extract_knotinfo.py

import xlrd
import json

def dump(o, fout):
    json.dump(o, fout, separators=(',', ':'))

def read_poly(s):
    """Puts the (Laurent) poly in polynomial vector notation "{mindeg, maxdeg, coeffs...}"
    into the form [mindeg, c0, c1, ..., cn]"""
    if s == "1":
        return [0,1]
    assert(s[0] == "{" and s[-1] == "}")
    ps = [int(p) for p in s[1:-1].split(",")]
    return [ps[0]] + ps[2:]

def convert_conway(p):
    """Take a conway polynomial in z^2 and make it be in z. """
    p2 = [p[0]*2] + [0]*(2*(len(p)-1)-1)
    for i,c in enumerate(p[1:]):
        p2[1+2*i] = c
    return normalize_conway(p2)

def convert_jones(p):
    """Take a jones polynomial for a knot (which is in t) and make it be in x=t^2."""
    p2 = [p[0]*2] + [0]*(2*(len(p)-1)-1)
    for i,c in enumerate(p[1:]):
        p2[1+2*i] = c
    return p2

def normalize_conway(p):
    cs = p[1:]
    minexp = p[0]
    while cs and cs[0] == 0:
        cs = cs[1:]
        minexp += 1
    return [minexp] + cs

def is_amphicheiral(symmetry_type):
    symmetry_type = symmetry_type.strip()
    if symmetry_type in ("", "fully amphicheiral", "negative amphicheiral", "positive amphicheiral"):
        return True
    elif symmetry_type in ("reversible", "chiral"):
        return False
    else:
        print(symmetry_type)
        raise Exception(symmetry_type)

def cut_katlas(url):
    if not url.startswith("http://katlas.math.toronto.edu/wiki/"):
        raise Exception(url)
    return url[len("http://katlas.math.toronto.edu/wiki/"):]

data = []

print("Processing knotinfo")
with xlrd.open_workbook("data/knotinfo_data_complete.xls") as book:
    sheet = book.sheet_by_index(0)
    cols = {}
    for i, cell in enumerate(sheet.row(0)):
        cols[cell.value] = i

    for row_idx in range(2, sheet.nrows):
        def get(colname):
            return sheet.cell(row_idx, cols[colname])

        entry={}
        entry['name'] = get('name').value
        if get('knot_atlas_anon').value:
            entry['katlas'] = cut_katlas(get('knot_atlas_anon').value)
        else:
            entry['katlas'] = ""
        entry['components'] = 1
        entry['crossing_number'] = int(get('crossing_number').value)
        entry['genus'] = int(get('three_genus').value)
        entry['signature'] = int(get('signature').value)
        entry['conway'] = convert_conway(read_poly(get('conway_polynomial_vector').value))
        entry['jones'] = convert_jones(read_poly(get('jones_polynomial_vector').value))
        entry['turaev_genus'] = json.loads(get('turaev_genus').value) # might be [lo, hi]
        entry['bridge_number'] = int(get('bridge_index').value)

        if get('pd_notation').value == "":
            entry['pd'] = [[1, 1]]
        else:
            entry['pd'] = json.loads(get('pd_notation').value)

        data.append(entry)

#        if not is_amphicheiral(get('symmetry_type').value):
#            entry = entry.copy()
#            entry['name'] = 'm' + entry['name']
#            entry['signature'] = -entry['signature']
#            entry['jones'] = poly_reverse(entry['jones'])
#            data.append(entry)

print("Processing linkinfo")

with open("data/linkinfo_conway_coeffs.json") as fin:
    conway = json.load(fin)

with xlrd.open_workbook("data/linkinfo_data_complete_resave.xls") as book:
    sheet = book.sheet_by_index(0)
    cols = {}
    for i, cell in enumerate(sheet.row(0)):
        cols[cell.value] = i

    for row_idx in range(2, sheet.nrows):
        def get(colname):
            return sheet.cell(row_idx, cols[colname])

        entry={}
        entry['name'] = get('name').value
        if not entry['name']:
            break

        if get('knot_atlas_anon').value:
            entry['katlas'] = cut_katlas(get('knot_atlas_anon').value)

        entry['components'] = int(get('components').value)
        entry['pd'] = json.loads(get('pd_notation_vector').value.replace("{","[").replace("}","]"))
        entry['crossing_number'] = int(get('crossing_number').value)
        entry['signature'] = int(get('signature').value)
        entry['conway'] = normalize_conway([0] + conway[entry['name']])
        entry['jones'] = read_poly(get('jones_polynomial_vector').value)

        data.append(entry)

print("Writing data files")

# Lazy loader description file
f_defs = open("build/knotinfo.js", "w")
f_defs.write("// Generated by extract_knotinfo.py from KnotInfo database\n")
f_defs.write("// Descriptions of available data files\n")

def write_knots(filename, crossings, components, properties):
    f_defs.write("provides_knot_data(")
    dump(filename, f_defs)
    f_defs.write(", ")
    dump(components, f_defs)
    f_defs.write(", ")
    dump(crossings, f_defs)
    f_defs.write(", ")
    dump(properties, f_defs)
    f_defs.write(");\n")

    fout = open("build/" + filename, "w")

    fout.write("// generated by extract_knotinfo.py from KnotInfo database\n")

    fout.write("add_knot_data(")
    dump(properties, fout)
    fout.write(",[\n")

    first = True
    for entry in data:
        if entry['crossing_number'] in crossings and entry['components'] in components:
            if not first:
                fout.write(",\n")
            first = False
            dump(entry['name'], fout)
            for p in properties:
                fout.write(",")
                dump(entry[p], fout)

    fout.write("]);\n")

    fout.write("loaded_knot_data(")
    dump(components, fout)
    fout.write(", ")
    dump(crossings, fout)
    fout.write(", ")
    dump(properties, fout)
    fout.write(");\n")

    fout.close()

properties = ['crossing_number',
              'components',
              'katlas',
              'genus',
              'signature',
              'conway',
              'jones',
              'turaev_genus',
              'bridge_number']

write_knots("knotinfo_0-10.js", [0,1,2,3,4,5,6,7,8,9,10], [1], properties);
write_knots("knotinfo_11-12.js", [11,12], [1], properties)
write_knots("knotinfo_0-10_pd.js", [0,1,2,3,4,5,6,7,8,9,10], [1], ["pd"])
write_knots("knotinfo_11-12_pd.js", [11,12], [1], ["pd"])

properties = ['crossing_number',
              'components',
              'katlas',
              'signature',
              'conway',
              'jones']

write_knots("linkinfo_0-10.js", [0,1,2,3,4,5,6,7,8,9,10], [2,3,4,5], properties);
write_knots("linkinfo_11.js", [11], [2,3,4,5], properties);
write_knots("linkinfo_0-10_pd.js", [0,1,2,3,4,5,6,7,8,9,10], [2,3,4,5], ["pd"]);
write_knots("linkinfo_11_pd.js", [11], [2,3,4,5], ["pd"]);

f_defs.close()

print("Done")