Frobby is a software system and project for computations with monomial ideals. Frobby is free software and it is intended as a vehicle for computational and mathematical research on monomial ideals.
The current functionality includes Euler characteristic, Hilbert series, maximal standard monomials, combinatorial optimization on monomial ideals, primary decomposition, irreducible decomposition, Alexander dual, associated primes, minimization and intersection of monomial ideals as well as the computation of Frobenius problems (using 4ti2) with very large numbers. Frobby is also able to translate between formats that can be used with several different computer systems, such as Macaulay2, Monos, 4ti2, CoCoA4 and Singular. Thus Frobby can be used with any of those systems.
The systems Macaulay2 and CoCoA include Frobby and use it to perform some of their computations on monomial ideals. Frobby is also available as an optional package for Sage.
Download Frobby from the GitHub releases page.
Frobby works with Linux and MacOS X, as well as with Windows through Cygwin. The short description for getting a Frobby executable is to download Frobby, unpack it with tar and type make and then make install. This requires that you have installed GMP with C++ support. There are more detailed installation instructions in the Frobby manual.
To try Frobby out after installation, you might generate a random monomial ideal and decompose it into irreducible components by typing
frobby genideal|frobby irrdecom
See the Frobby manual for a tutorial that shows how to do most of what Frobby can do. Frobby also has a built-in help system which contains complete information about what Frobby can do, though in a more compact and perhaps less accessible way. You access the built-in help system by typing
frobby help
NOTE: Frobby is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.
Some of the algorithms currently in Frobby are described in the following two papers.