plot::inequality
-- generate
a 2D plot of inequalitiesplot::inequality
([f1, f2,...], left..right,
bottom..top)
serves for displaying points (x,y) in
the rectangle Q=[left,right] x [bottom, top] satisfying the
inequalities
f1(x,y)>=0 and f2(x,y)>=0 and ..
plot::inequality([f1, f2...], left..right, bottom..top <,
n> <Colors = [c1, c2, c3]>)
f1, f2... |
- | real valued functions of two variables: procedures |
left, right, bottom, top |
- | real numerical values |
n |
- | a nonnegative integer determining the mesh size. The default value is 6. |
Colors = [c1, c2,
c3] |
- | each of the colors c1 , c2 ,
c3 must be an RGB
specification, i.e., a list of three real numerical values between
0 and 1. The default colors are c1 =
RGB::Green , c2 = RGB::Yellow , c3 =
RGB::Red . |
an object of the domain type plot::Group
.
n = 6
, the drawing
area is divided into 64 * 64 subrectangles. This default
produces a rather ``discretized'' plot. ``Smoother'' plots are
generated by larger values of n
. Note, however, that
increasing n
by 1 may increase the run time by
a factor of 4.c1
if all
its points (x,y) satisfy f1(x,y)>0 and
f2(x,y)>0 etc. Consequently, all points of this color are
guaranteed to satisfy (1).c3
if there
is at least one function f.i such that all points in the
subrectangle satisfy f.i(x,y)<0. Consequently, all points
of this color are guaranteed to violate (1).c2
. They cover the boundary of the region defined by the
inequalities (1).plot::inequality
may be passed
to the function plot::Scene
to create a graphical scene.
In the call to plot::Scene
, you may specify scene options. Call
plot(...)
to display the scene.
Alternatively, if the scene consists of only one ``inequality
object'', you can pass this object directly to plot
together with scene options.
f1(Dom::Interval(left..right), Dom::Interval(bottom..top))
etc. must produce valid intervals. In MuPAD, interval
implementations exist for most of the elementary functions such as
sin
, exp
, ln
etc. However, special functions such
as Bessel functions, polylogarithms etc. must not turn up in
f1, f2, ...
.>> f1:= (x,y) -> x^2 + y^2 - 1: p1:= plot::inequality([f1], -1..1, -1..1, 5)
plot::Group()
>> plot(p1, Scaling = Constrained, Axes = Box)
>> f2:= (x,y) -> cos(x) - y: f3:= (x,y) -> cos(x) + y: p23:= plot::inequality([f2, f3], -PI..PI, -2..2, 5)
plot::Group()
>> plot(p23, Scaling = Constrained, Axes = Box)
>> p123:= plot::inequality( [f1, f2, f3], -2..2, -1..1, 5, Colors = [RGB::Red, RGB::Black, RGB::White])
plot::Group()
>> plot(p123, Scaling = Constrained, Axes = Box)