{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "macro-china",
   "metadata": {},
   "source": [
    "# Counting indecomposable representations\n",
    "Given a quiver $Q$, we can compute its (absolutely) indecomposable representations over a finite field using the Hua formula. We use its formulation from [arXiv:math/0608321](https://arxiv.org/abs/math/0608321).\n",
    "\n",
    "For any $d\\in\\Gamma^+=\\mathbb N^{Q_0}$, we define its multi-partition to be a finite sequence of (nonzero) vectors $\\lambda=(\\lambda_1,\\dots,\\lambda_m)$ in $\\Gamma^+$ such that $\\lambda_1\\ge\\lambda_2\\ge\\dots\\ge\\lambda_m$ (meaning that $\\lambda_k-\\lambda_{k+1}\\in\\Gamma^+$) and $|\\lambda|=\\sum_k\\lambda_k=d$.\n",
    "Define\n",
    "$$R_\\lambda(q)=\\prod_{k=1}^m\\frac{q^{-\\chi(\\lambda_k,\\lambda_k)}}{(q^{-1})_{\\lambda_k-\\lambda_{k+1}}},$$\n",
    "where $(q)_d=\\prod_{i}(q)_{d_i}$ for $d\\in\\Gamma^+$ and $(q)_n=(1-q)\\dots(1-q^n)$ for $n\\in\\mathbb N$. \n",
    "Then the polynomials $A_d(q)$ counting absolutely indecomposable quiver representations having dimension vector $d$ are given by the formula\n",
    "$$\\sum_d A_d(q)x^d=(q-1)Log\\left(\\sum_{\\lambda}R_\\lambda(q)x^{|\\lambda|}\\right),$$\n",
    "where $Log$ is the plethystic logarithm. We use polynomials in $q=y^2$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "initial-savage",
   "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 *\n",
    "from msinvar.indecomposable import hua_formula\n",
    "set_plots()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "graduate-school",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "Graphics object consisting of 3 graphics primitives"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "{(1,): y^2, (2,): y^2, (3,): y^2}"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Q=JordanQuiver(1); show(Q)\n",
    "Q.prec([3])\n",
    "hua_formula(Q).dict()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "disciplinary-poland",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "Graphics object consisting of 4 graphics primitives"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "{(1, 0): 1, (0, 1): 1, (1, 1): 1}"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Q=Quiver('1-2'); show(Q)\n",
    "Q.prec([3,3])\n",
    "hua_formula(Q).dict()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "narrative-bunny",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "Graphics object consisting of 6 graphics primitives"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "{(1, 0): 1,\n",
       " (0, 1): 1,\n",
       " (1, 1): y^2 + 1,\n",
       " (2, 1): 1,\n",
       " (1, 2): 1,\n",
       " (2, 2): y^2 + 1,\n",
       " (3, 2): 1,\n",
       " (2, 3): 1,\n",
       " (3, 3): y^2 + 1}"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Q=KroneckerQuiver(2); show(Q)\n",
    "Q.prec([3,3])\n",
    "hua_formula(Q).dict()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "geological-anaheim",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "Graphics object consisting of 6 graphics primitives"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "{(1, 0): 1,\n",
       " (0, 1): 1,\n",
       " (1, 1): y^2 + 1,\n",
       " (2, 1): 1,\n",
       " (1, 2): 1,\n",
       " (2, 2): y^2 + 1,\n",
       " (3, 2): 1,\n",
       " (2, 3): 1,\n",
       " (3, 3): y^2 + 1}"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Q=KroneckerQuiver(2); show(Q)\n",
    "Q.prec([3,3])\n",
    "hua_formula(Q).dict()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "previous-coating",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "Graphics object consisting of 7 graphics primitives"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "{(1, 0, 0): 1,\n",
       " (0, 1, 0): 1,\n",
       " (1, 1, 0): 1,\n",
       " (0, 0, 1): 1,\n",
       " (1, 0, 1): 1,\n",
       " (0, 1, 1): 1,\n",
       " (1, 1, 1): y^2 + 2,\n",
       " (2, 1, 1): 1,\n",
       " (1, 2, 1): 1,\n",
       " (2, 2, 1): 1,\n",
       " (1, 1, 2): 1,\n",
       " (2, 1, 2): 1,\n",
       " (1, 2, 2): 1,\n",
       " (2, 2, 2): y^2 + 2,\n",
       " (3, 2, 2): 1,\n",
       " (2, 3, 2): 1,\n",
       " (3, 3, 2): 1,\n",
       " (2, 2, 3): 1,\n",
       " (3, 2, 3): 1,\n",
       " (2, 3, 3): 1,\n",
       " (3, 3, 3): y^2 + 2}"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Q=CyclicQuiver(3); show(Q)\n",
    "Q.prec([3,3,3])\n",
    "hua_formula(Q).dict()"
   ]
  },
  {
   "cell_type": "code",
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