GetRepresentation - Maple Help

Student[MultivariateCalculus]

 GetRepresentation
 obtain a representation of a line or plane

 Calling Sequence GetRepresentation(l, opts) GetRepresentation(p, opts)

Parameters

 l - Line ; Line defined by Student[MultivariateCalculus] opts - (optional) control the representation of a Line object p - Plane ; Plane defined by Student[MultivariateCalculus]

Options

 • 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: $x=-1,z=2$.
 – 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 $x=-1$.
 • 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 $t$.

Description

 • 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.

Examples

 > $\mathrm{with}\left(\mathrm{Student}:-\mathrm{MultivariateCalculus}\right):$
 > $\mathrm{l1}≔\mathrm{Line}\left(\left[1,2,3\right],\left[7,-2,-1\right],'\mathrm{variables}'=\left[u,v,w\right]\right)$
 ${\mathrm{l1}}{≔}{\mathrm{<< Line 1 >>}}$ (1)
 > $\mathrm{GetRepresentation}\left(\mathrm{l1}\right)$
 ${t}{·}\left[\begin{array}{c}{6}\\ {-4}\\ {-4}\end{array}\right]{+}\left[\begin{array}{c}{1}\\ {2}\\ {3}\end{array}\right]$ (2)
 > $\mathrm{GetRepresentation}\left(\mathrm{l1},'\mathrm{form}'='\mathrm{vectors}','\mathrm{parameter}'='k'\right)$
 ${k}{·}\left[\begin{array}{c}{6}\\ {-4}\\ {-4}\end{array}\right]{+}\left[\begin{array}{c}{1}\\ {2}\\ {3}\end{array}\right]$ (3)
 > $\mathrm{GetRepresentation}\left(\mathrm{l1},'\mathrm{form}'='\mathrm{combined_vector}'\right)$
 $\left[\begin{array}{c}{1}{+}{6}{}{t}\\ {2}{-}{4}{}{t}\\ {3}{-}{4}{}{t}\end{array}\right]$ (4)
 > $\mathrm{GetRepresentation}\left(\mathrm{l1},'\mathrm{form}'='\mathrm{parametric}'\right)$
 $\left[{u}{=}{1}{+}{6}{}{t}{,}{v}{=}{2}{-}{4}{}{t}{,}{w}{=}{3}{-}{4}{}{t}\right]$ (5)
 > $\mathrm{GetRepresentation}\left(\mathrm{l1},'\mathrm{form}'='\mathrm{symmetric}'\right)$
 $\frac{{u}}{{6}}{-}\frac{{1}}{{6}}{=}{-}\frac{{v}}{{4}}{+}\frac{{1}}{{2}}{=}{-}\frac{{w}}{{4}}{+}\frac{{3}}{{4}}$ (6)

The other symmetric forms.

 > $\mathrm{l2}≔\mathrm{Line}\left(\left[1,2,3\right],\left[7,-2,3\right],'\mathrm{variables}'=\left[u,v,w\right]\right)$
 ${\mathrm{l2}}{≔}{\mathrm{<< Line 2 >>}}$ (7)
 > $\mathrm{GetRepresentation}\left(\mathrm{l2},'\mathrm{form}'='\mathrm{symmetric}'\right)$
 $\frac{{u}}{{6}}{-}\frac{{1}}{{6}}{=}{-}\frac{{v}}{{4}}{+}\frac{{1}}{{2}}{,}{w}{=}{3}$ (8)
 > $\mathrm{l3}≔\mathrm{Line}\left(\left[1,2,3\right],\left[7,2,3\right],'\mathrm{variables}'=\left[u,v,w\right]\right)$
 ${\mathrm{l3}}{≔}{\mathrm{<< Line 3 >>}}$ (9)
 > $\mathrm{GetRepresentation}\left(\mathrm{l3},'\mathrm{form}'='\mathrm{symmetric}'\right)$
 ${v}{=}{2}{,}{w}{=}{3}$ (10)
 > $\mathrm{l4}≔\mathrm{Line}\left(\left[1,2\right],\left[7,-2\right],'\mathrm{variables}'=\left[u,v\right]\right)$
 ${\mathrm{l4}}{≔}{\mathrm{<< Line 4 >>}}$ (11)
 > $\mathrm{GetRepresentation}\left(\mathrm{l4},'\mathrm{form}'='\mathrm{symmetric}'\right)$
 $\frac{{u}}{{6}}{-}\frac{{1}}{{6}}{=}{-}\frac{{v}}{{4}}{+}\frac{{1}}{{2}}$ (12)
 > $\mathrm{l5}≔\mathrm{Line}\left(\left[1,2\right],\left[7,2\right],'\mathrm{variables}'=\left[u,v\right]\right)$
 ${\mathrm{l5}}{≔}{\mathrm{<< Line 5 >>}}$ (13)
 > $\mathrm{GetRepresentation}\left(\mathrm{l5},'\mathrm{form}'='\mathrm{symmetric}'\right)$
 ${v}{=}{2}$ (14)

The option $\mathrm{form}=\mathrm{equation}$ is available for lines in 2D, but not 3D.

 > $\mathrm{GetRepresentation}\left(\mathrm{l4},'\mathrm{form}'='\mathrm{equation}'\right)$
 $\frac{{2}{}{u}}{{3}}{+}{v}{=}\frac{{8}}{{3}}$ (15)
 > $\mathrm{GetRepresentation}\left(\mathrm{l4},'\mathrm{form}'='\mathrm{equations}'\right)$
 $\left\{\frac{{2}{}{u}}{{3}}{+}{v}{=}\frac{{8}}{{3}}\right\}$ (16)
 > $\mathrm{GetRepresentation}\left(\mathrm{l1},'\mathrm{form}'='\mathrm{equation}'\right)$
 > $\mathrm{GetRepresentation}\left(\mathrm{l1},'\mathrm{form}'='\mathrm{equations}'\right)$
 $\left\{\frac{{2}{}{u}}{{3}}{+}{v}{=}\frac{{8}}{{3}}{,}\frac{{2}{}{u}}{{3}}{+}{w}{=}\frac{{11}}{{3}}\right\}$ (17)
 > $\mathrm{p1}≔\mathrm{Plane}\left(\left[2,3,-3\right],⟨0,3,1⟩\right):$
 > $\mathrm{GetRepresentation}\left(\mathrm{p1}\right)$
 ${3}{}{y}{+}{z}{=}{6}$ (18)
 > $\mathrm{p2}≔\mathrm{Plane}\left(\left[9,4,-3\right],⟨9,-1,-3⟩,⟨-1,0,0⟩\right)$
 ${\mathrm{p2}}{≔}{\mathrm{<< Plane 2 >>}}$ (19)
 > $\mathrm{GetRepresentation}\left(\mathrm{p2}\right)$
 ${3}{}{y}{-}{z}{=}{15}$ (20)

u, v and x can be used in the equation.

 > $\mathrm{p3}≔\mathrm{Plane}\left(\left[3,6,1\right],\left[4,1,-5\right],\left[3,2,0\right],'\mathrm{variables}'=\left[u,v,x\right]\right):$
 > $\mathrm{GetRepresentation}\left(\mathrm{p3}\right)$
 ${-}{19}{}{u}{+}{v}{-}{4}{}{x}{=}{-55}$ (21)

Compatibility

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