Regina Calculation Engine
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This class offers routines for constructing ready-made examples of knots and links. More...
#include <link/examplelink.h>
Static Public Member Functions | |
static Link * | unknot () |
Returns a zero-crossing diagram of the unknot. More... | |
static Link * | monster () |
Returns the monster unknot, a 10-crossing diagram of the unknot that is difficult to untangle. More... | |
static Link * | gordian () |
Returns Haken's Gordian unknot, a 141-crossing diagram of the unknot that is difficult to untangle. More... | |
static Link * | trefoilLeft () |
Returns a three-crossing diagram of the left-hand trefoil. More... | |
static Link * | trefoilRight () |
Returns a three-crossing diagram of the right-hand trefoil. More... | |
static Link * | trefoil () |
Returns a three-crossing diagram of the right-hand trefoil. More... | |
static Link * | figureEight () |
Returns a four-crossing diagram of the figure eight knot. More... | |
static Link * | hopf () |
Returns a two-crossing diagram of the Hopf link. More... | |
static Link * | whitehead () |
Returns a five-crossing diagram of the Whitehead link. More... | |
static Link * | borromean () |
Returns a six-crossing diagram of the Borromean rings. More... | |
static Link * | conway () |
Returns the 11-crossing Conway knot. More... | |
static Link * | kinoshitaTerasaka () |
Returns the 11-crossing Kinoshita-Terasaka knot. More... | |
static Link * | torus (int p, int q) |
Returns the (p,q) torus link. More... | |
static Link * | gst () |
Returns a 48-crossing potential counterexample to the slice-ribbon conjecture, as described by Gompf, Scharlemann and Thompson. More... | |
This class offers routines for constructing ready-made examples of knots and links.
These examples may be useful for testing new code, or for simply getting a feel for how Regina works.
The sample links offered here may prove especially useful in Regina's scripting interface, where working with pre-existing files is more complicated than in the GUI.
All of the methods in this class will assign an appropriate packet label to the link that they return.
Note that each of these routines constructs a new link from scratch. It is up to the caller of each routine to destroy the link that is returned.
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Returns a six-crossing diagram of the Borromean rings.
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Returns the 11-crossing Conway knot.
This is the reflection of K11n34 in the Knot Atlas, and is a mutant of the Kinoshita-Terasaka knot.
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Returns a four-crossing diagram of the figure eight knot.
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Returns Haken's Gordian unknot, a 141-crossing diagram of the unknot that is difficult to untangle.
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Returns a 48-crossing potential counterexample to the slice-ribbon conjecture, as described by Gompf, Scharlemann and Thompson.
Specifically, this knot is Figure 2 from their paper "Fibered knots and potential counterexamples to the property 2R and slice-ribbon conjectures", arXiv:1103.1601.
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Returns a two-crossing diagram of the Hopf link.
This is the variant in which both crossings are positive.
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Returns the 11-crossing Kinoshita-Terasaka knot.
This is the reflection of K11n42 in the Knot Atlas, and is a mutant of the Conway knot. It has trivial Alexander polynomial.
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Returns the monster unknot, a 10-crossing diagram of the unknot that is difficult to untangle.
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Returns the (p,q) torus link.
The parameters p and q must be non-negative, but they do not need to be coprime.
All of the crossings in the resulting link will be positive.
p | the first parameter of the torus link; this must be strictly non-negative. |
q | the second parameter of the torus link; this must also be strictly non-negative. |
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Returns a three-crossing diagram of the right-hand trefoil.
This returns the same knot as trefoilRight().
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Returns a three-crossing diagram of the left-hand trefoil.
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Returns a zero-crossing diagram of the unknot.
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Returns a five-crossing diagram of the Whitehead link.