Metadata-Version: 2.1
Name: PyNormaliz
Version: 2.11
Summary: An interface to Normaliz
Home-page: https://github.com/Normaliz/PyNormaliz
Author: Sebastian Gutsche, Richard Sieg
Author-email: sebastian.gutsche@gmail.com
License: UNKNOWN
Description: [![Build Status](https://travis-ci.org/Normaliz/PyNormaliz.svg)](https://travis-ci.org/Normaliz/PyNormaliz)
        [![Code Coverage](https://codecov.io/github/Normaliz/PyNormaliz/coverage.svg)](https://codecov.io/gh/Normaliz/PyNormaliz)
        
        # PyNormaliz - A python interface to Normaliz
        
        
        PyNormaliz provides an interface to [Normaliz](https://www.normaliz.uni-osnabrueck.de) via libNormaliz.
        It offers the complete functionality of Normaliz, and can be used interactively from python.
        For a first example, see [this introduction](doc/PyNormaliz_Tutorial.pdf) by Richard Sieg (Slighty outdated: for the installation follow the instructions below).
        
        
        ## Requirements
        
        * python 2.7 or higher or python 3.4 or higher
        * Normaliz 3.8.3 or higher <https://github.com/Normaliz/Normaliz/releases>
        
        The source packages of the Normaliz realeases contain PyNormaliz.
        
        ## Installation
        
        The PyNormaliz install script assumes that you have executed
        
            ./install_normaliz_with_eantic.sh
        
        within the Normaliz directory. To install PyNormaliz navigate to the Normaliz directory and type
        
            ./install_pynormaliz.sh --user
        
        Also see Appendix E of the
        [Normaliz manual](https://github.com/Normaliz/Normaliz/blob/master/doc/Normaliz.pdf).
        
        ## Usage
        
        The command Cone creates a cone (and a lattice), and the member functions
        of Cone compute its properties. For a full list of input and output
        properties, see the Normaliz manual.
        
        We assume that you are running python 3.
        
        Start by
        
            import PyNormaliz
            from PyNormaliz import *
        
        To create a simple example, type
        
            C = Cone(cone = [[1,0],[0,1]])
        
        
        All possible Normaliz input types can be given as keyword arguments.
        
        The member functions allow the computation of the data of our cone.  For example,
        
            C.HilbertBasis()
        
        returns what its name says:
        
            [[0, 1], [1, 0]]
        
        is the matrix of the two Hilbert basis vectors.
        
        One can pass options to the compute functions as in
        
            C.HilbertSeries(HSOP = True)
        
        Note that some Normaliz output types must be specially encoded for python. Our Hilbert Series is returned as
        
            [[1], [1, 1], 0]
        
        to be read as follows: [1] is the numerator polynomial, [1,1] is the vector of exponents of t that occur in the denominator, which is (1-t)(1-t) in our case, and 0 is the shift.  So the Hilbert series is given by the rational function 1/(1-t)(1-t). (Also see [this introduction](doc/PyNormaliz_Tutorial.pdf).)
        
        One can also compute several data simultaneously and specify options ("PrimalMode" only added as an example, not because it is particularly useful here):
        
            C.Compute("LatticePoints", "Volume", "PrimalMode")
            
        Then
        
            C.Volume()
            
        retrieves the already computed result [1,1], which encodes the fraction 1/1 = 1. This is the lattice length of the diagonal in the square. The euclidean length, that has been computed simultaneously, is returned by
        
            C.EuclideanVolume()
            
        with the expected value
        
            1.4142135623730951
        
        By using Python functions, the functionality of Normaliz can be extended. For example, 
            
            def intersection(cone1, cone2):
                intersection_ineq = cone1.SupportHyperplanes()+cone2.SupportHyperplanes()
                C = Cone(inequalities = intersection_ineq)
                return C
                
        computes the intersection of two cones. So
        
            C1 = Cone(cone=[[1,2],[2,1]])
            C2 = Cone(cone=[[1,1],[1,3]])
            intersection(C1,C2).ExtremeRays()
            
        yields the result
        
            [[1, 1], [1, 2]]
            
        If you want to see what Normaliz is doing (especually in longer computations) activate the terminal output by
        
            C.setVerbose(True)
        
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