|  | Index Entry | Section | 
|---|
| 
 | 
| G |  |  | 
|---|
|  | G-algebra | 7.4.1 G-algebras | 
|  | G-algebra | Definition (G-algebra) | 
|  | G-algebra, setup | Setting up a G-algebra | 
|  | G_a -Invariants | A.5.1 G_a -Invariants | 
|  | galois field | 4.14 number | 
|  | Gamma | D.5.5.17 Gamma | 
|  | Gauss-Manin connection | C.5 Gauss-Manin connection | 
|  | Gauss-Manin connection | D.6.13 mondromy_lib | 
|  | Gauss-Manin connection | D.6.17.1 spectrumnd | 
|  | Gauss-Manin system | D.6.9 gmssing_lib | 
|  | Gauss-Manin system | D.6.9.1 gmsring | 
|  | Gauss-Manin system | D.6.9.2 gmsnf | 
|  | Gauss-Manin system | D.6.9.3 gmscoeffs | 
|  | Gauss-Manin system | D.6.9.4 bernstein | 
|  | Gauss-Manin system | D.6.9.5 monodromy | 
|  | Gauss-Manin system | D.6.9.6 spectrum | 
|  | Gauss-Manin system | D.6.9.7 sppairs | 
|  | Gauss-Manin system | D.6.9.8 vfilt | 
|  | Gauss-Manin system | D.6.9.9 vwfilt | 
|  | Gauss-Manin system | D.6.9.10 tmatrix | 
|  | Gauss-Manin system | D.6.9.11 endvfilt | 
|  | Gauss-Manin system | D.6.10 gmspoly_lib | 
|  | Gauss-Manin system | D.6.10.2 goodBasis | 
|  | gauss_col | D.3.1.14 gauss_col | 
|  | gauss_nf | D.3.2.13 gauss_nf | 
|  | gauss_row | D.3.1.15 gauss_row | 
|  | gaussred | D.3.2.11 gaussred | 
|  | gaussred_pivot | D.3.2.12 gaussred_pivot | 
|  | GBsolve | D.8.1.4 GBsolve | 
|  | GBWeight | 7.5.5.0. GBWeight | 
|  | gcd | 5.1.50 gcd | 
|  | gcddivisor | D.12.4.7 gcddivisor | 
|  | gcdMon | D.4.15.3 gcdMon | 
|  | Gelfand-Kirillov dimension | 7.10.3 fpaprops_lib | 
|  | gen | 5.1.51 gen | 
|  | General command syntax | 3.5.1 General command syntax | 
|  | General concepts | 3. General concepts | 
|  | general error-locator polynomial | General error-locator polynomial | 
|  | general neron. | D.15.19 GND_lib | 
|  | General purpose | D.2 General purpose | 
|  | General syntax of a ring declaration | 3.3.2 General syntax of a ring declaration | 
|  | general weighted lexicographical ordering | B.2.4 Local orderings | 
|  | general weighted reverse lexicographical ordering | B.2.4 Local orderings | 
|  | general.lib | D.2.3 general_lib | 
|  | general_lib | D.2.3 general_lib | 
|  | Generalized Hilbert Syzygy Theorem | Generalized Hilbert Syzygy Theorem | 
|  | Generalized Newton identities | C.8.3 Generalized Newton identities | 
|  | generalOrder | D.12.6.4 generalOrder | 
|  | generateG | D.12.3.31 generateG | 
|  | generator | D.15.12.3 diffAlgebraGens | 
|  | generator | D.15.12.13 difformIsGen | 
|  | generator | D.15.12.43 derivationContractionGen | 
|  | generators | D.6.1.8 charexp2generators | 
|  | generators | D.15.12.6 diffAlgebraListGen | 
|  | generators | D.15.12.8 difformCoef | 
|  | generators | D.15.12.9 difformGenToString | 
|  | generatorsOfLinealitySpace | D.13.1.21 generatorsOfLinealitySpace | 
|  | generatorsOfSpan | D.13.1.22 generatorsOfSpan | 
|  | generic representation | D.2.4.8 extendpoly | 
|  | genericid | D.2.9.1 genericid | 
|  | genericity | D.11.2.10 genericity | 
|  | genericmat | D.3.1.6 genericmat | 
|  | genMDSMat | D.10.2.11 genMDSMat | 
|  | genoutput | D.5.5.24 genoutput | 
|  | genSymId | D.4.29.1 genSymId | 
|  | genus | D.4.19.5 genus | 
|  | Geometric genus | D.5.4 paraplanecurves_lib | 
|  | Geometric Invariant Theory | A.6 Geometric Invariant Theory | 
|  | Geometric Theorems | D.2.4.21 ADGT | 
|  | geometrical locus | D.2.4.10 locus | 
|  | geometrical locus | D.2.4.11 locusdg | 
|  | geometrical locus | D.2.4.12 envelop | 
|  | geometrical locus | D.2.4.13 locusto | 
|  | geometrical locus | D.2.4.14 stdlocus | 
|  | geometrical locus | D.2.4.15 AssocTanToEnv | 
|  | geometrical locus | D.2.4.16 FamElemsAtEnvCompPoints | 
|  | German Umlaute | 6.1 Limitations | 
|  | getArguments | D.2.12.12 getArguments | 
|  | getCommand | D.2.12.11 getCommand | 
|  | getCone | D.13.1.48 getCone | 
|  | getcores | D.2.10.3 getcores | 
|  | getdump | 5.1.52 getdump | 
|  | getenv | 5.1.153 system | 
|  | getGradingGroup | D.15.25.3 getGradingGroup | 
|  | getLattice | D.15.25.4 getLattice | 
|  | getLinearForms | D.13.1.23 getLinearForms | 
|  | getModuleGrading | D.15.25.14 getModuleGrading | 
|  | getMultiplicity | D.13.1.24 getMultiplicity | 
|  | getOneVar | D.4.19.13 getOneVar | 
|  | getResult | D.2.12.13 getResult | 
|  | getSmallest | D.4.19.12 getSmallest | 
|  | getState | D.2.12.14 getState | 
|  | Getting started | 2.3 Getting started | 
|  | getVariableWeights | D.15.25.2 getVariableWeights | 
|  | gfan.lib | D.13.1 gfan_lib | 
|  | gfan_lib | D.13.1 gfan_lib | 
|  | gfanlib | 1. Preface | 
|  | GIT-Fans | A.6.1 GIT-Fans | 
|  | GITcone | D.15.18.6 GITcone | 
|  | gitCone | D.15.18.30 gitCone | 
|  | GITfan | D.15.18.7 GITfan | 
|  | gitfan.lib | D.15.18 gitfan_lib | 
|  | gitfan_lib | D.15.18 gitfan_lib | 
|  | GITfanFromOrbitCones | D.15.18.8 GITfanFromOrbitCones | 
|  | GITfanParallel | D.15.18.9 GITfanParallel | 
|  | GITfanParallelSymmetric | D.15.18.24 GITfanParallelSymmetric | 
|  | GITfanSymmetric | D.15.18.23 GITfanSymmetric | 
|  | GKdim | 7.5.9.0. GKdim | 
|  | gkdim.lib | 7.5.9 gkdim_lib | 
|  | gkdim_lib | 7.5.9 gkdim_lib | 
|  | GKZfan | D.15.18.10 GKZfan | 
|  | GKZsystem | 7.5.10.0. GKZsystem | 
|  | global | 5.1.2 attrib | 
|  | global Bernstein-Sato ideal | 7.5.6 dmodideal_lib | 
|  | global Bernstein-Sato polynomial | 7.5.2 bfun_lib | 
|  | global Bernstein-Sato polynomial | 7.5.4 dmod_lib | 
|  | global Bernstein-Sato polynomial for variety | 7.5.7 dmodvar_lib | 
|  | global homological dimension | 7.10.3 fpaprops_lib | 
|  | Global orderings | B.2.3 Global orderings | 
|  | globalSections | D.15.13.7 globalSections | 
|  | GMP | 1. Preface | 
|  | GMP | E.3 libSingular | 
|  | gmscoeffs | D.6.9.3 gmscoeffs | 
|  | gmsnf | D.6.9.2 gmsnf | 
|  | gmspoly.lib | D.6.10 gmspoly_lib | 
|  | gmspoly_lib | D.6.10 gmspoly_lib | 
|  | gmsring | D.6.9.1 gmsring | 
|  | gmssing.lib | D.6.9 gmssing_lib | 
|  | gmssing_lib | D.6.9 gmssing_lib | 
|  | GND.lib | D.15.19 GND_lib | 
|  | GND_lib | D.15.19 GND_lib | 
|  | Goettsche's formula | D.15.16 goettsche_lib | 
|  | goettsche.lib | D.15.16 goettsche_lib | 
|  | goettsche_lib | D.15.16 goettsche_lib | 
|  | GoettscheF | D.15.16.1 GoettscheF | 
|  | good basis | D.6.9 gmssing_lib | 
|  | good basis | D.6.9.10 tmatrix | 
|  | good basis | D.6.10 gmspoly_lib | 
|  | good basis | D.6.10.2 goodBasis | 
|  | goodBasis | D.6.10.2 goodBasis | 
|  | gorensteinIndex | D.13.2.21 gorensteinIndex | 
|  | gorensteinVector | D.13.2.22 gorensteinVector | 
|  | graal.lib | D.15.17 graal_lib | 
|  | graal_lib | D.15.17 graal_lib | 
|  | graalMixed | D.15.17.1 graalMixed | 
|  | graded | D.15.12.6 diffAlgebraListGen | 
|  | graded algebra | D.15.2 autgradalg_lib | 
|  | Graded commutative algebras | 7.6 Graded commutative algebras (SCA) | 
|  | graded Hilbert series | 7.10.5 ncHilb_lib | 
|  | graded module, graded piece | D.5.10.8 dimGradedPart | 
|  | graded modules, graded homomorphisms, syzygies | D.15.20 gradedModules_lib | 
|  | graded modules, handling of | A.3.5 Handling graded modules | 
|  | graded Weyl algebra | 7.5.2 bfun_lib | 
|  | graded-module, graded-resolution, homogenoues-matrix, R-module-homomorphism | D.15.23 modules_lib | 
|  | gradedModules.lib | D.15.20 gradedModules_lib | 
|  | gradedModules_lib | D.15.20 gradedModules_lib | 
|  | gradeNumber | 7.5.22.0. gradeNumber | 
|  | gradiator | D.15.25.47 gradiator | 
|  | graph | D.4.6.1 makeGraph | 
|  | graph | D.4.6.2 printGraph | 
|  | graph | D.15.33.21 makeGraphVE | 
|  | graph | D.15.33.22 printGraphG | 
|  | graphics.lib | D.9.1 graphics_lib | 
|  | graphics_lib | D.9.1 graphics_lib | 
|  | graphviz | 1. Preface | 
|  | Grassmannian | D.15.33.5 Grassmannian | 
|  | Grassmannian, abstract variety, Schubert calculus | D.15.33.5 Grassmannian | 
|  | graver4ti2 | D.4.28.3 graver4ti2 | 
|  | grconcat | D.15.20.23 grconcat | 
|  | grdeg | D.15.20.3 grdeg | 
|  | Greuel, Gert-Martin | Acknowledgements | 
|  | grgens | D.15.20.12 grgens | 
|  | grgroebner | D.15.20.22 grgroebner | 
|  | grlift | D.15.20.20 grlift | 
|  | grlifting | D.15.20.27 grlifting | 
|  | grlifting2 | D.15.20.28 grlifting2 | 
|  | grlifting3 | D.15.20.30 grlifting3 | 
|  | grneg | D.15.20.33 grneg | 
|  | Grob1Levels | D.2.4.24 Grob1Levels | 
|  | grobcov | D.2.4.1 grobcov | 
|  | grobcov.lib | D.2.4 grobcov_lib | 
|  | grobcov_lib | D.2.4 grobcov_lib | 
|  | grobj | D.15.20.1 grobj | 
|  | groebner | 5.1.53 groebner | 
|  | groebner | A.2.1 groebner and std | 
|  | Groebner Bases | A.2 Computing Groebner and Standard Bases | 
|  | Groebner bases for two-sided ideals in free associative algebras | 7.9.3 Groebner bases for two-sided ideals in free associative algebras | 
|  | Groebner bases in free associative algebras | 7.9.3 Groebner bases for two-sided ideals in free associative algebras | 
|  | Groebner bases in G-algebras | 7.4.2 Groebner bases in G-algebras | 
|  | Groebner bases, decodeGB | D.10.2 decodegb_lib | 
|  | Groebner bases, slim | A.2.3 slim Groebner bases | 
|  | groebner basis computations | 5.1.53 groebner | 
|  | Groebner basis conversion | A.2.2 Groebner basis conversion | 
|  | Groebner cover | D.2.4.1 grobcov | 
|  | Groebner cover | D.2.4.8 extendpoly | 
|  | Groebner cover | D.2.4.9 extendGC | 
|  | Groebner fan | D.13.2 polymake_lib | 
|  | Groebner walk | D.4.7.4 awalk2 | 
|  | Groebner walk | D.4.7.6 gwalk | 
|  | Groebner walk | D.15.32.1 prwalk | 
|  | Groebner walk | D.15.32.2 rwalk | 
|  | Groebner-Shirshov bases | 7.9.3 Groebner bases for two-sided ideals in free associative algebras | 
|  | Groebner-Shirshov bases in free associative algebras | 7.9.3 Groebner bases for two-sided ideals in free associative algebras | 
|  | groebnerComplex | D.13.4.42 groebnerComplex | 
|  | groebnerCone | D.13.4.36 groebnerCone | 
|  | groebnerFan | D.13.4.41 groebnerFan | 
|  | Groebnerwalk | D.4.7 grwalk_lib | 
|  | Groebnerwalk | D.15.24 modwalk_lib | 
|  | Groebnerwalk | D.15.32 rwalk_lib | 
|  | Groebnerwalk | D.15.34 swalk_lib | 
|  | Gromov-Witten invariants | D.4.6 ellipticcovers_lib | 
|  | Gromov-Witten invariants | D.4.6.6 gromovWitten | 
|  | Gromov-Witten invariants | D.4.6.7 computeGromovWitten | 
|  | Gromov-Witten invariants, lines on hypersurfaces | D.15.33.30 linesHypersurface | 
|  | Gromov-Witten invariants, multiple covers | D.15.33.29 multipleCover | 
|  | Gromov-Witten invariants, rational curves on Calabi-Yau threefolds | D.15.33.31 rationalCurve | 
|  | Gromov-Witten invariants, rational curves on Calabi-Yau threefolds | D.15.33.32 sumofquotients | 
|  | Gromov-Witten invariants. | D.15.33 schubert_lib | 
|  | gromovWitten | D.4.6.6 gromovWitten | 
|  | grorder | D.15.20.14 grorder | 
|  | ground field | 4.14 number | 
|  | group_reynolds | D.7.1.8 group_reynolds | 
|  | groupActionOnHashes | D.15.18.18 groupActionOnHashes | 
|  | groupActionOnQImage | D.15.18.17 groupActionOnQImage | 
|  | growth of algebra | 7.10.3 fpaprops_lib | 
|  | grpower | D.15.20.10 grpower | 
|  | grpres | D.15.20.13 grpres | 
|  | grprod | D.15.20.21 grprod | 
|  | grrange | D.15.20.32 grrange | 
|  | grres | D.15.20.19 grres | 
|  | grrndmap | D.15.20.25 grrndmap | 
|  | grrndmap2 | D.15.20.26 grrndmap2 | 
|  | grrndmat | D.15.20.24 grrndmat | 
|  | grshift | D.15.20.5 grshift | 
|  | grsum | D.15.20.9 grsum | 
|  | grsyz | D.15.20.18 grsyz | 
|  | grtest | D.15.20.2 grtest | 
|  | grtranspose | D.15.20.11 grtranspose | 
|  | grtranspose1 | D.15.20.15 grtranspose1 | 
|  | grtwist | D.15.20.7 grtwist | 
|  | grtwists | D.15.20.8 grtwists | 
|  | grview | D.15.20.4 grview | 
|  | grwalk.lib | D.4.7 grwalk_lib | 
|  | grwalk_lib | D.4.7 grwalk_lib | 
|  | grzero | D.15.20.6 grzero | 
|  | GTZmod | D.4.16.6 GTZmod | 
|  | GTZopt | D.4.16.13 GTZopt | 
|  | gwalk | D.4.7.6 gwalk | 
|  | Gweights | 7.5.19.0. Gweights | 
| 
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