from __future__ import division, print_function  # Python 3

from math import sqrt
sqrt(3)

from sympy import sqrt
sqrt(3)

sqrt(4)

sqrt(8)

from sympy import Symbol
a = Symbol("a")     # le symbole a est stocké dans la variable a
a

a + a + a + a * a + 1/a - a

from sympy.abc import a, epsilon
a + a * a + epsilon

from sympy import symbols
x4,x5,x6,x7,x8 = symbols("x4:9")
x4 + x5 + x6 + x7 + x8

from sympy import init_printing
init_printing(use_latex='mathjax')

from sympy.abc import a, epsilon
a + a * a + epsilon

from sympy.abc import a,b
(a + b)**2

from sympy import sin,cos
sin(a)**2 + cos(a)**2 + b

from sympy import Rational,pi,exp,I
from sympy.abc import x,y
Rational(3,2)*pi + exp(I*x) / (x**2 + y)

from sympy import srepr
expr = x - y
srepr(x - y)

from sympy.printing.dot import dotprint
s = dotprint(expr)

from sympy.abc import a,b,c
expression = a + 2*b + 3*c
expression.subs(a,9)

expression.subs({a:9, b:4})

expression.subs({a:9, b:4, c:100})

from sympy import log
from sympy.abc import x,y,z
expression.subs({a:x**2, b:log(y), c:z})

from sympy import pi
pi

from sympy import sin, pi
sin(pi/3)

from sympy import asin, Rational
asin(1)

asin(Rational(1,2))

from sympy.abc import x
sin(asin(x))

from sympy.abc import 
from math import sin
sin(x)

from sympy import sin,cos
from sympy.abc import a
r = sin(a)**2 + cos(a)**2
r

from sympy import simplify
simplify(r)

simplify((x**3 + x**2 - x - 1)/(x**2 + 2*x + 1))

from sympy import expand
from sympy.abc import a,b
(a + b)**2

expand((a + b)**2)

(a + b)**2 - (a - b)**2

expand(_)

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

from sympy import cancel
cancel(expr)

from sympy import factor
factor(x**3 - x**2 + x - 1)

factor(x**3 - x**2 + x - 1, gaussian=True)

factor(x**2 - 5)

factor(x**2 - 5, extension=sqrt(5))

expr = x*z + x**2 + x + x*y + x**2 * w + 5 - x**3
expr

from sympy import collect
collect(expr, x)

from sympy.abc import x,y,z
1/(x+1) + 1/y + 1/z

from sympy import ratsimp
ratsimp(1/(x+1) + 1/y + 1/z)

from sympy import together
together(1/(x+1) + 1/y + 1/z)

expr = (3*x**2  + 52*x - 265) / ((x - 7)*(x - 1)*(x + 34))
expr

from sympy import apart
apart(expr)

A = 1 / (1+sqrt(5))
A

from sympy import radsimp
radsimp(A)