Test Book



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import time
time.sleep(10)



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!gcc?









    



Object `gcc` not found.



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from ctypes import CDLL



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CDLL?



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dll = 'dylib'
libc = CDLL("libc.%s" % dll)



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libc?



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libc?



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message = 'The IPython notebook is great!'
# note: the echo command does not run on Windows, it's a unix command.
!echo $message









    



The IPython notebook is great!



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%load?



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%load http://matplotlib.sourceforge.net/mpl_examples/pylab_examples/integral_demo.py



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#!/usr/bin/env python

# implement the example graphs/integral from pyx
from pylab import *
from matplotlib.patches import Polygon

def func(x):
    return (x-3)*(x-5)*(x-7)+85

ax = subplot(111)

a, b = 2, 9 # integral area
x = arange(0, 10, 0.01)
y = func(x)
plot(x, y, linewidth=1)

# make the shaded region
ix = arange(a, b, 0.01)
iy = func(ix)
verts = [(a,0)] + list(zip(ix,iy)) + [(b,0)]
poly = Polygon(verts, facecolor='0.8', edgecolor='k')
ax.add_patch(poly)

text(0.5 * (a + b), 30,
     r"$\int_a^b f(x)\mathrm{d}x$", horizontalalignment='center',
     fontsize=20)

axis([0,10, 0, 180])
figtext(0.9, 0.05, 'x')
figtext(0.1, 0.9, 'y')
ax.set_xticks((a,b))
ax.set_xticklabels(('a','b'))
ax.set_yticks([])
show()









    



---------------------------------------------------------------------------
ImportError                               Traceback (most recent call last)
<ipython-input-20-766c9cf4d8d7> in <module>()
      2 
      3 # implement the example graphs/integral from pyx
----> 4 from pylab import *
      5 from matplotlib.patches import Polygon
      6 

ImportError: No module named pylab

What the hell!!

国家为了加强对房地产市场的宏观调控控制房价的过快上涨。（无用信息）
规定购买新房满五年后才可以上市转卖。（无用信息）
对二手房买卖征收差价的x%的附加税。（求解X）
某城市在不征收附加税时每年可成交十万套二手房。(已知常数：houses = 100000)
征收附加税后每年减少0.1x万套二手房交易。（newHouses = houses - 0.1x10000）
现已知每套二手房买卖的平均差价为10万元。(oneHouseProfit = 100000)
如果要是每年增收的附加税为16亿元，并且要使二手房市场保持一定的活力。(totalProfit = x/100 * newHouses * oneHouseProfit >= 1600000000)
每年二手房交易量不低于6万套。（newHouses >= 60000）
问。二手房交易附加税的税率应确定为多少？(Question: X = ?)

已知条件：
- 常数：
  - houses = 100000
  - oneHouseProfit = 100000
- 变量关系：
  - newHouses = houses - 0.1x10000
  - totalProfit = x/100 * newHouses * oneHouseProfit
- 限制条件：
  - totalProfit >= 1600000000
  - newHouses >= 60000
- 求解问题：
  - x=?



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x = 0
houses = 100000
oneHouseProfit = 100000
newHouses = houses - 0.1*x*10000
totalProfit = x/100*newHouses*oneHouseProfit

解题思路：
- 先考察x的范围：[0, 100]



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#x = 0
x = 0
houses = 100000
oneHouseProfit = 100000
newHouses = houses - 0.1*x*10000
totalProfit = x/100*newHouses*oneHouseProfit
print ("当税率为",x,"时：")
print ("可销售房屋数量为：", newHouses)
print ("税收为：", totalProfit)









    



当税率为 0 时：
可销售房屋数量为： 100000.0
税收为： 0.0



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#x = 100
x = 100
houses = 100000
oneHouseProfit = 100000
newHouses = houses - 0.1*x*10000
totalProfit = x/100*newHouses*oneHouseProfit
print ("当税率为",x,"时：")
print ("可销售房屋数量为：", newHouses)
print ("税收为：", totalProfit)









    



当税率为 100 时：
可销售房屋数量为： 0.0
税收为： 0.0

注意到销售数量和税收的关系，将其带入方程为：



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totalProfit = x/100 * (houses - 0.1*x*10000) * oneHouseProfit

原题转化为求解二次方程的极大值问题。

为了便于直观讲解，我们来画一下看看：



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fig, axes = subplots(1,2)
x = np.linspace(0,100,50)
totalProfit = x/100 * (houses - 0.1*x*10000) * oneHouseProfit

newHouses = houses - 0.1*x*10000

axes[0].plot(x, totalProfit)
axes[0].set_xlabel("X")
axes[0].set_ylabel("totalProfit")


axes[1].plot(x, newHouses)
axes[1].set_xlabel("x")
axes[1].set_ylabel("newHouses")
fig.tight_layout()
fig.show()

左图为税收随X的变化状况。右图为房屋销售数量的变化情况。

根据限制条件，则不难解出X的取值。
Done



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k = axes[0]



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%pylab inline









    



Populating the interactive namespace from numpy and matplotlib



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