Masahico Saito's Maple Program Library

This material is based upon work supported by the National Science Foundation under Grant No. 9988101 and No. 0301089.

Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

Chad's Maple programs

This is a package to compute quandle cocycle invariants for knots. Download the following files in the same directory (folder) and read cocysample.mws for instruction. In case you do not have Maple but want to see what these programs can compute, we includ the plain text file cocysample.txt.

• cocysample.mws
• cocysample.txt
• Knotpkg.m
• Knotpkg.mws
• knot_table
• extKnotTable
• overextKnotTable
• Quandle

The following are pachanges for the twisted case. See cocysampleTwisted.mws.

• cocysampleTwisted.mws
• KnotpkgT.m
• KnotpkgT.mws

The following are the tables of quandle 2- and 3-cocycle invariants with mod 2, 3, 5 coefficients computed using the above programs, for knots up to 8 crossings, and for quandles up to 6 elements with non-trivial torsion in their homology groups. For example, ``co3Q4m2'' stands for the list for 3-cocycle (shadow, or face-color) invariants for 4-element quandles with mod 2 coefficients. For twisted case, the coefficient Alexander quandles are indicated after a hyphen.

• Untwisted case, 2- and 3-cocycle invariants
• Twisted case, 2-cocycle invariants

Maple programs for computing quandle cocycle knot invariants for group 4- and 5-cycles

The following programs compute the cocycle invariants for the quandles (1) consisting of 4-cycles of S_4, and (2) consisting of 5-cycles of S_5 that are even permutations, respectively, for certain 2-cocycles. For (1), invariants for all 3-colorable knots up to 9 crossings excluding 5-braids, and for (2), all 2- and 3-braids up to 9 crossings, are computed.

• 4-cycles.
• 5-cycles that are even permutations.

Maple programs for computing generalized quandle cocycle knot invariants

The following programs are used in the paper ``Cocycle invariants from quandle modules and generalized quandle cohomology,'' (joint with J.S. Carter, M. Elhamdadi, M. Grana), to appear in Osaka J. Math.

Programs which compute the quandle module invariants for the dihedral quandle, up to 9 crossings.

• For 3-colorables.
• For 5-colorables, excluding 5-braids and up.
• For 7-colorables, excluding 5-braids and up.
• For 9-colorables, excluding 4-braids and up.

Programs which compute the generalized quandle cocycle invariants of classical knots for the dihedral quandle or order 3.

• Up to 9 crossings.
• For their mirror images.
• For a given closed braid.

Programs which compute the generalized quandle cocycle invariants of 2-twist spun knots for the dihedral quandle or order 3.

• Spins of up to 9 crossing 3-colorables.
• With orientations reversed.
• For any cocycle. This shows that the 2-twist spun trefoil has trivial invariant for any cocycle for one choice of orientation, and non-trivial for the other choice.
• For the trivial action on Z_3. This is for the cocycle that is of the diagonal form with the Z_3 coefficient (so the action is trivial) so that it gives the original cocycle invariant, with output in the diagonal vector form. For example, the contribution (1,1,1) means the contribution t in the value Z[t, t^{-1}]/(t^3-1).
• For the trivial action on Z_3 with orientation reversed. Comparing with the preceding program, this shows for which 2-twist spuns the original invariant detects non-invertibility.

Dan's Maple programs: Maple programs for computing quandle cohomology and cocycle knot invariants

The following programs are used in the paper ``Computations of quandle cocycle invariants for knotted curves and surfaces,'' (joint with J.S. Carter, D. Jelsovsky, S. Kamada), Advances in Math., 157 (2001) 36-94. The programs are written jointly with Dan Jelsovsky (currently a professor in Math at Florida Southern College in Lakeland). I like to thank Professor Edwin Clark at USF for his help in developing these programs.

Program which computes the 3rd cohomological dimensions of certain Alexander quandles.

Program which computes the values of the quandle cocycle invariants for knot table, using certain Alexander quandles.

Program which computes the quandle cocycle invariants for 3-twist spun trefoil with certain Alexander quandles.