BurauMatrix

The reduced Burau matrix of a braid, an $(n-1)\times(n-1)$ matrix over $\mathbb{Z}[t,t^{-1}]$ whose determinant gives the AlexanderPolynomial.

BurauMatrix(braid)the reduced Burau matrix itself

Typed signatures

Type	Package	Applies
(expression<Braid> | string) -> list<list<expression>>	braid	always

Domain: Braids and knots

Examples

Basic #

A $1\times 1$ matrix over $\mathbb{Z}[t,t^{-1}]$

live ↗

In$\mathrm{BurauMatrix}(\mathrm{Braid}(2, \bigl\lbrack1, 1, 1\bigr\rbrack))$Out$\bigl\lbrack\bigl\lbrack-t^3\bigr\rbrack\bigr\rbrack$

A $2\times 2$ matrix

live ↗

In$\mathrm{BurauMatrix}(\mathrm{Braid}(3, \bigl\lbrack1, 2\bigr\rbrack))$Out$\bigl\lbrack\bigl\lbrack0, -t\bigr\rbrack, \bigl\lbrack t, -t\bigr\rbrack\bigr\rbrack$

About

Examples	2

See also: AlexanderPolynomial, Braid