# Alexander Stoimenow

## Some programs

Here is C++ source code of some programs. My programs require the GNU C++
compiler g++ (version 2.7.2 f.) and a UNIX shell. Since even the GNU
compiler does not always handle correctly templates and offers internal
compiler errors, I cant exclude
funny results. *Please report any errors and problems you have!*

### A program for solid torus invariants and PostScript images

Here is a gzipped tar-file
gsinv.tgz

of some programs which can be used to
calculate the Fiedler solid torus invariants, generate PostScript
images of knots, links, and tangles (1/10 in size of those
rendered by
KnotScape and 1/100 of those rendered by the Adobe
Illustrator), and convert between different formats (including the
one of KnotScape's editor).

More information on what the programs do and instructions how they are
to be used may be found in the paper

- Th. Fiedler and A. Stoimenow,
*New
knot and link invariants*, Proceedings of the International
Conference on Knot Theory "Knots in Hellas, 98", Series
on Knots and Everything ** 24**, World Scientific, 2000.

The following papers and monographs use essentially calculations with
these programs:
- Th. Fiedler,
*Gauss Diagram Invariants for Knots
and Links*, Kluwer Academic Publishers, Mathematics and Its
Applications Vol ** 532** (2001).
- Th. Fiedler,
* Gauss diagram invariants for knots
which are not closed braids*, Math. Proc. Cambridge
Philos. Soc. ** 135(2)** (2003), 335--348.
- A. Stoimenow,
*Mutant links distinguished
by degree 3 Gauss sums*, Proceedings of the International
Conference on Knot Theory "Knots in Hellas, 98", Series
on Knots and Everything ** 24**, World Scientific, 2000.

Remarks:
- Compiling the main program may, however, take
*several minutes*.
- To run the program
`lsd2sp` requires also GNU's AWK program
`gawk` installed on your system.

### Odd crossing amphicheiral knots

A tar-file with 5 programs (and several input/data files)
written for calculations in the proof of the odd
crossing amphicheiral knots.
oddach.tar

The test messages what is computed compare well (not perfectly) to
this version of the paper.

Program aqv23tst7.C is for $15+4k$ crossings
(though it was updated to subsume the step of Jones polynomial
calculation explained in the paper). Programs aqv23tst8*.C are for
$17+4k$ crossings.

Compiling with g++ on UNIX and calling the program without any argument
should work (though some programs give no output, because there
are no diagrams of the sought type). There are some comments in
the programs, but better let me know if you like to try them out.
So far I give no detailed explanation, since
I'm not sure who will be interested...

### Hoste's conjecture for 2-bridge knots

h2br_m2.nb,
MATHEMATICA notebook with complete calculation (compiled with
version 10.2). Contains comments and some extraneous calculations.
(If you follow the comments you will be able to redo all
needed calculations, although a bit of fiddling may be necessary.)
alpha_bd.m, and
almax_bd_7a.m, two data files which can be read in from the
notebook file to avoid the most time consuming parts of the
calculation.

h2br_m2.pdf and
h2br_m2.ps.gz, printouts of the
MATHEMATICA notebook (with full graphics). PS is compressed
because it's 63M.

h2br3a.ps and
h2br3a.pdf, draft of the
paper, not in publication-ready form, but with full
explanation of all details of the calculation. Comments in
the MATHEMATICA notebook refer to this draft.

Alexander Stoimenow,

*stoimeno_stoimenov.net*