Example1: we first require to construct a vector field and a LHPDE object for representing the determining system for E(2).
E2 is a valid LAVF object and a collection of methods are available for E(2).
Basic properties of E2 can be obtained by:
Both X and S are Maple objects too, and have access to various methods too. For example,
We can check algebraic properties of E2.
Fetch structure constants of E2 & display it.
Some properties of E2 are also represented as LAVF objects (or lists of LAVF objects).
A LAVF object can be converted into a PDO for vector fields.
Solving E2 vector fields system to find vector fields.
Example2: now we consider three 3-d rotation vector fields that generating standard SO(3) action on R3(x,y,z). First we construct these vector fields.
Then a LAVF object as the vector fields system for SO(3) can be constructed by
Some geometric properties of SO(3).
Invariants may be found via integration.
We can explore the geometric properties of SO3 in further detail by extracting its orbit distribution.
OD is also a Maple object named Distribution, and it has access to various methods.