Initialize

Loading Student:-VectorCalculus

Define the Cartesian vector field F

$⟨u\left(x\,y\,z\right)\,v\left(x\,y\,z\right)\,w\left(x\,y\,z\right)⟩$ = $\stackrel{\text{to Vector Field}}{\to }$ $\stackrel{\text{assign to a name}}{\to }$$F$$$

Compute the divergence of the curl of F

$\nabla ·\left(\nabla \times \mathbf{F}\right)$ = $0$$$

Initialize

$$\begin{gathered} \mathrm{with}\left(\mathrm{Student}:-\mathrm{VectorCalculus}\right)\: \\ \mathrm{BasisFormat}\left(\mathrm{false}\right)\: \end{gathered}$$

Implement notational simplifications with the declare command in the PDEtools package

$\mathrm{PDEtools}:-\mathrm{declare}\left(u\left(x\,y\,z\right)\,v\left(x\,y\,z\right)\,w\left(x\,y\,z\right)\,\mathrm{quiet}\right)$

Use the VectorField command in the Student VectorCalculus package to define F

$\mathbf{F}≔\mathrm{VectorField}\left(⟨u\left(x\,y\,z\right)\,v\left(x\,y\,z\right)\,w\left(x\,y\,z\right)⟩\right)$ = $$

Verify $\nabla ·\left(\nabla \times \mathbf{F}\right)\=0$

$\mathrm{Divergence}\left(\mathrm{Curl}\left(\mathbf{F}\right)\right)$ = $0$$$