{{{id=1|
ZZ
///
Integer Ring
}}}

{{{id=2|
QQ
///
Rational Field
}}}

{{{id=3|
RR
///
Real Field with 53 bits of precision
}}}

{{{id=4|
CC
///
Complex Field with 53 bits of precision
}}}

{{{id=10|
QQbar
///
Algebraic Field
}}}

{{{id=36|
a = ZZ(3)
print a
print type(a)
///
3
<type 'sage.rings.integer.Integer'>
}}}

{{{id=35|
b = RR(5)
print b
type(b)
///
5.00000000000000
<type 'sage.rings.real_mpfr.RealNumber'>
}}}

{{{id=34|
c = QQ(4/5)
print c
print type(c)
///
4/5
<type 'sage.rings.rational.Rational'>
}}}

{{{id=32|
d = CC(4/5)
print d
print type(d)
///
0.800000000000000
<type 'sage.rings.complex_number.ComplexNumber'>
}}}

{{{id=39|
RR(sqrt(2))
///
1.41421356237310
}}}

{{{id=38|
a = QQbar(sqrt(2))
print a
print type(a)
///
1.414213562373095?
<class 'sage.rings.qqbar.AlgebraicNumber'>
}}}

{{{id=37|
a.minpoly()
///
x^2 - 2
}}}

{{{id=5|
Integers(24)
///
Ring of integers modulo 24
}}}

{{{id=6|
GF(11)
///
Finite Field of size 11
}}}

{{{id=27|
FiniteField(11)
///
Finite Field of size 11
}}}

{{{id=7|
GF(16)
///
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "_sage_input_12.py", line 10, in <module>
    exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 -*-\\n" + _support_.preparse_worksheet_cell(base64.b64decode("R0YoMTYp"),globals())+"\\n"); execfile(os.path.abspath("___code___.py"))' + '\n', '', 'single')
  File "", line 1, in <module>
    
  File "/tmp/tmpkjEdT8/___code___.py", line 3, in <module>
    exec compile(u'GF(_sage_const_16 )' + '\n', '', 'single')
  File "", line 1, in <module>
    
  File "factory.pyx", line 110, in sage.structure.factory.UniqueFactory.__call__ (sage/structure/factory.c:943)
  File "factory.pyx", line 138, in sage.structure.factory.UniqueFactory.get_object (sage/structure/factory.c:1146)
  File "/usr/local/sage-4.7.2-linux-64bit-ubuntu_10.04.3_lts-x86_64-Linux/local/lib/python2.6/site-packages/sage/rings/finite_rings/constructor.py", line 431, in create_object
    raise TypeError, "you must specify the generator name"
TypeError: you must specify the generator name
}}}

{{{id=8|
GF(16, 'a')
///
Finite Field in a of size 2^4
}}}

{{{id=9|
PolynomialRing(QQ, 'y', 3)
///
Multivariate Polynomial Ring in y0, y1, y2 over Rational Field
}}}

{{{id=11|
PolynomialRing(GF(101), x)
///
Univariate Polynomial Ring in x over Finite Field of size 101
}}}

{{{id=13|
##
///
}}}

{{{id=14|
T1.<x> = PolynomialRing(QQ)
///
}}}

{{{id=15|
f = x^2-1
///
}}}

{{{id=28|
f.factor()
///
(x - 1) * (x + 1)
}}}

{{{id=16|
f.factor()
///
(x - 1) * (x + 1)
}}}

{{{id=17|
T2.<x> = PolynomialRing(RR)
///
}}}

{{{id=18|
f = x^3-x-1
///
}}}

{{{id=29|

///
}}}

{{{id=19|
f.factor()
///
(x - 1.32471795724475) * (x^2 + 1.32471795724475*x + 0.754877666246693)
}}}

{{{id=20|
T3.<x> = PolynomialRing(CC)
///
}}}

{{{id=21|
f = x^3-x-1
///
}}}

{{{id=22|
f.factor()
///
(x - 1.32471795724475) * (x + 0.662358978622373 - 0.562279512062301*I) * (x + 0.662358978622373 + 0.562279512062301*I)
}}}

{{{id=23|
T4.<y> = PolynomialRing(GF(128, 'a'))
///
}}}

{{{id=24|
K.<a> = GF(128, 'a')
///
}}}

{{{id=25|
T4.<y> = PolynomialRing(K)
///
}}}

{{{id=26|
f = y^20-a
///
}}}

{{{id=30|
f.factor()
///
(y + a^4 + a^3 + 1)^4 * (y^4 + (a^4 + a^3 + 1)*y^3 + (a^6 + a^2 + a + 1)*y^2 + (a^4 + a^3 + a + 1)*y + a^6 + a^5 + a^4 + a^2 + 1)^4
}}}

{{{id=31|

///
}}}