bdry_run.py

# This program computes the boundary slopes of a Montesinos
# or two-bridge knot.
#
# You will need a Python interperator (version 1.5 or newer) to run
# these programs.  These are free and availible for virtually every
# platform from the Python home page <http://www.python.org>. If you're
# using UNIX, you can see if your system has python installed by
# typing which python. To run do
#
#    UNIX: While in the directory where you put all the files, type: python bdry_run.py
#    
#    MacOS: Run the Python program BuildApplet on bdry_run.py to
#     create an executable.  (Old versions of MacPython: Drag the file
#     bdry_run.py and drop it onto the main Python icon.)
#
#    Windoze: Double click the file bdry_run.py. If this doesn't
#     work, try the instructions for MacOS.
#
# Version 1.0   Dec  4, 1998.
# Version 1.1   Jan 29, 1999. Added more graceful handling of improper input.
# Version 1.1.1 Oct 16, 2000. Changed MacOS instructions.
# Version 1.3   Nov 14, 2020. Made work with Python 3.*
#
# Written by Nathan Dunfield <nathand@math.harvard.edu>

import os, re, sys
import two_bridge, montesinos, gcd_tools

out = print
get_input = sys.stdin.readline

# ask user Question and get back a one character response which must be from Answers

def ask_question(Question, Answers):
    while 1:
        out(Question)
        inp = get_input()[0]    
        if re.search(inp, Answers):
            break
        out("Sorry, input not understood.\n")
    return inp

# begin main program

out("This program computes the boundary slopes of a Montesinos knot.\n")
out("Written by Nathan Dunfield <nathan@dunfield.info>\n\n")
while 1:
    inp = ask_question("Do you want to do a t)wo-bridge knot or a m)ontesinos knot?: ", "tm")
    if inp == 't':
        while 1:
            out("Enter a fraction describing the two-bridge knot, e.g. 5/7: ")
            inp = get_input()[:-1]
            try:
                f = gcd_tools.string_to_frac(inp)
            except:
                out("Sorry, input not understood.\n")
                continue
            if f <= 0:
                out("Sorry, need fraction to be > 0.\n")
                continue
            break
        surfaces = two_bridge.branched_surfaces(f.t, f.b)
        out("K(%s) %s\n" % (f, two_bridge.slopes(surfaces)))
        inp = ask_question("Do you want more information? (y/n): ", "yn")
        if inp == 'y':
            out("\nContinued fraction expansion corresponding to each branched surface\n")
            out("followed by the slope.\n")
            two_bridge.print_surfaces(surfaces)

    else: #montesinos knot
        while 1:
            out("Enter fractions describing a montesinos knot, e.g. 1/3 1/3 -1/3 : ")
            tangles = []
            inp = get_input()[:-1]
            try:
                for item in re.split("\s+", inp):
                    tangles.append(gcd_tools.string_to_frac(item))
            except:
                out("Sorry, input not understood.\n")
                continue

            if not montesinos.defines_knot(tangles):
                out("Tangles give a link, not a knot.\n")
                continue
            if not montesinos.no_integer_tangles(tangles):
                out("No integer tangles allowed.\n")
                continue
            break

        surfaces = montesinos.compute_surfaces(tangles)
        out("K%s\t%s\n" % (tuple(tangles), montesinos.compute_boundary_slopes(surfaces) ))
        out("More info: (slope, number of sheets, euler char)\n")
        out(repr(montesinos.essential_info(surfaces)) + "\n")
        inp = ask_question("Do you want more information? (y/n): ", "yn")
        if inp == 'y':
            out("\n")
            for surface in surfaces:
                if surface.carries_incompressible:
                    out(repr(surface) + "\n")			

    if ask_question("Another knot? (y/n): ", "yn") == "n":
        break