ComponentForm

ComponentForm[ expr ] converts the vectors in an expression to component form.

Usages

`ComponentForm[ expr ]`

ComponentForm[ expr ] writes the vectors in expr in component form and adds them where possible. A polar vector or column vector becomes a column vector; a vector in basis form stays in basis form. In a script, wrap the command in Simplify.

Example	in	rendered
A polar vector.	`Simplify[ ComponentForm[ PolarVector[2, 1/4 Pi] ] ]`	$\begin{pmatrix}\sqrt{2}\\\sqrt{2}\end{pmatrix}$
A polar vector with the angle in degrees.	`Simplify[ ComponentForm[ PolarVector[2, Quantity[30, 'deg']] ] ]`	$\begin{pmatrix}\sqrt{3}\\1\end{pmatrix}$
The sum of two vectors in basis form.	`Simplify[ ComponentForm[ BaseVector[-4, 2] + BaseVector[2, -3] ] ]`	$\text{-}2\mathbf{i}-\mathbf{j}$

Options

`Format`

The form of the result: 'BaseVector' for basis form or 'CartesianVector' for a column vector.

Syntax	Example	rendered
`ComponentForm[ expr, Format=>'BaseVector' ]`	`Simplify[ ComponentForm[ CartesianVector[3, 4], Format=>'BaseVector' ] ]`	$3\mathbf{i}+4\mathbf{j}$
	`Simplify[ ComponentForm[ PolarVector[1, 0], Format=>'BaseVector' ] ]`	$\mathbf{i}$
`ComponentForm[ expr, Format=>'CartesianVector' ]`	`Simplify[ ComponentForm[ BaseVector[3, 4], Format=>'CartesianVector' ] ]`	$\begin{pmatrix}3\\4\end{pmatrix}$

Details

Without Simplify, the command is not calculated: in a script, ComponentForm[ PolarVector[2, 1/4 Pi] ] stays unevaluated.
An unknown value for Format is ignored without an error.
An expression without vectors, such as ComponentForm[ 5 ], is left unevaluated.