Introduction to techniques for solving equations in Python (code examples)

This article brings you an introduction to the techniques of solving equations in Python (code examples). It has certain reference value. Friends in need can refer to it. I hope it will be helpful to you.

numpy

numpy is a bit complicated to use to solve equations, and you need to use matrix thinking! I didn't learn matrices well and numpy can't solve nonlinear equations, so... I don't know how to do this either!

sympy

It is inferior to sage and z3, but it is also very good at solving equations!

from sympy import *
x = symbols('x')
y = symbols('y')
res = solve([x+y-3,x-y-1],[x,y])[0]
print(res)

sage

sage can solve both linear and nonlinear equations. It can be called an artifact in the world of equation solving. However, expressions do not support bit operations, such as: AND or Not, remainder and XOR. Equations where bit operations occur can only be solved using z3 to create constraints! The advantages of sage are also obvious: expressions are simple and easy to write, and calculation speed is fast!
Online sage solver

var('x y')
solve([x**3+y**2+666==142335262,x**2-y==269086,x+y==1834],[x,y])

z3

z3 is also called a constraint solver and can be used to solve any equation without any problem! But windows is not easy to install, so I basically run it on linux, both python2 and python3 are supported! The idea of ​​​​using it is very simple:

• First create a symbolic variable of the type you need

• Then initialize a constraint,

• Add constraints

• Finally determine whether the constraints have solutions and solve for variables

The commonly used functions are listed below. Az3-solver document

# 符号变量类型
Int('x')
Real('x')
Bool('x')
BitVec('x',N) # N bit的符号变量，用于位操作
BitVecVal(num,N) # N bit的数据 num
# 初始化约束器
solver = Solver()
# 添加约束
solver.add(x+y==10,x-y==0)
# 求解约束
solver.check()
ans = solver.mode()

# 初始化多个符号变量
x = [Int('x%d' % i) for i in range(n)]
# 取结果中某个变量的值
value = ans[x].as_long()

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