# QuiverCycles Package

QuiverCycles is a Macaulay2 package for computing the Grothendieck
classes of quiver cycles as well as the associated quiver
coefficients. The definitions are given in the paper Quiver
coefficients of Dynkin type, Michigan Math. J. 57 (2008), 93-120.

### Installation:

To install this software, do the following:

1) Download the file QuiverCycles.m2.

2) Start Macaulay2 and issue the command:

i1 : installPackage "QuiverCycles"

3) Browse the documentation, starting from:

i2 : viewHelp "QuiverCycles"

### Example:

The following gives an example of the capabilities:

i3 : Q = quiver(3, {0,1}, {1,2});
i4 : dv = {2,3,2};
i5 : rep = { matrix{{1,0},{0,0},{0,0}}, matrix{{0,0,0},{0,0,1}} };
i6 : cc = cycleClass(Q, dv, rep);
i7 : quiverCoefficients(Q, dv, cc)
---- (1)
---- (2)
---- (3)
---- (4)
{{}, {1, 1}, {2, 1}} => 1
{{}, {2, 1}, {2}} => 1
---- (5)
{{}, {2, 1}, {2, 1}} => -1
o7 = HashTable{{{}, {1, 1}, {2, 1}} => 1 }
{{}, {2, 1}, {2, 1}} => -1
{{}, {2, 1}, {2}} => 1
o7 : HashTable

I will be grateful for any comments or bug reports for this package.
Enjoy!

Anders Skovsted Buch

I enjoyed support from NSF grant DMS-0906148 during the development of
this software.