sage/text/sageを使ってみよう (竹本氏）¶
Demo of the Ipython notebook at Sage Paris group meeting, 6 Mar, 2014¶
IPython's Rich Display System¶
Made by Y.Sato, 16 Oct, 2014¶
In [1]:
%load_ext sage
In [2]:
a = 1/2 + 1/3
a
Out[2]:
5/6
In [3]:
# view(a) view に相当するものは？
In [4]:
from IPython.display import display, Math
def my_show(obj): return display(Math(latex(obj)))
#y = 1 / (x^2+1)
my_show(a)
$$\frac{5}{6}$$
多項式¶
In [5]:
x = var('x')
# f = x^3 -x^2 - 2*x
f = x**3 -x**2 - 2*x
#view(f)
f
Out[5]:
x^3 - x^2 - 2*x
In [6]:
my_show(f)
$$x^{3} - x^{2} - 2 \, x$$
In [7]:
factor(f)
Out[7]:
(x + 1)*(x - 2)*x
多項式のグラフ¶
In [8]:
from IPython.display import display, Image
In [9]:
plot(f, -2.5, 2.5, figsize=4).save("fig.png")
In [10]:
display(Image('fig.png'))
関数の極¶
In [11]:
df = diff(f, x); df
Out[11]:
3*x^2 - 2*x - 2
In [12]:
my_show(df)
$$3 \, x^{2} - 2 \, x - 2$$
関数の解¶
In [13]:
sol = solve(df, x); sol
Out[13]:
[x == -1/3*sqrt(7) + 1/3, x == 1/3*sqrt(7) + 1/3]
In [14]:
my_show(sol)
$$\left[x = -\frac{1}{3} \, \sqrt{7} + \frac{1}{3}, x = \frac{1}{3} \, \sqrt{7} + \frac{1}{3}\right]$$
In [15]:
plot(df, [x,-2.5,2.5], figsize=4).save('fig.png')
In [16]:
display(Image('fig.png'))
数値解¶
In [17]:
print find_root(df, -2, 0), find_root(df, 0, 2)
-0.548583770355 1.21525043702
In [ ]:
Demo of the Ipython notebook at Sage Paris group meeting, 6 Mar, 2014¶
Use latex in a markdown cell¶
Test $\alpha+\beta+\gamma$
Output in latex¶
In [18]:
from IPython.display import display, Math
def my_show(obj): return display(Math(latex(obj)))
y = 1 / (x^2+1)
my_show(y)
$$\frac{1}{x^{2} + 1}$$
In [19]:
#from IPython.display import Math
Math(r'F(k) = \int_{-\infty}^{\infty} f(x) e^{2\pi i k} dx')
Out[19]:
$$F(k) = \int_{-\infty}^{\infty} f(x) e^{2\pi i k} dx$$
Inline Matplotlib graphics¶
In [20]:
%matplotlib inline
import matplotlib.pyplot as plt
import numpy as np
x = np.linspace(0, 3*np.pi, 500)
plt.plot(x, np.sin(x**2))
plt.title('A simple chirp');
Sage 3D Graphics¶
In [21]:
sphere().save('fig3D.png')
In [22]:
#display(Image('fig3D.png'))
In [23]:
import os
os.system('convert -resize 350x fig3D.png fig3Ds.png')
display(Image('fig3Ds.png'))
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