Python's Mathematical Gotchas

mathematical_gotchas_in_python.ipynb

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    "Python's Mathematical Gotchas\n",
    "--------\n",
    "\n",
    "Python is a nice computer language for the \"maths\". I'm looking at you [`math.tau`](https://www.python.org/dev/peps/pep-0628/) and [SymPy](http://www.sympy.org/) But like all finite machine languages, Python can not flawlessly instantiate the rich world of mathematics.\n",
    "\n",
    "tl;dr: Choosing modern, specific tools within Python can assist. Sometimes it is worth being \"fancy\" to be more accurate.\n",
    "\n",
    "__Several Rough Edge Cases__:\n",
    "\n",
    "1. Mathematical Constants That Change\n",
    "1. Rational Number Shenanigans\n",
    "1. Specific Tools > General Tools\n",
    "\n",
    "All of these examples have been adapted from [Raymond Hettinger](https://twitter.com/raymondh?lang=en). Follow him and develop as a developer."
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    "Mathematical Constants That Change\n",
    "------"
   ]
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      "3.14159265359\n"
     ]
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   "source": [
    "%%python2\n",
    "from math import pi\n",
    "\n",
    "pi_py2 = pi\n",
    "print(pi_py2)"
   ]
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      "3.141592653589793\n"
     ]
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    "%%python3\n",
    "from math import pi\n",
    "\n",
    "pi_py3 = pi\n",
    "print(pi_py3)"
   ]
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    "Rational Number Shenanigans\n",
    "-------"
   ]
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   "source": [
    "# Should be the same...\n",
    ".1 + .2 == .3 # 😡"
   ]
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   "source": [
    "Other languages (e.g., Perl 6) internally represent some numbers as rational numbers, each with numerators and a denominators. \n",
    "\n",
    "In Python it would be like..."
   ]
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   "source": [
    "from fractions import Fraction"
   ]
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   "source": [
    "# Change the representation and they are equivalent\n",
    "Fraction(1, 10) + Fraction(2, 10) == Fraction(3, 10) # 🙂"
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   "source": [
    "Specfic Tools > General Tools\n",
    "------\n",
    "\n",
    "When given a choice in Python, use specialized tool.\n",
    "\n",
    "from this [Raymond tweet](https://twitter.com/raymondh/status/974018651308179456)"
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   "source": [
    "# General log\n",
    "from math import log"
   ]
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   "source": [
    "# Should be all be the same\n",
    "all(log(2**p, 2) == p for p in range(1024)) # 😡"
   ]
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   "execution_count": 41,
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   "source": [
    "# Special log base 2\n",
    "from math import log2"
   ]
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   "source": [
    "# Now they are all the same\n",
    "all(log2(2**p) == p for p in range(1024)) # 🙂"
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   "source": [
    "Summary\n",
    "------\n",
    "\n",
    "Python does __not__ always perform the way we expect. \n",
    "\n",
    "It is worth knowing about and collecting MathOps (Mathematical Operations) edge cases."
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   "source": [
    "<br>\n",
    "<br> \n",
    "<br>\n",
    "\n",
    "----"
   ]
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