Display areas where inequalities are fulfilled
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plot::Inequality(ineq
,x = x_{min} .. x_{max}
,y = y_{min} .. y_{max}
, <a = a_{min} .. a_{max}
>,options
) plot::Inequality([ineq_{1}, …]
,x = x_{min} .. x_{max}
,y = y_{min} .. y_{max}
, <a = a_{min} .. a_{max}
>,options
)
plot::Inequality(f(x, y) < g(x, y), x = `x_{min}`..`x_{max}`
, y = `y_{min}`..`y_{max}` )
fills the rectangle x_{min} ≤
x ≤ x_{max}
, y_{min} ≤
y ≤ y_{max}
with several colors,
indicating which points satisfy the inequality.
plot::Inequality
computes a (more or less
coarse) rasterization of the area specified by `x_{min}`..`x_{max}`
and `y_{min}`..`y_{max}`
and
colors subareas according to whether all of the given inequalities
are fulfilled (these are colored in FillColorTrue
), at least
one inequality is nowhere fulfilled in the subarea (FillColorFalse
)
or the granularity is insufficient to decide for either of these cases
(FillColorUnknown
).
You can control the density of the rasterization with the attribute Mesh
. Cf. Example 2.
plot::Inequality
uses interval numerics for evaluation, so
the results are reliable, but certain special functions (such as hypergeom
) cannot be
used because they are not supported for intervals.
Attribute  Purpose  Default Value 

AffectViewingBox  influence of objects on the ViewingBox of
a scene  TRUE 
AntiAliased  antialiased lines and points?  FALSE 
FillPattern  type of area filling  Solid 
FillColorTrue  the color for "true" areas (inequality plot)  RGB::Green 
FillColorFalse  the color for "false" areas (inequality plot)  RGB::Red 
FillColorUnknown  the color for "unknown" areas (inequality plot)  RGB::Black 
Frames  the number of frames in an animation  50 
Inequalities  inequalities displayed in inequality plots  
Legend  makes a legend entry  
LegendText  short explanatory text for legend  
LegendEntry  add this object to the legend?  FALSE 
LineColor  color of lines  RGB::Blue 
LineWidth  width of lines  0.35 
LineStyle  solid, dashed or dotted lines?  Solid 
LinesVisible  visibility of lines  FALSE 
Mesh  number of sample points  [256 , 256 ] 
Name  the name of a plot object (for browser and legend)  
ParameterEnd  end value of the animation parameter  
ParameterName  name of the animation parameter  
ParameterBegin  initial value of the animation parameter  
ParameterRange  range of the animation parameter  
TimeEnd  end time of the animation  10.0 
TimeBegin  start time of the animation  0.0 
TimeRange  the real time span of an animation  0.0 .. 10.0 
Title  object title  
TitleFont  font of object titles  [" sansserif " , 11 ] 
TitlePosition  position of object titles  
TitleAlignment  horizontal alignment of titles w.r.t. their coordinates  Center 
TitlePositionX  position of object titles, x component  
TitlePositionY  position of object titles, y component  
Visible  visibility  TRUE 
VisibleAfter  object visible after this time value  
VisibleBefore  object visible until this time value  
VisibleFromTo  object visible during this time range  
VisibleAfterEnd  object visible after its animation time ended?  TRUE 
VisibleBeforeBegin  object visible before its animation time starts?  TRUE 
XMax  final value of parameter "x"  
XMesh  number of sample points for parameter "x"  256 
XMin  initial value of parameter "x"  
XName  name of parameter "x"  
XRange  range of parameter "x"  
YMax  final value of parameter "y"  
YMesh  number of sample points for parameter "y"  256 
YMin  initial value of parameter "y"  
YName  name of parameter "y"  
YRange  range of parameter "y" 
With a single inequality, plot::Inequality
colors
the area where it is fulfilled or violated, with areas at the border
line, where the inequality is fulfilled in some parts of the rectangle
and violated in other parts:
plot(plot::Inequality(x^2 + y^2 < 1, x = 1.5..1.5, y = 1.5..1.5))
When giving more than one inequality, only those areas where all inequalities
are fulfilled are painted in blue (or whatever you set FillColorTrue
to),
while all rectangles where any inequality is
violated (over the whole rectangle) are colored red:
plot(plot::Inequality([x^2 + y^2 < 1, abs(x) > 1/3], x = 1.5..1.5, y = 1.5..1.5))
To get a more detailed image from plot::Inequality
,
increase the mesh density:
plot(plot::Inequality([x^2 + y^2 < 1, abs(x) > 1/3], x = 1.5..1.5, y = 1.5..1.5, Mesh = [120, 80]))
Almost all parameters of plot::Inequality
can
be animated (the mesh is one exception though):
plot(plot::Inequality([abs(x)^a + abs(y)^a < 1], x = 1.5+sin(a)..1.5+sin(a), y = 1.5+cos(a)..1.5+cos(a), Mesh = [64, 64], a = 1..2*PI+1))

Inequalities to plot: Expressions of the form


Identifiers or indexed identifiers. These denote the free variables spanning the plane. 

The ranges for


Animation parameter, specified as 