constructing a VectorField object
VectorField( components = compList, space = varList)
VectorField( DExpr, space = varList)
VectorField( listOfPairs, space = varList )
VectorField( 0, space = varList)
a list of scalar expressions [xi1, xi2,...,xin] the components of the vector field.
a list of names [x1, x2, ... ,xn], the coordinates of space
expression of the form xi1*D[x1] + xi2*D[x2] + ... + xin*D[xn]
a list of ordered pairs [[xi1,x1], [xi2,x2], ..., [xin,xn]] of component values and corresponding space coordinate
The command VectorField(...) is a constructor method for creating a VectorField object. Once a valid VectorField object is created, it has access to various methods which allow it to be manipulated and its contents queried. see Overview of VectorField object for more detail.
A vector field X is an expression of the form X=∑i=0nξix1,x2,…,xn living on a space with coordinates x1,x2,…,xn. The ξi are referred to as components, and x1,x2,…,xn are referred to as (coordinates of) space. ∂∂xiξi⁡x1,x2,..,xn
The VectorField command first validates the user input arguments and then constructs a VectorField object. A valid VectorField object consists of two data attributes: components ξ1,ξ2,…,ξn and space variables x1,x2,…,xn.
In the first calling sequence, both arguments components = compList, space=varList are required. These two lists must be of the same length.
The second calling sequence is a textual representation of the usual appearance of a vector field. The space = varList argument is optional; if present, its specification of the space overrides the space [x1, x2,..., xn] implied by DExpr.
In the third calling sequence, the space =varList argument is optional; if present, its specification of the space overrides the space [x1, x2,..., xn] implied by listOfPairs.
The fourth calling sequence is a special constructor for the zero vector field on the specified space; the space = varList argument is required.
This command is part of the VectorField package. For more detail, see Overview of the VectorField package.
This command can be used in the form VectorField(...) only after executing the command with(LieAlgebrasOfVectorFields), but can always be used by executing LieAlgebrasOfVectorFields:-VectorField(...).
First calling sequence:
X ≔ VectorField⁡components=x2,x⁢y,space=x,y
Second calling sequence:
X ≔ VectorField⁡x2⁢Dx+x⁢y⁢Dy
Third calling sequence, vector field specified by ordered pairs:
X ≔ VectorField⁡x2,x,x⁢y,y
Fourth calling sequence:
Z ≔ VectorField⁡0,space=x,y
The second calling sequence is especially useful as a sparse form entry, where only a few components are nonzero:
Tx ≔ VectorField⁡Dx,space=x,y,z,t
Although the coordinates y,z,t are not visible in the printed form of this vector field, they are present in the VectorField object:
VectorField (Object overview)
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