Preparing Data and NLP.ipynb

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   "source": [
    "# Modules\n",
    "import xml.etree.ElementTree as ET\n",
    "from lxml import etree\n",
    "import random\n",
    "import time\n",
    "import os\n",
    "import glob\n",
    "import pandas as pd\n",
    "import tarfile\n",
    "import nltk\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline  \n",
    "from sklearn import model_selection, preprocessing, linear_model, naive_bayes, metrics, svm\n",
    "from sklearn.feature_extraction.text import TfidfVectorizer, CountVectorizer\n",
    "from sklearn import decomposition, ensemble\n",
    "from tqdm import tqdm\n",
    "from collections import Counter\n",
    "from functools import partial\n",
    "\n",
    "from langdetect import detect\n",
    "from langdetect.lang_detect_exception import LangDetectException "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "%load_ext autoreload\n",
    "%autoreload 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Local\n",
    "import parsing_xml as px\n",
    "import peep_tar as peep"
   ]
  },
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      "9412_001/math.9412223/math.9412223.xml\n",
      "9412_001/math.9412220/math.9412220.xml\n",
      "9412_001/math.9412222/math.9412222.xml\n",
      "9412_001/math.9412209/sr2.xml\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "lang_lst = []\n",
    "for tar_name in tqdm(glob.glob('/mnt/promath/math94/*.tar.gz')):\n",
    "    for name,f in peep.tar_iter(tar_name, '.xml'):\n",
    "        print(name)\n",
    "        #try:\n",
    "        #    dd = px.DefinitionsXML(f, fname=name)\n",
    "        #    Lang = dd.det_language()\n",
    "        #    lang_lst.append(Lang)\n",
    "        #    if Lang != 'en':\n",
    "        #        print(Lang, 'in article: ', name)\n",
    "        #except ValueError as ee:\n",
    "        #    #print(\"\\n Probably empty article: %s \\n\"%name, ee) \n",
    "        #    pass\n",
    "        #except IndexError:\n",
    "        #    #print(f\"File {name} has no entries\")\n",
    "        #    pass\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " \n",
      " 𝕆ℕ ℂ𝕃𝕆𝕊𝔼𝔻 𝕌ℕ𝔹𝕆𝕌ℕ𝔻𝔼𝔻 𝕊𝔼𝕋𝕊 ℂ𝕆ℕ𝕊𝕀𝕊𝕋𝕀ℕ𝔾 \n",
      " 𝕆𝔽 𝔽𝕆ℝ𝕄𝔼ℝ ℝ𝔼𝔾𝕌𝕃𝔸ℝ𝕊 \n",
      " 𝕄⋊≈ℶ 𝔾ℶ≈ℶℸ \n",
      " 𝕊≂⋊⋊⋖ ⋊℧ 𝕄⅁≈≂⋗⅁≈ℶ⅁⋖ 𝕊ℶ⋉∼ 𝕊⅁ℸ⋖∖ 𝔽⅁≊⋖≈↷ ⋊℧ 𝔼↶⅁≈ 𝕊ℶ⋉∼ 𝕋⋖ 𝔸⪸ℶ⪸ 𝕌⋉ℶ⪸∖∼ℶ≈↷ ℝ⅁⋗⅁≈∤𝔸⪸ℶ⪸∦ ⋫↛↛⋪↚ 𝕀∼∖⅁⋖ \n",
      " 𝔸∼≈∖⅁≈ \n",
      " 𝔸 ⋗≈≂⋊ ⋊℧ ℶ≈∖⅁≈ℶ⋊⋉ ⋊℧ ℙ∖ℶℸ∖↷ ≈↷∣ ℧⋊∖ℶ⋉ð ⋉⋊≈ℶ⋊⋉∼ ⅁∼ ⪷⋖⋖ ⅁∼ ⅁ ℧⋊∖ℶ⋉ð ℧⋊∖ ⅁ℶ⋉ð ⋖≊∼ ℶ∼ ∣∖∼⋉≈∤ 𝕀≈ ℶ∼ ⅁∣∣⋖ℶ ≈⋊ ⋊⋉∼≈∖≊≈ ⅁ ⋗⋊⋖ ⪷ℶ≈≂ ⅁ ⋗⅁∼≊∖⅁⋖ ⅁∖ℶ⋉⅁⋖ ⋊⋉≈⅁ℶ⋉ℶ⋉ð ⅁ ⋖≊ ⋊℧ ℧⋊∖⋗∖ ∖ð≊⋖⅁∖∼∦ ∼≈⅁∖≈ℶ⋉ð ⪷ℶ≈≂ _inline_math_∤ 𝕆⋉ ≈≂ ⋊≈≂∖ ≂⅁⋉∦ ℶ≈ ℶ∼ ∼≂⋊⪷⋉ ≈≂⅁≈ ≈≂ ∼≈∖⋉ð≈≂ ⋊℧ ⅁⋊⪸ ℶ∼ ⅁≈ ⋖⅁∼≈ _inline_math_∤ \n",
      " 𝕊≊∣∣⋊∼ ≈≂⅁≈ _inline_math_ ℶ∼ ⅁⋉ ℶ⋉⅁∼∼ℶ⋖ ⅁∖ℶ⋉⅁⋖∤ 𝕎 ⪷ℶ∼≂ ≈⋊ ℧ℶ⋉ ⅁ ð⋉∖ℶ ↶≈⋉∼ℶ⋊⋉ ⊊≊∼≊⅁⋖⋖↷ ⅁∖ℶ⋉⅁⋖ ∣∖∼∖⪸ℶ⋉ð⊋ ∼≊≂ ≈≂⅁≈ _inline_math_ ℶ∼ ∖ð≊⋖⅁∖ ℶ⋉ _inline_math_ ⋊⋉≈⅁ℶ⋉∼ ⅁ ⋖≊∤ ℝ⅁ℶ⋉ ^ℝ⅁~ ℶ⋉≈∖⋊≊ ⅁ ⅁∼ℶ ⋗≈≂⋊ ≈⋊ ⋊ ≈≂ℶ∼∤ 𝕊ℶ⋗∣⋖↷ ∼≈⅁∖≈ ⪷ℶ≈≂ ⅁ ⋗⅁∼≊∖⅁⋖ _inline_math_ ⪷ℶ≈≂ _inline_math_ ⅁⋉ ≈≂⋉ ℧⋊∖ ⪷ℶ≈≂ ≈≂ ℝ⅁ℶ⋉ ℧⋊∖ℶ⋉ð ⋊⋉∼≈∖≊≈ ℧∖⋊⋗ _inline_math_∤ 𝕀℧ ⋊⋉ ⪷ℶ∼≂∼ ≈⋊ ℸ∣ _inline_math_ ⅁ ⋗⅁∼≊∖⅁⋖ ℶ⋉ ≈≂ ↶≈⋉∼ℶ⋊⋉∦ ≈≂⋉ ⅁ ⪷⅁ℸ ∖∣⅁≈ ∣⋊ℶ⋉≈ ∼≊℧℧ℶ∼∤ 𝔹⋊≈≂ ℧⅁≈∼ ⅁∖ ∣∖⋊⪸ ↷ 𝕄ℶ≈≂⋖⋖ ^𝕄ℶ⊮~∦ \n",
      " 𝕎 ∼≂⋊⪷ ≂⋊⪷ ≈⋊ ∖≊ ⅁∼∼≊⋗∣≈ℶ⋊⋉∼ ∖⋉∖ℶ⋉ð ≈≂ ⅁⋊⪸ ∣⋊∼∼ℶ⋖∤ \n",
      " 𝔸 ⋗≈≂⋊ ⋊℧ ℶ≈∖⅁≈ℶ⋊⋉ ð⋉∖⅁⋖ℶϝℶ⋉ð ≈≂⋊∼ ⋊℧ ^𝔾ℶ⊮~ ℶ∼ ∣∖∼⋉≈∤ 𝕋≂⋉ ⅁ ⪸⅁∖ℶ⅁⋉≈ ⋊℧ ℶ≈ ℶ∼ ≊∼ ≈⋊ ℶ≈∖⅁≈ ℧⋊∖ℶ⋉ð ℧⋊∖ ∼≂⋊⋊≈ℶ⋉ð ⋖≊∼∤ 𝕎 ≈≂ℶ⋉ℸ ≈≂⅁≈ ≈≂ℶ∼ ⋗≈≂⋊ ⋊℧ ℶ≈∖⅁≈ℶ⋊⋉ ⅁⋉ ⅁∣∣⋖ℶ ≈⋊ ⋊≈≂∖ ℶ∼≈∖ℶ≊≈ℶ⪸ ℧⋊∖ℶ⋉ð∼ ⅁∼ ⪷⋖⋖∤ \n",
      " 𝕎 ⋖ℶℸ ≈⋊ ≈≂⅁⋉ℸ ≈≂ ∖℧∖ ℧⋊∖ ∣⋊ℶ⋉≈ℶ⋉ð ⋊≊≈ ≈≂⅁≈ ≈≂ ∣∖⋊⋊℧ ⋊℧ ∼≈ℶ⋊⋉ ⊭ ðℶ⪸∼ ⋊⋉⋖↷ _inline_math_ ⅁⋉ ⋉⋊≈ _inline_math_ ⅁∼ ⪷⅁∼ ⋖⅁ℶ⋗ ℶ⋉ ≈≂ ∣∖⪸ℶ⋊≊∼ ⪸∖∼ℶ⋊⋉∦ ℧⋊∖ ⋖⋊⋉ð ⅁⋉ ≈⅁ℶ⋖ ⋖ℶ∼≈ ⋊℧ ⋊∖∖≈ℶ⋊⋉∼ ⅁⋉ ℧⋊∖ ≂ℶ∼ ∖∥≊∼≈∼ ⋊⋉ ↶∣⋖⅁ℶ⋉ℶ⋉ð ∖≈⅁ℶ⋉ ∣⅁∖≈∼ ⋊℧ ≈≂ ∣⅁∣∖∤ \n",
      " ⊮∤ 𝔸 𝔽⋊∖ℶ⋉ð ℂ⋊⋉∼≈∖≊≈ℶ⋊⋉ \n",
      " 𝕎 ⪷ℶ⋖⋖ ⋉⋊⪷ ∣∖⋊⪸ ≈≂ ℧⋊⋖⋖⋊⪷ℶ⋉ð ≈⪷⋊ ≈≂⋊∖⋗∼∤ \n",
      " 𝕊≊∣∣⋊∼ ≈≂⅁≈ _inline_math_ ℶ∼ ⅁⋉ ℶ⋉⅁∼∼ℶ⋖ ⅁∖ℶ⋉⅁⋖ ∼≊≂ ≈≂⅁≈ ℧⋊∖ ⪸∖↷ _inline_math_ ≈≂ ∼≈ ⋊℧ _inline_math_⫌∼ ⋖⋊⪷ _inline_math_ ⪷ℶ≈≂ _inline_math_ ℶ∼ ∼≈⅁≈ℶ⋊⋉⅁∖↷∤ 𝕋≂⋉ ≈≂∖ ℶ∼ ⅁ ⅁∖ℶ⋉⅁⋖ ∣∖∼∖⪸ℶ⋉ð ð⋉∖ℶ ↶≈⋉∼ℶ⋊⋉ ∼≊≂ ≈≂⅁≈ ≈≂ ∼≈ _inline_math_ ℶ∼ ∖ð≊⋖⅁∖ ℶ⋉ _inline_math_ ⋊⋉≈⅁ℶ⋉∼ ⅁ ⋖≊∤ \n",
      " 𝕊≊∣∣⋊∼ ≈≂⅁≈ _inline_math_ ℶ∼ ⅁ ⋗⅁∼≊∖⅁⋖ ⅁∖ℶ⋉⅁⋖ ⪷ℶ≈≂ _inline_math_∤ 𝕋≂⋉ ≈≂∖ ℶ∼ ⅁ ⅁∖ℶ⋉⅁⋖ ∣∖∼∖⪸ℶ⋉ð ↶≈⋉∼ℶ⋊⋉ ∼⅁≈ℶ∼℧↷ℶ⋉ð ≈≂ ℧⋊⋖⋖⋊⪷ℶ⋉ð⇍ ⊊⊮⊋ _inline_math_ ℶ∼ ⅁ ⋗⅁∼≊∖⅁⋖∦ ⊊⊭⊋ _inline_math_ ℶ∼ ⅁ ∖ð≊⋖⅁∖ ℶ⋉ _inline_math_ ⋊⋉≈⅁ℶ⋉∼ ⅁ ⋖≊_inline_math_∤ \n",
      " 𝕋≂ ∣∖⋊⋊℧∼ ⋊℧ ≈≂∼ ≈≂⋊∖⋗∼ ≊∼ ⅁⋉ ℶ≈∖⅁≈ℶ⋊⋉ ℙ∖ℶℸ∖↷ ≈↷∣ ℧⋊∖ℶ⋉ð ⋉⋊≈ℶ⋊⋉ ≈≂⅁≈ ⪷⅁∼ ℶ⋉≈∖⋊≊ ℶ⋉ ^𝔾ℶ⊮~∤ \n",
      " 𝔹⅁∼ℶ⅁⋖⋖↷ ℧⋊∖ ⪸∖↷ _inline_math_ ⪷ℶ≈≂ _inline_math_ ⪷ ⅁∖ ℧⋊∖ℶ⋉ð ⅁ ℙ∖ℶℸ∖↷ ⋊∖ 𝕄⅁ðℶ⋊∖ ∼∥≊⋉ ≈⋊ _inline_math_ ⪷ℶ≈≂⋊≊≈ ⅁ℶ⋉ð ⋉⪷ ⋊≊⋉ ∼≊∼≈∼∤ 𝕋≂ ⋊∖∖ ≈↷∣ ⋊℧ ≈≂ ∼∥≊⋉ ℶ∼ _inline_math_∦ ⪷≂∖ ≈≂ ↶∣⋊⋉⋉≈ℶ⅁≈ℶ⋊⋉ ℶ∼ ≈≂ ⋊∖ℶ⋉⅁⋖ ⋊⋉∤ 𝕋≂ ℧⋊∖ℶ⋉ð ≊∼ ℧⋊∖ ≈≂ℶ∼ ℶ∼ _inline_math_ ⪷≂ℶ≂ ⪷⅁∼ ℶ⋉≈∖⋊≊ ℶ⋉ ^𝔾ℶ⊮~∤ 𝕋≂ ℧ℶ⋉ℶ≈ℶ⋊⋉ ⋊℧ ℶ≈ ℶ∼ ∥≊ℶ≈ ⋖⋊⋉ð ⅁⋉ ⪷ℶ⋖⋖ ⋉⋊≈ ≊∼ ↶∣⋖ℶℶ≈⋖↷ ≂∖∤ 𝕋≂ ⋊⋉⋖↷ ℧⅁≈∼ ≊∼ ℶ⋉ ⋊⋉⋉≈ℶ⋊⋉ ⪷ℶ≈≂ ≈≂ℶ∼ ⅁∖ ∼≈⅁≈ ⋖⋊⪷∤ \n",
      " 𝔽⅁≈ ⊮∤ _inline_math_∦ _inline_math_∦ _inline_math_ ∼⅁≈ℶ∼℧ℶ∼ ℙ∖ℶℸ∖↷ ⋊⋉ℶ≈ℶ⋊⋉ ⅁⋉ ℶ≈ ℶ∼ _inline_math_∤⪷⅁ℸ⋖↷ ⋖⋊∼∦ ℶ∤∤ ⊊⅁⊋ _inline_math_⇏ ⊊⊋ ℧⋊∖ ⪸∖↷ _inline_math_ ⅁⋉ ⪸∖↷ ∼≈⅁≈⋗⋉≈ _inline_math_ ⋊℧ ≈≂ ℧⋊∖ℶ⋉ð _inline_math_ ≈≂∖ ℶ∼ _inline_math_ ℶℶ⋉ð _inline_math_⇏ ⊊⊋ _inline_math_ ℶ∼ _inline_math_∤⋖⋊∼∤ \n",
      "ko\n",
      "tar_file: arXiv_src_9401_001.tar\n",
      "extraction_tool: tarfile\n",
      "main .tex file club-reg.tex\n",
      "Finished in less than 2400 seconds\n",
      "\n"
     ]
    }
   ],
   "source": [
    "err, ddd = peep.tar('/mnt/promath/math94/9401_001.tar.gz', 'math.9401204')\n",
    "for D in ddd.para_list()[0:18]:\n",
    "    #print(etree.tostring(D, pretty_print=True).decode('utf-8'))\n",
    "    print(ddd.recutext(D))\n",
    "print(ddd.det_language(start_at=1))\n",
    "print(err)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 152,
   "metadata": {},
   "outputs": [],
   "source": [
    "with open('data/rm_me_05_article.xml', 'w') as fobj:\n",
    "    print(etree.tostring(ddd.exml, pretty_print=True).decode('utf-8'), file=fobj)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "from nltk.corpus import stopwords \n",
    "from nltk.stem.wordnet import WordNetLemmatizer\n",
    "import string\n",
    "stop = set(stopwords.words('english'))\n",
    "exclude = set(string.punctuation) \n",
    "lemma = WordNetLemmatizer()\n",
    "def clean(doc):\n",
    "    stop_free = \" \".join([i for i in doc.lower().split() if i not in stop])\n",
    "    punc_free = ''.join(ch for ch in stop_free if ch not in exclude)\n",
    "    normalized = \" \".join(lemma.lemmatize(word) for word in punc_free.split())\n",
    "    return normalized\n",
    "\n",
    "doc_clean = [clean(doc).split() for doc in para_text] "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Importing Gensim\n",
    "import gensim\n",
    "from gensim import corpora\n",
    "\n",
    "# Creating the term dictionary of our courpus, where every unique term is assigned an index. \n",
    "dictionary = corpora.Dictionary(doc_clean)\n",
    "\n",
    "# Converting list of documents (corpus) into Document Term Matrix using dictionary prepared above.\n",
    "doc_term_matrix = [dictionary.doc2bow(doc) for doc in doc_clean]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Creating the object for LDA model using gensim library\n",
    "Lda = gensim.models.ldamodel.LdaModel\n",
    "\n",
    "# Running and Trainign LDA model on the document term matrix.\n",
    "ldamodel = Lda(doc_term_matrix, num_topics=3, id2word = dictionary, passes=50)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(0, '0.023*\"extension\" + 0.023*\"system\" + 0.023*\"coherent\"')\n",
      "(1, '0.022*\"coherent\" + 0.022*\"system\" + 0.018*\"follows\"')\n",
      "(2, '0.034*\"value\" + 0.024*\"suppose\" + 0.023*\"critical\"')\n"
     ]
    }
   ],
   "source": [
    "for l in ldamodel.print_topics(num_topics=3, num_words=3):\n",
    "    print(l)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Title:\n",
    "#### ON THE GEOMETRY OF MODULI SPACES OF COHERENT SYSTEMS ON ALGEBRAIC CURVES"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "#prepare the dataset\n",
    "allData = pd.DataFrame()\n",
    "with open('../2000_defs.txt','r') as f1:\n",
    "    all_data_texts = f1.readlines()\n",
    "all_data_labels = len(all_data_texts)*[1.0]\n",
    "with open('../out_2000.txt', 'r') as f2:\n",
    "    all_data_texts_rand = f2.readlines()\n",
    "all_data_texts += all_data_texts_rand\n",
    "all_data_labels += len(all_data_texts_rand)*[0.0]\n",
    "\n",
    "# 1.0 will represent definitions is true 0.0 means it is false (not a definition)\n",
    "allData['labels'] = all_data_labels\n",
    "allData['texts'] = all_data_texts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "train_x, test_x, train_y, test_y = model_selection.train_test_split(allData['texts'], allData['labels'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "853     a triangulated category         is of finite t...\n",
       "1868           proof. by the expression of , all the r...\n",
       "255              let  be an open covering of m, with l...\n",
       "451              suppose we are given control data  on...\n",
       "752            the quantity  defined for a -tuple of c...\n",
       "1195    consider the following attributes of a cell   ...\n",
       "454              let  be a  function, let  be a -like ...\n",
       "43      for             put                           ...\n",
       "1982                                                   \\n\n",
       "169                    let  be a face of the triangula...\n",
       "1477    torus action and localization formula   \\mylab...\n",
       "832               is said to be pseudoeffective, if th...\n",
       "434     a subset           of a simplicial complex  ha...\n",
       "1411    we consider a prime divisor           on  whic...\n",
       "1693                                                   \\n\n",
       "936                                                    \\n\n",
       "552              the set of isomorphism classes of tri...\n",
       "802     let           be a normal complex variety with...\n",
       "895     let           be an -pointed, prestable curve ...\n",
       "981     this problem and the above mentioned corollary...\n",
       "1474    let           be a marked point of the curve ....\n",
       "426            for a given jnf  define its correspondi...\n",
       "442              for any -motive , we define its -th c...\n",
       "1494                         technical preliminaries   \\n\n",
       "1092         each  () is represented by a scheme  that...\n",
       "Name: texts, dtype: object"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "train_x.head(25)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "count_vect = CountVectorizer(analyzer='word', tokenizer=nltk.word_tokenize, ngram_range=(1,2))\n",
    "count_vect.fit(allData['texts'])\n",
    "xtrain = count_vect.transform(train_x)\n",
    "xtest = count_vect.transform(test_x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "             precision    recall  f1-score   support\n",
      "\n",
      "        0.0       0.61      0.93      0.73       174\n",
      "        1.0       0.95      0.68      0.79       327\n",
      "\n",
      "avg / total       0.83      0.77      0.77       501\n",
      "\n"
     ]
    }
   ],
   "source": [
    "clf = naive_bayes.MultinomialNB().fit(xtrain, train_y)\n",
    "predictions = clf.predict(xtest)\n",
    "print(metrics.classification_report(predictions,test_y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[20  3]\n",
      " [13 26]]\n"
     ]
    }
   ],
   "source": [
    "print(metrics.confusion_matrix(predictions,test_y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "         suppose that  holds with . then there exists a sequence of permissible monodial transforms  such that the following properties hold:                                                       (1)                                        holds.                                     (2)                                       all bad 2 points  satisfy ().                                     (3)                                       suppose that  is a curve which is r big at a 1 point. then there exists at most one 3 point  and  has a tangent direction at  distinct from those of  at . furthermore, if  is not r big, there exists only one 2 point . if  is the 2 curve containing , then  is not r-1 big or r small.                                   (4)                                       if  is a r small or r-1 big 2 curve containing a 2 point  such that  where  is a curve containing a 1 point and  is r big at , then  is r big.\n",
      "\n",
      " -------------1737\n",
      "if         is an oriented cycle in  then for any  there is a trace function                       where      . it is invariant under the action of .\n",
      "\n",
      " -------------1590\n",
      "let us take a sufficiently large positive integer           and let  be a general (nonzero) element of . we define a singular hermitian metric  on  by                             then                                      holds, where           denotes the closed positive current defined by the divisor . hence  is a closed positive current. let  be a positive number and let  denote the multiplier ideal sheaf of , i.e.,                             where           is an arbitrary -hermitian metric on . let us define a positive number  by                             since           is not locally integrable around , by the construction of , we see that                             holds. then one of the following two cases occurs.         case 1.1: for every small positive number ,  has -stalk at both  and . case 1.2: for every small positive number ,  has nonzero-stalk at one of  or  say .  \n",
      "\n",
      " -------------1503\n",
      "wenowexplainthemotivationbehindtheorems         andcomingfromthetheoryofmiddleperversityperversesheaves.letbeasinsection1.2.associatedtothepairisthecategoryofmiddleperversityperversesheavesonconstructiblewithrespectto.thiscategorywasfirstintroducedbybeilinson,bernstein,anddeligneintheseminalpaper[in1982.theydefined]asafullsubcategoryof,thebounded-constructiblederivedcategoryofsheaveson.thiswayinheritsanadditivestructurefrom.infact,itturnsouttobeanabeliancategory,unlikethederivedcategory.perversesheavesare“simpler”thanthederivedcategoryinseveralotherrespects.forexample,theyformastack(i.e.,objectsandmorphismsarelocallydefined),whichisnotthecasefor.forthesereasons,itwaslongfeltdesirabletohaveadefinitionofwhichdoesnotrelyonthemorecomplicatedderivedcategory,andwhichelucidatestheverysimpleformalpropertiesofperversesheaves.suchadefinitionwasproposedbymacphersoninhisamslecturesinsanfranciscoinjanuary1991.informalnotesofthoselectures[producedbymacpherson(anddated1990)weredistributedatthemeeting,butwereneverpublished.aslightlymodifiedversionofthesamedefinitionhasnowappearedinprintinthelecturenotes][fromthesummerinstituteheldinparkcity,utahinjuly1997.roughly,macpherson’sdefinition(the1997version)proceedsasfollows.aperversesheaf]isanassignment,pluscoboundaryandpull-backmaps,subjecttoasetofaxiomsmodeledaftertheeilenberg-steenrodaxioms.hereisastandardpairin,thatisapairofcompactsubsetsofacertainspecialkind.namely,isasmooth,realdimensionalsubmanifoldofwithcornersofcodimensiontwo,andisaunionofsomeofthewallsof,sothateachcornerisformedbyonewallfromandonewallnotfrom,andalltheboundarystrataofaretransverseto.itisaverypleasantfeatureofthisdefinitionthatweonlyneedtoconsiderstandardpairs.thestructuregroupiscalledthecohomologyofrelativetowithcoefficientsin;itisafinitedimensional,gradedvectorspaceover.turningnowtotheaxioms,allbutone(thedimensionaxiom)representamoreorlessstraightforwardadaptationoftheclassicaleilenberg-steenrodtothesettingofpairsinsideafixedspace.theremainingaxiomrunsasfollows.dimensionaxiom:letbeapropermorsefunction,andbeavaluesuchthatcontainsexactlyonecriticalpoint:.then                             for                      and_           .hereishowthisdefinitionfitswiththeideaofself-indexing.givenastandardpair,onecanuseavariantoftheoremtofindaself-indexingfunction                             whichis         adaptedtothepair.moreprecisely,thismeansthat,,andthelevelsetsof“looklikepagesofabook”nearthecorners.now,justasinclassicalmorsetheory,suchafunctiongivesrisetoafunctor                             withthepropertythat         forevery.ifwewrite,thenthefunctor                             breaksupintoadirectsumover                      oftheso-called_           morsegroupfunctors                             eachofthe       islocalizednear,i.e.,factorsthroughtherestrictiontoanyopenneighborhoodof.(perversesheavesonopensubsetsofandrestrictionfunctorsbetweenthemaredefinedintheobviousway.)moreover,asimpliedbythenotation,thefunctordependsononlythroughthedifferential.theexistenceoftheliftfromcohomologytocochaincomplexeswiththeaboveproperties,byitself,hasimportantconsequencesforthestructureofthecategory.forexample,itimmediatelyimpliesthatmorphismsofperversesheavesarelocallydefined.moreistruehowever:thefunctoris,insomesense,independentof;theonlyessentialdependenceisonthepair.tobeprecise,givenanytwoself-indexingfunctionsadaptedto,thefunctorsandarerelatedbyaquasi-isomorphismwhichisitselfcanonicaluptochainhomotopy.areaderfamiliarwithfloerhomologyhas,nodoubt,anticipatedthis.however,unlikeinfloerhomology,thisindependenceofthefunctionrequiresaproofwhichisrathermoreinvolvedthantheproofof.(thelaterisastraightforwardconsequenceoftheaxioms.)oncetheindependenceofthefunctionisestablishedinasuitablyflexibleform,allofthe(soft)formalpropertiesofperversesheavescanbederivedfromconsideringthecomplexesfordifferentfunctionsandstandardpairs.forexample,theabelianpropertyoffollowseasilyfromtheabelianpropertyofthecategoryofcochaincomplexes.finally,onecandevelopthetheoryofperversesheaves,startingwithmacpherson’sdefinition,tothepointofprovingthefollowing.{thm}macpherson’sdefinitionofagreeswiththeoriginaldefinitionduetobeilinson-bernstein-deligne.thepresentauthorhasrecentlyhadanopportunitytoworkthroughaproofoftheoreminagraduatecourseatmit,andafuturepaperdescribingthisproofisbeingplanned.thegoalofthepresentpaperistoprovidethemaingeometrictool:self-indexingmorsefunctions.weconcludethisintroductionwithaconjectureduetomacpherson.{conj}omittingthedimensionaxiomfrommacpherson’sdefinitionofgivesacategorywhichisequivalentto.acknowledgments.iwouldliketothanktheihesinbures-sur-yvettefortheirhospitalityduringaugust99whenmostofthisworkwasdone.myintellectualdebttobobmacphersonisclearfromtheprecedingintroduction.iamalsogratefultothestudentsinmycourseatmitforpatiently(butnotuncritically)allowingmetothinkthroughtheseideasoutloud.\n",
      "\n",
      " -------------1491\n",
      "despite from these facts,       and  are not isomorphic as bialgebras themselves. in fact, there exists no antipode which makes  a hopf algebra. recall that an antipode is a linear map , such that  and for each non-empty partition  we have , or equivalently                 where     isgivenby().takingwegetwhichimpliesthatwhere.sinceisequaltothesumoftheelementsforallpartitions,thisisnotanelementof.however,isnotfarfrombeingahopfalgebra.infact,ifweletbethelocalizationgeneratedbyand,thenisahopfalgebra.toseethis,noticethat()impliesthatwhereisthenumberofinnercornersof,i.e. thenumberofindicessuchthat.by()wethereforeseethatanantipodemustsatisfy                 thisequationcanbeusedtodefine     .theobtainedantipodeisfurthermorearinghomomorphism,sinceitmustagreewiththeantipodeontheringofsymmetricfunctionsextendedto.regardingthestructureofasanabstractring,weconjecture:{conj}(a)anystablepolynomialcanbewrittenasapolynomialintheelementsforrectangularpartitionscontainedin.(b)theelementscorrespondingtopartitionswithonlyoneroworonecolumnarealgebraicallyindependent.part(a)ofthisconjecturehasbeenverifiedforallpartitionsofweightatmost9.for(b),ifwedefinethedegreeofamonomialintheandtobethetotalnumberofboxesinthepartitionsofthefactors,thenallsuchmonomialsofdegreeupto9arelinearlyindependent.furthermore,itisnothardtoprovethatforanyinteger,theelementsarealgebraicallyindependent.namely,ifoneusesthelexicographicorderonpartitions,thenthemonomialsintheseelementsallhaveadifferentmaximalpartitionforwhichthecoefficientofisnon-zero.theconjecturehassomeinterestingconsequencesforthestructureof.if(a)istrue,thenisgeneratedbythetheelements,inadditionto.toseethis,noticethatifisarectangularpartitionwithatleasttworowsandtwocolumns,andisthepartitionobtainedbyremovingtheboxinthecornerof,then                 using(a)thisshowsthat     canbewrittenasapolynomialin,,andtheelementsforrectangleswhicharestrictlycontainedin.thisshowsthatisintheringgeneratedbytheelements,,andbyinductiononthesizeof.however,if(b)istruethentheelementsanddonotgenerateasaring.infact,theidentity                 impliesthat     can’tbewrittenasapolynomialintheseelementsiftheyarealgebraicallyindependent.geometrically,thefactthatisacommutativeandcocommutativebialgebraimpliesthatisanabeliansemigroupscheme.theexistenceofanantipodeonmeansthatthedenseopensubsetisagroupscheme.furthermore,if\\refconjconj_abistruethenthisopensubsetlookslikeaninfinitedimensionalaffinespacewithahyperplaneremoved.wewillfinishthispaperbyraisingsomeadditionalquestions.firstofall,severalpeoplehaveaskeduswhenasymmetricpowerseriesinisanelementin.evenwhenthevariablesaresettozero,wedonotknowtheanswertothis.inviewof\\refconjconj_abitwouldbeveryinterestingtoknowtherelationsbetweentheelementsforrectangularpartitions.wehavealsobeenwonderingifmightbeapolynomialring,i.e. aretherealgebraicallyindependentelementsinsuchthat?wethinkthisisnotthecasebuthaven’tbeenabletoproveit.itisnothardtoseethatthesinglegrothendieckpolynomialsforallpermutationsformabasisforthepolynomialring.forexample,onecancheckdirectlythatthegrothendieckpolynomialsforpermutationsingiveabasisforthelinearspanofallmonomialsforwhichforeach.alternativelyonecanuseastrongerresultoflenart[whichexpressesanysinglegrothendieckpolynomial]asanexplicitlinearcombinationofschubertpolynomialswithalternatingsigns,i.e. thesignofthecoefficientofis.ontheotherhand,lascouxhasconjecturedthateachsingleschubertpolynomialisanon-negativelinearcombinationofgrothendieckpolynomials.nowdefinegrothendieckstructureconstantsby                 theseconstantsaregeneralizationsofthestructureconstantsforschubertpolynomialsaswellasthecoefficients   discussedinthispaper.if,,andaregrassmannianpermutationsfor,,andwithdescentsatthesameposition,then.basedonourresultsforgrothendieckpolynomialsofgrassmannianpermutationsgiveninthispaper,aswellasonsomecomputationalevidence,wepose:{conj}thestructureconstantsforsinglegrothendieckpolynomialshavealternatingsigns,i.e. .\n",
      "\n",
      " -------------1299\n",
      "       . all points from  sufficiently close to  are good as well (this follows easily from the basic technical tool in the additive version). hence, the same polynomial  evaluated for  corresponding to points close to  is still a matrix with at least two distinct eigenvalues which will be close to two of the eigenvalues of  evaluated at  (denoted by , ). suppose that . hence, for all points from  close to  (denote their set by ) the polynomial  evaluated at them has an eigenvalue  with .\n",
      "\n",
      " -------------1821\n",
      "             the -module  is absolutely simple;\n",
      "\n",
      " -------------1126\n",
      "             let  be a scheme of finite type over  and  two morphisms, such that the pullbacks of  via  and  are equivalent. then, there exist an étale covering  and a morphism , such that the morphism  equals the morphism                                       \n",
      "\n",
      " -------------1440\n",
      "       m := fold((m, i) -> m ||\n",
      "\n",
      " -------------1578\n",
      "       being ,  is a projection of a rational normal scroll  of the same degree. the center  of such projection () is disjoint of , and is contained in the space generated by . moreover , being  or . conversely, every –dimensional rational normal scroll can be projected to  in this way, obtaining the focal scroll of a congruence of order  in the case ii without fixed points.\n",
      "\n",
      " -------------1138\n",
      "a quasi-projective variety is called        algebraic hyperbolic if it does not contain a curve whose normalization is an elliptic curve or a rational curve with two points removed, i.e., .\n",
      "\n",
      " -------------1144\n",
      "   problem. if a hypersurface  in  is isomorphic to a coordinate hyperplane, is it true that  vanishes nowhere? \n",
      "\n",
      " -------------1791\n",
      "if     are two partitions, let  denote the skew diagram of boxes in  which are not in , and let  be the number of boxes in this diagram. now choose a numbering of the north-west to south-east diagonals in the diagram with positive integers, which increase consecutively from south-west to north-east. for example, if  and , and if the bottom-left box in  is in diagonal number , then the numbering is given by the picture: \\[ \\tableauskew \\] let  be the sequence of diagonal numbers of the boxes in  when these boxes are read from right to left and then from bottom to top. we then let  be the product of the corresponding simple reflections. for the skew shape above this gives . notice that  depends on the numbering of the diagonals as well as the diagram . a theorem of billey, jockusch, and stanley \\citebilley.jockusch.ea:some says that a permutation  can be obtained from a skew diagram in this way, if and only if it is 321-avoiding, i.e. there are no integers  for which .\n",
      "\n",
      " -------------1290\n",
      "         step 1 : stability of smooth blow-downs. fix  in the smooth locus  of  and suppose that  is a fano -fold and there exists a smooth blow-down of  (denote by  the exceptional divisor,  its hilbert polynomial with respect to ). let  be the component of the hilbert scheme of -dimensional subschemes of  with hilbert polynomial  and  the universal family. finally, let  be the following subscheme of  :                             and         the proper algebraic map induced by the first projection. thanks to the analytic stability of smooth blow-downs due to kodaira (see [, theorem 5), the image ] contains an analytic open neighbourhood of  hence it also contains a zariski neighbourhood of . moreover, since exceptional divisors are rigid, the fiber  is a single point for  in a zariski neighbourhood of . finally, we get algebraic stability of smooth blow-downs (the -fibered structure of exceptional divisor is also analytically stable - [, theorem 4 - hence algebraically stable by the same kind of argument).]\n",
      "\n",
      " -------------1061\n",
      "consider the universal line through the origin        . it intersects  in two further points which correspond to the roots of the quadratic equation                       the equation is irreducible if       is irreducible. let its roots be .\n",
      "\n",
      " -------------1383\n",
      "let               be a radical ideal. then the symbolic powers  form a graded family of ideals that we denote by .\n",
      "\n",
      " -------------1357\n",
      "              for every \n",
      "\n",
      " -------------1700\n",
      "(2) for any birational morphism     from a normal variety, if we write , then all the coefficients of  are at most  (resp. strictly less than , at most  and strictly less than  for exceptional divisors).\n",
      "\n",
      " -------------1189\n",
      "we consider complete linear series on             arising from weierstrass non-gaps which will be useful for applications to optimal curves. let , set  and consider . then                                                  (1)                                                             is a  base-point-free on ;                          (2)                                             the                -orders are , .\n",
      "\n",
      " -------------1846\n",
      "let         be a positive integer that satisfies  and . then by [ and ][, there exists a ]-surface  with an action  of order  and . let  and . let  act on  by trivial action on  and the action above on . let  be the quotient of  by  with . then  is a log calabi-yau 3-fold with global index .\n",
      "\n",
      " -------------1139\n",
      "let       be the set of all matrices, which appear from  by permutation of columns. let  be the number of such matrices. put us                 where the sum is taken by all                    \n",
      "\n",
      " -------------1341\n",
      "we still denote by         a family of non-degenerate morphisms to  over . we will conclude this section by showing that there is a canonical closed subscheme structure on  making it the closed subscheme parameterizing all pre-deformable morphisms over .\n",
      "\n",
      " -------------1688\n",
      "for    , there is a natural contraction map  defined by composing the map  with  (so that the components of  carrying  special points become unstable) and contracting the unstable components. similarly, one can define the forgetting maps  by disregarding the -th marked point and contracting the component if it has become unstable.\n",
      "\n",
      " -------------1183\n",
      "       then for every positive integer , the -th plurigenus  is independent of .\n",
      "\n",
      " -------------1983\n",
      "in these terms, a system consisting of a period subgroup in       and compatible automorphy factors becomes simply a homomorphism, which we will call a multiplier,                 where     is a free abelian group of the same rank as  and  is a bijection. (we will find convenient in the future to weaken these restrictions).\n",
      "\n",
      " -------------1883\n",
      "         a function  defines an order  on  as follows:\n",
      "\n",
      " -------------1991\n",
      "let us center and scale the random variables          , that is, introduce the variables                             we have           and                             as          , where, see example ,                             here                                      it follows from our wick formula, see theorem          , that the leading asymptotics of averages of the form                             is given by the usual wick rule with the covariance matrix (       ). hence the variables  are asymptotically gaussian normal with mean zero and covariance (). they describe the gaussian fluctuation of a typical partition of  around its limit shape.\n",
      "\n",
      " -------------1506\n",
      "             restricted to the nontwisted sectors, i.e., the ordinary dolbeault cohomologies , the cup product  equals the ordinary wedge product on .\n",
      "\n",
      " -------------1431\n",
      "5. if the conditions of theorem           are satisfied for the collection , , then they are also satisfied for the collection ,  where  is any character. for example, for any characters  we have                                                                                                                                                                                                                                            \n",
      "\n",
      " -------------1132\n",
      "the subspace           is defined as follows. let  describes an deformation  where  is an artin algebra or a projective limit of artin algebras. to such deformation we associate an module  in  representing morphism . let  be rescaling operator:                             denote           the subspace of elements of the formthe action of  on arbitrary element from  is well-defined even in the case when  is a pro-artin algebra since  belongs to subspace of elements of the form .                            \n",
      "\n",
      " -------------1515\n",
      "              has a reduced component for a general point  of the discriminat locus of .\n",
      "\n",
      " -------------1809\n",
      "           the modified equivariant integral  corresponding to  is defined as follows                                 \n",
      "\n",
      " -------------1307\n",
      "let us denote       by , and let  be the canonical class of . \n",
      "\n",
      " -------------1732\n",
      "let           be an ample line bundle on  and let  be a -hermitian metric on  with strictly positive curvature. we may and do assume that for every pseudoeffective singular hermitian line bundle ,  is globally generated (cf. [). we set , proposition 1.1] and let  be the bundle projection. let  be the unit disk bundle associated with the hermitian line bundle . then  is a family of strongly pseudoconvex manifolds over . we denote the bundle projection  again by  and we shall identify  with the zero section of . let  be a -hermitian metric on . let  a -volume form on  and let  be the restriction of  to . we define (the diagonal part of) the -th bergman kernel  of  by                             where         is a complete orthonormal basis of the hilbert space  of -holomorphic sections of  with respect to  and  and .\n",
      "\n",
      " -------------1903\n",
      "     lemma 2.17.  fix  with . let  be of bidegree , and                      then,  is equal to the sum of the following two terms:                       and                                       where for each fixed  with ,  runs over all the maps                    satisfying . moreover, , , and .\n",
      "\n",
      " -------------1718\n",
      "the next lemma is valid for any       if  acts faithfully on  and if rank .\n",
      "\n",
      " -------------1908\n",
      "if         is dlt, then  is sdlt.\n",
      "\n",
      " -------------1249\n",
      "the sheaf                 is isomorphic to the canonical (dualizing) sheaf .\n",
      "\n",
      " -------------1677\n",
      "       for each , the divisor germ  is not -cartier.\n",
      "\n",
      " -------------1642\n",
      "consider the        -uple veronese embedding of  into , where . pick a line  skew to  in . let  be the linear join of the image  of  under this embedding and the line . blowing up  along  we obtain a fourfold  which is a -bundle over . now  is isomorphic to , where  is a rank  vector bundle over .\n",
      "\n",
      " -------------1897\n",
      "            is the projectivization of a rank  vector bundle over a smooth curve  and .\n",
      "\n",
      " -------------1226\n",
      "andrei căldăraru   \n",
      "\n",
      " -------------1949\n",
      "         b) is it true that the grassmannian -logarithm  admits a motivic construction?\n",
      "\n",
      " -------------1872\n",
      "(note that in general the preimage           is the same as the stack  introduced in sect.  and the map  becomes the map .)\n",
      "\n",
      " -------------1995\n",
      "let           and  be two -tuples of integers. we also think of  as elements of  in the following way:                             and through this identification we define an action of           on . we define also . once  are fixed we fix complex vector spaces  and  of dimensions  and  and we define the following spaces of maps:                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           more often, when it will not be ambiguous we will write         and  instead of  and .\n",
      "\n",
      " -------------1186\n",
      "our specialized matrix will look as follows:                                      applying linear operations in the rows and columns of           it can be transformed into:                              where the block         is square and of size \n",
      "\n",
      " -------------1544\n",
      "       proof of proposition  we take . as                       with the initial point         and put                       let us define a meromorphic function         on  by  then                     \n",
      "\n",
      " -------------1604\n",
      "tht1    \\psfragtht2 \\psfraglambda \\psfragsigma \\psfragmu \\psfragt1 \\psfragt2 \\psfragt3 \\psfragt4 \\psfragt5\n",
      "\n",
      " -------------1296\n",
      "       each proper normal algebraic surface admits a nonfree vector bundle.\n",
      "\n",
      " -------------1224\n",
      "assume that         contains . there is a non-trivial birational automorphism of                        clearly,       is the identity map and the set of fixed points of  coincides with .\n",
      "\n",
      " -------------1622\n",
      "         let  be of pure dimension and  a stable subset. if  is a countable covering of  by stable subsets with  as , then  is covered by a finite subcollection of .\n",
      "\n",
      " -------------1526\n",
      "set           and . note to begin with that  for all , from which it follows that the limit  exists. call this limit . we will prove the theorem by establishing (from right to left) the inequalities                           \n",
      "\n",
      " -------------1540\n",
      "let       be defined as in definition , then\n",
      "\n",
      " -------------1243\n",
      "the graph         is decorated as follows. any vertex  is decorated with three numbers. the first is the self–intersection . equivalently,  is the euler–number of the normal bundle of  in . the second is the genus  of . the third decoration is given by the multiplicity of . more precisely, for any , let  be the vanishing order of  along the irreducible divisor corresponding to . for example, if  defines an isolated singularity, then for any  one has .\n",
      "\n",
      " -------------1151\n",
      "before proving the lemma, we need the following easy consequence of the projectivity of        . we say a moment graph  is flexible at  if for any  and any , , there is a degree two section  so that , , and  for all vertices .\n",
      "\n",
      " -------------1637\n",
      "for       ,letbetheuniquefiberoftheellipticfibrationinwhichlies,andletbethepointofthatisintheimageofthesection.thentherestrictionisisomorphictooneofthesheavesconsideredinsection ,andthereforeitissemistableonthefiber.thisallowsustoconsiderasabasespace,parametrizingsheavesonthefibersof.allthesheavesaresemistableofrank1,degree0,sowegetanaturalmap,whichonlydependsonthechoiceofthesection.usingourknowledgeofthegeometryofthefibersofweseethatthemapisanisomorphismawayfromthefibersof,whereitcontractsthecomponentofthefiberthatisnothitbythesection.(onemustremarkherethatsinceisasection,itcannotpassthroughanyofthesingularpointsofthesingularfibersof.)sincethecontractedcomponentshavenormalbundleby ,thecontractionofsuchacomponentgivesanordinarydoublepoint(odp)in.reversingthepointofview,isasmallresolutionofthesingularitiesof.\n",
      "\n",
      " -------------1943\n",
      "keep notation as above. there exists a lift                                              of             with the following properties.         \n",
      "\n",
      " -------------1785\n",
      "(of proposition        ) we construct an auxiliary irreducible variety  and a zariski open subset . the subset  maps surjectively onto . the scheme  is a relative quot scheme over a subset  of a quot scheme  of vector bundles. we recall the construction of  following seshadri [.]\n",
      "\n",
      " -------------1733\n",
      "if       is a loopfree vertex (so ) there is a reflection  defined by , and a dual reflection  with . the reflection at vertex  is said to be admissible for the pair  if . in this case it is shown in [ that there are reflection functors relating ]-modules of dimension  with -modules of dimension . let  be the equivalence relation on  generated by  whenever the reflection at  is admissible for . we say that  is obtained from  by a sequence of admissible reflections if they are in the same equivalence class.\n",
      "\n",
      " -------------1589\n",
      "       the holomorphic family  defines an algebraic integrable system on the moduli space of three dimensional cy manifolds  in the sense of r. donagi and markman.\n",
      "\n",
      " -------------1240\n",
      "       suppose . then each weil divisor on  is numerically equivalent to a -cartier divisor. moreover,  is projective.\n",
      "\n",
      " -------------969\n",
      "               for any integers  we have                                                                                                                                                                                                                                                                                            \n",
      "\n",
      " -------------1964\n",
      "              is invariant under the actions of  and . \n",
      "\n",
      " -------------1348\n",
      "we describe this enumerative problem. let       be integers. the space  of maps  of degree  from  to , the grassmannian of -planes in , has dimension  [. given a point ] and an -plane  in , the set of maps  which satisfy  (the -plane  meets the -plane  non-trivially) is a divisor on this space of maps. we consider the following enumerative problem:\n",
      "\n",
      " -------------1932\n",
      "let         be a pseudoeffective singular hermitian line bundle on a complex manifold . the closure  of the multiplier ideal sheaf  can be analysed in terms of lelong numbers in the following way. we note that  is coherent ideal sheaf on  by theorem 2.1.\n",
      "\n",
      " -------------1904\n",
      "               if  is an integer such that  for , then there is a natural -equivariant inclusion                                             \n",
      "\n",
      " -------------1789\n",
      "       suppose that  is a smooth morphism to a nonsingular variety. suppose that  is a purely codimension  subscheme of , and that the composite  is proper and flat. for a closed point  of , let  be the fiber. if the segre classes , …,  specialize to the corresponding classes ,…, , then the same is true of the higher codimension segre classes , , etc.\n",
      "\n",
      " -------------1762\n",
      "(i) every          -fixed points of  is of the form , where  and  is an -fixed point of , and for any such point ,\n",
      "\n",
      " -------------1587\n",
      "             let  be a factorization of  into a product of two positive integers  and . then either there does not exist an absolutely simple -module of -dimension  or there does not exist an absolutely simple -module of -dimension .\n",
      "\n",
      " -------------1127\n",
      "as before we will sometimes write       and  for the moduli space  and its universal curve , respectively, if no confusion can arise.\n",
      "\n",
      " -------------1473\n",
      "having       andwecanapplythecriterionoftheorem totheextensionbyzeroofto.(onecanpushforward,sinceboththetwistingonandonispulledbackfrom.)notethatthesheavesforarepreciselyofproposition ,andtheyhavetheorthogonalitypropertyrequired.thereforetheintegraltransforminducedbyisfullandfaithful.finally,sincethecanonicalclassofthefibersofistrivial,thelastconditionoftheorem isvacuouslytrue,andhenceisanequivalenceofcategoriesbetweenand,thusfinishingtheproofoftheorem .\n",
      "\n",
      " -------------1939\n",
      "       for any  there exists a polynomial  such that  is a grã¶bner basis for every  not containing .\n",
      "\n",
      " -------------1182\n",
      "the        support of  is by definition the reduced support of , or equivalently of . if , where the  are distinct, then , where each  is supported at . we shall only be concerned in this paper with bundles  such that the support of  is contained in . we can see the structure of  concretely in this case: if  is a line bundle of degree zero, let . given a point , we let  be the corresponding line bundle of degree zero. then it is easy to check the following:\n",
      "\n",
      " -------------1841\n",
      "a (rational) hodge structure of weight           is a -vector space  with a decomposition of its complexification  (where complex conjugation is given by  for  and ):                             note that we insist on         and  being non-negative integers throughout this paper, so we only consider ‘effective’ hodge structures.\n",
      "\n",
      " -------------1630\n",
      "         one has the equalities                                    where given an ideal sheaf ,  denotes as above the least integer  such that  is globally generated.\n",
      "\n",
      " -------------1539\n",
      "now, assume (4.3.2b) holds and        . the sheaves  and  define natural maps  and . as above,  is defined along , and the projective subspace  spanned by  has dimension . in addition,  is defined along , and  spans . let  be the set of all linear maps  sending  to  for each . as above, we define an isomorphism .\n",
      "\n",
      " -------------1618\n",
      "we set                                      for a coherent sheaf           of ,                           \n",
      "\n",
      " -------------1652\n",
      "           let  be a multi-index . we have                                              where  and, as usual,                                              similarly,                                 \n",
      "\n",
      " -------------1505\n",
      "kawamata’s covering construction (see        [, 2.2) allows to choose a finite covering ] with  non singular. blowing up centers in fibres over , we obtain a non-singular variety  and a generically finite map , such that all the fibres of                       are normal crossing divisors. by abuse of notations we will add some points to      , hence some fibres to , and assume that  is smooth outside of  and that  is finite outside of . let  be the induced map. since  factors through a non-singular variety, finite over , the higher direct images  are zero for .\n",
      "\n",
      " -------------1066\n",
      "   dedicated to herb clemens\n",
      "\n",
      " -------------1716\n",
      "       definition. let the eigenvalues  not be strongly generic. hence, there holds at least one equality of the form\n",
      "\n",
      " -------------1322\n",
      "                                  1.                                 for each point            ,  lies in , the linear subspace of fixed points of .                    2.                                 the space of all             sections of , denoted by , has a structure of vector space over  (or ) as well as a -module structure.                  3.                                 the             sections  are in  correspondence with the underlying continuous maps .\n",
      "\n",
      " -------------1275\n",
      "to define the regulator map from this gadget to the complex         we specify it for each of  where . namely, we take the constructed in theorem () homomorphism  for  and multiply it by . notice that the distribution  depends only on the generic point of a subvariety . its image in the bicomplex described in the section 3.1 is in                       which is the triangle symmetric with respect to the diagonal in the         square presented on the picture below.     \n",
      "\n",
      " -------------1156\n",
      "let         be some cohomology classes of the toric manifold , and  some cycles poincaré dual to the classes : . then batyrev’s quantum intersection product in batyreví¦ ring  is defined by the requirement that                       for all        , and linearity. here the sum is over all  such that the intersection product in the sum is supposed to be of virtual dimension zero, i. e. such that                       where       is the number of one–dimensional cones in .\n",
      "\n",
      " -------------1720\n",
      "   corollary 4. if  is a contact projective manifold with , then  is a projectivized hyperplane bundle  associated with some projective manifold .\n",
      "\n",
      " -------------1252\n",
      "of course, the usual (real) variations are examples of complex variations. these satisfy the additional    reality constraint . conversely, a complex variation  together with its complex conjugate, defines a real variation of hodge structures on  in the obvious manner. in passing, we observe however that we can have complex variations of any given pure type. if for instance  has the property that it is preserved by  i.e., if it is a flat subbundle, it is itself a complex variation.\n",
      "\n",
      " -------------1568\n",
      "             if  belongs to  for all , then .\n",
      "\n",
      " -------------1997\n",
      "the        monodromic grothendieck group  is defined as the abelian group generated by symbols  (also denoted by , or simply ), for  an -variety with good -action, with the relations  if  and  are isomorphic as -varieties with  -ction, and  if  is zariski closed in  with the -action on  induced by the one on , and moreover  where  is the -dimensional affine space over  with any good -action, and  is taken with the trivial -action. there is a natural ring structure on , the product being induced by the fiber product over . we write  to denote the class in  of  with the trivial -action.\n",
      "\n",
      " -------------1447\n",
      "we return to the proof of theorem          . the maximal ideal of the polynomial ring  lying over  is of the form  for some monic polynomial  whose reduction  remains irreducible over . write  for a splitting field of , so that  with , and repeated factors if  is inseparable. let  be a ring extension as in , (i–ii). we write  and , and extend  to an isomorphism  given by the same formula . the extended rings  and  are gorenstein by proposition , (iii). thus                             is the unprojection ring constructed from the local ring         and the ideal .\n",
      "\n",
      " -------------1848\n",
      "         under the assumptions of the previous proposition, there is an exact sequence                                    where  denotes the full tate module of  and  is a finite abelian group whose prime-to- part is isomorphic to that of the (dual of) the group  considered above and whose -part is isomorphic to the (dual of) the -primary torsion subgroup of .\n",
      "\n",
      " -------------1662\n",
      "let         with  be two objects of . if  we define                     \n",
      "\n",
      " -------------1918\n",
      "       if  is a minimal smooth surface,  a disc in , and  any proper holomorphic map whose generic fiber  ( ) is irreducible and rational, then  is a (trivial) –bundle over .\n",
      "\n",
      " -------------1154\n",
      "if        :\n",
      "\n",
      " -------------964\n",
      "         the first three cohomology sheaves of  are                                                       •                                       .                                     •                                       .                                   •                                       . this symbol denotes the lagrangian obstructions, that is,  is the sheaf of obstructions to extend a lagrangian deformation to higher order regardless whether it can be extended as a flat deformation.\n",
      "\n",
      " -------------1028\n",
      "           definition: we call the homological chevalley complex of the dg lie algebroid  with coefficients in the right dg-module  the standard semiinfinite complex for the chiral module  over the lie-* algebra  and denote it by . remark: note that as the d-module on  the constructed complex looks as follows:                                                                                                        here as before           denotes the projection .\n",
      "\n",
      " -------------1414\n",
      "(c)    automorphy factors and theta functions on  any formal theta function (0.5) can be interpreted as a formal function on ., an infinite linear combination  this takes care of equations (0.1).\n",
      "\n",
      " -------------1884\n",
      "                for all .\n",
      "\n",
      " -------------1421\n",
      "let       be a generalized rational okamoto-painlevé pair. if  is of fibered type, that is, if there exists an elliptic fibration  with , pulling back non-constant regular algebraic functions on , we have many non-constant regular functions on . we can prove the converse of this fact.\n",
      "\n",
      " -------------1435\n",
      "letusstartbyexplainingthestatementofthetheorem.insection        wesawthattherelativejacobianissingular,havinganodpforeachfiberin,causedbythecontractionofawholes-equivalenceclassofproperlysemistablesheaveson.thelocalpicturewehavedevelopedsuggeststhatinordertoobtainawell-behavedreplacementfortheuniversalsheaf,oneshouldconsiderasmallresolutionoftheseodp’s.unfortunately,wecannotexpectsuchasmallresolutiontoexistinthealgebraiccategory:inordertoobtainone,weneedtoblowupaweildivisorwhichisnoteven-cartier,andthereforeweneedtohave.itisnothardtoprovethat,andhenceif(asisthecaseinbothexamples and )cannothaveanalgebraicsmallresolution(becausehasrankatleasthavingasectionandaprojectivebase).\n",
      "\n",
      " -------------1940\n",
      "          theorem 3.9  let  be a complex manifold and  be a sheaf over  then for any  we have  and               \n",
      "\n",
      " -------------1222\n",
      "let         be the partition . then . we see that we have an exact sequence                       where       is the bundle  constructed in a relative situation with  replacing .\n",
      "\n",
      " -------------1533\n",
      "a) the first condition means that that there is a holomorphic semistable          -bundle  with  and atiyah-bott point equal to , and the topological type of the -bundle  is uniquely determined by . this topological type is specified by an element . the second condition means that the point , or the corresponding stratum of -connections, is minimally unstable in the sense of [., definition 6.1.1]\n",
      "\n",
      " -------------1508\n",
      "     step 2. there exists a map  so that the induced map  is an isomorphism.\n",
      "\n",
      " -------------1614\n",
      "the eigenvalues of the matrix         (even when they are distinct) must satisfy certain equalities – for every diagonal block of size 2 (irreducible or not) of the triple  (resp. ) the eigenvalues  of  must satisfy the condition  (resp. ).\n",
      "\n",
      " -------------1856\n",
      "          lemma 2.8. if  is a -critical concave bundle, then in the -nonequivariant limit we have the following formula               \n",
      "\n",
      " -------------1569\n"
     ]
    }
   ],
   "source": [
    "#get values where prediction and value is different\n",
    "test_val = zip(test_y.keys(),test_y, predictions)\n",
    "div = [t for t in test_val if t[1] < 0.5 and t[2] > 0.5 ]\n",
    "for d in div:\n",
    "    print(allData['texts'][d[0]])\n",
    "    print(' -------------%s'%d[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "         suppose that  holds with . then there exists a sequence of permissible monodial transforms  such that the following properties hold:                                                       (1)                                        holds.                                     (2)                                       all bad 2 points  satisfy ().                                     (3)                                       suppose that  is a curve which is r big at a 1 point. then there exists at most one 3 point  and  has a tangent direction at  distinct from those of  at . furthermore, if  is not r big, there exists only one 2 point . if  is the 2 curve containing , then  is not r-1 big or r small.                                   (4)                                       if  is a r small or r-1 big 2 curve containing a 2 point  such that  where  is a curve containing a 1 point and  is r big at , then  is r big.\n",
      "\n",
      "------------------\n",
      "if         is an oriented cycle in  then for any  there is a trace function                       where      . it is invariant under the action of .\n",
      "\n",
      "------------------\n",
      "let us take a sufficiently large positive integer           and let  be a general (nonzero) element of . we define a singular hermitian metric  on  by                             then                                      holds, where           denotes the closed positive current defined by the divisor . hence  is a closed positive current. let  be a positive number and let  denote the multiplier ideal sheaf of , i.e.,                             where           is an arbitrary -hermitian metric on . let us define a positive number  by                             since           is not locally integrable around , by the construction of , we see that                             holds. then one of the following two cases occurs.         case 1.1: for every small positive number ,  has -stalk at both  and . case 1.2: for every small positive number ,  has nonzero-stalk at one of  or  say .  \n",
      "\n",
      "------------------\n",
      "wenowexplainthemotivationbehindtheorems         andcomingfromthetheoryofmiddleperversityperversesheaves.letbeasinsection1.2.associatedtothepairisthecategoryofmiddleperversityperversesheavesonconstructiblewithrespectto.thiscategorywasfirstintroducedbybeilinson,bernstein,anddeligneintheseminalpaper[in1982.theydefined]asafullsubcategoryof,thebounded-constructiblederivedcategoryofsheaveson.thiswayinheritsanadditivestructurefrom.infact,itturnsouttobeanabeliancategory,unlikethederivedcategory.perversesheavesare“simpler”thanthederivedcategoryinseveralotherrespects.forexample,theyformastack(i.e.,objectsandmorphismsarelocallydefined),whichisnotthecasefor.forthesereasons,itwaslongfeltdesirabletohaveadefinitionofwhichdoesnotrelyonthemorecomplicatedderivedcategory,andwhichelucidatestheverysimpleformalpropertiesofperversesheaves.suchadefinitionwasproposedbymacphersoninhisamslecturesinsanfranciscoinjanuary1991.informalnotesofthoselectures[producedbymacpherson(anddated1990)weredistributedatthemeeting,butwereneverpublished.aslightlymodifiedversionofthesamedefinitionhasnowappearedinprintinthelecturenotes][fromthesummerinstituteheldinparkcity,utahinjuly1997.roughly,macpherson’sdefinition(the1997version)proceedsasfollows.aperversesheaf]isanassignment,pluscoboundaryandpull-backmaps,subjecttoasetofaxiomsmodeledaftertheeilenberg-steenrodaxioms.hereisastandardpairin,thatisapairofcompactsubsetsofacertainspecialkind.namely,isasmooth,realdimensionalsubmanifoldofwithcornersofcodimensiontwo,andisaunionofsomeofthewallsof,sothateachcornerisformedbyonewallfromandonewallnotfrom,andalltheboundarystrataofaretransverseto.itisaverypleasantfeatureofthisdefinitionthatweonlyneedtoconsiderstandardpairs.thestructuregroupiscalledthecohomologyofrelativetowithcoefficientsin;itisafinitedimensional,gradedvectorspaceover.turningnowtotheaxioms,allbutone(thedimensionaxiom)representamoreorlessstraightforwardadaptationoftheclassicaleilenberg-steenrodtothesettingofpairsinsideafixedspace.theremainingaxiomrunsasfollows.dimensionaxiom:letbeapropermorsefunction,andbeavaluesuchthatcontainsexactlyonecriticalpoint:.then                             for                      and_           .hereishowthisdefinitionfitswiththeideaofself-indexing.givenastandardpair,onecanuseavariantoftheoremtofindaself-indexingfunction                             whichis         adaptedtothepair.moreprecisely,thismeansthat,,andthelevelsetsof“looklikepagesofabook”nearthecorners.now,justasinclassicalmorsetheory,suchafunctiongivesrisetoafunctor                             withthepropertythat         forevery.ifwewrite,thenthefunctor                             breaksupintoadirectsumover                      oftheso-called_           morsegroupfunctors                             eachofthe       islocalizednear,i.e.,factorsthroughtherestrictiontoanyopenneighborhoodof.(perversesheavesonopensubsetsofandrestrictionfunctorsbetweenthemaredefinedintheobviousway.)moreover,asimpliedbythenotation,thefunctordependsononlythroughthedifferential.theexistenceoftheliftfromcohomologytocochaincomplexeswiththeaboveproperties,byitself,hasimportantconsequencesforthestructureofthecategory.forexample,itimmediatelyimpliesthatmorphismsofperversesheavesarelocallydefined.moreistruehowever:thefunctoris,insomesense,independentof;theonlyessentialdependenceisonthepair.tobeprecise,givenanytwoself-indexingfunctionsadaptedto,thefunctorsandarerelatedbyaquasi-isomorphismwhichisitselfcanonicaluptochainhomotopy.areaderfamiliarwithfloerhomologyhas,nodoubt,anticipatedthis.however,unlikeinfloerhomology,thisindependenceofthefunctionrequiresaproofwhichisrathermoreinvolvedthantheproofof.(thelaterisastraightforwardconsequenceoftheaxioms.)oncetheindependenceofthefunctionisestablishedinasuitablyflexibleform,allofthe(soft)formalpropertiesofperversesheavescanbederivedfromconsideringthecomplexesfordifferentfunctionsandstandardpairs.forexample,theabelianpropertyoffollowseasilyfromtheabelianpropertyofthecategoryofcochaincomplexes.finally,onecandevelopthetheoryofperversesheaves,startingwithmacpherson’sdefinition,tothepointofprovingthefollowing.{thm}macpherson’sdefinitionofagreeswiththeoriginaldefinitionduetobeilinson-bernstein-deligne.thepresentauthorhasrecentlyhadanopportunitytoworkthroughaproofoftheoreminagraduatecourseatmit,andafuturepaperdescribingthisproofisbeingplanned.thegoalofthepresentpaperistoprovidethemaingeometrictool:self-indexingmorsefunctions.weconcludethisintroductionwithaconjectureduetomacpherson.{conj}omittingthedimensionaxiomfrommacpherson’sdefinitionofgivesacategorywhichisequivalentto.acknowledgments.iwouldliketothanktheihesinbures-sur-yvettefortheirhospitalityduringaugust99whenmostofthisworkwasdone.myintellectualdebttobobmacphersonisclearfromtheprecedingintroduction.iamalsogratefultothestudentsinmycourseatmitforpatiently(butnotuncritically)allowingmetothinkthroughtheseideasoutloud.\n",
      "\n",
      "------------------\n",
      "despite from these facts,       and  are not isomorphic as bialgebras themselves. in fact, there exists no antipode which makes  a hopf algebra. recall that an antipode is a linear map , such that  and for each non-empty partition  we have , or equivalently                 where     isgivenby().takingwegetwhichimpliesthatwhere.sinceisequaltothesumoftheelementsforallpartitions,thisisnotanelementof.however,isnotfarfrombeingahopfalgebra.infact,ifweletbethelocalizationgeneratedbyand,thenisahopfalgebra.toseethis,noticethat()impliesthatwhereisthenumberofinnercornersof,i.e. thenumberofindicessuchthat.by()wethereforeseethatanantipodemustsatisfy                 thisequationcanbeusedtodefine     .theobtainedantipodeisfurthermorearinghomomorphism,sinceitmustagreewiththeantipodeontheringofsymmetricfunctionsextendedto.regardingthestructureofasanabstractring,weconjecture:{conj}(a)anystablepolynomialcanbewrittenasapolynomialintheelementsforrectangularpartitionscontainedin.(b)theelementscorrespondingtopartitionswithonlyoneroworonecolumnarealgebraicallyindependent.part(a)ofthisconjecturehasbeenverifiedforallpartitionsofweightatmost9.for(b),ifwedefinethedegreeofamonomialintheandtobethetotalnumberofboxesinthepartitionsofthefactors,thenallsuchmonomialsofdegreeupto9arelinearlyindependent.furthermore,itisnothardtoprovethatforanyinteger,theelementsarealgebraicallyindependent.namely,ifoneusesthelexicographicorderonpartitions,thenthemonomialsintheseelementsallhaveadifferentmaximalpartitionforwhichthecoefficientofisnon-zero.theconjecturehassomeinterestingconsequencesforthestructureof.if(a)istrue,thenisgeneratedbythetheelements,inadditionto.toseethis,noticethatifisarectangularpartitionwithatleasttworowsandtwocolumns,andisthepartitionobtainedbyremovingtheboxinthecornerof,then                 using(a)thisshowsthat     canbewrittenasapolynomialin,,andtheelementsforrectangleswhicharestrictlycontainedin.thisshowsthatisintheringgeneratedbytheelements,,andbyinductiononthesizeof.however,if(b)istruethentheelementsanddonotgenerateasaring.infact,theidentity                 impliesthat     can’tbewrittenasapolynomialintheseelementsiftheyarealgebraicallyindependent.geometrically,thefactthatisacommutativeandcocommutativebialgebraimpliesthatisanabeliansemigroupscheme.theexistenceofanantipodeonmeansthatthedenseopensubsetisagroupscheme.furthermore,if\\refconjconj_abistruethenthisopensubsetlookslikeaninfinitedimensionalaffinespacewithahyperplaneremoved.wewillfinishthispaperbyraisingsomeadditionalquestions.firstofall,severalpeoplehaveaskeduswhenasymmetricpowerseriesinisanelementin.evenwhenthevariablesaresettozero,wedonotknowtheanswertothis.inviewof\\refconjconj_abitwouldbeveryinterestingtoknowtherelationsbetweentheelementsforrectangularpartitions.wehavealsobeenwonderingifmightbeapolynomialring,i.e. aretherealgebraicallyindependentelementsinsuchthat?wethinkthisisnotthecasebuthaven’tbeenabletoproveit.itisnothardtoseethatthesinglegrothendieckpolynomialsforallpermutationsformabasisforthepolynomialring.forexample,onecancheckdirectlythatthegrothendieckpolynomialsforpermutationsingiveabasisforthelinearspanofallmonomialsforwhichforeach.alternativelyonecanuseastrongerresultoflenart[whichexpressesanysinglegrothendieckpolynomial]asanexplicitlinearcombinationofschubertpolynomialswithalternatingsigns,i.e. thesignofthecoefficientofis.ontheotherhand,lascouxhasconjecturedthateachsingleschubertpolynomialisanon-negativelinearcombinationofgrothendieckpolynomials.nowdefinegrothendieckstructureconstantsby                 theseconstantsaregeneralizationsofthestructureconstantsforschubertpolynomialsaswellasthecoefficients   discussedinthispaper.if,,andaregrassmannianpermutationsfor,,andwithdescentsatthesameposition,then.basedonourresultsforgrothendieckpolynomialsofgrassmannianpermutationsgiveninthispaper,aswellasonsomecomputationalevidence,wepose:{conj}thestructureconstantsforsinglegrothendieckpolynomialshavealternatingsigns,i.e. .\n",
      "\n",
      "------------------\n",
      "       . all points from  sufficiently close to  are good as well (this follows easily from the basic technical tool in the additive version). hence, the same polynomial  evaluated for  corresponding to points close to  is still a matrix with at least two distinct eigenvalues which will be close to two of the eigenvalues of  evaluated at  (denoted by , ). suppose that . hence, for all points from  close to  (denote their set by ) the polynomial  evaluated at them has an eigenvalue  with .\n",
      "\n",
      "------------------\n",
      "             the -module  is absolutely simple;\n",
      "\n",
      "------------------\n",
      "             let  be a scheme of finite type over  and  two morphisms, such that the pullbacks of  via  and  are equivalent. then, there exist an étale covering  and a morphism , such that the morphism  equals the morphism                                       \n",
      "\n",
      "------------------\n",
      "       m := fold((m, i) -> m ||\n",
      "\n",
      "------------------\n",
      "       being ,  is a projection of a rational normal scroll  of the same degree. the center  of such projection () is disjoint of , and is contained in the space generated by . moreover , being  or . conversely, every –dimensional rational normal scroll can be projected to  in this way, obtaining the focal scroll of a congruence of order  in the case ii without fixed points.\n",
      "\n",
      "------------------\n",
      "a quasi-projective variety is called        algebraic hyperbolic if it does not contain a curve whose normalization is an elliptic curve or a rational curve with two points removed, i.e., .\n",
      "\n",
      "------------------\n",
      "   problem. if a hypersurface  in  is isomorphic to a coordinate hyperplane, is it true that  vanishes nowhere? \n",
      "\n",
      "------------------\n",
      "if     are two partitions, let  denote the skew diagram of boxes in  which are not in , and let  be the number of boxes in this diagram. now choose a numbering of the north-west to south-east diagonals in the diagram with positive integers, which increase consecutively from south-west to north-east. for example, if  and , and if the bottom-left box in  is in diagonal number , then the numbering is given by the picture: \\[ \\tableauskew \\] let  be the sequence of diagonal numbers of the boxes in  when these boxes are read from right to left and then from bottom to top. we then let  be the product of the corresponding simple reflections. for the skew shape above this gives . notice that  depends on the numbering of the diagonals as well as the diagram . a theorem of billey, jockusch, and stanley \\citebilley.jockusch.ea:some says that a permutation  can be obtained from a skew diagram in this way, if and only if it is 321-avoiding, i.e. there are no integers  for which .\n",
      "\n",
      "------------------\n",
      "         step 1 : stability of smooth blow-downs. fix  in the smooth locus  of  and suppose that  is a fano -fold and there exists a smooth blow-down of  (denote by  the exceptional divisor,  its hilbert polynomial with respect to ). let  be the component of the hilbert scheme of -dimensional subschemes of  with hilbert polynomial  and  the universal family. finally, let  be the following subscheme of  :                             and         the proper algebraic map induced by the first projection. thanks to the analytic stability of smooth blow-downs due to kodaira (see [, theorem 5), the image ] contains an analytic open neighbourhood of  hence it also contains a zariski neighbourhood of . moreover, since exceptional divisors are rigid, the fiber  is a single point for  in a zariski neighbourhood of . finally, we get algebraic stability of smooth blow-downs (the -fibered structure of exceptional divisor is also analytically stable - [, theorem 4 - hence algebraically stable by the same kind of argument).]\n",
      "\n",
      "------------------\n",
      "consider the universal line through the origin        . it intersects  in two further points which correspond to the roots of the quadratic equation                       the equation is irreducible if       is irreducible. let its roots be .\n",
      "\n",
      "------------------\n",
      "let               be a radical ideal. then the symbolic powers  form a graded family of ideals that we denote by .\n",
      "\n",
      "------------------\n",
      "              for every \n",
      "\n",
      "------------------\n",
      "(2) for any birational morphism     from a normal variety, if we write , then all the coefficients of  are at most  (resp. strictly less than , at most  and strictly less than  for exceptional divisors).\n",
      "\n",
      "------------------\n",
      "we consider complete linear series on             arising from weierstrass non-gaps which will be useful for applications to optimal curves. let , set  and consider . then                                                  (1)                                                             is a  base-point-free on ;                          (2)                                             the                -orders are , .\n",
      "\n",
      "------------------\n",
      "let         be a positive integer that satisfies  and . then by [ and ][, there exists a ]-surface  with an action  of order  and . let  and . let  act on  by trivial action on  and the action above on . let  be the quotient of  by  with . then  is a log calabi-yau 3-fold with global index .\n",
      "\n",
      "------------------\n",
      "let       be the set of all matrices, which appear from  by permutation of columns. let  be the number of such matrices. put us                 where the sum is taken by all                    \n",
      "\n",
      "------------------\n",
      "we still denote by         a family of non-degenerate morphisms to  over . we will conclude this section by showing that there is a canonical closed subscheme structure on  making it the closed subscheme parameterizing all pre-deformable morphisms over .\n",
      "\n",
      "------------------\n",
      "for    , there is a natural contraction map  defined by composing the map  with  (so that the components of  carrying  special points become unstable) and contracting the unstable components. similarly, one can define the forgetting maps  by disregarding the -th marked point and contracting the component if it has become unstable.\n",
      "\n",
      "------------------\n",
      "       then for every positive integer , the -th plurigenus  is independent of .\n",
      "\n",
      "------------------\n",
      "in these terms, a system consisting of a period subgroup in       and compatible automorphy factors becomes simply a homomorphism, which we will call a multiplier,                 where     is a free abelian group of the same rank as  and  is a bijection. (we will find convenient in the future to weaken these restrictions).\n",
      "\n",
      "------------------\n",
      "         a function  defines an order  on  as follows:\n",
      "\n",
      "------------------\n",
      "let us center and scale the random variables          , that is, introduce the variables                             we have           and                             as          , where, see example ,                             here                                      it follows from our wick formula, see theorem          , that the leading asymptotics of averages of the form                             is given by the usual wick rule with the covariance matrix (       ). hence the variables  are asymptotically gaussian normal with mean zero and covariance (). they describe the gaussian fluctuation of a typical partition of  around its limit shape.\n",
      "\n",
      "------------------\n",
      "             restricted to the nontwisted sectors, i.e., the ordinary dolbeault cohomologies , the cup product  equals the ordinary wedge product on .\n",
      "\n",
      "------------------\n",
      "5. if the conditions of theorem           are satisfied for the collection , , then they are also satisfied for the collection ,  where  is any character. for example, for any characters  we have                                                                                                                                                                                                                                            \n",
      "\n",
      "------------------\n",
      "the subspace           is defined as follows. let  describes an deformation  where  is an artin algebra or a projective limit of artin algebras. to such deformation we associate an module  in  representing morphism . let  be rescaling operator:                             denote           the subspace of elements of the formthe action of  on arbitrary element from  is well-defined even in the case when  is a pro-artin algebra since  belongs to subspace of elements of the form .                            \n",
      "\n",
      "------------------\n",
      "              has a reduced component for a general point  of the discriminat locus of .\n",
      "\n",
      "------------------\n",
      "           the modified equivariant integral  corresponding to  is defined as follows                                 \n",
      "\n",
      "------------------\n",
      "let us denote       by , and let  be the canonical class of . \n",
      "\n",
      "------------------\n",
      "let           be an ample line bundle on  and let  be a -hermitian metric on  with strictly positive curvature. we may and do assume that for every pseudoeffective singular hermitian line bundle ,  is globally generated (cf. [). we set , proposition 1.1] and let  be the bundle projection. let  be the unit disk bundle associated with the hermitian line bundle . then  is a family of strongly pseudoconvex manifolds over . we denote the bundle projection  again by  and we shall identify  with the zero section of . let  be a -hermitian metric on . let  a -volume form on  and let  be the restriction of  to . we define (the diagonal part of) the -th bergman kernel  of  by                             where         is a complete orthonormal basis of the hilbert space  of -holomorphic sections of  with respect to  and  and .\n",
      "\n",
      "------------------\n",
      "     lemma 2.17.  fix  with . let  be of bidegree , and                      then,  is equal to the sum of the following two terms:                       and                                       where for each fixed  with ,  runs over all the maps                    satisfying . moreover, , , and .\n",
      "\n",
      "------------------\n",
      "the next lemma is valid for any       if  acts faithfully on  and if rank .\n",
      "\n",
      "------------------\n",
      "if         is dlt, then  is sdlt.\n",
      "\n",
      "------------------\n",
      "the sheaf                 is isomorphic to the canonical (dualizing) sheaf .\n",
      "\n",
      "------------------\n",
      "       for each , the divisor germ  is not -cartier.\n",
      "\n",
      "------------------\n",
      "consider the        -uple veronese embedding of  into , where . pick a line  skew to  in . let  be the linear join of the image  of  under this embedding and the line . blowing up  along  we obtain a fourfold  which is a -bundle over . now  is isomorphic to , where  is a rank  vector bundle over .\n",
      "\n",
      "------------------\n",
      "            is the projectivization of a rank  vector bundle over a smooth curve  and .\n",
      "\n",
      "------------------\n",
      "andrei căldăraru   \n",
      "\n",
      "------------------\n",
      "         b) is it true that the grassmannian -logarithm  admits a motivic construction?\n",
      "\n",
      "------------------\n",
      "(note that in general the preimage           is the same as the stack  introduced in sect.  and the map  becomes the map .)\n",
      "\n",
      "------------------\n",
      "let           and  be two -tuples of integers. we also think of  as elements of  in the following way:                             and through this identification we define an action of           on . we define also . once  are fixed we fix complex vector spaces  and  of dimensions  and  and we define the following spaces of maps:                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           more often, when it will not be ambiguous we will write         and  instead of  and .\n",
      "\n",
      "------------------\n",
      "our specialized matrix will look as follows:                                      applying linear operations in the rows and columns of           it can be transformed into:                              where the block         is square and of size \n",
      "\n",
      "------------------\n",
      "       proof of proposition  we take . as                       with the initial point         and put                       let us define a meromorphic function         on  by  then                     \n",
      "\n",
      "------------------\n",
      "tht1    \\psfragtht2 \\psfraglambda \\psfragsigma \\psfragmu \\psfragt1 \\psfragt2 \\psfragt3 \\psfragt4 \\psfragt5\n",
      "\n",
      "------------------\n",
      "       each proper normal algebraic surface admits a nonfree vector bundle.\n",
      "\n",
      "------------------\n",
      "assume that         contains . there is a non-trivial birational automorphism of                        clearly,       is the identity map and the set of fixed points of  coincides with .\n",
      "\n",
      "------------------\n",
      "         let  be of pure dimension and  a stable subset. if  is a countable covering of  by stable subsets with  as , then  is covered by a finite subcollection of .\n",
      "\n",
      "------------------\n",
      "set           and . note to begin with that  for all , from which it follows that the limit  exists. call this limit . we will prove the theorem by establishing (from right to left) the inequalities                           \n",
      "\n",
      "------------------\n",
      "let       be defined as in definition , then\n",
      "\n",
      "------------------\n",
      "the graph         is decorated as follows. any vertex  is decorated with three numbers. the first is the self–intersection . equivalently,  is the euler–number of the normal bundle of  in . the second is the genus  of . the third decoration is given by the multiplicity of . more precisely, for any , let  be the vanishing order of  along the irreducible divisor corresponding to . for example, if  defines an isolated singularity, then for any  one has .\n",
      "\n",
      "------------------\n",
      "before proving the lemma, we need the following easy consequence of the projectivity of        . we say a moment graph  is flexible at  if for any  and any , , there is a degree two section  so that , , and  for all vertices .\n",
      "\n",
      "------------------\n",
      "for       ,letbetheuniquefiberoftheellipticfibrationinwhichlies,andletbethepointofthatisintheimageofthesection.thentherestrictionisisomorphictooneofthesheavesconsideredinsection ,andthereforeitissemistableonthefiber.thisallowsustoconsiderasabasespace,parametrizingsheavesonthefibersof.allthesheavesaresemistableofrank1,degree0,sowegetanaturalmap,whichonlydependsonthechoiceofthesection.usingourknowledgeofthegeometryofthefibersofweseethatthemapisanisomorphismawayfromthefibersof,whereitcontractsthecomponentofthefiberthatisnothitbythesection.(onemustremarkherethatsinceisasection,itcannotpassthroughanyofthesingularpointsofthesingularfibersof.)sincethecontractedcomponentshavenormalbundleby ,thecontractionofsuchacomponentgivesanordinarydoublepoint(odp)in.reversingthepointofview,isasmallresolutionofthesingularitiesof.\n",
      "\n",
      "------------------\n",
      "keep notation as above. there exists a lift                                              of             with the following properties.         \n",
      "\n",
      "------------------\n",
      "(of proposition        ) we construct an auxiliary irreducible variety  and a zariski open subset . the subset  maps surjectively onto . the scheme  is a relative quot scheme over a subset  of a quot scheme  of vector bundles. we recall the construction of  following seshadri [.]\n",
      "\n",
      "------------------\n",
      "if       is a loopfree vertex (so ) there is a reflection  defined by , and a dual reflection  with . the reflection at vertex  is said to be admissible for the pair  if . in this case it is shown in [ that there are reflection functors relating ]-modules of dimension  with -modules of dimension . let  be the equivalence relation on  generated by  whenever the reflection at  is admissible for . we say that  is obtained from  by a sequence of admissible reflections if they are in the same equivalence class.\n",
      "\n",
      "------------------\n",
      "       the holomorphic family  defines an algebraic integrable system on the moduli space of three dimensional cy manifolds  in the sense of r. donagi and markman.\n",
      "\n",
      "------------------\n",
      "       suppose . then each weil divisor on  is numerically equivalent to a -cartier divisor. moreover,  is projective.\n",
      "\n",
      "------------------\n",
      "               for any integers  we have                                                                                                                                                                                                                                                                                            \n",
      "\n",
      "------------------\n",
      "              is invariant under the actions of  and . \n",
      "\n",
      "------------------\n",
      "we describe this enumerative problem. let       be integers. the space  of maps  of degree  from  to , the grassmannian of -planes in , has dimension  [. given a point ] and an -plane  in , the set of maps  which satisfy  (the -plane  meets the -plane  non-trivially) is a divisor on this space of maps. we consider the following enumerative problem:\n",
      "\n",
      "------------------\n",
      "let         be a pseudoeffective singular hermitian line bundle on a complex manifold . the closure  of the multiplier ideal sheaf  can be analysed in terms of lelong numbers in the following way. we note that  is coherent ideal sheaf on  by theorem 2.1.\n",
      "\n",
      "------------------\n",
      "               if  is an integer such that  for , then there is a natural -equivariant inclusion                                             \n",
      "\n",
      "------------------\n",
      "       suppose that  is a smooth morphism to a nonsingular variety. suppose that  is a purely codimension  subscheme of , and that the composite  is proper and flat. for a closed point  of , let  be the fiber. if the segre classes , …,  specialize to the corresponding classes ,…, , then the same is true of the higher codimension segre classes , , etc.\n",
      "\n",
      "------------------\n",
      "(i) every          -fixed points of  is of the form , where  and  is an -fixed point of , and for any such point ,\n",
      "\n",
      "------------------\n",
      "             let  be a factorization of  into a product of two positive integers  and . then either there does not exist an absolutely simple -module of -dimension  or there does not exist an absolutely simple -module of -dimension .\n",
      "\n",
      "------------------\n",
      "as before we will sometimes write       and  for the moduli space  and its universal curve , respectively, if no confusion can arise.\n",
      "\n",
      "------------------\n",
      "having       andwecanapplythecriterionoftheorem totheextensionbyzeroofto.(onecanpushforward,sinceboththetwistingonandonispulledbackfrom.)notethatthesheavesforarepreciselyofproposition ,andtheyhavetheorthogonalitypropertyrequired.thereforetheintegraltransforminducedbyisfullandfaithful.finally,sincethecanonicalclassofthefibersofistrivial,thelastconditionoftheorem isvacuouslytrue,andhenceisanequivalenceofcategoriesbetweenand,thusfinishingtheproofoftheorem .\n",
      "\n",
      "------------------\n",
      "       for any  there exists a polynomial  such that  is a grã¶bner basis for every  not containing .\n",
      "\n",
      "------------------\n",
      "the        support of  is by definition the reduced support of , or equivalently of . if , where the  are distinct, then , where each  is supported at . we shall only be concerned in this paper with bundles  such that the support of  is contained in . we can see the structure of  concretely in this case: if  is a line bundle of degree zero, let . given a point , we let  be the corresponding line bundle of degree zero. then it is easy to check the following:\n",
      "\n",
      "------------------\n",
      "a (rational) hodge structure of weight           is a -vector space  with a decomposition of its complexification  (where complex conjugation is given by  for  and ):                             note that we insist on         and  being non-negative integers throughout this paper, so we only consider ‘effective’ hodge structures.\n",
      "\n",
      "------------------\n",
      "         one has the equalities                                    where given an ideal sheaf ,  denotes as above the least integer  such that  is globally generated.\n",
      "\n",
      "------------------\n",
      "now, assume (4.3.2b) holds and        . the sheaves  and  define natural maps  and . as above,  is defined along , and the projective subspace  spanned by  has dimension . in addition,  is defined along , and  spans . let  be the set of all linear maps  sending  to  for each . as above, we define an isomorphism .\n",
      "\n",
      "------------------\n",
      "we set                                      for a coherent sheaf           of ,                           \n",
      "\n",
      "------------------\n",
      "           let  be a multi-index . we have                                              where  and, as usual,                                              similarly,                                 \n",
      "\n",
      "------------------\n",
      "kawamata’s covering construction (see        [, 2.2) allows to choose a finite covering ] with  non singular. blowing up centers in fibres over , we obtain a non-singular variety  and a generically finite map , such that all the fibres of                       are normal crossing divisors. by abuse of notations we will add some points to      , hence some fibres to , and assume that  is smooth outside of  and that  is finite outside of . let  be the induced map. since  factors through a non-singular variety, finite over , the higher direct images  are zero for .\n",
      "\n",
      "------------------\n",
      "   dedicated to herb clemens\n",
      "\n",
      "------------------\n",
      "       definition. let the eigenvalues  not be strongly generic. hence, there holds at least one equality of the form\n",
      "\n",
      "------------------\n",
      "                                  1.                                 for each point            ,  lies in , the linear subspace of fixed points of .                    2.                                 the space of all             sections of , denoted by , has a structure of vector space over  (or ) as well as a -module structure.                  3.                                 the             sections  are in  correspondence with the underlying continuous maps .\n",
      "\n",
      "------------------\n",
      "to define the regulator map from this gadget to the complex         we specify it for each of  where . namely, we take the constructed in theorem () homomorphism  for  and multiply it by . notice that the distribution  depends only on the generic point of a subvariety . its image in the bicomplex described in the section 3.1 is in                       which is the triangle symmetric with respect to the diagonal in the         square presented on the picture below.     \n",
      "\n",
      "------------------\n",
      "let         be some cohomology classes of the toric manifold , and  some cycles poincaré dual to the classes : . then batyrev’s quantum intersection product in batyreví¦ ring  is defined by the requirement that                       for all        , and linearity. here the sum is over all  such that the intersection product in the sum is supposed to be of virtual dimension zero, i. e. such that                       where       is the number of one–dimensional cones in .\n",
      "\n",
      "------------------\n",
      "   corollary 4. if  is a contact projective manifold with , then  is a projectivized hyperplane bundle  associated with some projective manifold .\n",
      "\n",
      "------------------\n",
      "of course, the usual (real) variations are examples of complex variations. these satisfy the additional    reality constraint . conversely, a complex variation  together with its complex conjugate, defines a real variation of hodge structures on  in the obvious manner. in passing, we observe however that we can have complex variations of any given pure type. if for instance  has the property that it is preserved by  i.e., if it is a flat subbundle, it is itself a complex variation.\n",
      "\n",
      "------------------\n",
      "             if  belongs to  for all , then .\n",
      "\n",
      "------------------\n",
      "the        monodromic grothendieck group  is defined as the abelian group generated by symbols  (also denoted by , or simply ), for  an -variety with good -action, with the relations  if  and  are isomorphic as -varieties with  -ction, and  if  is zariski closed in  with the -action on  induced by the one on , and moreover  where  is the -dimensional affine space over  with any good -action, and  is taken with the trivial -action. there is a natural ring structure on , the product being induced by the fiber product over . we write  to denote the class in  of  with the trivial -action.\n",
      "\n",
      "------------------\n",
      "we return to the proof of theorem          . the maximal ideal of the polynomial ring  lying over  is of the form  for some monic polynomial  whose reduction  remains irreducible over . write  for a splitting field of , so that  with , and repeated factors if  is inseparable. let  be a ring extension as in , (i–ii). we write  and , and extend  to an isomorphism  given by the same formula . the extended rings  and  are gorenstein by proposition , (iii). thus                             is the unprojection ring constructed from the local ring         and the ideal .\n",
      "\n",
      "------------------\n",
      "         under the assumptions of the previous proposition, there is an exact sequence                                    where  denotes the full tate module of  and  is a finite abelian group whose prime-to- part is isomorphic to that of the (dual of) the group  considered above and whose -part is isomorphic to the (dual of) the -primary torsion subgroup of .\n",
      "\n",
      "------------------\n",
      "let         with  be two objects of . if  we define                     \n",
      "\n",
      "------------------\n",
      "       if  is a minimal smooth surface,  a disc in , and  any proper holomorphic map whose generic fiber  ( ) is irreducible and rational, then  is a (trivial) –bundle over .\n",
      "\n",
      "------------------\n",
      "if        :\n",
      "\n",
      "------------------\n",
      "         the first three cohomology sheaves of  are                                                       •                                       .                                     •                                       .                                   •                                       . this symbol denotes the lagrangian obstructions, that is,  is the sheaf of obstructions to extend a lagrangian deformation to higher order regardless whether it can be extended as a flat deformation.\n",
      "\n",
      "------------------\n",
      "           definition: we call the homological chevalley complex of the dg lie algebroid  with coefficients in the right dg-module  the standard semiinfinite complex for the chiral module  over the lie-* algebra  and denote it by . remark: note that as the d-module on  the constructed complex looks as follows:                                                                                                        here as before           denotes the projection .\n",
      "\n",
      "------------------\n",
      "(c)    automorphy factors and theta functions on  any formal theta function (0.5) can be interpreted as a formal function on ., an infinite linear combination  this takes care of equations (0.1).\n",
      "\n",
      "------------------\n",
      "                for all .\n",
      "\n",
      "------------------\n",
      "let       be a generalized rational okamoto-painlevé pair. if  is of fibered type, that is, if there exists an elliptic fibration  with , pulling back non-constant regular algebraic functions on , we have many non-constant regular functions on . we can prove the converse of this fact.\n",
      "\n",
      "------------------\n",
      "letusstartbyexplainingthestatementofthetheorem.insection        wesawthattherelativejacobianissingular,havinganodpforeachfiberin,causedbythecontractionofawholes-equivalenceclassofproperlysemistablesheaveson.thelocalpicturewehavedevelopedsuggeststhatinordertoobtainawell-behavedreplacementfortheuniversalsheaf,oneshouldconsiderasmallresolutionoftheseodp’s.unfortunately,wecannotexpectsuchasmallresolutiontoexistinthealgebraiccategory:inordertoobtainone,weneedtoblowupaweildivisorwhichisnoteven-cartier,andthereforeweneedtohave.itisnothardtoprovethat,andhenceif(asisthecaseinbothexamples and )cannothaveanalgebraicsmallresolution(becausehasrankatleasthavingasectionandaprojectivebase).\n",
      "\n",
      "------------------\n",
      "          theorem 3.9  let  be a complex manifold and  be a sheaf over  then for any  we have  and               \n",
      "\n",
      "------------------\n",
      "let         be the partition . then . we see that we have an exact sequence                       where       is the bundle  constructed in a relative situation with  replacing .\n",
      "\n",
      "------------------\n",
      "a) the first condition means that that there is a holomorphic semistable          -bundle  with  and atiyah-bott point equal to , and the topological type of the -bundle  is uniquely determined by . this topological type is specified by an element . the second condition means that the point , or the corresponding stratum of -connections, is minimally unstable in the sense of [., definition 6.1.1]\n",
      "\n",
      "------------------\n",
      "     step 2. there exists a map  so that the induced map  is an isomorphism.\n",
      "\n",
      "------------------\n",
      "the eigenvalues of the matrix         (even when they are distinct) must satisfy certain equalities – for every diagonal block of size 2 (irreducible or not) of the triple  (resp. ) the eigenvalues  of  must satisfy the condition  (resp. ).\n",
      "\n",
      "------------------\n",
      "          lemma 2.8. if  is a -critical concave bundle, then in the -nonequivariant limit we have the following formula               \n",
      "\n",
      "------------------\n"
     ]
    }
   ],
   "source": [
    "# find the lines where the predictions and test are different\n",
    "differ = test_y[test_y != predictions] \n",
    "\n",
    "true_differ = differ[differ > 0.5]\n",
    "for d in true_differ.keys():\n",
    "    print(allData['texts'][d])\n",
    "    print('------------------')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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      "article /mnt/math.AG/2000/math.0010053/pst-tree.xml has messed up para\n",
      "article /mnt/math.AG/2000/math.0010053/pst-tree.xml has messed up para\n",
      "article /mnt/math.AG/2000/math.0010053/pstricks.xml has few paragraphs\n",
      "article /mnt/math.AG/2000/math.0011014/envirdcls.xml has messed up para\n",
      "article /mnt/math.AG/2000/math.0011014/layoutdcls.xml has messed up para\n",
      "article /mnt/math.AG/2000/math.0011014/layoutdcls.xml has messed up para\n",
      "article /mnt/math.AG/2000/math.0011070/math.0011070.xml has few paragraphs\n",
      "article /mnt/math.AG/2000/math.0011080/math.0011080.xml has few paragraphs\n",
      "article /mnt/math.AG/2000/math.0011100/goksty.xml has few paragraphs\n",
      "article /mnt/math.AG/2000/math.0011176/math.0011176.xml has messed up para\n",
      "article /mnt/math.AG/2000/math.0012083/biblio.xml has few paragraphs\n",
      "article /mnt/math.AG/2000/math.0012083/conseq.xml has messed up para\n",
      "article /mnt/math.AG/2000/math.0012083/conseq.xml has messed up para\n",
      "article /mnt/math.AG/2000/math.0012083/defs.xml has messed up para\n",
      "article /mnt/math.AG/2000/math.0012083/defs.xml has messed up para\n",
      "article /mnt/math.AG/2000/math.0012083/dereqv.xml has messed up para\n",
      "article /mnt/math.AG/2000/math.0012083/dereqv.xml has messed up para\n",
      "article /mnt/math.AG/2000/math.0012083/dim1.xml has messed up para\n",
      "article /mnt/math.AG/2000/math.0012083/dim3.xml has messed up para\n",
      "article /mnt/math.AG/2000/math.0012083/dim3.xml has messed up para\n",
      "article /mnt/math.AG/2000/math.0012083/pagesize.xml has few paragraphs\n",
      "article /mnt/math.AG/2000/math.0012083/twsh.xml has messed up para\n",
      "article /mnt/math.AG/2000/math.0012210/smaps.xml has messed up para\n"
     ]
    }
   ],
   "source": [
    "out_file = open('../random_para_2015.txt','a')\n",
    "ns = {'latexml': 'http://dlmf.nist.gov/LaTeXML' }\n",
    "\n",
    "def check_sanity(p):\n",
    "    '''\n",
    "    Input:\n",
    "    p: element tree result of searching for para tags\n",
    "    Checks:\n",
    "    contains an ERROR tag \n",
    "    '''\n",
    "    if p.findall('.//latexml:ERROR', ns):\n",
    "        return False\n",
    "    else:\n",
    "        return True \n",
    "\n",
    "for f in glob.glob('/home/luis/media_home/math.AG/2015/*/*.xml'):\n",
    "    try:\n",
    "        exml = ET.parse(f)\n",
    "        para_lst_nonrand = exml.findall('.//latexml:para',ns)\n",
    "        para_lst = random.sample(para_lst_nonrand, 2)\n",
    "        for p in para_lst:\n",
    "            if check_sanity(p):\n",
    "                out_file.write(f + ':::' + px.recutext1(p) + \"\\n\")\n",
    "            else:\n",
    "                print('article %s has messed up para'%f)\n",
    "    except ET.ParseError:\n",
    "        pass\n",
    "    except ValueError:\n",
    "        print('article %s has few paragraphs'%f)\n",
    "out_file.close()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['                                                    \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm           \\\\eightrm                                     \\\\eightrm0             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm           \\\\eightrm                                     \\\\eightrm1             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm           \\\\eightrm                                     \\\\eightrm2             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm           \\\\eightrm                                     \\\\eightrm3             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm           \\\\eightrm                                     \\\\eightrm4             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm           \\\\eightrm                                     \\\\eightrm5             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm           \\\\eightrm                                     \\\\eightrm6             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm           \\\\eightrm                                     \\\\eightrm7             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm           \\\\eightrm                                    ...................                                     \\\\eightrm8             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm           \\\\eightrm                                     \\\\eightrm9             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm           \\\\eightrm                                     \\\\eightrm10             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm           \\\\eightrm                                   \\\\eightrm             \\\\eightrm1             \\\\eightrm2             \\\\eightrm3             \\\\eightrm4             \\\\eightrm5             \\\\eightrm6             \\\\eightrm7             \\\\eightrm8             \\\\eightrm9             \\\\eightrm10             \\\\eightrm11             \\\\eightrm12             \\\\eightrm13             \\\\eightrm14             \\\\eightrm15             \\\\eightrm16             \\\\eightrm17             \\\\eightrm18             \\\\eightrm19           \\\\eightrmr\\\\figure[table]\\\\label4surf.nc noncontractible quartic surfaces in  \\\\endfigure',\n",
       " '                                                         \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm           \\\\eightrm                                     \\\\eightrm2             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm           \\\\eightrm                                     \\\\eightrm3             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm           \\\\eightrm                                     \\\\eightrm4             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm           \\\\eightrm                                     \\\\eightrm5             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm           \\\\eightrm                                     \\\\eightrm6             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm                                    ...............                                    ...............             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm           \\\\eightrm                                     \\\\eightrm7             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm           \\\\eightrm                                     \\\\eightrm8             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm           \\\\eightrm                                     \\\\eightrm9             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm           \\\\eightrm                                     \\\\eightrm10             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm           \\\\eightrm                                     \\\\eightrm11             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm             \\\\eightrm           \\\\eightrm                                   \\\\eightrm             \\\\eightrm1             \\\\eightrm2             \\\\eightrm3             \\\\eightrm4             \\\\eightrm5             \\\\eightrm6             \\\\eightrm7             \\\\eightrm8             \\\\eightrm9             \\\\eightrm10             \\\\eightrm11             \\\\eightrm12             \\\\eightrm13             \\\\eightrm14             \\\\eightrm15             \\\\eightrm16             \\\\eightrm17             \\\\eightrm18             \\\\eightrm19             \\\\eightrm20           \\\\eightrmr\\\\figure[table]\\\\label4surf.c contractible quartic surfaces in  \\\\endfigure',\n",
       " '     \\\\eightpoint         and \\xa0stand for a surface of type\\xa0,  stands for a surface of type\\xa0, and  stands for a surface of type\\xa0. the surfaces of type\\xa0 denoted by \\xa0have  ( in table\\xa0\\\\ref4surf.nc) or  ( in table\\xa0\\\\ref4surf.c); the surfaces with  (the right edge of table\\xa0\\\\ref4surf.c) have ; the other surfaces have , where  and . the surfaces below (respectively, above) the dotted lines are (respectively, are not) rigidly isotopic to their mirror images. ']"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# checking for the words being stuck bug\n",
    "f = \"../math.0004134/f-4s-nc.xml\"\n",
    "#f = \"tests/latexmled_files/math.0402243.xml\"\n",
    "ns = {'latexml': 'http://dlmf.nist.gov/LaTeXML' }\n",
    "exml = ET.parse(f)\n",
    "para_lst = exml.findall('.//latexml:para',ns)\n",
    "[px.recutext1(p) for p in para_lst]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb1761bd8>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb1761818>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb1761368>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb1761138>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb1761098>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb175ae08>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb175acc8>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb175ab38>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb175a8b8>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb175a6d8>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb175a548>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb175a3b8>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb175a228>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb175a0e8>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb1753d18>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb1753908>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb1753548>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb17533b8>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb17b2778>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb17f2598>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb17f2b88>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb17f2db8>,\n",
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       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb21acbd8>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb21acd18>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb2375958>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb2367958>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb235ca98>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb90657c8>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb905a188>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb95efef8>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb95d4458>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb95d4318>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb95d4098>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb2cd5188>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb2cd5228>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb2cd58b8>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb2cd54f8>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb2cd5318>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb2cd55e8>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb2cd5868>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb2b2fd68>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb1d9bf98>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb1dbb728>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb24ae4f8>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb91fc048>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb92090e8>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb230c368>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb8142b38>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb106ad68>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb159bb88>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb8fb29f8>,\n",
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       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb95c34a8>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb1ced138>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb1cf9278>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb9c211d8>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb9c50e58>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb1f639a8>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeba6e15e8>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeba5629a8>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb2e3ba98>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb9b05d18>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb2ad3818>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeba6514a8>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb1bb1278>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb1bb1228>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb18b8318>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb2c33d68>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb2a067c8>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb2a2e2c8>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb9eb3ea8>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb9c064f8>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb9beea98>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb91956d8>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb2f8c098>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb2fa0188>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb2000c28>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb8173908>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeba0dc368>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeba0e1048>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeba0fe8b8>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb9d73638>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb8d37278>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb8d371d8>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb9317958>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb9317a98>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb8d739a8>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb8d737c8>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb9a6ccc8>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb99034a8>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb251f318>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb251f368>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb2586d68>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb2416e58>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb2388ef8>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb23af9f8>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb94a6318>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb94a65e8>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb94a6638>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb94a6458>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb94a6368>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb94a61d8>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb94a6048>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb94b5b38>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb94b5e08>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb94b51d8>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb8bff3b8>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeba783138>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb9ca7c28>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb1fe2f48>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb1ff93b8>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb8bbabd8>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb8bb3728>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb26da4f8>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb26da318>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb1d2cc78>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb1d2cea8>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb9425b88>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeba12bbd8>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeba19c688>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb27b9278>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb27b93b8>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeba0354a8>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb94eca98>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb2ba6728>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb2f1bf48>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb2f1be58>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb8b777c8>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb2ed3688>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb923f638>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeba462ea8>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeba462b38>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeba462bd8>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb18dcb38>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeba392278>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeba60fbd8>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeba60f048>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeba60f9a8>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb190d098>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb190dc28>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb190d0e8>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb190dc78>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeba3d1318>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeba3d19f8>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeba3d14a8>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeba3d1188>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeba3d1ea8>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb945ce08>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb945cc28>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb945cae8>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb945c728>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb945c0e8>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb945c818>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb945c4a8>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb945cd18>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb945c4f8>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb1956e08>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeba5e9228>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeba5e9318>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeba5e9638>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeba5e90e8>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeba5e93b8>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeba5e9688>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb2607908>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb8b8f048>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb8b68c28>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb8b685e8>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb8b68048>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb8b68138>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb8b68688>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb8b682c8>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb8b68f48>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb8b68278>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb8b686d8>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb8b68c78>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb8b689a8>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb8b689f8>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb8b68bd8>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb289b368>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb289b048>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb289b3b8>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb289b278>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb289b458>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb23fc9a8>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb23fc368>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb23fcf48>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb23fcdb8>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb23fcb38>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb23fc4a8>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb23fc728>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb23fcb88>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb23fc3b8>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb23fc6d8>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb23fc4f8>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb23fc778>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb23fc9f8>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb23fca98>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb8bef0e8>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb8bef318>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb8bef958>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb8bef5e8>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb8bef6d8>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb8bef048>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb8bef778>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb8befef8>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb8bef3b8>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb8bef4f8>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb8bef9a8>,\n",
       " <Element '{http://dlmf.nist.gov/LaTeXML}ERROR' at 0x7fdeb8beff98>]"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "el = para_lst[0]\n",
    "el.findall('.//latexml:ERROR', ns)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(para_lst)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "def count_words_per_line(file_path):\n",
    "    with open(file_path, 'r') as defs_file:\n",
    "        def_lines = defs_file.readlines()\n",
    "    len_lst = [len(l.split()) for l in def_lines]\n",
    "    return len_lst\n",
    "len_lst = count_words_per_line('../out_2000.txt')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([285., 185., 152., 119.,  93.,  64.,  49.,  31.,  20.,  16.,   8.,\n",
       "         10.,   7.,   4.,   4.]),\n",
       " array([  0.        ,  13.33333333,  26.66666667,  40.        ,\n",
       "         53.33333333,  66.66666667,  80.        ,  93.33333333,\n",
       "        106.66666667, 120.        , 133.33333333, 146.66666667,\n",
       "        160.        , 173.33333333, 186.66666667, 200.        ]),\n",
       " <a list of 15 Patch objects>)"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(len_lst, range=(0,200), bins=15)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([132., 287., 202., 146.,  62.,  33.,  35.,  16.,   5.,   5.,   4.,\n",
       "          2.,   3.,   0.,   1.]),\n",
       " array([  0.        ,  12.93333333,  25.86666667,  38.8       ,\n",
       "         51.73333333,  64.66666667,  77.6       ,  90.53333333,\n",
       "        103.46666667, 116.4       , 129.33333333, 142.26666667,\n",
       "        155.2       , 168.13333333, 181.06666667, 194.        ]),\n",
       " <a list of 15 Patch objects>)"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(count_words_per_line('../2000_defs.txt'), bins=15)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}