r"""
This file was *autogenerated* from sagetex.tex with sagetex.sty
version 2015/08/26 v3.0-92d9f7a. It contains the contents of all the
sageexample environments from sagetex.tex. You should be able to
doctest this file with "sage -t sagetex_doctest.sage".
It is always safe to delete this file; it is not used in typesetting your
document.
Sage example, line 426::
sage: 2+2
4
sage: print 'middle'
middle
sage: factor(x^2 + 2*x + 1)
(x + 1)^2
Sage example, line 448::
sage: print 'middle'
middle
Sage example, line 455::
sage: is_prime(57)
toothpaste
Sage example, line 463::
sage: gcd([5656565656,
....: 4747474747,
....: 123456789])
1
sage: mystr = '''my
....: string
....: has
....: several
....: lines.'''
sage: len(mystr)
28
sage: def f(a):
....: '''This function is really quite nice,
....: although perhaps not very useful.'''
....: print "f called with a = ", a
....: y = integrate(SR(cyclotomic_polynomial(10)) + a, x)
....: return y + 1
sage: f(x)
f called with a = x
1/5*x^5 - 1/4*x^4 + 1/3*x^3 + x + 1
Sage example, line 512::
sage: 1; 2; a=4; 3; a
1
2
3
4
Sage example, line 521::
sage: f(a)
f called with a = 4
1/5*x^5 - 1/4*x^4 + 1/3*x^3 - 1/2*x^2 + 5*x + 1
Sage commandline, line 622::
sage: 1+1
sage: is_prime(57)
sage: if is_prime(57):
....: print 'prime'
....: else:
....: print 'composite'
Sage commandline, line 639::
sage: x = 2010; len(x.divisors())
sage: print 'Hola, mundo!'
Sage commandline, line 651::
sage: l = matrix([[1,0,0],[3/5,1,0],[-2/5,-2,1]])
sage: d = diagonal_matrix([15, -1, 4]) #@\label{diagonal}
sage: u = matrix([[1,0,1/3],[0,1,2],[0,0,1]]) #@\label{anotherlabel} \# foo
sage: l*d*u # this is a comment
Sage commandline, line 667::
sage: l*d*u
sage: x = var('x')
sage: (1-cos(x)^2).trig_simplify()
Sage commandline, line 683::
sage: pi.n(100)
Sage commandline, line 693::
sage: plot(sin(x), (x, 0, 2*pi))
Sage commandline, line 709::
sage: factor(x^2 + 2*x + 1)
(x + 999)^2
"""