from sympy import *

3 + math.sqrt(3)

expr = 3 * sqrt(3)
expr

init_printing(use_latex='mathjax')

expr

expr = sqrt(8)
expr

x, y = symbols("x y")

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

expr = (x+y)**3
expr

a = Symbol("a")

a.is_imaginary

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

b.is_imaginary

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

c.is_positive

c.is_imaginary

I

I ** 2

Rational(1,3)

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

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

N(pi, 100)

pi.evalf(100)

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

expr.subs(x, 1)

expr = pi * x**2
expr

expr.subs(x, 3)

N(_)

expr = (x + y) ** 2
expr

expand(expr)

factor(_)

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

simplify(expr)

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

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

simplify(expr)

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

apart(expr)

together(_)

diff(sin(x), x)

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

integrate(cos(x), x)

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

N(_)

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

expr.doit()

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

expr.doit()

expr = 2*x + 1
solve(expr)

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

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

from sympy.physics import units as u

5. * u.milligram

1./2 * u.inch

1. * u.nano

u.watt

u.ohm

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

N(mph / kmph)

80 * N(mph / kmph)

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

sympy_expr(3)

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

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

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

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

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

lf = lambdify(x, expr)

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

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();