X7ROOT File Manager
Current Path:
/usr/share/doc/python3-docs/html/library
usr
/
share
/
doc
/
python3-docs
/
html
/
library
/
π
..
π
2to3.html
(60.26 KB)
π
__future__.html
(15.42 KB)
π
__main__.html
(8.81 KB)
π
_dummy_thread.html
(8.98 KB)
π
_thread.html
(22.06 KB)
π
abc.html
(40.42 KB)
π
aifc.html
(27.46 KB)
π
allos.html
(31.48 KB)
π
archiving.html
(11.71 KB)
π
argparse.html
(268.54 KB)
π
array.html
(32.76 KB)
π
ast.html
(38.67 KB)
π
asynchat.html
(31.78 KB)
π
asyncio-dev.html
(50.65 KB)
π
asyncio-eventloop.html
(108.61 KB)
π
asyncio-eventloops.html
(32.25 KB)
π
asyncio-protocol.html
(85.38 KB)
π
asyncio-queue.html
(23.4 KB)
π
asyncio-stream.html
(59.58 KB)
π
asyncio-subprocess.html
(56.66 KB)
π
asyncio-sync.html
(34.84 KB)
π
asyncio-task.html
(82 KB)
π
asyncio.html
(27.37 KB)
π
asyncore.html
(41.71 KB)
π
atexit.html
(18 KB)
π
audioop.html
(34.61 KB)
π
base64.html
(35.6 KB)
π
bdb.html
(42.41 KB)
π
binary.html
(12.42 KB)
π
binascii.html
(24.17 KB)
π
binhex.html
(11.4 KB)
π
bisect.html
(25 KB)
π
builtins.html
(11.33 KB)
π
bz2.html
(32.58 KB)
π
calendar.html
(38.61 KB)
π
cgi.html
(54.57 KB)
π
cgitb.html
(12.47 KB)
π
chunk.html
(16.48 KB)
π
cmath.html
(33.37 KB)
π
cmd.html
(42.78 KB)
π
code.html
(27.23 KB)
π
codecs.html
(130.93 KB)
π
codeop.html
(13.97 KB)
π
collections.abc.html
(59.48 KB)
π
collections.html
(151.31 KB)
π
colorsys.html
(12.33 KB)
π
compileall.html
(27.6 KB)
π
concurrency.html
(20.71 KB)
π
concurrent.futures.html
(59.24 KB)
π
concurrent.html
(7.77 KB)
π
configparser.html
(137.75 KB)
π
constants.html
(17.09 KB)
π
contextlib.html
(86.72 KB)
π
copy.html
(13.52 KB)
π
copyreg.html
(14.38 KB)
π
crypt.html
(19.85 KB)
π
crypto.html
(10.66 KB)
π
csv.html
(67.42 KB)
π
ctypes.html
(258.33 KB)
π
curses.ascii.html
(24.61 KB)
π
curses.html
(171.44 KB)
π
curses.panel.html
(16.31 KB)
π
custominterp.html
(8.53 KB)
π
datatypes.html
(23.39 KB)
π
datetime.html
(299.25 KB)
π
dbm.html
(42.11 KB)
π
debug.html
(13.66 KB)
π
decimal.html
(228.01 KB)
π
development.html
(24.53 KB)
π
difflib.html
(93.9 KB)
π
dis.html
(103.7 KB)
π
distribution.html
(10.26 KB)
π
distutils.html
(10.63 KB)
π
doctest.html
(175.54 KB)
π
dummy_threading.html
(9.1 KB)
π
email.charset.html
(25.81 KB)
π
email.compat32-message.html
(84.13 KB)
π
email.contentmanager.html
(29.32 KB)
π
email.encoders.html
(13.92 KB)
π
email.errors.html
(19.24 KB)
π
email.examples.html
(56.52 KB)
π
email.generator.html
(40.82 KB)
π
email.header.html
(30.49 KB)
π
email.headerregistry.html
(56.32 KB)
π
email.html
(27.09 KB)
π
email.iterators.html
(13.21 KB)
π
email.message.html
(85.17 KB)
π
email.mime.html
(35.24 KB)
π
email.parser.html
(46.32 KB)
π
email.policy.html
(73.48 KB)
π
email.util.html
(33.06 KB)
π
ensurepip.html
(18.26 KB)
π
enum.html
(130.81 KB)
π
errno.html
(40.36 KB)
π
exceptions.html
(83.16 KB)
π
faulthandler.html
(22.85 KB)
π
fcntl.html
(26.68 KB)
π
filecmp.html
(24.45 KB)
π
fileformats.html
(10.87 KB)
π
fileinput.html
(29.33 KB)
π
filesys.html
(13.1 KB)
π
fnmatch.html
(16.59 KB)
π
formatter.html
(36.78 KB)
π
fpectl.html
(17.13 KB)
π
fractions.html
(29.22 KB)
π
frameworks.html
(13.16 KB)
π
ftplib.html
(53.15 KB)
π
functional.html
(8.79 KB)
π
functions.html
(196.76 KB)
π
functools.html
(63.43 KB)
π
gc.html
(28.83 KB)
π
getopt.html
(24.76 KB)
π
getpass.html
(11.78 KB)
π
gettext.html
(74.84 KB)
π
glob.html
(18 KB)
π
grp.html
(12.09 KB)
π
gzip.html
(31.9 KB)
π
hashlib.html
(77.69 KB)
π
heapq.html
(34.7 KB)
π
hmac.html
(17.41 KB)
π
html.entities.html
(11.09 KB)
π
html.html
(10.85 KB)
π
html.parser.html
(40.86 KB)
π
http.client.html
(63.72 KB)
π
http.cookiejar.html
(93.94 KB)
π
http.cookies.html
(38.41 KB)
π
http.html
(36.72 KB)
π
http.server.html
(56.83 KB)
π
i18n.html
(10.22 KB)
π
idle.html
(47.28 KB)
π
imaplib.html
(65.76 KB)
π
imghdr.html
(13.14 KB)
π
imp.html
(47.02 KB)
π
importlib.html
(169.05 KB)
π
index.html
(66.18 KB)
π
inspect.html
(127.3 KB)
π
internet.html
(30.36 KB)
π
intro.html
(9.67 KB)
π
io.html
(119.81 KB)
π
ipaddress.html
(103.39 KB)
π
ipc.html
(32.95 KB)
π
itertools.html
(129.71 KB)
π
json.html
(79.18 KB)
π
keyword.html
(8.71 KB)
π
language.html
(13.33 KB)
π
linecache.html
(13.18 KB)
π
locale.html
(60.1 KB)
π
logging.config.html
(83.49 KB)
π
logging.handlers.html
(109.76 KB)
π
logging.html
(131.69 KB)
π
lzma.html
(55.16 KB)
π
macpath.html
(9.04 KB)
π
mailbox.html
(153.63 KB)
π
mailcap.html
(14.33 KB)
π
markup.html
(18.9 KB)
π
marshal.html
(17.89 KB)
π
math.html
(52.4 KB)
π
mimetypes.html
(30.67 KB)
π
misc.html
(7.93 KB)
π
mm.html
(9.79 KB)
π
mmap.html
(33.49 KB)
π
modulefinder.html
(18.12 KB)
π
modules.html
(10.66 KB)
π
msilib.html
(55.86 KB)
π
msvcrt.html
(21.47 KB)
π
multiprocessing.html
(356.92 KB)
π
netdata.html
(17.06 KB)
π
netrc.html
(14.23 KB)
π
nis.html
(11.39 KB)
π
nntplib.html
(67.97 KB)
π
numbers.html
(40.46 KB)
π
numeric.html
(15.17 KB)
π
operator.html
(79.55 KB)
π
optparse.html
(244.08 KB)
π
os.html
(388.71 KB)
π
os.path.html
(52.56 KB)
π
ossaudiodev.html
(46.82 KB)
π
othergui.html
(10.02 KB)
π
parser.html
(41.41 KB)
π
pathlib.html
(113.99 KB)
π
pdb.html
(51.43 KB)
π
persistence.html
(14.92 KB)
π
pickle.html
(112.36 KB)
π
pickletools.html
(16.69 KB)
π
pipes.html
(15.62 KB)
π
pkgutil.html
(31.13 KB)
π
platform.html
(32.94 KB)
π
plistlib.html
(28.6 KB)
π
poplib.html
(30.21 KB)
π
posix.html
(17.2 KB)
π
pprint.html
(40.99 KB)
π
profile.html
(70.16 KB)
π
pty.html
(17.18 KB)
π
pwd.html
(12.79 KB)
π
py_compile.html
(15.14 KB)
π
pyclbr.html
(16.13 KB)
π
pydoc.html
(15.62 KB)
π
pyexpat.html
(86.85 KB)
π
python.html
(16.73 KB)
π
queue.html
(27.54 KB)
π
quopri.html
(13.53 KB)
π
random.html
(59.22 KB)
π
re.html
(186.7 KB)
π
readline.html
(41.15 KB)
π
reprlib.html
(24.38 KB)
π
resource.html
(35.7 KB)
π
rlcompleter.html
(14.05 KB)
π
runpy.html
(25.98 KB)
π
sched.html
(19.56 KB)
π
secrets.html
(24.15 KB)
π
select.html
(61.35 KB)
π
selectors.html
(35 KB)
π
shelve.html
(28.1 KB)
π
shlex.html
(47.83 KB)
π
shutil.html
(72.47 KB)
π
signal.html
(53.77 KB)
π
site.html
(31.49 KB)
π
smtpd.html
(35.05 KB)
π
smtplib.html
(66.83 KB)
π
sndhdr.html
(12.15 KB)
π
socket.html
(191.48 KB)
π
socketserver.html
(80 KB)
π
spwd.html
(12.04 KB)
π
sqlite3.html
(158.08 KB)
π
ssl.html
(260.08 KB)
π
stat.html
(43.67 KB)
π
statistics.html
(48.88 KB)
π
stdtypes.html
(454.74 KB)
π
string.html
(93.03 KB)
π
stringprep.html
(18.22 KB)
π
struct.html
(49.9 KB)
π
subprocess.html
(138.6 KB)
π
sunau.html
(31.01 KB)
π
superseded.html
(13.46 KB)
π
symbol.html
(8.64 KB)
π
symtable.html
(25.5 KB)
π
sys.html
(138.35 KB)
π
sysconfig.html
(29.55 KB)
π
syslog.html
(20.53 KB)
π
tabnanny.html
(11.98 KB)
π
tarfile.html
(94.49 KB)
π
telnetlib.html
(29.7 KB)
π
tempfile.html
(40.42 KB)
π
termios.html
(17.75 KB)
π
test.html
(76.71 KB)
π
text.html
(13.46 KB)
π
textwrap.html
(37.11 KB)
π
threading.html
(101.04 KB)
π
time.html
(77.76 KB)
π
timeit.html
(44.19 KB)
π
tk.html
(22.75 KB)
π
tkinter.html
(80.99 KB)
π
tkinter.scrolledtext.html
(9.72 KB)
π
tkinter.tix.html
(50.64 KB)
π
tkinter.ttk.html
(108.08 KB)
π
token.html
(22.13 KB)
π
tokenize.html
(31.4 KB)
π
trace.html
(28.46 KB)
π
traceback.html
(56.24 KB)
π
tracemalloc.html
(98.77 KB)
π
tty.html
(10.29 KB)
π
turtle.html
(244.5 KB)
π
types.html
(36.19 KB)
π
typing.html
(135.91 KB)
π
undoc.html
(8.97 KB)
π
unicodedata.html
(20.61 KB)
π
unittest.html
(244.81 KB)
π
unittest.mock-examples.html
(164.2 KB)
π
unittest.mock.html
(293.06 KB)
π
unix.html
(11.5 KB)
π
urllib.error.html
(14.13 KB)
π
urllib.html
(9.34 KB)
π
urllib.parse.html
(74.54 KB)
π
urllib.request.html
(173.05 KB)
π
urllib.robotparser.html
(16.75 KB)
π
uu.html
(11.92 KB)
π
uuid.html
(31.21 KB)
π
venv.html
(72.18 KB)
π
warnings.html
(49.14 KB)
π
wave.html
(29.17 KB)
π
weakref.html
(63.76 KB)
π
webbrowser.html
(26.27 KB)
π
windows.html
(10.38 KB)
π
winreg.html
(65.17 KB)
π
winsound.html
(20.77 KB)
π
wsgiref.html
(92.28 KB)
π
xdrlib.html
(32.96 KB)
π
xml.dom.html
(95.28 KB)
π
xml.dom.minidom.html
(40.51 KB)
π
xml.dom.pulldom.html
(23.65 KB)
π
xml.etree.elementtree.html
(132.32 KB)
π
xml.html
(18.81 KB)
π
xml.sax.handler.html
(41.66 KB)
π
xml.sax.html
(24.92 KB)
π
xml.sax.reader.html
(44.79 KB)
π
xml.sax.utils.html
(16.53 KB)
π
xmlrpc.client.html
(70.26 KB)
π
xmlrpc.html
(8.33 KB)
π
xmlrpc.server.html
(48.04 KB)
π
zipapp.html
(44.05 KB)
π
zipfile.html
(78.16 KB)
π
zipimport.html
(22.51 KB)
π
zlib.html
(33.75 KB)
Editing: fractions.html
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"> <html xmlns="http://www.w3.org/1999/xhtml"> <head> <meta http-equiv="X-UA-Compatible" content="IE=Edge" /> <meta http-equiv="Content-Type" content="text/html; charset=utf-8" /> <title>9.5. fractions β Rational numbers — Python 3.6.7 documentation</title> <link rel="stylesheet" href="../_static/pydoctheme.css" type="text/css" /> <link rel="stylesheet" href="../_static/pygments.css" type="text/css" /> <script type="text/javascript" id="documentation_options" data-url_root="../" src="../_static/documentation_options.js"></script> <script type="text/javascript" src="../_static/jquery.js"></script> <script type="text/javascript" src="../_static/underscore.js"></script> <script type="text/javascript" src="../_static/doctools.js"></script> <script type="text/javascript" src="../_static/sidebar.js"></script> <link rel="search" type="application/opensearchdescription+xml" title="Search within Python 3.6.7 documentation" href="../_static/opensearch.xml"/> <link rel="author" title="About these documents" href="../about.html" /> <link rel="index" title="Index" href="../genindex.html" /> <link rel="search" title="Search" href="../search.html" /> <link rel="copyright" title="Copyright" href="../copyright.html" /> <link rel="next" title="9.6. random β Generate pseudo-random numbers" href="random.html" /> <link rel="prev" title="9.4. decimal β Decimal fixed point and floating point arithmetic" href="decimal.html" /> <link rel="shortcut icon" type="image/png" href="../_static/py.png" /> <link rel="canonical" href="https://docs.python.org/3/library/fractions.html" /> <script type="text/javascript" src="../_static/copybutton.js"></script> </head><body> <div class="related" role="navigation" aria-label="related navigation"> <h3>Navigation</h3> <ul> <li class="right" style="margin-right: 10px"> <a href="../genindex.html" title="General Index" accesskey="I">index</a></li> <li class="right" > <a href="../py-modindex.html" title="Python Module Index" >modules</a> |</li> <li class="right" > <a href="random.html" title="9.6. random β Generate pseudo-random numbers" accesskey="N">next</a> |</li> <li class="right" > <a href="decimal.html" title="9.4. decimal β Decimal fixed point and floating point arithmetic" accesskey="P">previous</a> |</li> <li><img src="../_static/py.png" alt="" style="vertical-align: middle; margin-top: -1px"/></li> <li><a href="https://www.python.org/">Python</a> »</li> <li> <a href="../index.html">3.6.7 Documentation</a> » </li> <li class="nav-item nav-item-1"><a href="index.html" >The Python Standard Library</a> »</li> <li class="nav-item nav-item-2"><a href="numeric.html" accesskey="U">9. Numeric and Mathematical Modules</a> »</li> <li class="right"> <div class="inline-search" style="display: none" role="search"> <form class="inline-search" action="../search.html" method="get"> <input placeholder="Quick search" type="text" name="q" /> <input type="submit" value="Go" /> <input type="hidden" name="check_keywords" value="yes" /> <input type="hidden" name="area" value="default" /> </form> </div> <script type="text/javascript">$('.inline-search').show(0);</script> | </li> </ul> </div> <div class="document"> <div class="documentwrapper"> <div class="bodywrapper"> <div class="body" role="main"> <div class="section" id="module-fractions"> <span id="fractions-rational-numbers"></span><h1>9.5. <a class="reference internal" href="#module-fractions" title="fractions: Rational numbers."><code class="xref py py-mod docutils literal notranslate"><span class="pre">fractions</span></code></a> β Rational numbers<a class="headerlink" href="#module-fractions" title="Permalink to this headline">ΒΆ</a></h1> <p><strong>Source code:</strong> <a class="reference external" href="https://github.com/python/cpython/tree/3.6/Lib/fractions.py">Lib/fractions.py</a></p> <hr class="docutils" /> <p>The <a class="reference internal" href="#module-fractions" title="fractions: Rational numbers."><code class="xref py py-mod docutils literal notranslate"><span class="pre">fractions</span></code></a> module provides support for rational number arithmetic.</p> <p>A Fraction instance can be constructed from a pair of integers, from another rational number, or from a string.</p> <dl class="class"> <dt id="fractions.Fraction"> <em class="property">class </em><code class="descclassname">fractions.</code><code class="descname">Fraction</code><span class="sig-paren">(</span><em>numerator=0</em>, <em>denominator=1</em><span class="sig-paren">)</span><a class="headerlink" href="#fractions.Fraction" title="Permalink to this definition">ΒΆ</a></dt> <dt> <em class="property">class </em><code class="descclassname">fractions.</code><code class="descname">Fraction</code><span class="sig-paren">(</span><em>other_fraction</em><span class="sig-paren">)</span></dt> <dt> <em class="property">class </em><code class="descclassname">fractions.</code><code class="descname">Fraction</code><span class="sig-paren">(</span><em>float</em><span class="sig-paren">)</span></dt> <dt> <em class="property">class </em><code class="descclassname">fractions.</code><code class="descname">Fraction</code><span class="sig-paren">(</span><em>decimal</em><span class="sig-paren">)</span></dt> <dt> <em class="property">class </em><code class="descclassname">fractions.</code><code class="descname">Fraction</code><span class="sig-paren">(</span><em>string</em><span class="sig-paren">)</span></dt> <dd><p>The first version requires that <em>numerator</em> and <em>denominator</em> are instances of <a class="reference internal" href="numbers.html#numbers.Rational" title="numbers.Rational"><code class="xref py py-class docutils literal notranslate"><span class="pre">numbers.Rational</span></code></a> and returns a new <a class="reference internal" href="#fractions.Fraction" title="fractions.Fraction"><code class="xref py py-class docutils literal notranslate"><span class="pre">Fraction</span></code></a> instance with value <code class="docutils literal notranslate"><span class="pre">numerator/denominator</span></code>. If <em>denominator</em> is <code class="xref py py-const docutils literal notranslate"><span class="pre">0</span></code>, it raises a <a class="reference internal" href="exceptions.html#ZeroDivisionError" title="ZeroDivisionError"><code class="xref py py-exc docutils literal notranslate"><span class="pre">ZeroDivisionError</span></code></a>. The second version requires that <em>other_fraction</em> is an instance of <a class="reference internal" href="numbers.html#numbers.Rational" title="numbers.Rational"><code class="xref py py-class docutils literal notranslate"><span class="pre">numbers.Rational</span></code></a> and returns a <a class="reference internal" href="#fractions.Fraction" title="fractions.Fraction"><code class="xref py py-class docutils literal notranslate"><span class="pre">Fraction</span></code></a> instance with the same value. The next two versions accept either a <a class="reference internal" href="functions.html#float" title="float"><code class="xref py py-class docutils literal notranslate"><span class="pre">float</span></code></a> or a <a class="reference internal" href="decimal.html#decimal.Decimal" title="decimal.Decimal"><code class="xref py py-class docutils literal notranslate"><span class="pre">decimal.Decimal</span></code></a> instance, and return a <a class="reference internal" href="#fractions.Fraction" title="fractions.Fraction"><code class="xref py py-class docutils literal notranslate"><span class="pre">Fraction</span></code></a> instance with exactly the same value. Note that due to the usual issues with binary floating-point (see <a class="reference internal" href="../tutorial/floatingpoint.html#tut-fp-issues"><span class="std std-ref">Floating Point Arithmetic: Issues and Limitations</span></a>), the argument to <code class="docutils literal notranslate"><span class="pre">Fraction(1.1)</span></code> is not exactly equal to 11/10, and so <code class="docutils literal notranslate"><span class="pre">Fraction(1.1)</span></code> does <em>not</em> return <code class="docutils literal notranslate"><span class="pre">Fraction(11,</span> <span class="pre">10)</span></code> as one might expect. (But see the documentation for the <a class="reference internal" href="#fractions.Fraction.limit_denominator" title="fractions.Fraction.limit_denominator"><code class="xref py py-meth docutils literal notranslate"><span class="pre">limit_denominator()</span></code></a> method below.) The last version of the constructor expects a string or unicode instance. The usual form for this instance is:</p> <div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="n">sign</span><span class="p">]</span> <span class="n">numerator</span> <span class="p">[</span><span class="s1">'/'</span> <span class="n">denominator</span><span class="p">]</span> </pre></div> </div> <p>where the optional <code class="docutils literal notranslate"><span class="pre">sign</span></code> may be either β+β or β-β and <code class="docutils literal notranslate"><span class="pre">numerator</span></code> and <code class="docutils literal notranslate"><span class="pre">denominator</span></code> (if present) are strings of decimal digits. In addition, any string that represents a finite value and is accepted by the <a class="reference internal" href="functions.html#float" title="float"><code class="xref py py-class docutils literal notranslate"><span class="pre">float</span></code></a> constructor is also accepted by the <a class="reference internal" href="#fractions.Fraction" title="fractions.Fraction"><code class="xref py py-class docutils literal notranslate"><span class="pre">Fraction</span></code></a> constructor. In either form the input string may also have leading and/or trailing whitespace. Here are some examples:</p> <div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span> <span class="nn">fractions</span> <span class="k">import</span> <span class="n">Fraction</span> <span class="gp">>>> </span><span class="n">Fraction</span><span class="p">(</span><span class="mi">16</span><span class="p">,</span> <span class="o">-</span><span class="mi">10</span><span class="p">)</span> <span class="go">Fraction(-8, 5)</span> <span class="gp">>>> </span><span class="n">Fraction</span><span class="p">(</span><span class="mi">123</span><span class="p">)</span> <span class="go">Fraction(123, 1)</span> <span class="gp">>>> </span><span class="n">Fraction</span><span class="p">()</span> <span class="go">Fraction(0, 1)</span> <span class="gp">>>> </span><span class="n">Fraction</span><span class="p">(</span><span class="s1">'3/7'</span><span class="p">)</span> <span class="go">Fraction(3, 7)</span> <span class="gp">>>> </span><span class="n">Fraction</span><span class="p">(</span><span class="s1">' -3/7 '</span><span class="p">)</span> <span class="go">Fraction(-3, 7)</span> <span class="gp">>>> </span><span class="n">Fraction</span><span class="p">(</span><span class="s1">'1.414213 </span><span class="se">\t\n</span><span class="s1">'</span><span class="p">)</span> <span class="go">Fraction(1414213, 1000000)</span> <span class="gp">>>> </span><span class="n">Fraction</span><span class="p">(</span><span class="s1">'-.125'</span><span class="p">)</span> <span class="go">Fraction(-1, 8)</span> <span class="gp">>>> </span><span class="n">Fraction</span><span class="p">(</span><span class="s1">'7e-6'</span><span class="p">)</span> <span class="go">Fraction(7, 1000000)</span> <span class="gp">>>> </span><span class="n">Fraction</span><span class="p">(</span><span class="mf">2.25</span><span class="p">)</span> <span class="go">Fraction(9, 4)</span> <span class="gp">>>> </span><span class="n">Fraction</span><span class="p">(</span><span class="mf">1.1</span><span class="p">)</span> <span class="go">Fraction(2476979795053773, 2251799813685248)</span> <span class="gp">>>> </span><span class="kn">from</span> <span class="nn">decimal</span> <span class="k">import</span> <span class="n">Decimal</span> <span class="gp">>>> </span><span class="n">Fraction</span><span class="p">(</span><span class="n">Decimal</span><span class="p">(</span><span class="s1">'1.1'</span><span class="p">))</span> <span class="go">Fraction(11, 10)</span> </pre></div> </div> <p>The <a class="reference internal" href="#fractions.Fraction" title="fractions.Fraction"><code class="xref py py-class docutils literal notranslate"><span class="pre">Fraction</span></code></a> class inherits from the abstract base class <a class="reference internal" href="numbers.html#numbers.Rational" title="numbers.Rational"><code class="xref py py-class docutils literal notranslate"><span class="pre">numbers.Rational</span></code></a>, and implements all of the methods and operations from that class. <a class="reference internal" href="#fractions.Fraction" title="fractions.Fraction"><code class="xref py py-class docutils literal notranslate"><span class="pre">Fraction</span></code></a> instances are hashable, and should be treated as immutable. In addition, <a class="reference internal" href="#fractions.Fraction" title="fractions.Fraction"><code class="xref py py-class docutils literal notranslate"><span class="pre">Fraction</span></code></a> has the following properties and methods:</p> <div class="versionchanged"> <p><span class="versionmodified">Changed in version 3.2: </span>The <a class="reference internal" href="#fractions.Fraction" title="fractions.Fraction"><code class="xref py py-class docutils literal notranslate"><span class="pre">Fraction</span></code></a> constructor now accepts <a class="reference internal" href="functions.html#float" title="float"><code class="xref py py-class docutils literal notranslate"><span class="pre">float</span></code></a> and <a class="reference internal" href="decimal.html#decimal.Decimal" title="decimal.Decimal"><code class="xref py py-class docutils literal notranslate"><span class="pre">decimal.Decimal</span></code></a> instances.</p> </div> <dl class="attribute"> <dt id="fractions.Fraction.numerator"> <code class="descname">numerator</code><a class="headerlink" href="#fractions.Fraction.numerator" title="Permalink to this definition">ΒΆ</a></dt> <dd><p>Numerator of the Fraction in lowest term.</p> </dd></dl> <dl class="attribute"> <dt id="fractions.Fraction.denominator"> <code class="descname">denominator</code><a class="headerlink" href="#fractions.Fraction.denominator" title="Permalink to this definition">ΒΆ</a></dt> <dd><p>Denominator of the Fraction in lowest term.</p> </dd></dl> <dl class="method"> <dt id="fractions.Fraction.from_float"> <code class="descname">from_float</code><span class="sig-paren">(</span><em>flt</em><span class="sig-paren">)</span><a class="headerlink" href="#fractions.Fraction.from_float" title="Permalink to this definition">ΒΆ</a></dt> <dd><p>This class method constructs a <a class="reference internal" href="#fractions.Fraction" title="fractions.Fraction"><code class="xref py py-class docutils literal notranslate"><span class="pre">Fraction</span></code></a> representing the exact value of <em>flt</em>, which must be a <a class="reference internal" href="functions.html#float" title="float"><code class="xref py py-class docutils literal notranslate"><span class="pre">float</span></code></a>. Beware that <code class="docutils literal notranslate"><span class="pre">Fraction.from_float(0.3)</span></code> is not the same value as <code class="docutils literal notranslate"><span class="pre">Fraction(3,</span> <span class="pre">10)</span></code>.</p> <div class="admonition note"> <p class="first admonition-title">Note</p> <p class="last">From Python 3.2 onwards, you can also construct a <a class="reference internal" href="#fractions.Fraction" title="fractions.Fraction"><code class="xref py py-class docutils literal notranslate"><span class="pre">Fraction</span></code></a> instance directly from a <a class="reference internal" href="functions.html#float" title="float"><code class="xref py py-class docutils literal notranslate"><span class="pre">float</span></code></a>.</p> </div> </dd></dl> <dl class="method"> <dt id="fractions.Fraction.from_decimal"> <code class="descname">from_decimal</code><span class="sig-paren">(</span><em>dec</em><span class="sig-paren">)</span><a class="headerlink" href="#fractions.Fraction.from_decimal" title="Permalink to this definition">ΒΆ</a></dt> <dd><p>This class method constructs a <a class="reference internal" href="#fractions.Fraction" title="fractions.Fraction"><code class="xref py py-class docutils literal notranslate"><span class="pre">Fraction</span></code></a> representing the exact value of <em>dec</em>, which must be a <a class="reference internal" href="decimal.html#decimal.Decimal" title="decimal.Decimal"><code class="xref py py-class docutils literal notranslate"><span class="pre">decimal.Decimal</span></code></a> instance.</p> <div class="admonition note"> <p class="first admonition-title">Note</p> <p class="last">From Python 3.2 onwards, you can also construct a <a class="reference internal" href="#fractions.Fraction" title="fractions.Fraction"><code class="xref py py-class docutils literal notranslate"><span class="pre">Fraction</span></code></a> instance directly from a <a class="reference internal" href="decimal.html#decimal.Decimal" title="decimal.Decimal"><code class="xref py py-class docutils literal notranslate"><span class="pre">decimal.Decimal</span></code></a> instance.</p> </div> </dd></dl> <dl class="method"> <dt id="fractions.Fraction.limit_denominator"> <code class="descname">limit_denominator</code><span class="sig-paren">(</span><em>max_denominator=1000000</em><span class="sig-paren">)</span><a class="headerlink" href="#fractions.Fraction.limit_denominator" title="Permalink to this definition">ΒΆ</a></dt> <dd><p>Finds and returns the closest <a class="reference internal" href="#fractions.Fraction" title="fractions.Fraction"><code class="xref py py-class docutils literal notranslate"><span class="pre">Fraction</span></code></a> to <code class="docutils literal notranslate"><span class="pre">self</span></code> that has denominator at most max_denominator. This method is useful for finding rational approximations to a given floating-point number:</p> <div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span> <span class="nn">fractions</span> <span class="k">import</span> <span class="n">Fraction</span> <span class="gp">>>> </span><span class="n">Fraction</span><span class="p">(</span><span class="s1">'3.1415926535897932'</span><span class="p">)</span><span class="o">.</span><span class="n">limit_denominator</span><span class="p">(</span><span class="mi">1000</span><span class="p">)</span> <span class="go">Fraction(355, 113)</span> </pre></div> </div> <p>or for recovering a rational number thatβs represented as a float:</p> <div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span> <span class="nn">math</span> <span class="k">import</span> <span class="n">pi</span><span class="p">,</span> <span class="n">cos</span> <span class="gp">>>> </span><span class="n">Fraction</span><span class="p">(</span><span class="n">cos</span><span class="p">(</span><span class="n">pi</span><span class="o">/</span><span class="mi">3</span><span class="p">))</span> <span class="go">Fraction(4503599627370497, 9007199254740992)</span> <span class="gp">>>> </span><span class="n">Fraction</span><span class="p">(</span><span class="n">cos</span><span class="p">(</span><span class="n">pi</span><span class="o">/</span><span class="mi">3</span><span class="p">))</span><span class="o">.</span><span class="n">limit_denominator</span><span class="p">()</span> <span class="go">Fraction(1, 2)</span> <span class="gp">>>> </span><span class="n">Fraction</span><span class="p">(</span><span class="mf">1.1</span><span class="p">)</span><span class="o">.</span><span class="n">limit_denominator</span><span class="p">()</span> <span class="go">Fraction(11, 10)</span> </pre></div> </div> </dd></dl> <dl class="method"> <dt id="fractions.Fraction.__floor__"> <code class="descname">__floor__</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#fractions.Fraction.__floor__" title="Permalink to this definition">ΒΆ</a></dt> <dd><p>Returns the greatest <a class="reference internal" href="functions.html#int" title="int"><code class="xref py py-class docutils literal notranslate"><span class="pre">int</span></code></a> <code class="docutils literal notranslate"><span class="pre"><=</span> <span class="pre">self</span></code>. This method can also be accessed through the <a class="reference internal" href="math.html#math.floor" title="math.floor"><code class="xref py py-func docutils literal notranslate"><span class="pre">math.floor()</span></code></a> function:</p> <div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span> <span class="nn">math</span> <span class="k">import</span> <span class="n">floor</span> <span class="gp">>>> </span><span class="n">floor</span><span class="p">(</span><span class="n">Fraction</span><span class="p">(</span><span class="mi">355</span><span class="p">,</span> <span class="mi">113</span><span class="p">))</span> <span class="go">3</span> </pre></div> </div> </dd></dl> <dl class="method"> <dt id="fractions.Fraction.__ceil__"> <code class="descname">__ceil__</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#fractions.Fraction.__ceil__" title="Permalink to this definition">ΒΆ</a></dt> <dd><p>Returns the least <a class="reference internal" href="functions.html#int" title="int"><code class="xref py py-class docutils literal notranslate"><span class="pre">int</span></code></a> <code class="docutils literal notranslate"><span class="pre">>=</span> <span class="pre">self</span></code>. This method can also be accessed through the <a class="reference internal" href="math.html#math.ceil" title="math.ceil"><code class="xref py py-func docutils literal notranslate"><span class="pre">math.ceil()</span></code></a> function.</p> </dd></dl> <dl class="method"> <dt id="fractions.Fraction.__round__"> <code class="descname">__round__</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#fractions.Fraction.__round__" title="Permalink to this definition">ΒΆ</a></dt> <dt> <code class="descname">__round__</code><span class="sig-paren">(</span><em>ndigits</em><span class="sig-paren">)</span></dt> <dd><p>The first version returns the nearest <a class="reference internal" href="functions.html#int" title="int"><code class="xref py py-class docutils literal notranslate"><span class="pre">int</span></code></a> to <code class="docutils literal notranslate"><span class="pre">self</span></code>, rounding half to even. The second version rounds <code class="docutils literal notranslate"><span class="pre">self</span></code> to the nearest multiple of <code class="docutils literal notranslate"><span class="pre">Fraction(1,</span> <span class="pre">10**ndigits)</span></code> (logically, if <code class="docutils literal notranslate"><span class="pre">ndigits</span></code> is negative), again rounding half toward even. This method can also be accessed through the <a class="reference internal" href="functions.html#round" title="round"><code class="xref py py-func docutils literal notranslate"><span class="pre">round()</span></code></a> function.</p> </dd></dl> </dd></dl> <dl class="function"> <dt id="fractions.gcd"> <code class="descclassname">fractions.</code><code class="descname">gcd</code><span class="sig-paren">(</span><em>a</em>, <em>b</em><span class="sig-paren">)</span><a class="headerlink" href="#fractions.gcd" title="Permalink to this definition">ΒΆ</a></dt> <dd><p>Return the greatest common divisor of the integers <em>a</em> and <em>b</em>. If either <em>a</em> or <em>b</em> is nonzero, then the absolute value of <code class="docutils literal notranslate"><span class="pre">gcd(a,</span> <span class="pre">b)</span></code> is the largest integer that divides both <em>a</em> and <em>b</em>. <code class="docutils literal notranslate"><span class="pre">gcd(a,b)</span></code> has the same sign as <em>b</em> if <em>b</em> is nonzero; otherwise it takes the sign of <em>a</em>. <code class="docutils literal notranslate"><span class="pre">gcd(0,</span> <span class="pre">0)</span></code> returns <code class="docutils literal notranslate"><span class="pre">0</span></code>.</p> <div class="deprecated"> <p><span class="versionmodified">Deprecated since version 3.5: </span>Use <a class="reference internal" href="math.html#math.gcd" title="math.gcd"><code class="xref py py-func docutils literal notranslate"><span class="pre">math.gcd()</span></code></a> instead.</p> </div> </dd></dl> <div class="admonition seealso"> <p class="first admonition-title">See also</p> <dl class="last docutils"> <dt>Module <a class="reference internal" href="numbers.html#module-numbers" title="numbers: Numeric abstract base classes (Complex, Real, Integral, etc.)."><code class="xref py py-mod docutils literal notranslate"><span class="pre">numbers</span></code></a></dt> <dd>The abstract base classes making up the numeric tower.</dd> </dl> </div> </div> </div> </div> </div> <div class="sphinxsidebar" role="navigation" aria-label="main navigation"> <div class="sphinxsidebarwrapper"> <h4>Previous topic</h4> <p class="topless"><a href="decimal.html" title="previous chapter">9.4. <code class="docutils literal notranslate"><span class="pre">decimal</span></code> β Decimal fixed point and floating point arithmetic</a></p> <h4>Next topic</h4> <p class="topless"><a href="random.html" title="next chapter">9.6. <code class="docutils literal notranslate"><span class="pre">random</span></code> β Generate pseudo-random numbers</a></p> <div role="note" aria-label="source link"> <h3>This Page</h3> <ul class="this-page-menu"> <li><a href="../bugs.html">Report a Bug</a></li> <li> <a href="https://github.com/python/cpython/blob/3.6/Doc/library/fractions.rst" rel="nofollow">Show Source </a> </li> </ul> </div> </div> </div> <div class="clearer"></div> </div> <div class="related" role="navigation" aria-label="related navigation"> <h3>Navigation</h3> <ul> <li class="right" style="margin-right: 10px"> <a href="../genindex.html" title="General Index" >index</a></li> <li class="right" > <a href="../py-modindex.html" title="Python Module Index" >modules</a> |</li> <li class="right" > <a href="random.html" title="9.6. random β Generate pseudo-random numbers" >next</a> |</li> <li class="right" > <a href="decimal.html" title="9.4. decimal β Decimal fixed point and floating point arithmetic" >previous</a> |</li> <li><img src="../_static/py.png" alt="" style="vertical-align: middle; margin-top: -1px"/></li> <li><a href="https://www.python.org/">Python</a> »</li> <li> <a href="../index.html">3.6.7 Documentation</a> » </li> <li class="nav-item nav-item-1"><a href="index.html" >The Python Standard Library</a> »</li> <li class="nav-item nav-item-2"><a href="numeric.html" >9. Numeric and Mathematical Modules</a> »</li> <li class="right"> <div class="inline-search" style="display: none" role="search"> <form class="inline-search" action="../search.html" method="get"> <input placeholder="Quick search" type="text" name="q" /> <input type="submit" value="Go" /> <input type="hidden" name="check_keywords" value="yes" /> <input type="hidden" name="area" value="default" /> </form> </div> <script type="text/javascript">$('.inline-search').show(0);</script> | </li> </ul> </div> <div class="footer"> © <a href="../copyright.html">Copyright</a> 2001-2023, Python Software Foundation. <br /> The Python Software Foundation is a non-profit corporation. <a href="https://www.python.org/psf/donations/">Please donate.</a> <br /> Last updated on Dec 18, 2023. <a href="../bugs.html">Found a bug</a>? <br /> Created using <a href="http://sphinx.pocoo.org/">Sphinx</a> 1.7.6. </div> </body> </html>
Upload File
Create Folder