KauffmanBracket

The Kauffman bracket $\langle L\rangle$ of a knot or link, in $A$ — defined for links too, unlike the Jones polynomial, and not itself an invariant until the writhe is corrected for (see BracketInvariant).

KauffmanBracket(knot)$\langle L\rangle$ in $A$

Typed signatures

Type	Package	Applies
(expression<Braid> | expression<FigureEightKnot> | expression<Link> | expression<PretzelKnot> | expression<TorusKnot> | expression<TwistKnot> | string) -> expression	braid	always

Domain: Braids and knots

Examples

Basic #

Not yet corrected for writhe

live ↗

In$\mathrm{KauffmanBracket}(\mathrm{TorusKnot}(2, 3))$Out$-A^5-\frac{1}{A^3}+\frac{1}{A^7}$

Defined for links too

live ↗

In$\mathrm{KauffmanBracket}(\mathrm{Braid}(2, \bigl\lbrack1, 1\bigr\rbrack))$Out$-A^4-\frac{1}{A^4}$

About

Examples	2

See also: BracketInvariant, JonesPolynomial