rational_overflow.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "using BSeries\n",
    "using Latexify\n",
    "using RootedTrees\n",
    "using Symbolics\n",
    "import SymPy; sp=SymPy;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$F_{f}\\mathopen{}\\left( \\varnothing \\right)\\mathclose{} + h F_{f}\\mathopen{}\\left( \\rootedtree[] \\right)\\mathclose{} + \\frac{h^{2}}{2} F_{f}\\mathopen{}\\left( \\rootedtree[[]] \\right)\\mathclose{} + \\frac{h^{3}}{8 \\alpha} F_{f}\\mathopen{}\\left( \\rootedtree[[][]] \\right)\\mathclose{}$"
      ],
      "text/plain": [
       "L\"$F_{f}\\mathopen{}\\left( \\varnothing \\right)\\mathclose{} + h F_{f}\\mathopen{}\\left( \\rootedtree[] \\right)\\mathclose{} + \\frac{h^{2}}{2} F_{f}\\mathopen{}\\left( \\rootedtree[[]] \\right)\\mathclose{} + \\frac{h^{3}}{8 \\alpha} F_{f}\\mathopen{}\\left( \\rootedtree[[][]] \\right)\\mathclose{}$\""
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "α = sp.symbols(\"α\", real=true)\n",
    "A = [0 0; 1/(2*α) 0]; b = [1-α, α]; c = [0, 1/(2*α)]\n",
    "coeffs = bseries(A,b,c,3)\n",
    "latexify(coeffs, cdot=false)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "ename": "LoadError",
     "evalue": "OverflowError: -499541949138073 * 25441 overflowed for type Int64",
     "output_type": "error",
     "traceback": [
      "OverflowError: -499541949138073 * 25441 overflowed for type Int64",
      "",
      "Stacktrace:",
      " [1] throw_overflowerr_binaryop(op::Symbol, x::Int64, y::Int64)",
      "   @ Base.Checked ./checked.jl:154",
      " [2] checked_mul",
      "   @ ./checked.jl:288 [inlined]",
      " [3] +(x::Rational{Int64}, y::Rational{Int64})",
      "   @ Base ./rational.jl:286",
      " [4] dot(x::Vector{Rational{Int64}}, y::Vector{Rational{Int64}})",
      "   @ LinearAlgebra /Users/julia/buildbot/worker/package_macos64/build/usr/share/julia/stdlib/v1.6/LinearAlgebra/src/generic.jl:916",
      " [5] elementary_weight",
      "   @ ~/.julia/packages/RootedTrees/J2eWh/src/RootedTrees.jl:1223 [inlined]",
      " [6] bseries(A::Matrix{Rational{Int64}}, b::Vector{Rational{Int64}}, c::Vector{Rational{Int64}}, order::Int64)",
      "   @ BSeries ~/.julia/packages/BSeries/Uz1I9/src/BSeries.jl:210",
      " [7] top-level scope",
      "   @ In[3]:5",
      " [8] eval",
      "   @ ./boot.jl:360 [inlined]",
      " [9] include_string(mapexpr::typeof(REPL.softscope), mod::Module, code::String, filename::String)",
      "   @ Base ./loading.jl:1116"
     ]
    }
   ],
   "source": [
    "A = [0 0 0 0 0 0 0 0;(-1//6) (1//2) 0 0 0 0 0 0;(-1//10) (1//10) (1//2) 0 0 0 0 0;(-21463//39375) (21017//26250) (-5//9) (1//2) 0 0 0 0;(-59588//54675) (118717//36450) (-4375//2187) 0 (1//2) 0 0 0;(-19993033//9443328) (28508695//3147776) (-13577105//2360832) (-4090625//3147776) (1136025//3147776) (1//2) 0 0;(367020141781//199294617600) (814214904871//22143846400) (-29834937659//1992946176) (-1983358776875//87689631744) (-6702625935//885753856) (688576//109395) (1//2) 0;(1081252805//134140608) (2639189439//74522560) (33646441//4191894) (-7873511875//210792384) (-504040617//14904512) (2110843561//115277085) (13//7) (1//2)];\n",
    "b = [(1081252805//134140608),(2639189439//74522560),(33646441//4191894),(-7873511875//210792384),(-504040617//14904512),(2110843561//115277085),(13//7),(1//2)];\n",
    "c = [0,(1//3),(1//2),(1//5),(2//3),(3//4),(1//4),1];\n",
    "\n",
    "coeffs = bseries(A,b,c,5)\n",
    "latexify(coeffs, cdot=false)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Julia 1.6.3",
   "language": "julia",
   "name": "julia-1.6"
  },
  "language_info": {
   "file_extension": ".jl",
   "mimetype": "application/julia",
   "name": "julia",
   "version": "1.6.3"
  },
  "toc": {
   "base_numbering": 1,
   "nav_menu": {},
   "number_sections": true,
   "sideBar": true,
   "skip_h1_title": false,
   "title_cell": "Table of Contents",
   "title_sidebar": "Contents",
   "toc_cell": false,
   "toc_position": {},
   "toc_section_display": true,
   "toc_window_display": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}