Plotting Nonlinear Inequalities

Description

There are some inequalities where the relationship between $x$ and $y$ cannot be expressed as a function, such as

(1)
\begin{align} cos(x^2 + y^2) \leq 0 \end{align}

To plot these, we can use the region_plot command.

Sage Cell

Code

y = var('y')
region_plot(cos(x^2 + y^2) <= 0, (x, -5, 5), (y, -5, 5))


Options

Style Options

We can change the look of the graph by setting the bordercol (color of the border), incol (color of the fill) and alpha (transparency of the fill).

Code

y = var('y')
region_plot(cos(x^2 + y^2) <= 0, (x, -5, 5), (y, -5, 5), bordercol='black', incol='yellow', alpha=2/3)


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