4.3.1.1 RealField Objects

class RealField
The field of real numbers.
RealField( )

sage: R = RealField_mpf(); R
Multi-precision Real Field
sage: R('1/3')
0.333333333333333333333

Note that the second argument is the number of *bits* of precision, not the number of digits of precision:

sage: R('1/3',100)
0.3333333333333333333333333333333333333333
sage: R('1/3',200)
0.3333333333333333333333333333333333333333333333333333333333333
33333333

If we create a real without quotes, we loose precision, because the real is turned into a Python float:

sage: R(0.333333333333333333333)
0.33333333333333331483

We can also coerce rational numbers and integers into R, but coercing a polynomial in raising an exception.

sage: Q = RationalField()
sage: R(Q('1/3'))
0.333333333333333333333
sage: S = PolynomialRing(Q)
sage: R(S.gen())
Traceback (most recent call last):
...
TypeError: unable to coerce x to a RealNumber_mpf
sage: R.is_field()
True
sage: R.characteristic()
0
sage: R.name()
'R'
sage: R == R
True
sage: R == 5
False

Instances of class RealField have the following methods (in addition to inherited methods and special methods):

characteristic,$  $ euler_constant,$  $ is_atomic_repr,$  $ is_field,$  $ name,$  $ pi

These methods are defined as follows:

characteristic( )

Returns the characteristic of the real field, which is 0.

euler_constant( [n=0])

Returns Euler's constant gamma = 0.57721566... = lim 1 + 1/2 + 1/3 + 1/4 + 1/5 + ... + 1/m - log m. to at most 219 decimal digits of precision.

IMPLEMENTATION: PARI C library.

sage: RealField_mpf().euler_constant()
0.577215664901532865549

is_atomic_repr( )

is_field( )

Returns True, since the real field is a field.

name( )

Returns a short string 'R' that describes the real field.

pi( [n=0])

Returns pi to (at least) the given precision.

sage: RealField().pi(3)
3.14

Instances of class RealField also have the following special methods:

__call__( x, [prec=0])

__cmp__( other)

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