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Graphics`InequalityGraphics`

This package provides functions for visualizing logical combinations of inequalities over the reals in 2D and 3D. It also provides functionality for visualizing regions over the complexes.

Visualization of inequalities.

This loads the package.

In[1]:= <<Graphics`InequalityGraphics`

This plots the region .

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In this case there is a logical combination of inequalities to describe the region .

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This plots the symmetric difference between the two regions and . Since the region is bounded, you will not need to give additional bounds in the range specification.

In[4]:=

This plots the region . The full region is an infinite x shaped figure.

In[5]:=

This is an array of various norm-related regions. The center diagonal corresponds to the unit balls in , , and respectively or the regions for and .

In[6]:=

Out[6]=

This plots the intersection of a double cone with a ball.

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This plots the ellipsoid intersected by the halfspace .

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This is a slightly more complex figure.

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Out[9]=

You can also specify regions in the complex plane using inequalities. All operations on complex numbers need eventually to involve real quantities before using inequalities to specify these regions. Typically this means that complex arithmetic expressions are eventually wrapped in real-valued functions such as Abs, Re, and Im.

Visualizing complex regions.

Here is the simplest complex region.

In[10]:=

This is the region .

In[11]:=

This constructs an animation of a set of regions given by a bilinear or Möbius transformation.

In[12]:=