\contentsline {chapter}{\numberline {1}\textcolor {Chapter }{Introduction}}{3}{chapter.1}%
\contentsline {section}{\numberline {1.1}\textcolor {Chapter }{What is the purpose of the this package?}}{3}{section.1.1}%
\contentsline {chapter}{\numberline {2}\textcolor {Chapter }{Functions}}{4}{chapter.2}%
\contentsline {section}{\numberline {2.1}\textcolor {Chapter }{Create a NmzCone}}{4}{section.2.1}%
\contentsline {subsection}{\numberline {2.1.1}\textcolor {Chapter }{NmzCone}}{4}{subsection.2.1.1}%
\contentsline {section}{\numberline {2.2}\textcolor {Chapter }{Use a NmzCone}}{5}{section.2.2}%
\contentsline {subsection}{\numberline {2.2.1}\textcolor {Chapter }{NmzHasConeProperty}}{5}{subsection.2.2.1}%
\contentsline {subsection}{\numberline {2.2.2}\textcolor {Chapter }{NmzKnownConeProperties}}{5}{subsection.2.2.2}%
\contentsline {subsection}{\numberline {2.2.3}\textcolor {Chapter }{NmzSetVerboseDefault}}{6}{subsection.2.2.3}%
\contentsline {subsection}{\numberline {2.2.4}\textcolor {Chapter }{NmzSetVerbose}}{6}{subsection.2.2.4}%
\contentsline {subsection}{\numberline {2.2.5}\textcolor {Chapter }{NmzCompute}}{6}{subsection.2.2.5}%
\contentsline {subsection}{\numberline {2.2.6}\textcolor {Chapter }{NmzConeProperty}}{6}{subsection.2.2.6}%
\contentsline {subsection}{\numberline {2.2.7}\textcolor {Chapter }{NmzPrintConeProperties}}{8}{subsection.2.2.7}%
\contentsline {section}{\numberline {2.3}\textcolor {Chapter }{Cone properties}}{8}{section.2.3}%
\contentsline {subsection}{\numberline {2.3.1}\textcolor {Chapter }{NmzAffineDim}}{8}{subsection.2.3.1}%
\contentsline {subsection}{\numberline {2.3.2}\textcolor {Chapter }{NmzAllGeneratorsTriangulation}}{8}{subsection.2.3.2}%
\contentsline {subsection}{\numberline {2.3.3}\textcolor {Chapter }{NmzAmbientAutomorphisms}}{9}{subsection.2.3.3}%
\contentsline {subsection}{\numberline {2.3.4}\textcolor {Chapter }{NmzApproximate}}{9}{subsection.2.3.4}%
\contentsline {subsection}{\numberline {2.3.5}\textcolor {Chapter }{NmzAutomorphisms}}{9}{subsection.2.3.5}%
\contentsline {subsection}{\numberline {2.3.6}\textcolor {Chapter }{NmzAxesScaling}}{9}{subsection.2.3.6}%
\contentsline {subsection}{\numberline {2.3.7}\textcolor {Chapter }{NmzBasicStanleyDec}}{9}{subsection.2.3.7}%
\contentsline {subsection}{\numberline {2.3.8}\textcolor {Chapter }{NmzBasicTriangulation}}{9}{subsection.2.3.8}%
\contentsline {subsection}{\numberline {2.3.9}\textcolor {Chapter }{NmzBigInt}}{9}{subsection.2.3.9}%
\contentsline {subsection}{\numberline {2.3.10}\textcolor {Chapter }{NmzBottomDecomposition}}{10}{subsection.2.3.10}%
\contentsline {subsection}{\numberline {2.3.11}\textcolor {Chapter }{NmzClassGroup}}{10}{subsection.2.3.11}%
\contentsline {subsection}{\numberline {2.3.12}\textcolor {Chapter }{NmzCombinatorialAutomorphisms}}{10}{subsection.2.3.12}%
\contentsline {subsection}{\numberline {2.3.13}\textcolor {Chapter }{NmzConeDecomposition}}{10}{subsection.2.3.13}%
\contentsline {subsection}{\numberline {2.3.14}\textcolor {Chapter }{NmzCongruences}}{10}{subsection.2.3.14}%
\contentsline {subsection}{\numberline {2.3.15}\textcolor {Chapter }{NmzCoveringFace}}{10}{subsection.2.3.15}%
\contentsline {subsection}{\numberline {2.3.16}\textcolor {Chapter }{NmzDefaultMode}}{11}{subsection.2.3.16}%
\contentsline {subsection}{\numberline {2.3.17}\textcolor {Chapter }{NmzDeg1Elements}}{11}{subsection.2.3.17}%
\contentsline {subsection}{\numberline {2.3.18}\textcolor {Chapter }{NmzDehomogenization}}{11}{subsection.2.3.18}%
\contentsline {subsection}{\numberline {2.3.19}\textcolor {Chapter }{NmzDescent}}{11}{subsection.2.3.19}%
\contentsline {subsection}{\numberline {2.3.20}\textcolor {Chapter }{NmzDistributedComp}}{11}{subsection.2.3.20}%
\contentsline {subsection}{\numberline {2.3.21}\textcolor {Chapter }{NmzDualFVector}}{11}{subsection.2.3.21}%
\contentsline {subsection}{\numberline {2.3.22}\textcolor {Chapter }{NmzDualFaceLattice}}{11}{subsection.2.3.22}%
\contentsline {subsection}{\numberline {2.3.23}\textcolor {Chapter }{NmzDualIncidence}}{12}{subsection.2.3.23}%
\contentsline {subsection}{\numberline {2.3.24}\textcolor {Chapter }{NmzDualMode}}{12}{subsection.2.3.24}%
\contentsline {subsection}{\numberline {2.3.25}\textcolor {Chapter }{NmzDynamic}}{12}{subsection.2.3.25}%
\contentsline {subsection}{\numberline {2.3.26}\textcolor {Chapter }{NmzEhrhartQuasiPolynomial}}{12}{subsection.2.3.26}%
\contentsline {subsection}{\numberline {2.3.27}\textcolor {Chapter }{NmzEhrhartSeries}}{12}{subsection.2.3.27}%
\contentsline {subsection}{\numberline {2.3.28}\textcolor {Chapter }{NmzEmbeddingDimension}}{12}{subsection.2.3.28}%
\contentsline {subsection}{\numberline {2.3.29}\textcolor {Chapter }{NmzEquations}}{12}{subsection.2.3.29}%
\contentsline {subsection}{\numberline {2.3.30}\textcolor {Chapter }{NmzEuclideanAutomorphisms}}{13}{subsection.2.3.30}%
\contentsline {subsection}{\numberline {2.3.31}\textcolor {Chapter }{NmzEuclideanIntegral}}{13}{subsection.2.3.31}%
\contentsline {subsection}{\numberline {2.3.32}\textcolor {Chapter }{NmzEuclideanVolume}}{13}{subsection.2.3.32}%
\contentsline {subsection}{\numberline {2.3.33}\textcolor {Chapter }{NmzExcludedFaces}}{13}{subsection.2.3.33}%
\contentsline {subsection}{\numberline {2.3.34}\textcolor {Chapter }{NmzExploitAutomsVectors}}{13}{subsection.2.3.34}%
\contentsline {subsection}{\numberline {2.3.35}\textcolor {Chapter }{NmzExploitIsosMult}}{13}{subsection.2.3.35}%
\contentsline {subsection}{\numberline {2.3.36}\textcolor {Chapter }{NmzExternalIndex}}{14}{subsection.2.3.36}%
\contentsline {subsection}{\numberline {2.3.37}\textcolor {Chapter }{NmzExtremeRays}}{14}{subsection.2.3.37}%
\contentsline {subsection}{\numberline {2.3.38}\textcolor {Chapter }{NmzExtremeRaysFloat}}{14}{subsection.2.3.38}%
\contentsline {subsection}{\numberline {2.3.39}\textcolor {Chapter }{NmzFVector}}{14}{subsection.2.3.39}%
\contentsline {subsection}{\numberline {2.3.40}\textcolor {Chapter }{NmzFaceLattice}}{14}{subsection.2.3.40}%
\contentsline {subsection}{\numberline {2.3.41}\textcolor {Chapter }{NmzFixedPrecision}}{14}{subsection.2.3.41}%
\contentsline {subsection}{\numberline {2.3.42}\textcolor {Chapter }{NmzFullConeDynamic}}{14}{subsection.2.3.42}%
\contentsline {subsection}{\numberline {2.3.43}\textcolor {Chapter }{NmzGeneratorOfInterior}}{15}{subsection.2.3.43}%
\contentsline {subsection}{\numberline {2.3.44}\textcolor {Chapter }{NmzGenerators}}{15}{subsection.2.3.44}%
\contentsline {subsection}{\numberline {2.3.45}\textcolor {Chapter }{NmzGrading}}{15}{subsection.2.3.45}%
\contentsline {subsection}{\numberline {2.3.46}\textcolor {Chapter }{NmzGradingDenom}}{15}{subsection.2.3.46}%
\contentsline {subsection}{\numberline {2.3.47}\textcolor {Chapter }{NmzGradingIsPositive}}{15}{subsection.2.3.47}%
\contentsline {subsection}{\numberline {2.3.48}\textcolor {Chapter }{NmzHSOP}}{15}{subsection.2.3.48}%
\contentsline {subsection}{\numberline {2.3.49}\textcolor {Chapter }{NmzHilbertBasis}}{15}{subsection.2.3.49}%
\contentsline {subsection}{\numberline {2.3.50}\textcolor {Chapter }{NmzHilbertQuasiPolynomial}}{16}{subsection.2.3.50}%
\contentsline {subsection}{\numberline {2.3.51}\textcolor {Chapter }{NmzHilbertSeries}}{16}{subsection.2.3.51}%
\contentsline {subsection}{\numberline {2.3.52}\textcolor {Chapter }{NmzIncidence}}{16}{subsection.2.3.52}%
\contentsline {subsection}{\numberline {2.3.53}\textcolor {Chapter }{NmzInclusionExclusionData}}{16}{subsection.2.3.53}%
\contentsline {subsection}{\numberline {2.3.54}\textcolor {Chapter }{NmzInputAutomorphisms}}{16}{subsection.2.3.54}%
\contentsline {subsection}{\numberline {2.3.55}\textcolor {Chapter }{NmzIntegerHull}}{17}{subsection.2.3.55}%
\contentsline {subsection}{\numberline {2.3.56}\textcolor {Chapter }{NmzIntegral}}{17}{subsection.2.3.56}%
\contentsline {subsection}{\numberline {2.3.57}\textcolor {Chapter }{NmzInternalIndex}}{17}{subsection.2.3.57}%
\contentsline {subsection}{\numberline {2.3.58}\textcolor {Chapter }{NmzIsDeg1ExtremeRays}}{17}{subsection.2.3.58}%
\contentsline {subsection}{\numberline {2.3.59}\textcolor {Chapter }{NmzIsDeg1HilbertBasis}}{17}{subsection.2.3.59}%
\contentsline {subsection}{\numberline {2.3.60}\textcolor {Chapter }{NmzIsEmptySemiOpen}}{17}{subsection.2.3.60}%
\contentsline {subsection}{\numberline {2.3.61}\textcolor {Chapter }{NmzIsGorenstein}}{17}{subsection.2.3.61}%
\contentsline {subsection}{\numberline {2.3.62}\textcolor {Chapter }{NmzIsInhomogeneous}}{18}{subsection.2.3.62}%
\contentsline {subsection}{\numberline {2.3.63}\textcolor {Chapter }{NmzIsIntegrallyClosed}}{18}{subsection.2.3.63}%
\contentsline {subsection}{\numberline {2.3.64}\textcolor {Chapter }{NmzIsPointed}}{18}{subsection.2.3.64}%
\contentsline {subsection}{\numberline {2.3.65}\textcolor {Chapter }{NmzIsReesPrimary}}{18}{subsection.2.3.65}%
\contentsline {subsection}{\numberline {2.3.66}\textcolor {Chapter }{NmzIsTriangulationNested}}{18}{subsection.2.3.66}%
\contentsline {subsection}{\numberline {2.3.67}\textcolor {Chapter }{NmzIsTriangulationPartial}}{18}{subsection.2.3.67}%
\contentsline {subsection}{\numberline {2.3.68}\textcolor {Chapter }{NmzKeepOrder}}{19}{subsection.2.3.68}%
\contentsline {subsection}{\numberline {2.3.69}\textcolor {Chapter }{NmzLatticePointTriangulation}}{19}{subsection.2.3.69}%
\contentsline {subsection}{\numberline {2.3.70}\textcolor {Chapter }{NmzLatticePoints}}{19}{subsection.2.3.70}%
\contentsline {subsection}{\numberline {2.3.71}\textcolor {Chapter }{NmzMaximalSubspace}}{19}{subsection.2.3.71}%
\contentsline {subsection}{\numberline {2.3.72}\textcolor {Chapter }{NmzModuleGenerators}}{19}{subsection.2.3.72}%
\contentsline {subsection}{\numberline {2.3.73}\textcolor {Chapter }{NmzModuleGeneratorsOverOriginalMonoid}}{19}{subsection.2.3.73}%
\contentsline {subsection}{\numberline {2.3.74}\textcolor {Chapter }{NmzModuleRank}}{19}{subsection.2.3.74}%
\contentsline {subsection}{\numberline {2.3.75}\textcolor {Chapter }{NmzMultiplicity}}{20}{subsection.2.3.75}%
\contentsline {subsection}{\numberline {2.3.76}\textcolor {Chapter }{NmzNoBottomDec}}{20}{subsection.2.3.76}%
\contentsline {subsection}{\numberline {2.3.77}\textcolor {Chapter }{NmzNoDescent}}{20}{subsection.2.3.77}%
\contentsline {subsection}{\numberline {2.3.78}\textcolor {Chapter }{NmzNoGradingDenom}}{20}{subsection.2.3.78}%
\contentsline {subsection}{\numberline {2.3.79}\textcolor {Chapter }{NmzNoLLL}}{20}{subsection.2.3.79}%
\contentsline {subsection}{\numberline {2.3.80}\textcolor {Chapter }{NmzNoNestedTri}}{20}{subsection.2.3.80}%
\contentsline {subsection}{\numberline {2.3.81}\textcolor {Chapter }{NmzNoPeriodBound}}{21}{subsection.2.3.81}%
\contentsline {subsection}{\numberline {2.3.82}\textcolor {Chapter }{NmzNoProjection}}{21}{subsection.2.3.82}%
\contentsline {subsection}{\numberline {2.3.83}\textcolor {Chapter }{NmzNoRelax}}{21}{subsection.2.3.83}%
\contentsline {subsection}{\numberline {2.3.84}\textcolor {Chapter }{NmzNoSignedDec}}{21}{subsection.2.3.84}%
\contentsline {subsection}{\numberline {2.3.85}\textcolor {Chapter }{NmzNoSubdivision}}{21}{subsection.2.3.85}%
\contentsline {subsection}{\numberline {2.3.86}\textcolor {Chapter }{NmzNoSymmetrization}}{21}{subsection.2.3.86}%
\contentsline {subsection}{\numberline {2.3.87}\textcolor {Chapter }{NmzNumberLatticePoints}}{21}{subsection.2.3.87}%
\contentsline {subsection}{\numberline {2.3.88}\textcolor {Chapter }{NmzOriginalMonoidGenerators}}{22}{subsection.2.3.88}%
\contentsline {subsection}{\numberline {2.3.89}\textcolor {Chapter }{NmzPlacingTriangulation}}{22}{subsection.2.3.89}%
\contentsline {subsection}{\numberline {2.3.90}\textcolor {Chapter }{NmzPrimalMode}}{22}{subsection.2.3.90}%
\contentsline {subsection}{\numberline {2.3.91}\textcolor {Chapter }{NmzProjectCone}}{22}{subsection.2.3.91}%
\contentsline {subsection}{\numberline {2.3.92}\textcolor {Chapter }{NmzProjection}}{22}{subsection.2.3.92}%
\contentsline {subsection}{\numberline {2.3.93}\textcolor {Chapter }{NmzProjectionFloat}}{22}{subsection.2.3.93}%
\contentsline {subsection}{\numberline {2.3.94}\textcolor {Chapter }{NmzPullingTriangulation}}{22}{subsection.2.3.94}%
\contentsline {subsection}{\numberline {2.3.95}\textcolor {Chapter }{NmzPullingTriangulationInternal}}{23}{subsection.2.3.95}%
\contentsline {subsection}{\numberline {2.3.96}\textcolor {Chapter }{NmzRank}}{23}{subsection.2.3.96}%
\contentsline {subsection}{\numberline {2.3.97}\textcolor {Chapter }{NmzRationalAutomorphisms}}{23}{subsection.2.3.97}%
\contentsline {subsection}{\numberline {2.3.98}\textcolor {Chapter }{NmzRecessionRank}}{23}{subsection.2.3.98}%
\contentsline {subsection}{\numberline {2.3.99}\textcolor {Chapter }{NmzReesPrimaryMultiplicity}}{23}{subsection.2.3.99}%
\contentsline {subsection}{\numberline {2.3.100}\textcolor {Chapter }{NmzRenfVolume}}{23}{subsection.2.3.100}%
\contentsline {subsection}{\numberline {2.3.101}\textcolor {Chapter }{NmzSignedDec}}{24}{subsection.2.3.101}%
\contentsline {subsection}{\numberline {2.3.102}\textcolor {Chapter }{NmzStanleyDec}}{24}{subsection.2.3.102}%
\contentsline {subsection}{\numberline {2.3.103}\textcolor {Chapter }{NmzStatic}}{24}{subsection.2.3.103}%
\contentsline {subsection}{\numberline {2.3.104}\textcolor {Chapter }{NmzStrictIsoTypeCheck}}{24}{subsection.2.3.104}%
\contentsline {subsection}{\numberline {2.3.105}\textcolor {Chapter }{NmzSublattice}}{24}{subsection.2.3.105}%
\contentsline {subsection}{\numberline {2.3.106}\textcolor {Chapter }{NmzSuppHypsFloat}}{24}{subsection.2.3.106}%
\contentsline {subsection}{\numberline {2.3.107}\textcolor {Chapter }{NmzSupportHyperplanes}}{24}{subsection.2.3.107}%
\contentsline {subsection}{\numberline {2.3.108}\textcolor {Chapter }{NmzSymmetrize}}{25}{subsection.2.3.108}%
\contentsline {subsection}{\numberline {2.3.109}\textcolor {Chapter }{NmzTestArithOverflowDescent}}{25}{subsection.2.3.109}%
\contentsline {subsection}{\numberline {2.3.110}\textcolor {Chapter }{NmzTestArithOverflowDualMode}}{25}{subsection.2.3.110}%
\contentsline {subsection}{\numberline {2.3.111}\textcolor {Chapter }{NmzTestArithOverflowFullCone}}{25}{subsection.2.3.111}%
\contentsline {subsection}{\numberline {2.3.112}\textcolor {Chapter }{NmzTestArithOverflowProjAndLift}}{25}{subsection.2.3.112}%
\contentsline {subsection}{\numberline {2.3.113}\textcolor {Chapter }{NmzTestLargePyramids}}{25}{subsection.2.3.113}%
\contentsline {subsection}{\numberline {2.3.114}\textcolor {Chapter }{NmzTestLibNormaliz}}{26}{subsection.2.3.114}%
\contentsline {subsection}{\numberline {2.3.115}\textcolor {Chapter }{NmzTestLinearAlgebraGMP}}{26}{subsection.2.3.115}%
\contentsline {subsection}{\numberline {2.3.116}\textcolor {Chapter }{NmzTestSimplexParallel}}{26}{subsection.2.3.116}%
\contentsline {subsection}{\numberline {2.3.117}\textcolor {Chapter }{NmzTestSmallPyramids}}{26}{subsection.2.3.117}%
\contentsline {subsection}{\numberline {2.3.118}\textcolor {Chapter }{NmzTriangulation}}{26}{subsection.2.3.118}%
\contentsline {subsection}{\numberline {2.3.119}\textcolor {Chapter }{NmzTriangulationDetSum}}{26}{subsection.2.3.119}%
\contentsline {subsection}{\numberline {2.3.120}\textcolor {Chapter }{NmzTriangulationSize}}{27}{subsection.2.3.120}%
\contentsline {subsection}{\numberline {2.3.121}\textcolor {Chapter }{NmzUnimodularTriangulation}}{27}{subsection.2.3.121}%
\contentsline {subsection}{\numberline {2.3.122}\textcolor {Chapter }{NmzUnitGroupIndex}}{27}{subsection.2.3.122}%
\contentsline {subsection}{\numberline {2.3.123}\textcolor {Chapter }{NmzVerticesFloat}}{27}{subsection.2.3.123}%
\contentsline {subsection}{\numberline {2.3.124}\textcolor {Chapter }{NmzVerticesOfPolyhedron}}{27}{subsection.2.3.124}%
\contentsline {subsection}{\numberline {2.3.125}\textcolor {Chapter }{NmzVirtualMultiplicity}}{27}{subsection.2.3.125}%
\contentsline {subsection}{\numberline {2.3.126}\textcolor {Chapter }{NmzVolume}}{27}{subsection.2.3.126}%
\contentsline {subsection}{\numberline {2.3.127}\textcolor {Chapter }{NmzWeightedEhrhartQuasiPolynomial}}{28}{subsection.2.3.127}%
\contentsline {subsection}{\numberline {2.3.128}\textcolor {Chapter }{NmzWeightedEhrhartSeries}}{28}{subsection.2.3.128}%
\contentsline {subsection}{\numberline {2.3.129}\textcolor {Chapter }{NmzWitnessNotIntegrallyClosed}}{28}{subsection.2.3.129}%
\contentsline {subsection}{\numberline {2.3.130}\textcolor {Chapter }{NmzBasisChange}}{28}{subsection.2.3.130}%
\contentsline {chapter}{\numberline {3}\textcolor {Chapter }{Examples}}{29}{chapter.3}%
\contentsline {section}{\numberline {3.1}\textcolor {Chapter }{Generators}}{29}{section.3.1}%
\contentsline {section}{\numberline {3.2}\textcolor {Chapter }{System of equations}}{29}{section.3.2}%
\contentsline {section}{\numberline {3.3}\textcolor {Chapter }{System of inhomogeneous equations}}{29}{section.3.3}%
\contentsline {section}{\numberline {3.4}\textcolor {Chapter }{Combined input}}{30}{section.3.4}%
\contentsline {section}{\numberline {3.5}\textcolor {Chapter }{Using the dual mode}}{31}{section.3.5}%
\contentsline {chapter}{\numberline {4}\textcolor {Chapter }{Installing NormalizInterface}}{32}{chapter.4}%
\contentsline {section}{\numberline {4.1}\textcolor {Chapter }{Compiling}}{32}{section.4.1}%
\contentsline {chapter}{References}{33}{chapter*.2}%
\contentsline {chapter}{Index}{34}{section*.3}%
