getKnotType: Given a polynomial invariant, obtain information on the knot...

In Rknots: Topological Analysis of Knotted Proteins, Biopolymers and 3D Structures

Description

Given a polynomial invariant, obtain information on the knot type. Additionally, other polynomials are returned if wished

Usage

getKnotType( polynomial, invariant = 'HOMFLY', full.output = FALSE )

Arguments

polynomial	a single element character vector containing a polynomial invariant as returned by computeInvariant
invariant	the type of polynomial. It can assume values among 'HOMFLY', 'Jones' and 'Alexander'
full.output	logical, define the output type. If TRUE, the polynomial provided in input is converted to other polynomials. The knot type, an URL to retrieve additional information on the knot type and the full set of invariants are returned. If FALSE, only the knot type is returned. Default to FALSE.

Value

The knot type (the simplest knot having the input polynomial). Optionally, additional informations on it.

Author(s)

Federico Comoglio, [e-mail]

References

The Rolfsen Knot Table on Knot Atlas, http://www.math.toronto.edu/~drorbn/KAtlas/Knots

See Also

computeInvariant

Examples

#suppose you obtain the following HOMFLY polynomial (e.g. via computeInvariant)
polynomial <- 'l^(-4) - 1/l^2 + l^2 - m^2 - m^2/l^2'
getKnotType(polynomial = polynomial, invariant='HOMFLY')
#get more information of the Stevedore's knot
getKnotType(polynomial = polynomial, invariant='HOMFLY', full.output = TRUE)

Example output

Loading required package: rgl
Loading required package: rSymPy
Loading required package: rJython
Loading required package: rJava
Loading required package: rjson
Loading required package: bio3d
Warning messages:
1: In rgl.init(initValue, onlyNULL) : RGL: unable to open X11 display
2: 'rgl_init' failed, running with rgl.useNULL = TRUE 
3: .onUnload failed in unloadNamespace() for 'rgl', details:
  call: fun(...)
  error: object 'rgl_quit' not found 
[1] "Stevedore's knot (6_1)"
                                 Knot.type 
                  "Stevedore's knot (6_1)" 
                                    HOMFLY 
    "l^(-4) - 1/l^2 + l^2 - m^2 - m^2/l^2" 
                                     Jones 
"2 - 2*t - 1/t + t^(-2) + t^2 - t^3 + t^4" 
                                 Alexander 
                         "5 - 2*t1 - 2/t1" 
                           link.Knot.Atlas 
              "http://katlas.org/wiki/6_1" 

Rknots documentation built on May 1, 2019, 10:19 p.m.