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<script src="https://code.jquery.com/jquery-3.3.1.min.js"></script>

Degree (unknown) extensions of ℚ(unknown)

Polynomial Galois group

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<script type="text/javascript"> $('document').ready(function (){ // Read a page's GET URL variables and return them as an associative array. function getUrlVars() { var vars = [], hash; var hashes = window.location.href.slice(window.location.href.indexOf('?') + 1).split('&'); for(var i = 0; i < hashes.length; i++) { hash = hashes[i].split('='); vars.push(hash[0]); vars[hash[0]] = hash[1]; } return vars; } 
// given coefficients, makes a polynomial in HTML
function polynomialToHTML(coeffs) {
  let html = '';
  for (var i=coeffs.length-1; i>=0; i--) {
    let c = coeffs[i];
    if (c === 0) { 
      continue;
    }
    let xi = (i===0) ? '' : (i===1) ? 'x' : ('x<sup>'+i+'</sup>');
    if (html.length === 0) {
      html += '' + (c===1?'':c===-1?'-':c) + xi;
    } else {
      if (c > 0) {
        html += ' + ' + (c===1?xi?'':c:c) + xi;
      } else {
        html += ' - ' + (c===-1?xi?'':-c:-c) + xi;
      }
    }
  }
  if (html.length === 0) {
    html = '0';
  }
  return html;
}

// given the string contents of a CSV file, populates the table
function CSVtoTable($table, data, deg) {
  // get the rows of the table
  let allLines = data.split(/\r\n|\n/);
  let headers = allLines[0].split(',');
  let rows = [];
  for (var i = 1; i < allLines.length; i++) {
    if (allLines[i].length === 0) { continue; }
    let x = allLines[i].split(',')
    let coeffs = [];
    for (var j = 0; j <= deg; j++) {
      coeffs.push(parseInt(x[j], 10));
    }
    let tnum = parseInt(x[deg+1], 10);
    rows.push([coeffs, tnum]);
  }
  rows.sort(function (a,b) { return a[1] - b[1]; });
  // make the table
  let numunknown = 0;
  for (var i = 0; i<rows.length; i++) {
    let row = rows[i];
    let coeffs = row[0];
    let tnum = row[1];
    if (tnum === 0) {
      $table.append($('<tr></tr>').append($('<td>'+polynomialToHTML(coeffs)+'</td>')).append($('<td>unknown</td>')));
      numunknown += 1;
    } else {
      $table.append($('<tr></tr>').append($('<td>'+polynomialToHTML(coeffs)+'</td>')).append($('<td style="white-space: nowrap;">'+deg+'T'+tnum+' (<a href="https://hobbes.la.asu.edu/Groups/group-data/d'+deg+'t'+tnum+'.html" target="_blank">JJ</a>, <a href="http://groupnames.org/#?'+deg+'T'+tnum+'" target="_blank">GN</a>)</td>')));
    }
  }
  if (numunknown > 0) {
    $('#info').append($('<p>Note: '+numunknown+' unknown Galois groups</p>'));
  }
}

function suffixToText(x) {
  if (x==='e2') {
    return 'All fields with ramification degree 2';
  } else if (x==='e14') {
    return 'All fields with ramification degree 14';
  } else if (x==='tr') {
    return 'All totally ramified fields';
  } else if (x==='e4a') {
    return 'All fields with ramification degree 4, singly ramified and elementary abelian over its maximal unramified subfield';
  } else if (x==='e8a') {
    return 'All fields with ramification degree 8, singly ramified and elementary abelian over its maximal unramified subfield';
  } else {
    return 'Some unknown restriction'
  }
}

let getvars = getUrlVars();
let prime = parseInt(getvars.prime, 10);
let degree = parseInt(getvars.degree, 10);
let suffix = getvars.suffix;
let csvfile = 'p'+prime+'_d'+degree+(suffix?'_'+suffix:'')+'.csv';
let csvurl = 'https://raw.githubusercontent.com/cjdoris/pAdicGaloisGroupTables/master/' + csvfile;
$('#prime').text(prime);
$('#degree').text(degree);
if (suffix) {
  $('#info').append('<p>Note: ' + suffixToText(suffix) + '</p>')
}
if (getvars.dupes) {
  $('#info').append($('<p>Note: Possibly several polynomials per field</p>'))
}
$('#info').append($('<p>File: <a href="'+csvurl+'">'+csvfile+'</a></p>'))
if (degree <= 12) {
  $('#info').append($('<p>Also in: <a href="https://hobbes.la.asu.edu/LocalFields/basic-table.cgi?prime='+prime+'&degree='+degree+'" target="_blank">LFDB</a>, <a href="http://www.lmfdb.org/LocalNumberField/?p='+prime+'&n='+degree+'" target="_blank">LMFDB</a></p>'))
}
else if (degree <= 14) {
  $('#info').append($('<p>Also in: <a href="http://www.lmfdb.org/LocalNumberField/?p='+prime+'&n='+degree+'" target="_blank">LMFDB</a></p>'))
}
$.ajax({
  type: 'GET',
  url: csvurl,
  dataType: 'text',
  success: function (data) { $('#loading').remove(); CSVtoTable($('table'), data, degree); },
  error: function (xhr,st,err) { $('#loading').empty().text('Error loading CSV file! (check URL parameters)').css('color','red'); },
});

}) </script>