import sympy

a = sympy.Rational(5, 3)
a **= 60
print(a)

x = sympy.Symbol('x')
y = sympy.Symbol('y')
p = y + y * 2 * y * y
print(p)

sympy.plotting.plot(p, (y, -3, 3))
print(p * sympy.sqrt(p))
p = (x + x * y) / x
p = sympy.sin(x)**2 + sympy.cos(x)**2
p = sympy.cos(sympy.pi / 3 - x)
print(p, "=", sympy.simplify(p))

p = (x + 5) ** 7
print(p.subs(x, 10))
print(p.subs(x, x**2))
q = sympy.expand(p)
print(q)
print(sympy.factor(6 * x ** 2 + 5 * x + 1))
print(sympy.factor(sympy.log(x) ** 2 - x ** 2))
print(sympy.sqrt(x) + x ** sympy.Rational(1/2))
print(sympy.factor(sympy.expand((x + 1) * (x + 0.3))), "BUG")
print(sympy.limit(sympy.sin(x * y) / x, x, 0))
print(sympy.limit(1 / x, x, 0, dir="-"))
p = sympy.sin(x)**2 + sympy.cos(x)**2
q = sympy.cos(x)**2 + sympy.sin(x)**2
print(p == q)
print(sympy.diff(sympy.tan(x) ** 2))
print(sympy.series(sympy.cos(x), n=9))
p = sympy.integrate(x ** 2 + 1)
p = sympy.integrate(1 / x ** 2, (x, 5, sympy.oo))
p = sympy.integrate(sympy.exp(-x**2), (x, -sympy.oo, sympy.oo))
p = sympy.integrate(sympy.exp(sympy.tan(x)), (x, 3, 4))
print(p)