals( PDESYS, DepVars, S, options = value ) Compute the infinitesimals of symmetry groups admitted by a given PDE system