knot-calculations

Calculate some knot invariants. Try it now!

To draw a knot, click on the canvas to draw line segments that will connect to form a polygonal line. By clicking "Print Knot", you can get your knot data in the console. You can import the knot by calling setKnot(...) with your data. There are also buttons to click to make certain preset knots.

Letting A(t) be the Alexander polynomial, |A(-1)| is the largest number such that there exists a Fox n-coloring of the knot. It is normal that the Alexander polynomial calculated by determinant might differ from other sources by a factor of t^n or by sign.

Features:

• Input knots using setKnot() from the console, or by drawing the knot
• PRESETS["3_1"] until PRESETS["6_3"] are available
• Alexander polynomial calculation using skein relation
• Alexander polynomial calculation using determinant
• Jones polynomial works
• HOMFLY polynomial uses the skein relation of (a L+) - (1/a L-) = z L0 as described here
• HOMFLY (l, z) polynomial tested against Wolfram MathWorld

These are tested on the sample knots given in the code, compared here.

Other data sources for checking:

• 3_1
• 4_1
• 5_1
• (no source for 5_2)
• 6_1
• 6_2

TODO:

• Add feature for links (need to specify orientation)
• Fox n-coloring generator