#!/usr/bin/env python
# coding: utf-8

# # Table of Contents
#  <p><div class="lev1 toc-item"><a href="#連立方程式" data-toc-modified-id="連立方程式-1"><span class="toc-item-num">1&nbsp;&nbsp;</span>連立方程式</a></div><div class="lev1 toc-item"><a href="#展開(expand)-因数分解(factor)" data-toc-modified-id="展開(expand)-因数分解(factor)-2"><span class="toc-item-num">2&nbsp;&nbsp;</span>展開(expand) 因数分解(factor)</a></div><div class="lev1 toc-item"><a href="#3点を通る２次方程式" data-toc-modified-id="3点を通る２次方程式-3"><span class="toc-item-num">3&nbsp;&nbsp;</span>3点を通る２次方程式</a></div>

# In[3]:


from sympy import Symbol, pprint
a = 3
b = 2
pprint(a+b)


# In[7]:


x = Symbol('x')
eq1 = a*x+b
pprint(eq1)


# In[8]:


from sympy import solve
solve(eq1, x)


# # 連立方程式
# 

# In[9]:


from sympy import Matrix, solve_linear_system
from sympy.abc import x, y

system = Matrix(( (1, 4, 2), (-2, 1, 14)))
solve_linear_system(system, x, y)


# # 展開(expand) 因数分解(factor)

# In[13]:


from sympy import *
pprint(expand((x+y)**2))


# In[15]:


pprint(factor(x**3 - x**2 + x - 1))


# # 3点を通る２次方程式
# 3点(1,2),(-3,4),(-1,1)を通る２次方程式を求めよ．

# In[33]:


from sympy import *
f, x, a, b, c = symbols('f x a b c')
f = a*x**2 + b*x + c


# In[34]:


print(f)


# In[35]:


class my_func(Function):
    @classmethod
    def eval(cls, x):
        return a*x**2 + b*x + c


# In[36]:


pprint(my_func(x))


# In[37]:


eq1 = my_func(1)
eq2 = my_func(-3)
eq3 = my_func(-1)


# In[38]:


pprint(eq1)
pprint(eq2)
pprint(eq3)


# In[40]:


from sympy.abc import a, b, c

system = Matrix(( (1, 1, 1, 2), (9, -3, 1, 4),
(1, -1, 1, 1)))
s1 = solve_linear_system(system, a, b, c)


# In[42]:


pprint(s1)


# In[48]:


pprint(s1[a])
pprint(s1[b])
pprint(s1[c])


# In[52]:


from sympy import sin
eq = sin(x+1) - x**2


# In[54]:


solve(eq, x)


# In[ ]: