Download the two dos programs mkp2.exe and lmp1.exe. Then click on mkp2.exe when in file manager (in windows) or run it under DOS.

First input the number of components your link is to have.

Use Left mouse button to make the vertices of your link. Left or Right mouse button to make crossings - the program prompts with a beep. Finally press C to close the loop.

To modify a tangle select an area with the left mouse button: click on the vertices. Then right mouse button (not C this time) to close the loop.

To join two cut ends: click on an end then make new vertices by left clicking to get an extension of the end. When ready to close press C then click on a second end to join up. Repeat this procedure until all cut ends are joined up. The beeping is to tell you to choose either over or under - easiest to click any button after a beep then put it right afterwards.

 WARNING: The polynomials produced for links with more than one component do not agree with polynomials defined in the course. ie the program works for knots only. The coefficients of the Jones polynomial are displayed in descending order. The coefficient in square brackets is the constant coefficient.

 Output of last line of prog:

 V''(1), det=|Alex(-1)|, V(i) determines Arf, V(exp(i*Pi/3)),

mkp2.exe was written by M.G.V. Bogle, of Water Engineering and Modelling in Pasadena California. It allows one to draw a link with a mouse and generates Ewing-Millett coding in the .crs file, which is then fed to the lmp1 program which calculates the homfly polynomial of the link and then mkp2.exe calculates the V-polynomial. Both results are written on the screen and written to a file called kp.out. lmp1 was written by Ewing and Millett.
MA3F2 page