Depending on the options enabled (see
setNmzOption),
Normaliz writes additional output files. To obtain the content of these files within Macaulay2, use
readNmzData or
allComputations. The following files may be written, provided certain conditions are satisfied and the information that should go into them has been computed. We denote the files simply by their types. In types 0,1,4,5 the ambient lattice is ℤ
n if the input of Normaliz is a matrix of n columns. In types 2 and 3 the ambient lattice is ℤ
n+1 since the input vectors are extended by 1 component. In type 6 the ambient lattice is ℤ
n, in type 10 ℤ
r where n-r is the rank of the input matrix. The essential lattice is gp(M) where M is the monoid computed by Normaliz. See the documentation for Normaliz at
http://www.math.uos.de/normaliz/Normaliz2.2Documentation for more details.
- gen The Hilbert basis is written to this file, provided it has been computed.
- ext The file ext contains the extreme rays, provided they have ben computed.
- cst The file cst contains the constraints defining the cone and the lattice in the same format as they would appear in the input: matrices of types 4,5,6 following each other. Each matrix is concluded by the integer denoting its type. Empty matrices are indicated by 0 as the number of rows. Therefore there will always be 3 matrices. Using this file as input for Normaliz will reproduce the Hilbert basis and all the other data computed.
- egn, esp These contain the Hilbert basis and the support hyperplanes respectively, however with respect to the essential lattice and a basis of it.
- typ This is the product of the matrices corresponding to egn and esp. That is, the support hyperplanes of the cone are evaluated (as linear forms) on the generators.
- tri The file tri contains a triangulation of the cone computed by Normaliz. Each of the rows of the matrix specifies a simplicial cone D: the entries except the last are the indices (with respect to the order in tgn) of those generators that span D, and the last entry is the multiplicity of D in the essential lattice, i.e. the absolute value of the determinant of the matrix of the spanning vectors (as elements of the essential lattice).
- tgn The file tgn contains a matrix of vectors (in the coordinates of the ambient lattice) spanning the simplicial cones in the triangulation.
- ht1 If the associated semigroup is homogeneous, the file ht1 contains the height 1 elements of the cone.
- inv The file inv contains all the information computed that is not contained in any of the other files, i.e. the h-vector, the number of height 1 elements, the cardinality of the Hilbert basis, the Hilbert polynomial, whether the semigroup is homogeneous, the index, the multiplicity, the number of extreme rays, the number of support hyperplanes, whether the ideal is primary and the rank.