Overview of the VectorField Object
VectorField Object Methods
The VectorField object is designed and created to represent a vector field as a mathematical object. It can be queried for basic properties of a vector field, and can be used in computing vector field arithmetic, Lie derivatives and Lie brackets. A VectorField object can also act as an operator.
Some existing Maple builtins have been overloaded so that they work for a VectorField object.
All methods of the VectorField object become available only once a valid VectorField object is constructed successfully. See LieAlgebrasOfVectorFields[VectorField] command for more detail about constructing a VectorField object.
The VectorField object is one of the main Maple objects exported by the VectorField package. See Overview of the VectorField package for more detail.
For a space with coordinates x1,x2,…,xn a vector field X is an expression of the form X=∑i=0nξix1,x2,…,xn⋅axi. The ξi are referred to as components, and x1,x2,…,xn are referred as space. Therefore, a VectorField object is mathematically represented by two data attributes: "components" and "space". The data attributes of a VectorField object can be accessed via the GetComponents and GetSpace methods.
After a VectorField object X is successfully constructed, each method in the VectorField object can be accessed by either the short form method(X, arguments) or the long form X:-method(X, arguments).
After a VectorField object is constructed, the following methods are available:
A VectorField object can also act as a derivation operator. See VectorField Object as Derivation Operator for more detail.
The following arithmetic operators (=, +, -, ?) are overloaded for use on VectorField object. See VectorField Object Operator Methods for more detail.
The following Maple builtins functions are extended so that they work for a VectorField object: type, expand, has, hastype, indets, map, normal, simplify, subs. See VectorField Object Overloaded Builtins for more detail.
Inserting option static gives a list of exports of the VectorField object.
R ≔ VectorField⁡−y⁢Dx+x⁢Dy,space=x,y
Tx ≔ VectorField⁡Dx,space=x,y
Retrieve data attributes of R
Vector field arithmetic
Vector field acting as a derivation operator
The Overview of the VectorField Object command was introduced in Maple 2020.
For more information on Maple 2020 changes, see Updates in Maple 2020.
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