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Function, XFunction, YFunction, ZFunction

Function expression or procedure

Value Summary

Function, XFunction, YFunction, ZFunctionMandatoryMuPAD® expression

Description

Function, XFunction, YFunction, ZFunction correspond to function expressions or procedures in various plot objects given by a mathematical function.

The attribute Function is used for graphs of functions in 2D and 3D, implicit plots, conformal plots etc. which are characterized by a single function.

The attributes XFunction etc. refer to the parametrization of the x, y or z-coordinate of parametrized curves and surfaces. In vector field plots they correspond to the components of the vector field.

When defining a graphical primitive such as a function plot, the mathematical expression defining the function is passed directly to the plot routine generating this object. E.g., one calls plot::Function2d(x*sin(x), x = -5 .. 5) to define the graph of f(x) = xsin(x). Internally, the attribute Function = x*sin(x) is associated with the graphical object.

Wherever function expressions are expected, also piecewise objects or MuPAD procedures can be used. E.g., the calls plot::Function2d(sin(x), x = 0..PI) and plot::Function2d(x -> sin(x), x = 0..PI) are equivalent and associate the attributes Function = sin(x) or Function = x -> sin(x), respectively, with the plot objects.

Examples

Example 1

We define an object of type plot::Function2d representing the graph of f(x) = xsin(x):

f := plot::Function2d(x*sin(x), x = -4 .. 4):
plot(f)

Internally, the expression defining the function is turned into the attribute Function = x*sin(x). It is accessible via a corresponding slot of the object:

f::Function

One can change the object by reassigning a new value to this attribute:

f::Function := 1/x:
plot(f):

delete f:

Example 2

For implicit plots as produced by plot::Implicit2d and plot::Implicit3d, the attribute Function refers to the function whose zero set is to be plotted:

p := plot::Implicit2d(y*sin(x) - x*cos(y), x=-5..5, y=-5..5):

Internally, the expression defining the function is turned into the attribute Function = y*sin(x) - x*cos(y). It is accessible via a corresponding slot of the object:

p::Function

delete p:

Example 3

For parametrized curves and surfaces, the attributes XFunction, YFunction etc. correspond to the parametrization of the coordinates x, y etc:

c2 := plot::Curve2d([u*cos(u), u*sin(u)], u = 0..5*PI):
c2::XFunction, c2::YFunction

c3 := plot::Curve3d([u*cos(u), u*sin(u), u^2], u = 0..5*PI):
c3::XFunction, c3::YFunction, c3::ZFunction

s := plot::Surface([u*cos(v), u*sin(v), u^2*sin(2*v)],
                   u = 0..1, v = 0..2*PI):
s::XFunction, s::YFunction, s::ZFunction

delete c2, c3, s:

Example 4

Wherever a function expression is expected, also a piecewise object or a procedure can be used:

f1 := piecewise([x < 0, 0], [x >= 0, x]):
f2 := proc(x) begin
         if x < 0 then
              1
         else 1 - x^2/2
         end_if;
      end_proc:
F1 := plot::Function2d(f1, x = -1..PI/2):
F2 := plot::Function2d(f2, x = -1..PI/2):
F1::Function, F2::Function

plot(F1, F2)

delete f1, f2, F1, F2:

See Also

MuPAD Functions

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