Bugs: Difference between revisions
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* The <code>PD</code> notation used by <code>KnotTheory`</code> is inadequate when a knot diagram contains kinks. For example, there is no way to tell the orientation of <code>PD[X[1,1,2,2]]</code>. |
* The <code>PD</code> notation used by <code>KnotTheory`</code> is inadequate when a knot diagram contains kinks. For example, there is no way to tell the orientation of <code>PD[X[1,1,2,2]]</code>. You can define [[Braid_Representatives|braids]] with kinks, though: <code>Kink = BR[2, {1}]</code>. All knot invariants defined for braid representatives will be correctly evaluated. For example, the previously defined <code>Kink</code> will of course have the same invariants as the unknot. However, don't try to transform the braid into a planar diagram (<code>PD[BR[2, {1}]]</code>), as mathematica might hang up on that. |
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* Many knot invariants (including <code>Jones</code>) do not understand the (artificial but necessary) <code>PD</code> construct "<code>Loop</code>". |
* Many knot invariants (including <code>Jones</code>) do not understand the (artificial but necessary) <code>PD</code> construct "<code>Loop</code>". |
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* Mathematica 9 defines its own tensor product, which causes bugs with the QuantumGroups` package. Stick with Mathematica 7 or 8 until Scott has it fixed. |
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* For some unexplicable bugs (in Mathematica 8 only?), it appears helpful to state the "context" explicitly, e.g. <code>KnotTheory`BR</code> instead of <code>BR</code>, or <code>MirrorTrefoil = PD[KnotTheory`X[1, 5, 2, 4], KnotTheory`X[3, 1, 4, 6], KnotTheory`X[5, 3, 6, 2]]</code> instead of <code>MirrorTrefoil = PD[X[1, 5, 2, 4], X[3, 1, 4, 6], X[5, 3, 6, 2]]</code>. |
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Latest revision as of 11:49, 25 April 2013
- The
PDnotation used byKnotTheory`is inadequate when a knot diagram contains kinks. For example, there is no way to tell the orientation ofPD[X[1,1,2,2]]. You can define braids with kinks, though:Kink = BR[2, {1}]. All knot invariants defined for braid representatives will be correctly evaluated. For example, the previously definedKinkwill of course have the same invariants as the unknot. However, don't try to transform the braid into a planar diagram (PD[BR[2, {1}]]), as mathematica might hang up on that.
- Many knot invariants (including
Jones) do not understand the (artificial but necessary)PDconstruct "Loop".
- Mathematica 9 defines its own tensor product, which causes bugs with the QuantumGroups` package. Stick with Mathematica 7 or 8 until Scott has it fixed.
- For some unexplicable bugs (in Mathematica 8 only?), it appears helpful to state the "context" explicitly, e.g.
KnotTheory`BRinstead ofBR, orMirrorTrefoil = PD[KnotTheory`X[1, 5, 2, 4], KnotTheory`X[3, 1, 4, 6], KnotTheory`X[5, 3, 6, 2]]instead ofMirrorTrefoil = PD[X[1, 5, 2, 4], X[3, 1, 4, 6], X[5, 3, 6, 2]].
