Sympy符号计算

1、sympy库的安装（cmd输入pip install sympy）

C:\Users\17865>pip install sympy

2、根号运算的精确表达

小数形式的计算：

import math
print (math.sqrt(8))

PS C:\Users\17865> & C:/Users/17865/AppData/Local/Microsoft/WindowsApps/python3.11.exe d:/Python/sympy1.py
2.8284271247461903

import sympy
print (sympy.sqrt(8))

PS C:\Users\17865> & C:/Users/17865/AppData/Local/Microsoft/WindowsApps/python3.11.exe d:/Python/sympy1.py
2*sqrt(2)

3、符号的表达式运算

from sympy import symbols
x,y,z = symbols('x y z')
expr = x + 2*y +3*z
print(expr*expr)

PS C:\Users\17865> & C:/Users/17865/AppData/Local/Microsoft/WindowsApps/python3.11.exe d:/Python/sympy1.py
(x + 2*y + 3*z)**2

4、因式分解计算

from sympy import symbols,factor
x,y,z = symbols('x y z')
expr = x*x+y*y+z*z+2*x*y+2*y*z+2*x*z
print(factor(expr))

PS C:\Users\17865> & C:/Users/17865/AppData/Local/Microsoft/WindowsApps/python3.11.exe d:/Python/sympy1.py
(x + y + z)**2

5、求导

from sympy import *
x = symbols('x')
print ( diff(sin(x)*exp(x),x) )

PS C:\Users\17865> & C:/Users/17865/AppData/Local/Microsoft/WindowsApps/python3.11.exe d:/Python/sympy1.py
exp(x)*sin(x) + exp(x)*cos(x)

6、求不定积分

from sympy import *
x = symbols('x')
print ( integrate (sin(x)*exp(x),x) )

exp(x)*sin(x)/2 - exp(x)*cos(x)/2

7、求极限

from sympy import *
x = symbols('x')
print ( limit (sin(x)/x,x,0) )

PS C:\Users\17865> & C:/Users/17865/AppData/Local/Microsoft/WindowsApps/python3.11.exe d:/Python/sympy1.py
1