Sym Paclet Symbol

GetOptimalSystemRawData

GetOptimalSystemRawData[L]
gives from a Lie algebra L the required information for calculating its optimal system.

To use GetOptimalSystemRawData, you first need to load the SYM Package using Needs["SYM`"].

The Lie algebra L can be provided either from their structure constants or their infinitesimal generator representation.

GetOptimalSystemRawData provides a list containing the orbits of the action of each base element of the Lie algebra to a random element of the algebra, the invariants constraints and the set of the coeficients of the random element.

GetOptimalSystemRawData is an intermediary command. For a fully automated function use GetOptimalSystem.

Let the following representation of

(2):

Out[3]=

The orbits of the action of each base element X₁, X₂, X₃ to a random element of the Lie algebra k₁X₁+k₂X₂+k₃X₃

Out[4]//MatrixForm=

The invariant for this case is: