PyFunction.ipynb

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   "source": [
    "import sympy\n",
    "from symengine import *\n",
    "x,y,z=symbols(\"x y z\")\n",
    "from symengine.lib.symengine_wrapper import *\n",
    "import sage.all as sage"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x + loggamma(x)\n"
     ]
    }
   ],
   "source": [
    "e = x + sympy.loggamma(x); print(e)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(symengine.lib.symengine_wrapper.PyFunction, loggamma(x)),\n",
       " (symengine.lib.symengine_wrapper.Symbol, x)]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[(type(t), t) for t in e.args]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x + 2*loggamma(x)\n"
     ]
    }
   ],
   "source": [
    "e = e + sympy.loggamma(x); print(e)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10 + 2*log(362880)\n"
     ]
    }
   ],
   "source": [
    "f=e.subs({x:10}); print(f)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(symengine.lib.symengine_wrapper.Integer, 10),\n",
       " (symengine.lib.symengine_wrapper.Mul, 2*log(362880))]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[(type(t), t) for t in f.args]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x + y + 2*loggamma(x + y)\n"
     ]
    }
   ],
   "source": [
    "f=e.subs({x:x+y}); print(f)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f=e.subs({x:2});\n",
    "f"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "symengine.lib.symengine_wrapper.Integer"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "818.268410739151 + 0.0*I\n"
     ]
    }
   ],
   "source": [
    "f=e.subs({x:100});\n",
    "n=f.n(53);\n",
    "print(n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "symengine.lib.symengine_wrapper.ComplexDouble"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(x + 2*loggamma(x))**2\n",
      "2*(1 + 2*polygamma(0, x))*(x + 2*loggamma(x))\n"
     ]
    }
   ],
   "source": [
    "print(e**2)\n",
    "print((e**2).diff(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "polygamma(0, x)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sympy.loggamma(x).diff(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{loggamma: <symengine.lib.symengine_wrapper.PyFunctionClass at 0x7ff25e7c1c88>,\n",
       " polygamma: <symengine.lib.symengine_wrapper.PyFunctionClass at 0x7ff25e7c1d78>}"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "funcs"
   ]
  }
 ],
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