{
 "cells": [
  {
   "cell_type": "code",
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   "metadata": {
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   "source": [
    "using Symata"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Differences from Wolfram\n",
    "\n",
    "Symata is similar to the Wolfram language. But, there are difference in notation and behavior."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Notation\n",
    "\n",
    "#### List\n",
    "Mathematica lists are delimited by `{ }`. Symata lists are delimited by `[ ]`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$  \\left[ a,b,c \\right]  $$"
      ],
      "text/plain": [
       "L\"$$  \\left[ a,b,c \\right]  $$\""
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[a,b,c]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Curly braces may also be used to enter lists in Symata. This may change in the future."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$  \\left[ a,b,c \\right]  $$"
      ],
      "text/plain": [
       "L\"$$  \\left[ a,b,c \\right]  $$\""
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "{a,b,c}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Elements in a list may be separated by commas, as above. But, in Symata they may also be separated by a newline after a complete expression."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$  \\left[ a,c + d,\\text{\"cat\"},x^{2} + 2 \\ x \\ y + y^{2} \\right]  $$"
      ],
      "text/plain": [
       "L\"$$  \\left[ a,c + d,\\text{\\\"cat\\\"},x^{2} + 2 \\ x \\ y + y^{2} \\right]  $$\""
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[\n",
    "    a\n",
    "    c + d\n",
    "    \"cat\"\n",
    "    Expand((x+y)^2)\n",
    "]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Functions\n",
    "\n",
    "Function arguments are delimited by `[ ]` in Mathematica. In Symata, arguments are delimited by `( )`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$ f \\!  \\left( x \\right)  $$"
      ],
      "text/plain": [
       "L\"$$ f \\!  \\left( x \\right)  $$\""
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Infix notation for `Map`, `Apply`, `Rule`, `ReplaceAll`, etc."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`Map`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$ \\text{Map} \\!  \\left( f,list \\right)  $$"
      ],
      "text/plain": [
       "L\"$$ \\text{Map} \\!  \\left( f,list \\right)  $$\""
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f % list"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$  \\left[ f \\!  \\left( a \\right) ,f \\!  \\left( b \\right) ,f \\!  \\left( c \\right)  \\right]  $$"
      ],
      "text/plain": [
       "L\"$$  \\left[ f \\!  \\left( a \\right) ,f \\!  \\left( b \\right) ,f \\!  \\left( c \\right)  \\right]  $$\""
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f % [a,b,c]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`Apply`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$ \\text{Apply} \\!  \\left( x,y \\right)  $$"
      ],
      "text/plain": [
       "L\"$$ \\text{Apply} \\!  \\left( x,y \\right)  $$\""
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x .%  y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$ f \\!  \\left( 1,2 \\right)  $$"
      ],
      "text/plain": [
       "L\"$$ f \\!  \\left( 1,2 \\right)  $$\""
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f .% g(1,2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`Rule`\n",
    "\n",
    "`Rule` can be entered in the following ways."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$  \\left[ a \\Rightarrow b,a \\Rightarrow b,a \\Rightarrow b \\right]  $$"
      ],
      "text/plain": [
       "L\"$$  \\left[ a \\Rightarrow b,a \\Rightarrow b,a \\Rightarrow b \\right]  $$\""
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[Rule(a,b), a => b , a ⇒ b]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`RuleDelayed`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$  \\left[ a\\text{:>}b,a\\text{:>}b \\right]  $$"
      ],
      "text/plain": [
       "L\"$$  \\left[ a\\text{:>}b,a\\text{:>}b \\right]  $$\""
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[RuleDelayed(a,b),  a .> b]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`ReplaceAll`\n",
    "\n",
    "The short \"infix\" symbol for `ReplaceAll` is `./`. In Mathematica, it is `/.`.\n",
    "Also note the parentheses surrounding the rule."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$  \\left[ a,g \\!  \\left(  \\left[ 2 \\right] ,x \\right) ,g \\!  \\left(  \\left[ 3 \\right] ,b \\right) ,g \\!  \\left(  \\left[ 3 \\right] ,a + b \\right)  \\right]  $$"
      ],
      "text/plain": [
       "L\"$$  \\left[ a,g \\!  \\left(  \\left[ 2 \\right] ,x \\right) ,g \\!  \\left(  \\left[ 3 \\right] ,b \\right) ,g \\!  \\left(  \\left[ 3 \\right] ,a + b \\right)  \\right]  $$\""
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[a, x^2, b^3, (a+b)^3]  ./ ( x_^n_ => g([n],x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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