> | ### D.4.18 normaliz_lib Library: normaliz.lib Purpose: Provides an interface for the use of Normaliz 2.8 or newer within SINGULAR. Authors: Winfried Bruns, Winfried.Bruns@Uni-Osnabrueck.de Christof Soeger, Christof.Soeger@Uni-Osnabrueck.de Overview: The library normaliz.lib provides an interface for the use of Normaliz 2.8 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. Therefore SINGULAR can be used as a comfortable environment for the work with 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 function. Singular and Normaliz exchange data via files. 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. Use of this library requires the program Normaliz to be installed. You can download it from http://www.mathematik.uni-osnabrueck.de/normaliz/. Please make sure that the executables are in the search path or use setNmzExecPath ( setNmzExecPath). Procedures:
> D.4.18.1 intclToricRing |  | computes the integral closure of the toric ring generated by the leading monomials of the elements of I in the basering
> D.4.18.2 normalToricRing |  | computes the normalization of the toric ring generated by the leading monomials of the elements of I
> D.4.18.3 normalToricRingFromBinomials |  | computes the normalization of the polynomial ring modulo the unique minimal binomial prime ideal of the binomial ideal I
> D.4.18.4 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.4.18.5 intclMonIdeal |  | Computes the integral closure of the Rees algebra of the ideal generated by the leading monomials of the elements of I
> D.4.18.6 torusInvariants |  | computes the ring of invariants of a torus action
> D.4.18.7 finiteDiagInvariants |  | computes the ring of invariants of a finite abelian group acting diagonally on a polynomial ring
> D.4.18.8 diagInvariants |  | computes the ring of invariants of a diagonalizable group
> D.4.18.9 intersectionValRings |  | computes the intersection of the polynomial ring with the valuation rings of monomial valuations
> D.4.18.10 intersectionValRingIdeals |  | computes ideals of monomial valuations
> D.4.18.11 showNuminvs |  | prints the numerical invariants found by Normaliz
> D.4.18.12 exportNuminvs |  | exports the numerical invariants found by Normaliz
> D.4.18.13 setNmzOption |  | sets the option s to onoff
> D.4.18.14 showNmzOptions |  | prints the enabled options to the standard output
> D.4.18.15 normaliz |  | applies Normaliz
> D.4.18.16 setNmzExecPath |  | sets the path to the Normaliz executable
> D.4.18.17 writeNmzData |  | creates an input file for Normaliz
> D.4.18.18 readNmzData |  | reads the Normaliz output file with the specified suffix
> D.4.18.19 setNmzFilename |  | sets the filename for the exchange of data
> D.4.18.20 setNmzDataPath |  | sets the directory for the exchange of data
> D.4.18.21 writeNmzPaths |  | writes the path names into two files
> D.4.18.22 startNmz |  | retrieves the path names written by writeNmzPaths
> D.4.18.23 rmNmzFiles |  | removes the files created for and by Normaliz
> D.4.18.24 mons2intmat |  | returns the intmat whose rows represent the leading exponents of the elements of I
> D.4.18.25 intmat2mons |  | returns the ideal generated by the monomials which have the rows of expo_vecs as exponent vector
> D.4.18.26 binomials2intmat |  | returns the intmat whose rows represent the exponents of the elements of the binomial ideal I

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