# SymmetryAnalysis(JB1, xi, eta)¶

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.