Rknots (version 1.3.0)

AlexanderBriggs: Alexander-Briggs reduction of a polygonal knot or link

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

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, $M\leq N$
• ends
  if a non empty ends has been provided as an input, a vector of positive integers defining the separators of the reduced structure

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.

See Also

msr

Examples

#reducing a knot
k <- makeExampleKnot(k = TRUE)
AlexanderBriggs(points3D = k)

#reducing a link
k <- makeExampleKnot(k = FALSE)
AlexanderBriggs(points3D = k$points3D, ends = k$ends)