{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "vocational-obligation",
   "metadata": {},
   "source": [
    "## Flow tree formulas\n",
    "Here we will test the attractor tree formula (see [arXiv:1910.03098](https://arxiv.org/abs/1910.03098) and [arXiv:2101.07636](https://arxiv.org/abs/2101.07636)) and the flow tree formula (see [arXiv:1804.06928](https://arxiv.org/abs/1804.06928) and [arXiv:2102.11200](https://arxiv.org/abs/2102.11200)). They allow us to find rational DT invariants for any stability parameter from rational attractor invariants.\n",
    "We will compare these computations to the algorithm from [arXiv:math/0204059](https://arxiv.org/abs/math/0204059) that allows us to find the same invariants from the total invariant (stacky invariant for the trivial stability). We will also compare implementation speeds of all algorithms."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "involved-village",
   "metadata": {},
   "outputs": [],
   "source": [
    "import os, sys\n",
    "module_path = os.path.abspath(os.path.join('..'))\n",
    "if module_path not in sys.path:\n",
    "    sys.path.append(module_path)\n",
    "from msinvar import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "prescription-recipe",
   "metadata": {},
   "outputs": [],
   "source": [
    "Q=KroneckerQuiver(3, prec=[3,3])\n",
    "z=Stability([1,0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "universal-reggae",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 442 ms, sys: 2.62 ms, total: 444 ms\n",
      "Wall time: 443 ms\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "{(1, 0): 1,\n",
       " (2, 0): 1/2*y/(y^2 + 1),\n",
       " (3, 0): 1/3*y^2/(y^4 + y^2 + 1),\n",
       " (0, 1): 1,\n",
       " (1, 1): (y^4 + y^2 + 1)/y^2,\n",
       " (2, 1): (y^4 + y^2 + 1)/y^2,\n",
       " (3, 1): 1,\n",
       " (0, 2): 1/2*y/(y^2 + 1),\n",
       " (1, 2): (y^4 + y^2 + 1)/y^2,\n",
       " (2,\n",
       "  2): (-y^12 - 3/2*y^10 - 2*y^8 - 3/2*y^6 - 2*y^4 - 3/2*y^2 - 1)/(y^7 + y^5),\n",
       " (3, 2): (y^12 + y^10 + 3*y^8 + 3*y^6 + 3*y^4 + y^2 + 1)/y^6,\n",
       " (0, 3): 1/3*y^2/(y^4 + y^2 + 1),\n",
       " (1, 3): 1,\n",
       " (2, 3): (y^12 + y^10 + 3*y^8 + 3*y^6 + 3*y^4 + y^2 + 1)/y^6,\n",
       " (3,\n",
       "  3): (y^24 + 2*y^22 + 4*y^20 + 16/3*y^18 + 6*y^16 + 6*y^14 + 19/3*y^12 + 6*y^10 + 6*y^8 + 16/3*y^6 + 4*y^4 + 2*y^2 + 1)/(y^14 + y^12 + y^10)}"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Omb1=Q.attr_tree_formula(z,Q.ratAtt_default())\n",
    "%time Omb1.dict()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "promising-allergy",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 695 ms, sys: 5.35 ms, total: 700 ms\n",
      "Wall time: 704 ms\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "{(1, 0): 1,\n",
       " (2, 0): 1/2*y/(y^2 + 1),\n",
       " (3, 0): 1/3*y^2/(y^4 + y^2 + 1),\n",
       " (0, 1): 1,\n",
       " (1, 1): (y^4 + y^2 + 1)/y^2,\n",
       " (2, 1): (y^4 + y^2 + 1)/y^2,\n",
       " (3, 1): 1,\n",
       " (0, 2): 1/2*y/(y^2 + 1),\n",
       " (1, 2): (y^4 + y^2 + 1)/y^2,\n",
       " (2,\n",
       "  2): (-y^12 - 3/2*y^10 - 2*y^8 - 3/2*y^6 - 2*y^4 - 3/2*y^2 - 1)/(y^7 + y^5),\n",
       " (3, 2): (y^12 + y^10 + 3*y^8 + 3*y^6 + 3*y^4 + y^2 + 1)/y^6,\n",
       " (0, 3): 1/3*y^2/(y^4 + y^2 + 1),\n",
       " (1, 3): 1,\n",
       " (2, 3): (y^12 + y^10 + 3*y^8 + 3*y^6 + 3*y^4 + y^2 + 1)/y^6,\n",
       " (3,\n",
       "  3): (y^24 + 2*y^22 + 4*y^20 + 16/3*y^18 + 6*y^16 + 6*y^14 + 19/3*y^12 + 6*y^10 + 6*y^8 + 16/3*y^6 + 4*y^4 + 2*y^2 + 1)/(y^14 + y^12 + y^10)}"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Omb2=Q.flow_tree_formula(z,Q.ratAtt_default())\n",
    "%time Omb2.dict()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "integral-execution",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 47.4 ms, sys: 2.69 ms, total: 50.1 ms\n",
      "Wall time: 50.1 ms\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "{(1, 0): 1,\n",
       " (2, 0): 1/2*y/(y^2 + 1),\n",
       " (3, 0): 1/3*y^2/(y^4 + y^2 + 1),\n",
       " (0, 1): 1,\n",
       " (1, 1): (-y^4 - y^2 - 1)/(-y^2),\n",
       " (2, 1): (-y^4 - y^2 - 1)/(-y^2),\n",
       " (3, 1): 1,\n",
       " (0, 2): 1/2*y/(y^2 + 1),\n",
       " (1, 2): (-y^4 - y^2 - 1)/(-y^2),\n",
       " (2,\n",
       "  2): (y^12 + 3/2*y^10 + 2*y^8 + 3/2*y^6 + 2*y^4 + 3/2*y^2 + 1)/(-y^7 - y^5),\n",
       " (3, 2): (y^12 + y^10 + 3*y^8 + 3*y^6 + 3*y^4 + y^2 + 1)/y^6,\n",
       " (0, 3): 1/3*y^2/(y^4 + y^2 + 1),\n",
       " (1, 3): 1,\n",
       " (2, 3): (-y^12 - y^10 - 3*y^8 - 3*y^6 - 3*y^4 - y^2 - 1)/(-y^6),\n",
       " (3,\n",
       "  3): (y^24 + 2*y^22 + 4*y^20 + 16/3*y^18 + 6*y^16 + 6*y^14 + 19/3*y^12 + 6*y^10 + 6*y^8 + 16/3*y^6 + 4*y^4 + 2*y^2 + 1)/(y^14 + y^12 + y^10)}"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Omb3=Q.rat_from_total(z)\n",
    "%time Omb3.dict()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "engaged-willow",
   "metadata": {},
   "source": [
    "### Another example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "leading-establishment",
   "metadata": {},
   "outputs": [],
   "source": [
    "r=6\n",
    "Q=ChainQuiver(r)\n",
    "Q.prec([1]*r)\n",
    "z=Stability([1]*r).randomize()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "human-machine",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 14.1 s, sys: 18.4 ms, total: 14.1 s\n",
      "Wall time: 14.1 s\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "{(1, 0, 0, 0, 0, 0): 1,\n",
       " (0, 1, 0, 0, 0, 0): 1,\n",
       " (0, 0, 1, 0, 0, 0): 1,\n",
       " (0, 0, 0, 1, 0, 0): 1,\n",
       " (0, 0, 1, 1, 0, 0): 1,\n",
       " (0, 1, 1, 1, 0, 0): 1,\n",
       " (0, 0, 0, 0, 1, 0): 1,\n",
       " (0, 0, 1, 1, 1, 0): 1,\n",
       " (0, 1, 1, 1, 1, 0): 1,\n",
       " (0, 0, 0, 0, 0, 1): 1,\n",
       " (0, 0, 0, 0, 1, 1): 1,\n",
       " (0, 0, 1, 1, 1, 1): 1,\n",
       " (0, 1, 1, 1, 1, 1): 1}"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Omb1=Q.attr_tree_formula(z,Q.ratAtt_default())\n",
    "%time Omb1.dict()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "isolated-telling",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 500 ms, sys: 2.9 ms, total: 503 ms\n",
      "Wall time: 502 ms\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "{(1, 0, 0, 0, 0, 0): 1,\n",
       " (0, 1, 0, 0, 0, 0): 1,\n",
       " (0, 0, 1, 0, 0, 0): 1,\n",
       " (0, 0, 0, 1, 0, 0): 1,\n",
       " (0, 0, 1, 1, 0, 0): 1,\n",
       " (0, 1, 1, 1, 0, 0): 1,\n",
       " (0, 0, 0, 0, 1, 0): 1,\n",
       " (0, 0, 1, 1, 1, 0): 1,\n",
       " (0, 1, 1, 1, 1, 0): 1,\n",
       " (0, 0, 0, 0, 0, 1): 1,\n",
       " (0, 0, 0, 0, 1, 1): 1,\n",
       " (0, 0, 1, 1, 1, 1): 1,\n",
       " (0, 1, 1, 1, 1, 1): 1}"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Omb2=Q.flow_tree_formula(z,Q.ratAtt_default())\n",
    "%time Omb2.dict()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "starting-gender",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 143 ms, sys: 2.01 ms, total: 145 ms\n",
      "Wall time: 144 ms\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "{(1, 0, 0, 0, 0, 0): 1,\n",
       " (0, 1, 0, 0, 0, 0): 1,\n",
       " (0, 0, 1, 0, 0, 0): 1,\n",
       " (0, 0, 0, 1, 0, 0): 1,\n",
       " (0, 0, 1, 1, 0, 0): 1,\n",
       " (0, 1, 1, 1, 0, 0): 1,\n",
       " (0, 0, 0, 0, 1, 0): 1,\n",
       " (0, 0, 1, 1, 1, 0): 1,\n",
       " (0, 1, 1, 1, 1, 0): 1,\n",
       " (0, 0, 0, 0, 0, 1): 1,\n",
       " (0, 0, 0, 0, 1, 1): 1,\n",
       " (0, 0, 1, 1, 1, 1): 1,\n",
       " (0, 1, 1, 1, 1, 1): 1}"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Omb3=Q.rat_from_total(z)\n",
    "%time Omb3.dict()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "bulgarian-shoulder",
   "metadata": {},
   "outputs": [],
   "source": [
    "r=7\n",
    "Q=ChainQuiver(r)\n",
    "Q.prec([1]*r)\n",
    "z=Stability([1]*r).randomize()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "headed-force",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 8.19 s, sys: 11 ms, total: 8.2 s\n",
      "Wall time: 8.2 s\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "{(1, 0, 0, 0, 0, 0, 0): 1,\n",
       " (0, 1, 0, 0, 0, 0, 0): 1,\n",
       " (1, 1, 0, 0, 0, 0, 0): 1,\n",
       " (0, 0, 1, 0, 0, 0, 0): 1,\n",
       " (0, 0, 0, 1, 0, 0, 0): 1,\n",
       " (0, 0, 0, 0, 1, 0, 0): 1,\n",
       " (0, 0, 0, 1, 1, 0, 0): 1,\n",
       " (0, 0, 1, 1, 1, 0, 0): 1,\n",
       " (0, 0, 0, 0, 0, 1, 0): 1,\n",
       " (0, 0, 0, 0, 0, 0, 1): 1,\n",
       " (0, 0, 0, 0, 0, 1, 1): 1,\n",
       " (0, 0, 0, 0, 1, 1, 1): 1,\n",
       " (0, 0, 0, 1, 1, 1, 1): 1,\n",
       " (0, 0, 1, 1, 1, 1, 1): 1}"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Omb2=Q.flow_tree_formula(z,Q.ratAtt_default())\n",
    "%time Omb2.dict()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "divided-indonesian",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 400 ms, sys: 2.18 ms, total: 402 ms\n",
      "Wall time: 401 ms\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "{(1, 0, 0, 0, 0, 0, 0): 1,\n",
       " (0, 1, 0, 0, 0, 0, 0): 1,\n",
       " (1, 1, 0, 0, 0, 0, 0): 1,\n",
       " (0, 0, 1, 0, 0, 0, 0): 1,\n",
       " (0, 0, 0, 1, 0, 0, 0): 1,\n",
       " (0, 0, 0, 0, 1, 0, 0): 1,\n",
       " (0, 0, 0, 1, 1, 0, 0): 1,\n",
       " (0, 0, 1, 1, 1, 0, 0): 1,\n",
       " (0, 0, 0, 0, 0, 1, 0): 1,\n",
       " (0, 0, 0, 0, 0, 0, 1): 1,\n",
       " (0, 0, 0, 0, 0, 1, 1): 1,\n",
       " (0, 0, 0, 0, 1, 1, 1): 1,\n",
       " (0, 0, 0, 1, 1, 1, 1): 1,\n",
       " (0, 0, 1, 1, 1, 1, 1): 1}"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Omb3=Q.rat_from_total(z)\n",
    "%time Omb3.dict()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "sized-change",
   "metadata": {},
   "outputs": [],
   "source": [
    "r=8\n",
    "Q=ChainQuiver(r)\n",
    "Q.prec([1]*r)\n",
    "z=Stability([1]*r).randomize()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "boxed-median",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 1min 39s, sys: 103 ms, total: 1min 39s\n",
      "Wall time: 1min 39s\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Omb2=Q.flow_tree_formula(z,Q.ratAtt_default())\n",
    "%time Omb2([1]*r)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "passing-intranet",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 292 ms, sys: 2.3 ms, total: 294 ms\n",
      "Wall time: 293 ms\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Omb3=Q.rat_from_total(z)\n",
    "%time Omb3([1]*r)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "satellite-tattoo",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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  "kernelspec": {
   "display_name": "SageMath 9.2",
   "language": "sage",
   "name": "sagemath"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
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   "file_extension": ".py",
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