## Solve Equations in Python

The following tutorials are an introduction to solving linear and nonlinear equations with Python. The solution to linear equations is through matrix operations while sets of nonlinear equations require a solver to numerically find a solution.

#### Solve Linear Equations with Python

#### Source Code for Linear Solutions

A = np.array([ [3,-9], [2,4] ])

b = np.array([-42,2])

z = np.linalg.solve(A,b)

print(z)

M = np.array([ [1,-2,-1], [2,2,-1], [-1,-1,2] ])

c = np.array([6,1,1])

y = np.linalg.solve(M,c)

print(y)

#### Solve Nonlinear Equations with Python

#### Source Code for Nonlinear Solution

from scipy.optimize import *

def myFunction(z):

x = z[0]

y = z[1]

w = z[2]

F = empty((3))

F[0] = pow(x,2)+pow(y,2)-20

F[1] = y - pow(x,2)

F[2] = w + 5 - x*y

return F

zGuess = array([1,1,1])

z = fsolve(myFunction,zGuess)

print(z)

#### Additional Tutorials

Linear and nonlinear equations can also be solved with Excel and MATLAB. Click on the appropriate link for additional information and source code.

The APMonitor Modeling Language with a Python interface is optimization software for mixed-integer and differential algebraic equations. It is coupled with large-scale solvers for linear, quadratic, nonlinear, and mixed integer programming (LP, QP, NLP, MILP, MINLP). Modes of operation include data reconciliation, real-time optimization, dynamic simulation, and nonlinear predictive control. It is freely available through MATLAB, Python, Julia, or from a web browser interface.

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