The Equivariant Schubert Calculator is a Maple package able to perform
computations in the equivariant K-theory ring K_{T}(X) of any
generalized flag variety X=G/P. For cominuscule varieties it can also
do calculations in the (small) equivariant quantum K-theory ring
QK_{T}(X). In addition, the package can present its results
in (and perform conversions between) several common indexing
conventions for Schubert classes.

At its core, this software package implements general functions for doing calculations with Weyl groups and root systems. These functions are used to implement calculations in equivariant (quantum) K-theory, as well as computations of curve neighborhoods of Schubert varieties.

To install the Equivariant Schubert Calculator, download the fileEquivCalc-1.0.1.tar.gzand unpack it using the (unix) command:

% tar zxvf EquivCalc-1.0.1.tar.gz

This will create a directory called
`EquivCalc-1.0.1`

that contains
the Maple program file
`equivcalc`

, a (very
preliminary)
user manual, and several
examples. The user manual will be expanded later.

For a quick demonstration of the capabilities, the following Maple commands will compute the multiplication table of the quantum K-theory ring of the Grassmannian Gr(2,4):

% cd EquivCalc-1.0.1 % maple > read equivcalc; > with(equivcalc): > Gr(2,4); > for u in weyl_group() do for v in weyl_group() do > lprint(weyl_comin(X[op(u)] * X[op(v)] = comin_qkmult(u, v))); > od; od;

More examples can be found in the files
`ex_twostep`

.
`ex_qkgrass`

,
`ex_qktP2`

,
`ex_kminu`

,
`ex_curvenbhd`

,
`ex_kpieri`

, and
`ex_qkcayley`

.
For example, the first example can be executed with the (unix) command:

% maple -q < ex_twostepNotice that the examples

`ex_kpieri`

and `ex_qkcayley`

take a while to execute, and some
versions of Maple require a large amount of memory to complete these
examples. All of the examples can be executed using Maple 14 on my
own computer with 4GB of RAM. However, I have not been able to
execute the last two examples with Maple 15 or Maple 16. I expect
that Maple 17 will perform better.
I will be grateful for any comments or bug reports for this package. Enjoy!

During the development of this software, the author was partially supported by NSF grants DMS-0603822, DMS-0906148, and DMS-1205351.