sympy

基础

from sympy import *
# x,y = symbols('x,y')
x = Symbol('x')
y = Symbol('y')

print('>> limit极限')
print(limit(sin(x)/x,x,0))

print('>> diff微分')
print(diff(x**3,x))
#1.
print(diff(x**3,x,1))
print(diff(x**3,x,2))
print(diff(x**3,x,3))
#2.diff 和1.等价
print(diff(x**3,x))
print(diff(x**3,x,x))
print(diff(x**3,x,x,x))


print('>> ingegrate积分')
print(integrate(6,x))
print(integrate(6,x,x))
print(integrate(6,x,x,x))

print('>> ingegrate定积分')
print(integrate(x,(x,0,3)))


print('>> series级数展开')
s = exp(x).series(x,0,10)
# print(s)
pprint(s)


print('>> expand表达式展开')
expr = (sin(x + y)).expand(trig=True)
print(expr)
print('>> subs变量替换/求表达式的值')
print(expr.subs(x,pi/2))
print(expr.subs(y,pi))

print('>> factor提取公因式')
expr = x**2 + 2*x*y
pprint(factor(expr))


print('>> qsrt开平方根（以根号形式显示）')
pprint(sqrt(8))

print('>> Rational有理数(分子，分母)')
print(Rational(1,3))

print('>> latex打印公式')
l = latex(Integral(expr, (x, 0, pi)))
print(l)

print('>> factorial阶乘')
print(factorial(x))

print('>> 解方程 x**2-1=0')
ret = solve('x**2 - 1',x)
print(ret)


print('>> 矩阵运算')	# 可以带符号
M = Matrix(([1,2,3],[4,5,6],[7,8,9]))
N = Matrix(([1,x,0],[0,1,0],[0,0,1]))
pprint(M)
pprint(N)
pprint(M*N)

微风方程

# ----------------------------
# 1.0 学习一下sympy的使用
# 2.0 针对rc延时电路做了简单的分析
# 3.0 求解某函数式极限
# ----------------------------

# from sympy import *
from sympy import symbols,Function,dsolve
from sympy import pprint,limit,cos,pi

## print(dir(sympy))
r,c,t = symbols('r,c t')
f = Function('f')

s = r*c * f(t).diff(t) + f(t)
r = dsolve(s,f(t))
pprint(r)

print("")
r = r.expand(power_exp=True)
pprint(r)

#----------------------------------------------
## 这个图也太简陋了点吧。。
## 果然直接使用sympy没法看
## 还得matplotlib啊

# t = symbols('t')
# plot(exp(t),(t,-4,1))

#----------------------------------------------
r = limit(cos(t-pi/2)/t,t,0)
print(r)

input("请按任意键退出")

拉普拉斯变换

from sympy import *
t,x,y,s = symbols('t,x,y,s')
eq = 5*(1-exp(-t/1))
ret = solve(eq,[t])
print(ret)
# plot(eq,(t,0,5))
# ret = solve([0.7*exp(-t/0.2) + 5*(1-exp(-t/0.2))],[t])
# print(ret)
# ret = solve([x+2,y*2+1],[x,y])
# print(ret)
# ret = solve([x+2,y**2+1],[x,y])
# print(ret)

ret = laplace_transform(1,t,s)
print(ret)
ret = laplace_transform(t,t,s)
print(ret)
ret = laplace_transform(t**2,t,s)
print(ret)

r = limit(pow(1+1/x,x),x,oo)
print(r)
r = limit(pow(1+x,1/x),x,0)
pprint(r)