SymmetryAnalysis(JB1, xi, eta)¶

JB1: JetBundleCategory
xi: Union(Symbol, List Symbol)
eta: Union(Symbol, List Symbol)

SymmetryAnalysis(JB, xi, eta) provides procedures for the symmetry analysis of differential equations over a given jet bundle. Currently there exist only some procedures to set up the determining system for the symmetry generators of Lie point symmetries.

ansatz: () -> JetVectorField(JB1, JetBundleExpression JB1): ansatz() returns a general ansatz for a symmetry generator.

detSys: (List JetBundleExpression JB1, JetVectorField(JB1, JetBundleExpression JB1)) -> List JetBundleExpression JB1: detSys(sys, vf) computes the determining system for symmetry generators of the system sys with a given ansatz for the generators. It is assumed that each equation can be solved for its leading derivative.

detSys: (List JetBundleExpression JB1, List JB1, JetVectorField(JB1, JetBundleExpression JB1)) -> List JetBundleExpression JB1: detSys(sys, sjb, vf) computes the determining system for symmetry generators of the system sys with a given ansatz for the generators. sjb contains jet variables for which the individual equations can be solved.

detSys: List JetBundleExpression JB1 -> List JetBundleExpression JetBundleSymAna(JB1, xi, eta): detSys(sys) computes the determining system for symmetry generators of the system sys. It is assumed that each equation can be solved for its leading derivative.

detSysNS: (List JetBundleExpression JB1, JetVectorField(JB1, JetBundleExpression JB1)) -> List JetBundleExpression JB1: detSysNS(sys, vf) computes the determining system for symmetry generators without assuming solvability of the equations for some derivatives.

detSysNS: List JetBundleExpression JB1 -> List JetBundleExpression JetBundleSymAna(JB1, xi, eta): detSysNS(sys, vf) computes the determining system for symmetry generators without assuming solvability of the equations for some derivatives.

linearize: List JetBundleExpression JetBundleSymAna(JB1, xi, eta) -> List JetBundleLinearFunction(JetBundleSymAna(JB1, xi, eta), JetBundleXExpression JetBundleSymAna(JB1, xi, eta)): linearize(sys) tries to retract all equations in sys to a linear one. If that is not possible, an error occurs.

ncDetSys: (List JetBundleExpression JB1, JetVectorField(JB1, JetBundleExpression JB1)) -> List JetBundleExpression JB1: ncDetSys(sys, vf) computes the determining system for generators of conditional symmetries of sys with a given ansatz for the vector fields.

ncDetSys: (List JetBundleExpression JB1, List JB1, JetVectorField(JB1, JetBundleExpression JB1)) -> List JetBundleExpression JB1: ncDetSys(sys, sjb, vf) computes the determining system for generators of conditional symmetries of sys. The meaning of the further arguments is the same as in detSys.

ncDetSys: List JetBundleExpression JB1 -> List JetBundleExpression JetBundleSymAna(JB1, xi, eta): ncDetSys(sys) computes the determining system for generators of conditional symmetries of sys. It makes the same assumptions as detSys.

transform: JetBundleExpression JB1 -> JetBundleExpression JetBundleSymAna(JB1, xi, eta): transform(f) transforms expressions between the different function types involved.