# AlexanderBriggs: Alexander-Briggs reduction of a polygonal knot or link In Rknots: Topological Analysis of Knotted Proteins, Biopolymers and 3D Structures

## Description

Apply the Alexander-Briggs reduction to a polygonal knot or link. This method is based on the concept of elementary deformation, which consists in the replacement of two sides of a triangle with the third provided that the triangle is empty. From version 1.1 a fast implementation for links is provided.

## Usage

 `1` ```AlexanderBriggs(points3D, ends = c()) ```

## Arguments

 `points3D` an N x 3 matrix of the x, y, z coordinates of a polygonal link `ends` a vector of positive integers defining the separators of the polygonal link

## Value

A list of two slots:

 `points3D` an M x 3 matrix of the x, y, z coordinates of the reduced structure, M≤q N `ends` if a non empty `ends` has been provided as an input, a vector of positive integers defining the separators of the reduced structure

## Note

This is a low-level function.

## Author(s)

Federico Comoglio, [email protected]

Maurizio Rinaldi, [email protected]

## References

Reidemeister K (1926), Abh Math Sem Univ Hamburg 5: 24-32.

Alexander JW, Briggs GB (1926) On types of knotted curves. Ann of Math 28: 562-586.

`msr`
 ```1 2 3 4 5 6 7``` ```#reducing a knot k <- makeExampleKnot(k = TRUE) AlexanderBriggs(points3D = k) #reducing a link k <- makeExampleKnot(k = FALSE) AlexanderBriggs(points3D = k\$points3D, ends = k\$ends) ```