Hence, mathematical expressions are expressed like any Python expression would be processed. Because j was used as a substitute for x, the result is a simplified and easily solvable linear equation.įirst, as a demonstration of how eval() works, in that it can evaluate any Python command given in a string: When the expression is evaluated, the answer comes out to be a*j + b, which Python believes is a complex number. By substituting an unknown variable x with the natively understood j (i), Python treats two categories of expression elements - variables and constants - as separate. The eval function takes in an expression.
Note that var was specified to equal 'x' at function initialization. grouped = eval(expression.replace(var,'1j') This uses Python’s built-in complex number handling, where j is used to denote the mathematical constant i = √-1.
#Solving three equation systems with python code
The second line of code evaluates the new expression, into a form ax + b = 0. expression = equation.replace("="," - (")+")"Īll the 'information' in the equation has been shifted to one side, and while the equals sign has been discarded, remember that this expression is equal to 0. The first line transforms the equation into an expression to be evaluated by moving the entire expression on the right side of the equation to the left side. As an example, we will be using the following linear equation as a demonstration. Let’s break down the function step-by-step. As long as it abides by these definitions of a linear equation, it is solvable by our function. A two-variable equation would require multiple linear equations (a system of equations) to be solved.Ī linear equation consists of three primary components - constants, variables, and multipliers.Īny number or combination of operations - addition, subtraction, multiplication, and division - are valid, with any parenthesis scope. This means that it can only have one variable, usually written as x. replace(var, '1j'))įirst, let’s define what a linear equation is - it must be solvable in its pure form.
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