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# Symmetries

## Category Documents

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PDEtools/CharacteristicQ

compute the characteristic of a point symmetry represented by its infinitesimals

compute the characteristic of a point symmetry represented by its infinitesimals

PDEtools/CharacteristicQInvariants

computes the differential invariants associated to a given list of symmetries directly from their CharacteristicQ

computes the differential invariants associated to a given list of symmetries directly from their CharacteristicQ

PDEtools/ConservedCurrents

computes the conserved currents of a system of ordinary or partial differential equations (PDE)

computes the conserved currents of a system of ordinary or partial differential equations (PDE)

PDEtools/D_Dx

differentiate expressions in function or jet notation, with respect to independent or dependent (function) variables of the jet space.

differentiate expressions in function or jet notation, with respect to independent or dependent (function) variables of the jet space.

PDEtools/DeterminingPDE

computes the determining PDE system satisfied by the infinitesimals of the symmetry groups, or the integrating factors or the conserved currents, admitted by a given PDE system

computes the determining PDE system satisfied by the infinitesimals of the symmetry groups, or the integrating factors or the conserved currents, admitted by a given PDE system

PDEtools/Eta_k

construct a table-procedure that computes, on request, any prolongation of the infinitesimals of a symmetry generator

construct a table-procedure that computes, on request, any prolongation of the infinitesimals of a symmetry generator

PDEtools/Euler

Euler's operator - return the conditions that a DE system must satisfy in order to be the divergence of a current

Euler's operator - return the conditions that a DE system must satisfy in order to be the divergence of a current

PDEtools/InfinitesimalGenerator

receives a list with the infinitesimals of a symmetry generator and returns the corresponding infinitesimal generator as a differential operator procedure

receives a list with the infinitesimals of a symmetry generator and returns the corresponding infinitesimal generator as a differential operator procedure

PDEtools/Infinitesimals

compute the infinitesimals of symmetry groups admitted by a given PDE system

compute the infinitesimals of symmetry groups admitted by a given PDE system

PDEtools/IntegratingFactors

computes generalized integrating factors for a system of differential equations (DE)

computes generalized integrating factors for a system of differential equations (DE)

PDEtools/InvariantSolutions

computes the group invariant (symmetry) solutions for a given PDE system

computes the group invariant (symmetry) solutions for a given PDE system

PDEtools/InvariantTransformation

computes transformations reducing by k the number of independent variables of PDE systems admitting a given k-dimensional symmetry group

computes transformations reducing by k the number of independent variables of PDE systems admitting a given k-dimensional symmetry group

PDEtools/PolynomialSolutions

computes polynomial solutions for (differential or not) system of equations.

computes polynomial solutions for (differential or not) system of equations.

PDEtools/SimilaritySolutions

computes the group invariant (point symmetry) solutions for a given PDE system

computes the group invariant (point symmetry) solutions for a given PDE system

PDEtools/SimilarityTransformation

computes a transformation reducing by one the number of independent variables of PDE systems possessing a given symmetry

computes a transformation reducing by one the number of independent variables of PDE systems possessing a given symmetry

PDEtools/SymmetrySolutions

computes the group invariant (point symmetry) solutions for a given PDE system

computes the group invariant (point symmetry) solutions for a given PDE system

PDEtools/SymmetryTest

tests whether a given list of infinitesimals represents a symmetry of a given PDE system.

tests whether a given list of infinitesimals represents a symmetry of a given PDE system.

PDEtools/SymmetryTransformation

computes the finite form of the (symmetry) transformation leaving invariant any PDE system admitting a given symmetry

computes the finite form of the (symmetry) transformation leaving invariant any PDE system admitting a given symmetry

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