Interfaces most of the functionality of the software 4ti2 available at http://www.4ti2.de/. (The user needs to have 4ti2 installed on his/her machine.)
A d×n integral matrix A (with nonnegative entries) specifies a map from a polynomial ring in d variables to a polynomial ring with n variables by specifying exponents of the variables indexing its columns. For example, if A is a matrix
3 2 1 0 0 1 2 3
The toric ideal IA is the kernel of this map. It is minimally generated by the 2-minors of the matrix
x y z y z w
For more theoretical details (and more generality), see the standard reference: B. Sturmfels, Gröbner bases and convex polytopes. American Mathematical Society, University Lectures Series, No 8, Providence, Rhode Island, 1996.
Note for cygwin users: If a problem occurs during package installation and/or loading, it should be fixed by setting the path inside the file .Macaulay2/init-FourTiTwo.m2 to whatever folder 4ti2 is installed. For example, if 4ti2 has been installed in C:/cygwin/4ti2/win32, then the line inside the init-FourTiTwo.m2 file will look like this: "path" => "C:/cygwin/4ti2/win32/" . Alternately, the path for 4ti2 may be set when loading the package using the following command: loadPackage("FourTiTwo", Configuration=>"path"=>"C:/cygwin/4ti2/win32/") assuming that 4ti2 has been installed in C:/cygwin/4ti2/win32.