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



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


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

See also

Ways to use isVectorField :

For the programmer

The object isVectorField is a method function.