isVectorField -- test whether a module or matrix can be interpreted as a collection of vector fields

Synopsis

Usage:

b=isVectorField(m)

b=isVectorField(M)
Inputs:
- m, a module,
- M, a matrix,
Outputs:
- b, a Boolean value, whether the provided module or matrix can be interpreted as a collection of vector fields

Description

This determines whether the provided Module or Matrix can be interpreted as a collection of vector fields.

For a Module to be interpreted as a module of vector fields, the module must be presented as a submodule of a free module whose rank equals the number of variables in the ring.

i1 : R=QQ[x,y];

i2 : isVectorField(image matrix {{x,y^2}})

o2 = false

i3 : isVectorField(image matrix {{x,y^2},{0,0}})

o3 = true

For a Matrix, it must have the correct number of rows.

i4 : isVectorField(matrix {{x,y^2}})

o4 = false

i5 : isVectorField(matrix {{x,y^2},{0,0}})

o5 = true

Caveat

Despite the name, the function does not check the number of vector fields provided.

Ways to use isVectorField :

isVectorField(Matrix)
isVectorField(Module)

For the programmer