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Calling Sequence
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GetRepresentation(l, opts)
GetRepresentation(p, opts)
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Parameters
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Options
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The following options are available.
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form = equation, equations, vectors, combined_vector, parametric, symmetric (if called on a Line object)
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form = equation, equations (if called on a Plane object)
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The standard representations for the given object. The default is vectors for a Line and equation for a Plane.
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In vectors form, the result is an expression of the form .
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In combined_vector form, the two vectors of vectors form are combined to obtain an expression of the form .
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In parametric form, the expressions from combined_vector form are used in equations to obtain a list of
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In symmetric form, the result is a little more complicated to describe:
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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: . 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.
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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: .
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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: .
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For a line in 2D, Maple typically returns an equation of the form .
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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 .
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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 .
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Description
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The GetRepresentation command returns a representation of a line or plane.
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For a Plane object p, the command returns the equation of p in the form .
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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.
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For a Line object l, several forms of representation are available. These are selected by the form option (see below).
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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.
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Examples
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The other symmetric forms.
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The option is available for lines in 2D, but not 3D.
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u, v and x can be used in the equation.
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Compatibility
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The Student[MultivariateCalculus][GetRepresentation] command was introduced in Maple 17.
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