How to graph curves that are not functions (in Python, using SymPy)

Task

Assume we have an equation in which $y$ cannot be isolated as a function of $x$ . (The standard example is the formula for the unit circle, $x^{2} + y^{2} = 1$ .) We would still like to be able to use software to plot such curves. How?

Related tasks:

Solution

This answer assumes you have imported SymPy as follows.

from sympy import *                   # load all math functions
init_printing( use_latex='mathjax' )  # use pretty math output

Let’s consider the example of the unit circle, $x^{2} + y^{2} = 1$ .

To plot it, SymPy first expects us to move everything to the left-hand side of the equation, so in this case, we would have $x^{2} + y^{2} - 1 = 0$ .

We then use that left hand side to represent the equation as a single formula, and we can plot it with SymPy’s plot_implicit function.

var( 'x y' )
formula = x**2 + y**2 - 1   # to represent x^2+y^2=1
plot_implicit( formula )

png

<sympy.plotting.plot.Plot at 0x7f67130cb460>

Content last modified on 24 July 2023.

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Contributed by Nathan Carter (ncarter@bentley.edu)