The following options are available.

form = equation, equations, vectors, combined_vector, parametric, symmetric (if called on a Line object)

form = equation, equations (if called on a Plane object)

The standard representations for the given object. The default is vectors for a Line and equation for a Plane.

In vectors form, the result is an expression of the form $t.\left[\begin{array}{c}1\\ 2\end{array}\right]+\left[\begin{array}{c}3\\ 4\end{array}\right]$.

In combined_vector form, the two vectors of vectors form are combined to obtain an expression of the form $\left[\begin{array}{c}t+3\\ 2t+4\end{array}\right]$.

In parametric form, the expressions from combined_vector form are used in equations to obtain a list of

In symmetric form, the result is a little more complicated to describe:

For a line in 3D space, symmetric form is typically an object displayed as an equation with three parts, each of which is a linear expression in one of the coordinate variables. This is an example: $\frac{x}{4}-\frac{1}{4}=\frac{y}{5}-\frac{2}{5}=\frac{z}{6}-\frac{1}{2}$. Such 'equations' cannot be handled by Maple, and indeed this is not an equation that you can use in other parts of Maple - only for display.

If a line in 3D is parallel to one of the coordinate planes, then there is no equation of that form that describes the line. Instead, GetRepresentation returns a sequence of two equations, like this: $\frac{x}{4}-\frac{1}{4}=\frac{y}{5}-\frac{2}{5},z=2$.

If a line in 3D is parallel to two of the coordinate planes (that is, it is parallel to one of the coordinate axes), then GetRepresentation returns a sequence of two equations, like this: $x=\mathrm{-1},z=2$.

For a line in 2D, Maple typically returns an equation of the form $\frac{x}{4}-\frac{1}{4}=\frac{y}{5}-\frac{2}{5}$.

If a line in 2D is parallel to a coordinate axis, then there is no equation of that form that describes the line. Instead, GetRepresentation returns an equation of the form $x=\mathrm{-1}$.

parameter = name

The free variable used in vectors, combined_vector, and parametric form.  The default is the parameter used when constructing the line. In turn, the default for that is $t$.

The GetRepresentation command returns a representation of a line or plane.

For a Plane object p, the command returns the equation of p in the form $ax+by+cz=d$.

For consistency with lines in 3D (see below), one can pass the option form = equations (plural) to GetRepresentation to get this equation in a set. The only other valid value for form is equation (singular), which is the default - it returns just the equation.

For a Line object l, several forms of representation are available. These are selected by the form option (see below).

When form = symmetric is selected for a typical line in 3D space (see the options below), the result is not a normal Maple equation - Maple does not support equations involving three expressions. The value returned can only be used for displaying this 'equation'. The other forms all result in normal Maple equations and expressions.

$\mathrm{with}\left(\mathrm{Student}:-\mathrm{MultivariateCalculus}\right)\:$

$\mathrm{l1}≔\mathrm{Line}\left(\left[1\,2\,3\right]\,\left[7\,-2\,-1\right]\,'\mathrm{variables}'=\left[u\,v\,w\right]\right)$

$\mathrm{l1}≔\mathrm{<<\; Line\; 1\; >>}$

$\mathrm{GetRepresentation}\left(\mathrm{l1}\right)$

$t·\left[\begin{array}{c}6\\ \mathrm{-4}\\ \mathrm{-4}\end{array}\right]+\left[\begin{array}{c}1\\ 2\\ 3\end{array}\right]$

$\mathrm{GetRepresentation}\left(\mathrm{l1}\&comma;'\mathrm{form}'='\mathrm{vectors}'\&comma;'\mathrm{parameter}'='k'\right)$

$k·\left[\begin{array}{c}6\\ \mathrm{-4}\\ \mathrm{-4}\end{array}\right]+\left[\begin{array}{c}1\\ 2\\ 3\end{array}\right]$

$\mathrm{GetRepresentation}\left(\mathrm{l1}\&comma;'\mathrm{form}'='\mathrm{combined\_vector}'\right)$

$\left[\begin{array}{c}1+6t\\ 2-4t\\ 3-4t\end{array}\right]$

$\mathrm{GetRepresentation}\left(\mathrm{l1}\&comma;'\mathrm{form}'='\mathrm{parametric}'\right)$

$\left[u=1+6t\&comma;v=2-4t\&comma;w=3-4t\right]$

$\mathrm{GetRepresentation}\left(\mathrm{l1}\&comma;'\mathrm{form}'='\mathrm{symmetric}'\right)$

$\frac{u}{6}-\frac{1}{6}=-\frac{v}{4}+\frac{1}{2}=-\frac{w}{4}+\frac{3}{4}$

$\mathrm{l2}≔\mathrm{Line}\left(\left[1\&comma;2\&comma;3\right]\&comma;\left[7\&comma;-2\&comma;3\right]\&comma;'\mathrm{variables}'=\left[u\&comma;v\&comma;w\right]\right)$

$\mathrm{l2}≔\mathrm{<<\; Line\; 2\; >>}$

$\mathrm{GetRepresentation}\left(\mathrm{l2}\&comma;'\mathrm{form}'='\mathrm{symmetric}'\right)$

$\frac{u}{6}-\frac{1}{6}=-\frac{v}{4}+\frac{1}{2},w=3$

$\mathrm{l3}≔\mathrm{Line}\left(\left[1\&comma;2\&comma;3\right]\&comma;\left[7\&comma;2\&comma;3\right]\&comma;'\mathrm{variables}'=\left[u\&comma;v\&comma;w\right]\right)$

$\mathrm{l3}≔\mathrm{<<\; Line\; 3\; >>}$

$\mathrm{GetRepresentation}\left(\mathrm{l3}\&comma;'\mathrm{form}'='\mathrm{symmetric}'\right)$

$v=2,w=3$

$\mathrm{l4}≔\mathrm{Line}\left(\left[1\&comma;2\right]\&comma;\left[7\&comma;-2\right]\&comma;'\mathrm{variables}'=\left[u\&comma;v\right]\right)$

$\mathrm{l4}≔\mathrm{<<\; Line\; 4\; >>}$

$\mathrm{GetRepresentation}\left(\mathrm{l4}\&comma;'\mathrm{form}'='\mathrm{symmetric}'\right)$

$\frac{u}{6}-\frac{1}{6}=-\frac{v}{4}+\frac{1}{2}$

$\mathrm{l5}≔\mathrm{Line}\left(\left[1\&comma;2\right]\&comma;\left[7\&comma;2\right]\&comma;'\mathrm{variables}'=\left[u\&comma;v\right]\right)$

$\mathrm{l5}≔\mathrm{<<\; Line\; 5\; >>}$

$\mathrm{GetRepresentation}\left(\mathrm{l5}\&comma;'\mathrm{form}'='\mathrm{symmetric}'\right)$

$v=2$

$\mathrm{GetRepresentation}\left(\mathrm{l4}\&comma;'\mathrm{form}'='\mathrm{equation}'\right)$

$\frac{2u}{3}+v=\frac{8}{3}$

$\mathrm{GetRepresentation}\left(\mathrm{l4}\&comma;'\mathrm{form}'='\mathrm{equations}'\right)$

$\left\{\frac{2u}{3}+v=\frac{8}{3}\right\}$

$\mathrm{GetRepresentation}\left(\mathrm{l1}\&comma;'\mathrm{form}'='\mathrm{equation}'\right)$

Error, (in Student:-MultivariateCalculus:-Line:-GetRepresentation) a line in 3 dimensions cannot be given by a single equation; try 'form = equations' instead

$\mathrm{GetRepresentation}\left(\mathrm{l1}\&comma;'\mathrm{form}'='\mathrm{equations}'\right)$

$\left\{\frac{2u}{3}+v=\frac{8}{3}\&comma;\frac{2u}{3}+w=\frac{11}{3}\right\}$

$\mathrm{p1}≔\mathrm{Plane}\left(\left[2\&comma;3\&comma;-3\right]\&comma;⟨0\&comma;3\&comma;1⟩\right)\&colon;$

$\mathrm{GetRepresentation}\left(\mathrm{p1}\right)$

$3y+z=6$

$\mathrm{p2}≔\mathrm{Plane}\left(\left[9\&comma;4\&comma;-3\right]\&comma;⟨9\&comma;-1\&comma;-3⟩\&comma;⟨-1\&comma;0\&comma;0⟩\right)$

$\mathrm{p2}≔\mathrm{<<\; Plane\; 2\; >>}$

$\mathrm{GetRepresentation}\left(\mathrm{p2}\right)$

$3y-z=15$

$\mathrm{p3}≔\mathrm{Plane}\left(\left[3\&comma;6\&comma;1\right]\&comma;\left[4\&comma;1\&comma;-5\right]\&comma;\left[3\&comma;2\&comma;0\right]\&comma;'\mathrm{variables}'=\left[u\&comma;v\&comma;x\right]\right)\&colon;$

$\mathrm{GetRepresentation}\left(\mathrm{p3}\right)$

$-19u+v-4x=\mathrm{-55}$

The Student[MultivariateCalculus][GetRepresentation] command was introduced in Maple 17.

For more information on Maple 17 changes, see Updates in Maple 17.