Python 函数绘图及函数图像微分与积分

# Python 3.x
import turtle
from random import *
from math import *
from time import *

def draw():
  turtle.pencolor(random(), random(), random())
  global n, sf
  n = 0
  sf = 0
  while n > width / (-2 * zoom):
    f = evale(express, n)
    drawf(n, f)
    n -= (1 / zoom)
  n = 0
  sf = 0
  while n < width / (2 * zoom):
    f = evale(express, n)
    drawf(n, f)
    n += (1 / zoom)

def drawf(n, f):
  if n == 0 or isnan(f.real):
    turtle.penup()
  else:
    turtle.pendown()
  if isnan(f.real):
    f = 0
  elif n.imag != 0:
    f = abs(f)
  if hight / -zoom < f.real < hight / zoom:
    turtle.goto(n * zoom, f.real * zoom)

def drawxy():
  turtle.clear()
  turtle.pencolor(0, 0, 0)
  turtle.penup()
  turtle.goto(0, 0)
  turtle.pendown()
  turtle.goto(width / -2, 0)
  turtle.goto(width / 2, 0)
  turtle.goto(0, 0)
  turtle.goto(0, hight / 2)
  turtle.goto(0, hight / -2)

def format(s):
  s = s.replace("^","**")
  s = s.replace("@","differentiate")
  s = s.replace("$","integral")
  return s

def evale(s, n):
  x = n
  try:
    return eval(s)
  except BaseException:
    return nan

def differentiate(s):
  dx = 0.1 / zoom
  f1 = evale(s, n)
  df = evale(s, n + dx) - f1
  return df / dx

def integral(s):
  global sf
  dx = copysign(1 / zoom, n)
  f1 = evale(s, n)
  df = (f1 + evale(s, n + dx)) / 2
  sf = sf + df * dx
  return sf

def rezoom(n):
  global zoom
  zoom = n
  drawxy()
  draw()

zoom = eval(input("zoom = "))
width = 1280
hight = 720

turtle.setup(width, hight)
turtle.hideturtle()
turtle.delay(0)
turtle.pensize(2)
drawxy()

while True:
  express = format(input("f(x) = "))
  draw()

  while True:
    i = input(": ")
    if i == "break":
      break
    else:
      try:
        print(eval(i))
      except BaseException:
        print("Input error.")