D.4.24 normaliz_lib

Library:

normaliz.lib

Purpose:

Provides an interface for the use of Normaliz 3.10.0 or newer within SINGULAR.

Authors:

Winfried Bruns, [email protected]
Christof Soeger, [email protected]

Overview:

The library normaliz.lib provides an interface for the use of Normaliz 3.10.0 or newer within SINGULAR. The exchange of data is via files. In addition to the top level functions that aim at objects of type ideal or ring, several other auxiliary functions allow the user to apply Normaliz to data of type intmat. Options such as compoutationn goals or algorithmic variants can be activated.To some extent, SINGULAR can therefore be used as an environment for interactive access to Normaliz.
Please see the Normaliz.pdf (included in the Normaliz distribution) for a more extensive documentation of Normaliz.

Normaliz allows the use of a grading. In the Singular functions that access Normaliz the parameter grading is an intvec that assigns a (not necessarily positive) degree to every variable of the ambient polynomial ring. But it must give positive degrees to the generators given to the function.

Singular and Normaliz exchange data via files. The input files use the Normaliz 3 syntax. These files are automatically created and erased behind the scenes. As long as one wants to use only the ring-theoretic functions there is no need for file management.
Note that the numerical invariants computed by Normaliz can be accessed in this "automatic file mode".
However, if Singular is used as a frontend for Normaliz or the user wants to inspect data not automatically returned to Singular, then an explicit filename and a path can be specified for the exchange of data. Moreover, the library provides functions for access to these files. Deletion of the files is left to the user. (Not all output files of Normaliz can be read by this library.)

Use of this library requires the program Normaliz >=3.10.0 to be installed. You can download it from https://github.com/Normaliz/Normaliz/releases. Please make sure that the executable is in the search path or use setNmzExecPath ( setNmzExecPath).

Procedures:

D.4.24.1 intclToricRing		computes the integral closure of the toric ring generated by the leading monomials of the elements of I in the basering
D.4.24.2 normalToricRing		computes the normalization of the toric ring generated by the leading monomials of the elements of I proc hilbertSeriesToricRing(ideal I) computes the Hilbert series of the toric ring generated by the lead monomials of the elements in I. A grading can be specified
D.4.24.3 normalToricRingFromBinomials		computes the normalization of the polynomial ring modulo the unique minimal binomial prime ideal of the binomial ideal I
D.4.24.4 toricRingFromBinomials		computes the polynomial ring modulo the unique inimal binomial prime ideal of the binomial ideal I
D.4.24.5 ehrhartRing		considers the exponent vectors of the elements of I as points of a lattice polytope and computes the integral cloure of the polytopal algebra
D.4.24.6 intclMonIdeal		Computes the integral closure of the Rees algebra of the ideal generated by the leading monomials of the elements of I
D.4.24.7 definingBinomialIdeal		computes the defining binomail ideal of the toric ring generated by the leading monomials of the elements of I
D.4.24.8 latticeIdeal		computes the lattice ideal defined by the binomial ideal I
D.4.24.9 groebnerBasis		computes a Gröbner basis of the lattice ideal defined by the binomial ideal I
D.4.24.10 torusInvariants		computes the ring of invariants of a torus action
D.4.24.11 finiteDiagInvariants		computes the ring of invariants of a finite abelian group acting diagonally on a polynomial ring
D.4.24.12 diagInvariants		computes the ring of invariants of a diagonalizable group
D.4.24.13 intersectionValRings		computes the intersection of the polynomial ring with the valuation rings of monomial valuations
D.4.24.14 intersectionValRingIdeals		computes ideals of monomial valuations
D.4.24.15 showNuminvs		prints the numerical invariants found by Normaliz
D.4.24.16 exportNuminvs		exports the numerical invariants found by Normaliz
D.4.24.17 allNmzOptions		prints all available Normaliz options with thei naming string, the default value and the string passed to Normaliz
D.4.24.18 setNmzOption		sets the option s to onoff
D.4.24.19 addNmzOption		adds a Normaliz option to the list of predefined ones and activates it
D.4.24.20 showNmzOptions		prints the enabled options to the standard output
D.4.24.21 resetNmzOptions		resets the options to the default choice
D.4.24.22 normaliz		applies Normaliz to the input matrix of type nmz_type. Further arguments can be additional matrices and integer parameters.
D.4.24.23 setNmzExecPath		sets the path to the Normaliz executable
D.4.24.24 writeNmzData		creates an input file for Normaliz (also from a list of pairs sgr, nmz_type)
D.4.24.25 readNmzData		reads the Normaliz output file with the specified suffix
D.4.24.26 setNmzFilename		sets the filename for the exchange of data
D.4.24.27 setNmzDataPath		sets the directory for the exchange of data
D.4.24.28 writeNmzPaths		writes the path names into two files
D.4.24.29 startNmz		retrieves the path names written by writeNmzPaths
D.4.24.30 rmNmzFiles		removes the files created for and by Normaliz
D.4.24.31 mons2intmat		returns the intmat whose rows represent the leading exponents of the elements of I
D.4.24.32 intmat2mons		returns the ideal generated by the monomials which have the rows of expo_vecs as exponent vector
D.4.24.33 binomials2intmat		returns the intmat whose rows represent the exponents of the elements of the binomial ideal I
D.4.24.34 intmat2binomials		returns the ideal generated by the binomials represent by the rows of the intmat expo_vecs