How to write symbolic equations (in Python, using SymPy)

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Task

In programming, when we write a=b, the computer interprets it as an instruction, to change the value of a to b. But in mathematics, $a=b$ is a statement that $a$ and $b$ are equal; it’s often a starting point for algebraic work. How can we write a mathematical equation using software?

Related tasks:

• How to solve symbolic equations
• How to isolate one variable in an equation

Solution

This answer assumes you have imported SymPy as follows.

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

Let’s say we want to write the equation $x^2+y^2=2$. We must first define $x$ and $y$ as mathematical variables, then use SymPy’s Eq function to build an equation. This helps SymPy distinguish a mathematical equation from a Python assignment statement.

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var( 'x y' )
Eq( x**2 + y**2, 2 )    # Two parameters: left and right sides of equation

$\displaystyle x^{2} + y^{2} = 2$

You can make a system of equations just by placing several equations in a Python list.

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system = [
    Eq( x + 2*y, 1 ),
    Eq( x - 9*y, 5 )
]
system

$\displaystyle \left[ x + 2 y = 1, \ x - 9 y = 5\right]$

Content last modified on 24 July 2023.

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Contributed by Nathan Carter (ncarter@bentley.edu)