D.15.19 sagbiNormaliz_lib

Library:

sagbiNormaliz.lib

Purpose:

Provides an interface for the computation of Sagbi bases. It uses normaliz.lib (version 4... or higher) for combinatorial computations.

Authors:

Winfried Bruns, [email protected]

Overview:

The library sagbiNormaliz.lib provides functions for the computations of Sagbi bases. It is based on normaliz.lib. Its functions compute Sagbi bases with or without the control by Hilbert functions and/orv degrees. Hilbert functions and degrees require that bthe ambient polynomial ring is standard gtraded. (An extension to general positive gradinmgs would not be difficult.)

Use of this library requires the program Normaliz to be installed and the availability of normaliz.lib. You can download both from @uref{https://github.com/Normaliz/Normaliz/releases}. Please make sure that the executable is in the search path or use setNmzExecPath (defined in normaliz.lib).

The computations of this library require reading Normaliz output files and therefore a file name must be set. The standard file name chosen by the library is NmzSagbiExchange in the current directory. The user can overwrite it by setting another name.

Procedures:

D.15.19.1 sagbiGeneral		computes the Sagbi basis of the subalgebra of the current polynomial ring that is generated by the elements of Q. The computation is stopped after at most sagbiMaxRounds rounds if trhe parameter is set. If sorting is set, the compouted elements are degrevlex sorted before a round of the algorithm. The optional parameter verb sets the terminal output. Fefault is 1 = on..
D.15.19.2 sagbiByDegree		computes the Sagbi basis degree by degree until thwe degree bound is reached or the Sagbi basis has been computed compltely.
D.15.19.3 sagbiHilbControlled		computes the Sagbi basis up to the degree bound. The Hilbert series of the subalgebra generated by the elements of Q is given by its numerator and denominator as a rational function. HS_denom_algebra lists the exponents g_i in the factors 1 -t^g_i of the denominator. If tehe degree bound is reached and the optional argument inalCheck is set, the Hilbert series is checked again for completion.