{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "alien-benchmark",
   "metadata": {},
   "source": [
    "# Complex projective space and a wedge of spheres"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "encouraging-gauge",
   "metadata": {
    "execution": {
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    }
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   "outputs": [],
   "source": [
    "from steenroder import barcodes, wedge, sphere, suspension, cone\n",
    "from examples import cp2\n",
    "import numpy as np\n",
    "\n",
    "def print_rel_barcodes(k, filtration):\n",
    "    '''Auxiliary function to print outputs in the\n",
    "    persistent relative cohomology context'''\n",
    "    barcode, steenrod_barcode = barcodes(k, filtration)\n",
    "    print(f'*) Regular (infinite only):')\n",
    "    for d, bars in enumerate(barcode):\n",
    "        print(d, bars[np.where(bars == -1)[0],:])\n",
    "    print(f'*) Sq^{k} (non-zero only):')\n",
    "    for d, bars in enumerate(steenrod_barcode):\n",
    "        if bars.size > 0:\n",
    "            print(d, bars)\n",
    "            \n",
    "def print_abs_barcodes(k, filtration, length=1):\n",
    "    '''Auxiliary function to print outputs in the\n",
    "    persistent absolute cohomology context'''\n",
    "    barcode, steenrod_barcode = barcodes(k, filtration, absolute=True)\n",
    "    print(f'*) Regular (length > {length} only):')\n",
    "    for d, bars in enumerate(barcode):\n",
    "        print(d, bars[np.where(bars[:,1]-bars[:,0] > length)])\n",
    "    print(f'*) Sq^{k} (non-zero only):')\n",
    "    for d, bars in enumerate(steenrod_barcode):\n",
    "        if bars.size > 0:\n",
    "            print(d, bars)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "amino-buyer",
   "metadata": {},
   "source": [
    "We will be mostly interested in $Sq^k$ when $k = 2$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "associate-pursuit",
   "metadata": {
    "execution": {
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    }
   },
   "outputs": [],
   "source": [
    "k = 2"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "supported-buddy",
   "metadata": {},
   "source": [
    "## $\\mathbb CP^2$ and $S^2 \\vee S^4$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "violent-local",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-05-29T19:44:55.960976Z",
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     "shell.execute_reply": "2022-05-29T19:45:44.996410Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Persistent relative cohomology:\n",
      "\n",
      "**) CP^2:\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "*) Regular (infinite only):\n",
      "0 [[-1  0]]\n",
      "1 []\n",
      "2 [[-1 13]]\n",
      "3 []\n",
      "4 [[ -1 254]]\n",
      "*) Sq^2 (non-zero only):\n",
      "4 [[-1 13]]\n",
      "\n",
      "**) S^2 v S^4:\n",
      "*) Regular (infinite only):\n",
      "0 [[-1  0]]\n",
      "1 []\n",
      "2 [[-1 13]]\n",
      "3 []\n",
      "4 [[-1 74]]\n",
      "*) Sq^2 (non-zero only):\n"
     ]
    }
   ],
   "source": [
    "print('Persistent relative cohomology:')\n",
    "print('\\n**) CP^2:')\n",
    "print_rel_barcodes(k, cp2)\n",
    "print('\\n**) S^2 v S^4:')\n",
    "s2_s4 = wedge(sphere(2), sphere(4))\n",
    "print_rel_barcodes(k, s2_s4)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "metallic-wisconsin",
   "metadata": {},
   "source": [
    "## $\\Sigma\\mathbb CP^2$ and $\\Sigma(S^2 \\vee S^4)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "functioning-active",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-05-29T19:45:45.000431Z",
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     "shell.execute_reply": "2022-05-29T19:45:57.908258Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Persistent relative cohomology:\n",
      "**) Suspension of CP^2:\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "*) Regular (infinite only):\n",
      "0 [[-1  0]]\n",
      "1 []\n",
      "2 []\n",
      "3 [[ -1 525]]\n",
      "4 []\n",
      "5 [[ -1 766]]\n",
      "*) Sq^2 (non-zero only):\n",
      "5 [[254 269]\n",
      " [ -1 525]]\n",
      "\n",
      "**) Suspension of S^2 v S^4:\n",
      "*) Regular (infinite only):\n",
      "0 [[-1  0]]\n",
      "1 []\n",
      "2 []\n",
      "3 [[ -1 165]]\n",
      "4 []\n",
      "5 [[ -1 226]]\n",
      "*) Sq^2 (non-zero only):\n"
     ]
    }
   ],
   "source": [
    "print('Persistent relative cohomology:')\n",
    "print('**) Suspension of CP^2:')\n",
    "sus_cp2 = suspension(cp2)\n",
    "print_rel_barcodes(2, sus_cp2)\n",
    "\n",
    "print('\\n**) Suspension of S^2 v S^4:')\n",
    "sus_s2_s4 = suspension(s2_s4)\n",
    "print_rel_barcodes(2, sus_s2_s4)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "martial-implement",
   "metadata": {},
   "source": [
    "## $\\mathrm{C}\\,\\Sigma\\,\\mathbb CP^2$ and $\\mathrm{C}\\,\\Sigma(S^2 \\vee S^4)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "impaired-might",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-05-29T19:45:57.912437Z",
     "iopub.status.busy": "2022-05-29T19:45:57.912164Z",
     "iopub.status.idle": "2022-05-29T19:46:10.976551Z",
     "shell.execute_reply": "2022-05-29T19:46:10.975748Z"
    },
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Persistent absolute cohomology\n",
      "**) Cone on the suspension of CP^2:\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "*) Regular (length > 30 only):\n",
      "0 []\n",
      "1 []\n",
      "2 [[ 13 269]]\n",
      "3 [[ 525 1293]\n",
      " [ 781 1037]]\n",
      "4 [[254 510]]\n",
      "5 [[ 766 1534]\n",
      " [1022 1278]]\n",
      "6 []\n",
      "*) Sq^2 (non-zero only):\n",
      "4 [[254 269]]\n",
      "5 [[1022 1037]\n",
      " [ 766 1293]]\n",
      "\n",
      "**) Cone on the suspension of S^2 v S^4:\n",
      "*) Regular (length > 30 only):\n",
      "0 []\n",
      "1 []\n",
      "2 [[13 89]]\n",
      "3 [[165 393]\n",
      " [241 317]]\n",
      "4 [[ 74 150]]\n",
      "5 [[226 454]\n",
      " [302 378]]\n",
      "6 []\n",
      "*) Sq^2 (non-zero only):\n"
     ]
    }
   ],
   "source": [
    "print('Persistent absolute cohomology')\n",
    "min_length_bars = 30\n",
    "\n",
    "print('**) Cone on the suspension of CP^2:')\n",
    "cone_sus_cp2 = cone(sus_cp2)\n",
    "print_abs_barcodes(k, cone_sus_cp2, min_length_bars)\n",
    "\n",
    "print('\\n**) Cone on the suspension of S^2 v S^4:')\n",
    "cone_sus_s2_s4 = cone(sus_s2_s4)\n",
    "print_abs_barcodes(k, cone_sus_s2_s4, min_length_bars)"
   ]
  }
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