notebooks/python-1.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Calculator\n",
    "\n",
    "You can use Python as a calculator. Operators are similar to C or Fortran."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "3 + 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "3 * 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "3 ** 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "3 - 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Older versions of python perform integer division for / operator. Latest version does float division. To force integer division, use // operator. Make sure either numerator or denominator is a float to ask for float division."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "a = 3 // 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.5"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "3.0 / 2.0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "int"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(a)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can import a module to start using all the features of that module. The math module is important to offer you the features of a scientific calculator."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "import math"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using the function dir, you can inspect the methods and the data offered by any object or module. You can use it at any depth of the object heirarchy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['__doc__',\n",
       " '__file__',\n",
       " '__loader__',\n",
       " '__name__',\n",
       " '__package__',\n",
       " '__spec__',\n",
       " 'acos',\n",
       " 'acosh',\n",
       " 'asin',\n",
       " 'asinh',\n",
       " 'atan',\n",
       " 'atan2',\n",
       " 'atanh',\n",
       " 'ceil',\n",
       " 'copysign',\n",
       " 'cos',\n",
       " 'cosh',\n",
       " 'degrees',\n",
       " 'e',\n",
       " 'erf',\n",
       " 'erfc',\n",
       " 'exp',\n",
       " 'expm1',\n",
       " 'fabs',\n",
       " 'factorial',\n",
       " 'floor',\n",
       " 'fmod',\n",
       " 'frexp',\n",
       " 'fsum',\n",
       " 'gamma',\n",
       " 'gcd',\n",
       " 'hypot',\n",
       " 'inf',\n",
       " 'isclose',\n",
       " 'isfinite',\n",
       " 'isinf',\n",
       " 'isnan',\n",
       " 'ldexp',\n",
       " 'lgamma',\n",
       " 'log',\n",
       " 'log10',\n",
       " 'log1p',\n",
       " 'log2',\n",
       " 'modf',\n",
       " 'nan',\n",
       " 'pi',\n",
       " 'pow',\n",
       " 'radians',\n",
       " 'remainder',\n",
       " 'sin',\n",
       " 'sinh',\n",
       " 'sqrt',\n",
       " 'tan',\n",
       " 'tanh',\n",
       " 'tau',\n",
       " 'trunc']"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dir(math)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8414709848078965"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "math.sin(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.141592653589793"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "math.pi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "float"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(math.pi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.718281828459045"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "math.e"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The module sys has information about the limits of the system representation of data types."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "import sys"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['__breakpointhook__',\n",
       " '__displayhook__',\n",
       " '__doc__',\n",
       " '__excepthook__',\n",
       " '__interactivehook__',\n",
       " '__loader__',\n",
       " '__name__',\n",
       " '__package__',\n",
       " '__spec__',\n",
       " '__stderr__',\n",
       " '__stdin__',\n",
       " '__stdout__',\n",
       " '_clear_type_cache',\n",
       " '_current_frames',\n",
       " '_debugmallocstats',\n",
       " '_framework',\n",
       " '_getframe',\n",
       " '_git',\n",
       " '_home',\n",
       " '_xoptions',\n",
       " 'abiflags',\n",
       " 'api_version',\n",
       " 'argv',\n",
       " 'base_exec_prefix',\n",
       " 'base_prefix',\n",
       " 'breakpointhook',\n",
       " 'builtin_module_names',\n",
       " 'byteorder',\n",
       " 'call_tracing',\n",
       " 'callstats',\n",
       " 'copyright',\n",
       " 'displayhook',\n",
       " 'dont_write_bytecode',\n",
       " 'exc_info',\n",
       " 'excepthook',\n",
       " 'exec_prefix',\n",
       " 'executable',\n",
       " 'exit',\n",
       " 'flags',\n",
       " 'float_info',\n",
       " 'float_repr_style',\n",
       " 'get_asyncgen_hooks',\n",
       " 'get_coroutine_origin_tracking_depth',\n",
       " 'get_coroutine_wrapper',\n",
       " 'getallocatedblocks',\n",
       " 'getcheckinterval',\n",
       " 'getdefaultencoding',\n",
       " 'getdlopenflags',\n",
       " 'getfilesystemencodeerrors',\n",
       " 'getfilesystemencoding',\n",
       " 'getprofile',\n",
       " 'getrecursionlimit',\n",
       " 'getrefcount',\n",
       " 'getsizeof',\n",
       " 'getswitchinterval',\n",
       " 'gettrace',\n",
       " 'hash_info',\n",
       " 'hexversion',\n",
       " 'implementation',\n",
       " 'int_info',\n",
       " 'intern',\n",
       " 'is_finalizing',\n",
       " 'maxsize',\n",
       " 'maxunicode',\n",
       " 'meta_path',\n",
       " 'modules',\n",
       " 'path',\n",
       " 'path_hooks',\n",
       " 'path_importer_cache',\n",
       " 'platform',\n",
       " 'prefix',\n",
       " 'ps1',\n",
       " 'ps2',\n",
       " 'ps3',\n",
       " 'set_asyncgen_hooks',\n",
       " 'set_coroutine_origin_tracking_depth',\n",
       " 'set_coroutine_wrapper',\n",
       " 'setcheckinterval',\n",
       " 'setdlopenflags',\n",
       " 'setprofile',\n",
       " 'setrecursionlimit',\n",
       " 'setswitchinterval',\n",
       " 'settrace',\n",
       " 'stderr',\n",
       " 'stdin',\n",
       " 'stdout',\n",
       " 'thread_info',\n",
       " 'version',\n",
       " 'version_info',\n",
       " 'warnoptions']"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dir(sys)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Use the help function to ask for help on any module or a method or data under it. You can also use it to ask for names of modules that you can import."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Please wait a moment while I gather a list of all available modules...\n",
      "\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/SageMath/sage-9.0/local/lib/python3.7/site-packages/IPython/kernel/__init__.py:13: ShimWarning: The `IPython.kernel` package has been deprecated since IPython 4.0.You should import from ipykernel or jupyter_client instead.\n",
      "  \"You should import from ipykernel or jupyter_client instead.\", ShimWarning)\n",
      "/opt/SageMath/sage-9.0/local/lib/python3.7/site-packages/nbconvert/exporters/exporter_locator.py:28: DeprecationWarning: `nbconvert.exporters.exporter_locator` is deprecated in favor of `nbconvert.exporters.base` since nbconvert 5.0.\n",
      "  DeprecationWarning)\n",
      "/opt/SageMath/sage-9.0/local/lib/python3.7/site-packages/rpy2/ipython/rmagic.py:65: UserWarning: The Python package 'pandas' is stronglyrecommended when using `rpy2.ipython`. Unfortunately it could not be loaded, but at least we found 'numpy'.\n",
      "  warnings.warn(' '.join((\"The Python package 'pandas' is strongly\"\n",
      "/opt/SageMath/sage-9.0/local/lib/python3.7/site-packages/sphinx/websupport/__init__.py:25: RemovedInSphinx20Warning: sphinx.websupport module is now provided as sphinxcontrib-websupport. sphinx.websupport will be removed at Sphinx-2.0. Please use the package instead.\n",
      "  RemovedInSphinx20Warning)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cython              bisect              jsonschema          secrets\n",
      "IPython             bleach              jupyter             select\n",
      "PIL                 brial               jupyter_client      selectors\n",
      "__future__          builtins            jupyter_core        send2trash\n",
      "_abc                bz2                 keyword             setuptools\n",
      "_ast                cProfile            kiwisolver          setuptools_scm\n",
      "_asyncio            calendar            lib2to3             shelve\n",
      "_bisect             certifi             libfuturize         shlex\n",
      "_blake2             cgi                 libpasteurize       shutil\n",
      "_bootlocale         cgitb               linecache           signal\n",
      "_bz2                chunk               locale              simplegeneric\n",
      "_codecs             cmath               logging             singledispatch\n",
      "_codecs_cn          cmd                 lzma                singledispatch_helpers\n",
      "_codecs_hk          code                macpath             site\n",
      "_codecs_iso2022     codecs              mailbox             six\n",
      "_codecs_jp          codeop              mailcap             smtpd\n",
      "_codecs_kr          collections         markupsafe          smtplib\n",
      "_codecs_tw          colorsys            marshal             sndhdr\n",
      "_collections        compileall          math                snowballstemmer\n",
      "_collections_abc    concurrent          matplotlib          socket\n",
      "_compat_pickle      configparser        mimetypes           socketserver\n",
      "_compression        contextlib          mistune             speaklater\n",
      "_contextvars        contextvars         mmap                sphinx\n",
      "_crypt              copy                modulefinder        spwd\n",
      "_csv                copyreg             mpmath              sqlite3\n",
      "_ctypes             crypt               multiprocessing     sre_compile\n",
      "_ctypes_test        csv                 nbconvert           sre_constants\n",
      "_curses             ctypes              nbformat            sre_parse\n",
      "_curses_panel       curses              netrc               ssl\n",
      "_datetime           cvxopt              networkx            stat\n",
      "_decimal            cycler              nis                 statistics\n",
      "_dummy_thread       cypari2             nntplib             storemagic\n",
      "_elementtree        cysignals           nose                string\n",
      "_functools          cython              notebook            stringprep\n",
      "_hashlib            cythonmagic         ntpath              struct\n",
      "_heapq              dataclasses         nturl2path          subprocess\n",
      "_imp                datetime            numbers             sunau\n",
      "_io                 dateutil            numpy               surface3d_demo\n",
      "_json               dbm                 opcode              symbol\n",
      "_locale             decimal             openid              sympy\n",
      "_lsprof             decorator           operator            sympyprinting\n",
      "_lzma               defusedxml          optparse            symtable\n",
      "_markupbase         difflib             os                  sys\n",
      "_md5                dis                 ossaudiodev         sysconfig\n",
      "_multibytecodec     distutils           packaging           syslog\n",
      "_multiprocessing    doctest             pandocfilters       tabnanny\n",
      "_opcode             docutils            parser              tarfile\n",
      "_operator           dummy_threading     past                telnetlib\n",
      "_osx_support        easy_install        path                tempfile\n",
      "_pickle             email               pathlib             terminado\n",
      "_posixsubprocess    encodings           pathlib2            termios\n",
      "_py_abc             ensurepip           pdb                 test\n",
      "_pydecimal          entrypoints         pexpect             test_path\n",
      "_pyio               enum                pickle              testpath\n",
      "_queue              errno               pickleshare         tests\n",
      "_random             faulthandler        pickletools         textwrap\n",
      "_scandir            fcntl               pip                 this\n",
      "_sha1               filecmp             pipes               threading\n",
      "_sha256             fileinput           pkg_resources       time\n",
      "_sha3               flask               pkgconfig           timeit\n",
      "_sha512             flask_autoindex     pkgutil             tkinter\n",
      "_signal             flask_babel         platform            token\n",
      "_sitebuiltins       flask_oldsessions   plistlib            tokenize\n",
      "_socket             flask_openid        poplib              tornado\n",
      "_sqlite3            flask_silk          posix               trace\n",
      "_sre                fnmatch             posixpath           traceback\n",
      "_ssl                formatter           ppl                 tracemalloc\n",
      "_stat               fpylll              pprint              traitlets\n",
      "_string             fractions           profile             trisurf3d_demo\n",
      "_strptime           ftplib              prometheus_client   tty\n",
      "_struct             functools           prompt_toolkit      turtle\n",
      "_symtable           future              pstats              turtledemo\n",
      "_sysconfigdata_m_linux_x86_64-linux-gnu gc                  psutil              twisted\n",
      "_testbuffer         genericpath         pty                 types\n",
      "_testcapi           getopt              ptyprocess          typing\n",
      "_testimportmultiple getpass             pwd                 unicodedata\n",
      "_testmultiphase     gettext             py_compile          unittest\n",
      "_thread             glob                pyclbr              urllib\n",
      "_threading_local    gmpy2               pydoc               uu\n",
      "_tkinter            grp                 pydoc_data          uuid\n",
      "_tracemalloc        gzip                pyexpat             vcversioner\n",
      "_warnings           hashlib             pygments            venv\n",
      "_weakref            heapq               pylab               warnings\n",
      "_weakrefset         hmac                pyparsing           wave\n",
      "_xxtestfuzz         html                pytz                wcwidth\n",
      "abc                 html5lib            pyximport           weakref\n",
      "aifc                http                queue               webbrowser\n",
      "alabaster           idlelib             quopri              webencodings\n",
      "antigravity         imagesize           random              werkzeug\n",
      "argparse            imaplib             re                  widgetsnbextension\n",
      "array               imghdr              readline            wire3d_demo\n",
      "ast                 imp                 reprlib             wsgiref\n",
      "asynchat            importlib           requests            xdrlib\n",
      "asyncio             inspect             resource            xml\n",
      "asyncore            io                  rlcompleter         xmlrpc\n",
      "atexit              ipaddress           rmagic              xxlimited\n",
      "audioop             ipykernel           rpy2                xxsubtype\n",
      "autoreload          ipykernel_launcher  runpy               zipapp\n",
      "babel               ipython_genutils    sage                zipfile\n",
      "backports           ipywidgets          sage_setup          zipimport\n",
      "backports_abc       isympy              sagenb_export       zlib\n",
      "base64              itertools           sagetex             zmq\n",
      "bdb                 itsdangerous        scandir             \n",
      "binascii            jinja2              sched               \n",
      "binhex              json                scipy               \n",
      "\n",
      "Enter any module name to get more help.  Or, type \"modules spam\" to search\n",
      "for modules whose name or summary contain the string \"spam\".\n",
      "\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/SageMath/sage-9.0/local/lib/python3.7/pkgutil.py:107: VisibleDeprecationWarning: zmq.eventloop.minitornado is deprecated in pyzmq 14.0 and will be removed.\n",
      "    Install tornado itself to use zmq with the tornado IOLoop.\n",
      "    \n",
      "  yield from walk_packages(path, info.name+'.', onerror)\n"
     ]
    }
   ],
   "source": [
    "help('modules')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "import sys"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['__add__',\n",
       " '__class__',\n",
       " '__contains__',\n",
       " '__delattr__',\n",
       " '__dir__',\n",
       " '__doc__',\n",
       " '__eq__',\n",
       " '__format__',\n",
       " '__ge__',\n",
       " '__getattribute__',\n",
       " '__getitem__',\n",
       " '__getnewargs__',\n",
       " '__gt__',\n",
       " '__hash__',\n",
       " '__init__',\n",
       " '__init_subclass__',\n",
       " '__iter__',\n",
       " '__le__',\n",
       " '__len__',\n",
       " '__lt__',\n",
       " '__mul__',\n",
       " '__ne__',\n",
       " '__new__',\n",
       " '__reduce__',\n",
       " '__reduce_ex__',\n",
       " '__repr__',\n",
       " '__rmul__',\n",
       " '__setattr__',\n",
       " '__sizeof__',\n",
       " '__str__',\n",
       " '__subclasshook__',\n",
       " 'count',\n",
       " 'dig',\n",
       " 'epsilon',\n",
       " 'index',\n",
       " 'mant_dig',\n",
       " 'max',\n",
       " 'max_10_exp',\n",
       " 'max_exp',\n",
       " 'min',\n",
       " 'min_10_exp',\n",
       " 'min_exp',\n",
       " 'n_fields',\n",
       " 'n_sequence_fields',\n",
       " 'n_unnamed_fields',\n",
       " 'radix',\n",
       " 'rounds']"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dir(sys.float_info)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.2250738585072014e-308"
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     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "sys.float_info.min"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
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     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
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   "source": [
    "sys.float_info.max"
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  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.220446049250313e-16"
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     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "sys.float_info.epsilon"
   ]
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  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
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     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "0.1**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "a = 1e14"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "b = 25.44"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "c = 0.74"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "100000000000026.17"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(a+b)+c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "100000000000026.19"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a+(b+c)"
   ]
  }
 ],
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