Quantum Calculator

The Quantum Calculator is a Maple program that can carry out computations in the small quantum cohomology ring of any Grassmannian of classical type. More precisely, it covers ordinary Grassmannians (type A) and Grassmannians of isotropic subspaces in a symplectic vector space (type C) or in an orthogonal vector space (type B or D). This software was written as part of a joint project with Andrew Kresch and Harry Tamvakis, aimed at studying the small quantum cohomology rings of submaximal isotropic and orthogonal Grassmannians. The Quantum Calculator is open source software (under the GNU General Public License).

To use the Quantum Calculator, download the file qcalc, place it in the current directory, and issue the Maple commands "read qcalc;" and "with(qcalc);". This makes several functions available. A detailed description can be found in the User Manual. The following example gives an impression of the capabilities:

% maple
    |\^/|     Maple 10 (IBM INTEL LINUX)
._|\|   |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2005
 \  MAPLE  /  All rights reserved. Maple is a trademark of
 <____ ____>  Waterloo Maple Inc.
      |       Type ? for help.
> read qcalc:
> with(qcalc):
> Gr(3,7):
> qtoS(S[2,1]^3);
     4 S[4, 4, 1] + 8 S[4, 3, 2] + 2 S[3, 3, 3] + 5 q S[2] + 4 q S[1, 1]

I will be grateful for any comments or bug reports regarding this package. Thanks to Weihong Xu for one such report. Enjoy!

Anders Skovsted Buch

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