Component(A, n) returns the nth. component of the vector A when A is a projected vector expression, or an unevaluated representation of the nth component when A is a non-projected vector or n is an unresolved name representing one of 1, 2 or 3. If A is not a vector then an error message is returned. Regarding how a vector is identified as such in the context of the Physics/Vectors package, see Identify and type, PhysicsVectors.

The %Component is the inert form of Component, that is: it represents the same mathematical operation while holding the operation unperformed. To activate the operation use value.

When Component returns unevaluated, the display on the screen shows the vectorial expression between parentheses, and indexed (as usual when working by hand). This is done using a `print/Component` procedure.

$\mathrm{with}\left(\mathrm{Physics}\left[\mathrm{Vectors}\right]\right)$

$\left[\mathrm{\&x}\,\mathrm{`+`}\,\mathrm{`.`}\,\mathrm{Assume}\,\mathrm{ChangeBasis}\,\mathrm{ChangeCoordinates}\,\mathrm{CompactDisplay}\,\mathrm{Component}\,\mathrm{Curl}\,\mathrm{DirectionalDiff}\,\mathrm{Divergence}\,\mathrm{Gradient}\,\mathrm{Identify}\,\mathrm{Laplacian}\,\nabla \,\mathrm{Norm}\,\mathrm{ParametrizeCurve}\,\mathrm{ParametrizeSurface}\,\mathrm{ParametrizeVolume}\,\mathrm{Setup}\,\mathrm{Simplify}\,\mathrm{`^`}\,\mathrm{diff}\,\mathrm{int}\right]$

$\mathrm{Setup}\left(\mathrm{mathematicalnotation}=\mathrm{true}\right)$

$\left[\mathrm{mathematicalnotation}=\mathrm{true}\right]$

$R≔a\left(x\,y\,z\right)\mathrm{\_i}+b\left(x\,y\,z\right)\mathrm{\_j}+c\left(x\,y\,z\right)\mathrm{\_k}$

$R≔a\left(x\,y\,z\right)\stackrel{\wedge }{i}+b\left(x\,y\,z\right)\stackrel{\wedge }{j}+c\left(x\,y\,z\right)\stackrel{\wedge }{k}$

$\mathrm{Component}\left(R\,1\right)$

$a\left(x\,y\,z\right)$

$\mathrm{Component}\left(R\,3\right)$

$c\left(x\,y\,z\right)$

$\mathrm{Component}\left(R\,n\right)$

${\left(a\left(x\,y\,z\right)\stackrel{\wedge }{i}+b\left(x\,y\,z\right)\stackrel{\wedge }{j}+c\left(x\,y\,z\right)\stackrel{\wedge }{k}\right)}_n$

$\mathrm{eval}\left(\,n=1\right)$

$a\left(x\,y\,z\right)$

$\mathrm{type}\left(\mathrm{A\_}\,\mathrm{PhysicsVectors}\right)$

$\mathrm{true}$

$\mathrm{Component}\left(\mathrm{A\_}\,2\right)$

${\left(\overrightarrow{A}\right)}_2$

$\mathrm{eval}\left(\,\mathrm{A\_}=R\right)$

$b\left(x\,y\,z\right)$

$\mathrm{Component}\left(\mathrm{A\_}\,n\right)$

${\left(\overrightarrow{A}\right)}_n$

$\mathrm{type}\left(\mathrm{A\_}+\mathrm{B\_}\,\mathrm{PhysicsVectors}\right)$

$\mathrm{true}$

$\mathrm{Component}\left(\mathrm{A\_}+\mathrm{B\_}\,n\right)$

${\left(\overrightarrow{A}+\overrightarrow{B}\right)}_n$

$\mathrm{type}\left(A\,\mathrm{PhysicsVectors}\right)$

$\mathrm{false}$

$\mathrm{Component}\left(A\,n\right)$

Error, (in Physics:-Vectors:-Component) first argument is not a vector