In [1]:

    

from sympy import *


    

In [2]:

    

3 + math.sqrt(3)


    

    
Out[2]:





4.732050807568877

In [3]:

    

expr = 3 * sqrt(3)
expr


    

    
Out[3]:





3*sqrt(3)

In [4]:

    

init_printing(use_latex='mathjax')


    

In [5]:

    

expr


    

    
Out[5]:





$$3 \sqrt{3}$$

In [6]:

    

expr = sqrt(8)
expr


    

    
Out[6]:





$$2 \sqrt{2}$$

In [7]:

    

x, y = symbols("x y")


    

In [8]:

    

expr = x**2 + y**2
expr


    

    
Out[8]:





$$x^{2} + y^{2}$$

In [9]:

    

expr = (x+y)**3
expr


    

    
Out[9]:





$$\left(x + y\right)^{3}$$

In [10]:

    

a = Symbol("a")


    

In [11]:

    

a.is_imaginary


    

In [12]:

    

b = Symbol("b", integer=True)


    

In [13]:

    

b.is_imaginary


    

    
Out[13]:





False

In [14]:

    

c = Symbol("c", positive=True)


    

In [15]:

    

c.is_positive


    

    
Out[15]:





True

In [16]:

    

c.is_imaginary


    

    
Out[16]:





False

In [17]:

    

I


    

    
Out[17]:





$$i$$

In [18]:

    

I ** 2


    

    
Out[18]:





$$-1$$

In [19]:

    

Rational(1,3)


    

    
Out[19]:





$$\frac{1}{3}$$

In [20]:

    

Rational(1,3) + Rational(1,2)


    

    
Out[20]:





$$\frac{5}{6}$$

In [21]:

    

expr = Rational(1,3) + Rational(1,2)
N(expr)


    

    
Out[21]:





$$0.833333333333333$$

In [22]:

    

N(pi, 100)


    

    
Out[22]:





$$3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117068$$

In [23]:

    

pi.evalf(100)


    

    
Out[23]:





$$3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117068$$

In [24]:

    

expr = x**2 + 2*x + 1
expr


    

    
Out[24]:





$$x^{2} + 2 x + 1$$

In [25]:

    

expr.subs(x, 1)


    

    
Out[25]:





$$4$$

In [26]:

    

expr = pi * x**2
expr


    

    
Out[26]:





$$\pi x^{2}$$

In [27]:

    

expr.subs(x, 3)


    

    
Out[27]:





$$9 \pi$$

In [28]:

    

N(_)


    

    
Out[28]:





$$28.2743338823081$$

In [29]:

    

expr = (x + y) ** 2
expr


    

    
Out[29]:





$$\left(x + y\right)^{2}$$

In [30]:

    

expand(expr)


    

    
Out[30]:





$$x^{2} + 2 x y + y^{2}$$

In [31]:

    

factor(_)


    

    
Out[31]:





$$\left(x + y\right)^{2}$$

In [32]:

    

expr = (2*x + Rational(1,3)*x + 4) / x
expr


    

    
Out[32]:





$$\frac{1}{x} \left(\frac{7 x}{3} + 4\right)$$

In [33]:

    

simplify(expr)


    

    
Out[33]:





$$\frac{7}{3} + \frac{4}{x}$$

In [34]:

    

expr = "(2*x + 1/3*x + 4)/x"
simplify(expr)


    

    
Out[34]:





$$\frac{7}{3} + \frac{4}{x}$$

In [35]:

    

expr = sin(x)/cos(x)
expr


    

    
Out[35]:





$$\frac{\sin{\left (x \right )}}{\cos{\left (x \right )}}$$

In [36]:

    

simplify(expr)


    

    
Out[36]:





$$\tan{\left (x \right )}$$

In [37]:

    

expr = 1/(x**2 + 2*x)
expr


    

    
Out[37]:





$$\frac{1}{x^{2} + 2 x}$$

In [38]:

    

apart(expr)


    

    
Out[38]:





$$- \frac{1}{2 x + 4} + \frac{1}{2 x}$$

In [39]:

    

together(_)


    

    
Out[39]:





$$\frac{1}{x \left(x + 2\right)}$$

In [40]:

    

diff(sin(x), x)


    

    
Out[40]:





$$\cos{\left (x \right )}$$

In [41]:

    

diff(log(x**2 + 1) + 2*x, x)


    

    
Out[41]:





$$\frac{2 x}{x^{2} + 1} + 2$$

In [42]:

    

integrate(cos(x), x)


    

    
Out[42]:





$$\sin{\left (x \right )}$$

In [43]:

    

Integral(sin(x), (x,0,pi))


    

    
Out[43]:





$$\int_{0}^{\pi} \sin{\left (x \right )}\, dx$$

In [44]:

    

N(_)


    

    
Out[44]:





$$2.0$$

In [45]:

    

expr = Sum(1/(x**2 + 2*x), (x, 1, 10))
expr


    

    
Out[45]:





$$\sum_{x=1}^{10} \frac{1}{x^{2} + 2 x}$$

In [46]:

    

expr.doit()


    

    
Out[46]:





$$\frac{175}{264}$$

In [47]:

    

expr = Product(1/(x**2 + 2*x), (x, 1, 10))
expr


    

    
Out[47]:





$$\prod_{x=1}^{10} \frac{1}{x^{2} + 2 x}$$

In [48]:

    

expr.doit()


    

    
Out[48]:





$$\frac{1}{869100503040000}$$

In [49]:

    

expr = 2*x + 1
solve(expr)


    

    
Out[49]:





$$\begin{bmatrix}- \frac{1}{2}\end{bmatrix}$$

In [50]:

    

expr = x**2 - 1
solve(expr)


    

    
Out[50]:





$$\begin{bmatrix}-1, & 1\end{bmatrix}$$

In [51]:

    

expr_1 = 2*x + y + 3
expr_2 = 2*y - x
solve([expr_1, expr_2],(x,y))


    

    
Out[51]:





$$\begin{Bmatrix}x : - \frac{6}{5}, & y : - \frac{3}{5}\end{Bmatrix}$$

In [52]:

    

from sympy.physics import units as u


    

In [53]:

    

5. * u.milligram


    

    
Out[53]:





$$5.0 \cdot 10^{-6} kg$$

In [54]:

    

1./2 * u.inch


    

    
Out[54]:





$$0.0127 m$$

In [55]:

    

1. * u.nano


    

    
Out[55]:





$$1.0 \cdot 10^{-9}$$

In [56]:

    

u.watt


    

    
Out[56]:





$$\frac{kg m^{2}}{s^{3}}$$

In [57]:

    

u.ohm


    

    
Out[57]:





$$\frac{kg m^{2}}{A^{2} s^{3}}$$

In [58]:

    

kmph = u.km / u.hour
mph = u.mile / u.hour

N(mph / kmph)


    

    
Out[58]:





$$1.609344$$

In [69]:

    

80 * N(mph / kmph)


    

    
Out[69]:





$$128.74752$$

In [59]:

    

def sympy_expr(x_val):
    expr = x**2 + sqrt(3)*x - Rational(1,3)
    return expr.subs(x, x_val)


    

In [60]:

    

sympy_expr(3)


    

    
Out[60]:





$$3 \sqrt{3} + \frac{26}{3}$$

In [61]:

    

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt


    

In [62]:

    

list1 = np.arange(1,1000)
list2 = pd.Series(list1)


    

In [63]:

    

%timeit [sympy_expr(item) for item in list1]
%timeit [sympy_expr(item) for item in list2]


    

    




1 loops, best of 3: 103 ms per loop
10 loops, best of 3: 105 ms per loop

In [64]:

    

%timeit np.vectorize(sympy_expr)(list1)
%timeit list2.apply(sympy_expr)


    

    




10 loops, best of 3: 776 ms per loop
1 loops, best of 3: 1.09 s per loop

In [65]:

    

expr = x**2 + sqrt(3)*x - Rational(1,3)

lf = lambdify(x, expr)


    

In [66]:

    

%timeit lf(list1)
%timeit lf(list2)


    

    




1000 loops, best of 3: 242 µs per loop
100 loops, best of 3: 4.8 ms per loop

In [67]:

    

fig = plt.figure()
axes = fig.add_subplot(111)

x_vals = np.linspace(-5.,5.)
y_vals = lf(x_vals)

axes.grid()
axes.plot(x_vals, y_vals)

plt.show();