In [1]: 
import sympy
In [2]: 
x = sympy.Symbol('x')
In [3]: 
x
Out[3]:
x
In [4]: 
x + x
Out[4]:
2*x
In [5]: 
x ** 2
Out[5]:
x**2
In [6]: 
y 

---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
<ipython-input-6-a29c36ce3331> in <module>()
----> 1 y

NameError: name 'y' is not defined
In [7]: 
y + y

---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
<ipython-input-7-cb09bc56781f> in <module>()
----> 1 y + y

NameError: name 'y' is not defined
In [8]: 
from sympy.abc import y, z
In [9]: 
(x + y)**2
Out[9]:
(x + y)**2
In [10]: 
sympy.expand((x + y)**2)
Out[10]:
x**2 + 2*x*y + y**2
In [11]: 
sympy.init_printing()
In [12]: 
sympy.expand((x + y)**2)
Out[12]:
$$x^{2} + 2 x y + y^{2}$$
In [13]: 
t = (x + y)**2
In [14]: 
t
Out[14]:
$$\left(x + y\right)^{2}$$
In [15]: 
sympy.printing.latex(t)
Out[15]:
'\\left(x + y\\right)^{2}'
In [16]: 
t
Out[16]:
$$\left(x + y\right)^{2}$$
In [17]: 
t.subs(x, 3)
Out[17]:
$$\left(y + 3\right)^{2}$$
In [20]: 
v = t.subs(x, 3).subs(y, sympy.pi)
In [21]: 
v
Out[21]:
$$\left(3 + \pi\right)^{2}$$
In [22]: 
v.evalf()
Out[22]:
$$37.7191603226281$$
In [23]: 
v.evalf(20)
Out[23]:
$$37.71916032262811805$$
In [24]: 
sympy.pi.evalf(100)
Out[24]:
$$3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117068$$
In [25]: 
from sympy import limit, sin, oo
In [26]: 
oo
Out[26]:
$$\infty$$
In [27]: 
limit(1/x, x, 50)
Out[27]:
$$\frac{1}{50}$$
In [28]: 
limit(1/x, x, oo)
Out[28]:
$$0$$
In [29]: 
limit(sin(x) / x, x, 0)
Out[29]:
$$1$$
In [30]: 
from sympy import series
In [31]: 
series(sin(x), x, 0)
Out[31]:
$$x - \frac{x^{3}}{6} + \frac{x^{5}}{120} + \mathcal{O}\left(x^{6}\right)$$
In [32]: 
series(sin(x) / x, x, 0)
Out[32]:
$$1 - \frac{x^{2}}{6} + \frac{x^{4}}{120} + \mathcal{O}\left(x^{6}\right)$$
In [33]: 
from sympy import integrate
In [34]: 
from sympy.abc import a, b
In [37]: 
integrate(2*x, (x, 0.1, b))
Out[37]:
$$b^{2} - 0.01$$
In [36]: 
integrate(2*x, x)
Out[36]:
$$x^{2}$$
In [39]: 
r = (x + 2) * (x - 3)
In [40]: 
sympy.solve(r, x)
Out[40]:
$$\begin{bmatrix}-2, & 3\end{bmatrix}$$
In []: