Description Usage Arguments Value Author(s) References See Also Examples
Given a polynomial invariant, obtain information on the knot type. Additionally, other polynomials are returned if wished
1 | getKnotType( polynomial, invariant = 'HOMFLY', full.output = FALSE )
|
polynomial |
a single element character vector containing a polynomial invariant as returned by |
invariant |
the type of |
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. |
The knot type (the simplest knot having the input polynomial). Optionally, additional informations on it.
Federico Comoglio, federico.comoglio@bsse.ethz.ch
The Rolfsen Knot Table on Knot Atlas, http://www.math.toronto.edu/~drorbn/KAtlas/Knots
1 2 3 4 5 | #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)
|
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"
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