|  | Index Entry | Section | 
|---|
| 
 | 
| J |  |  | 
|---|
|  | J-marked schemes | D.5.11 JMBTest_lib | 
|  | J-marked schemes, Borel ideals | D.5.12 JMSConst_lib | 
|  | jacob | 5.1.66 jacob | 
|  | Jacobi | D.12.3.6 Jacobi | 
|  | jacoblift | D.6.13.3 jacoblift | 
|  | jacobson | D.11.3.2 jacobson | 
|  | Jacobson form | D.11.3 jacobson_lib | 
|  | Jacobson normal form | D.11.3 jacobson_lib | 
|  | jacobson.lib | D.11.3 jacobson_lib | 
|  | jacobson_lib | D.11.3 jacobson_lib | 
|  | janet | 5.1.67 janet | 
|  | janet basis | D.15.31 rstandard_lib | 
|  | Janet basis | D.15.31.4 modJanet | 
|  | Janet division, Janet basis | D.15.31.3 rJanet | 
|  | jet | 5.1.68 jet | 
|  | jInvariant | D.13.4.10 jInvariant | 
|  | JMarkedScheme | D.5.12.2 JMarkedScheme | 
|  | JMBTest.lib | D.5.11 JMBTest_lib | 
|  | JMBTest_lib | D.5.11 JMBTest_lib | 
|  | JMSConst.lib | D.5.12 JMSConst_lib | 
|  | JMSConst_lib | D.5.12 JMSConst_lib | 
|  | jOft | D.12.2.9 jOft | 
|  | jordan | D.3.2.22 jordan | 
|  | jordanbasis | D.3.2.23 jordanbasis | 
|  | jordanmatrix | D.3.2.24 jordanmatrix | 
|  | jordannf | D.3.2.25 jordannf | 
|  | jordanVecField | D.15.36.3 jordanVecField | 
|  | jungfib | D.5.7.3 jungfib | 
|  | jungnormal | D.5.7.2 jungnormal | 
|  | jungresolve | D.5.7.1 jungresolve | 
|  | JuReTopDim | D.5.2.6 JuReTopDim | 
|  | JuReZeroDim | D.5.2.7 JuReZeroDim | 
| 
 | 
| K |  |  | 
|---|
|  | K-basis | 7.10.1 fpadim_lib | 
|  | K-dimension | 7.10.1 fpadim_lib | 
|  | katsura | D.2.8.3 katsura | 
|  | kbase | 5.1.69 kbase | 
|  | kbase (plural) | 7.3.10 kbase (plural) | 
|  | keepring | 5.2.11 keepring | 
|  | KeneshlouMatrixPresentation | D.15.20.17 KeneshlouMatrixPresentation | 
|  | Ker | D.15.23.25 Ker | 
|  | kerHom | D.15.23.45 kerHom | 
|  | kernel | 5.1.70 kernel | 
|  | Kernel of module homomorphisms | A.3.11 Kernel of module homomorphisms | 
|  | kernelLattice | D.15.25.18 kernelLattice | 
|  | kill | 5.1.71 kill | 
|  | killall | D.2.3.10 killall | 
|  | killattrib | 5.1.72 killattrib | 
|  | killTask | D.2.12.2 killTask | 
|  | kmemory | D.2.3.9 kmemory | 
|  | kohom | D.4.8.16 kohom | 
|  | kontrahom | D.4.8.17 kontrahom | 
|  | koszul | 5.1.73 koszul | 
|  | KoszulHomology | D.4.8.18 KoszulHomology | 
|  | Kronecker module | D.15.16 goettsche_lib | 
|  | Kronecker product | 5.1.155 tensor | 
|  | KScoef | D.6.12.4 KScoef | 
|  | KSconvert | D.6.12.2 KSconvert | 
|  | KSker | D.6.12.1 KSker | 
|  | kskernel.lib | D.6.12 kskernel_lib | 
|  | kskernel_lib | D.6.12 kskernel_lib | 
|  | KSlinear | D.6.12.3 KSlinear | 
|  | KSpencerKernel | D.6.16.9 KSpencerKernel | 
| 
 | 
| L |  |  | 
|---|
|  | L, ordering | B.2.9 Pseudo ordering L | 
|  | l-adic numbers | p-adic numbers | 
|  | laguerre | 5.1.74 laguerre | 
|  | laguerre_solve | D.8.3.1 laguerre_solve | 
|  | lastvarGeneral | D.12.6.3 lastvarGeneral | 
|  | latex.lib | D.9.2 latex_lib | 
|  | latex_lib | D.9.2 latex_lib | 
|  | lattice | D.14.1.38 arrLattice | 
|  | latticeArea | D.13.2.11 latticeArea | 
|  | latticeBasis | D.15.25.19 latticeBasis | 
|  | latticeCodegree | D.13.2.37 latticeCodegree | 
|  | latticeDegree | D.13.2.38 latticeDegree | 
|  | latticePoints | D.13.2.39 latticePoints | 
|  | latticeVolume | D.13.2.40 latticeVolume | 
|  | Laurent series | D.4.6.4 computeConstant | 
|  | laxfrT | D.15.15.4 laxfrT | 
|  | laxfrX | D.15.15.5 laxfrX | 
|  | lazy, option | 5.1.110 option | 
|  | lcm | D.2.8.6 lcm | 
|  | lcmMon | D.4.15.4 lcmMon | 
|  | lcmN | D.12.3.3 lcmN | 
|  | lcmofall | D.5.5.19 lcmofall | 
|  | lead | 5.1.75 lead | 
|  | leadcoef | 5.1.76 leadcoef | 
|  | leadexp | 5.1.77 leadexp | 
|  | leadmonom | 5.1.78 leadmonom | 
|  | leadmonomial | D.12.5.4 leadmonomial | 
|  | Left and two-sided Groebner bases | A.7.1 Left and two-sided Groebner bases | 
|  | left annihilator ideal | 7.5.4 dmod_lib | 
|  | left annihilator ideal | 7.5.6 dmodideal_lib | 
|  | Left ideal membership (plural) | Left ideal membership (plural) | 
|  | Left normal form | Left Normal Form | 
|  | leftInverse | D.11.2.7 leftInverse | 
|  | leftKernel | D.11.2.5 leftKernel | 
|  | leftOre | 7.5.20.0. leftOre | 
|  | length | D.15.30.2 length | 
|  | length, option | 5.1.110 option | 
|  | LengthSym | 7.5.23.0. LengthSym | 
|  | LengthSymElement | 7.5.23.0. LengthSymElement | 
|  | letplaceGBasis | 7.10.4.9 letplaceGBasis | 
|  | letterplace | 5.1.88 maxideal | 
|  | Letterplace | 7.7 LETTERPLACE | 
|  | LETTERPLACE | 7.7 LETTERPLACE | 
|  | letterplace | 5.1.129 reduce | 
|  | Letterplace correspondence | 7.9.5 Letterplace correspondence | 
|  | Letterplace Groebner basis | 7.10.1 fpadim_lib | 
|  | Letterplace Groebner basis | 7.10.3 fpaprops_lib | 
|  | Letterplace Groebner basis | 7.10.4 freegb_lib | 
|  | Letterplace libraries | 7.10 LETTERPLACE libraries | 
|  | LETTERPLACE libraries | 7.10 LETTERPLACE libraries | 
|  | Letterplace ring | 5.1.149 std | 
|  | Levels | D.2.4.23 Levels | 
|  | lex_solve | D.8.3.7 lex_solve | 
|  | Lexicographic Groebner bases, computation of | A.2.2 Groebner basis conversion | 
|  | lexicographical ordering | B.2.3 Global orderings | 
|  | LIB | 5.1.79 LIB | 
|  | LIB commands | 3.8.5 LIB commands | 
|  | lib2doc | 3.8.9 Documentation Tool | 
|  | libcdd | 1. Preface | 
|  | libfac | 1. Preface | 
|  | libparse | 3.9.6 libparse | 
|  | Libraries | 3.8 Libraries | 
|  | Libraries | A.1.2 Writing procedures and libraries | 
|  | Libraries in the SINGULAR Documentation | 3.8.1 Libraries in the SINGULAR Documentation | 
|  | library | D.14.4 polybori_lib | 
|  | Library versioning | Library versioning | 
|  | library, gitfan, GIT, geometric invariant theory, quotients | D.15.18 gitfan_lib | 
|  | library, info string | 3.8.7 template_lib | 
|  | library, polybori.lib | D.14.4 polybori_lib | 
|  | library, template | 3.8.7 template_lib | 
|  | library, template.lib | 3.8.7 template_lib | 
|  | LIBs | D. SINGULAR libraries | 
|  | libSingular | E.3 libSingular | 
|  | Lie | D.15.12.45 derivationLie | 
|  | Lie algebra | D.5.3.1 tangentGens | 
|  | Lie bracket | 7.3.2 bracket | 
|  | Lie group | D.5.3.4 parametrizeOrbit | 
|  | Lie group | D.5.3.5 maxZeros | 
|  | lieBracket | 7.10.4.10 lieBracket | 
|  | lift | 5.1.80 lift | 
|  | lift | 7.5.1 bimodules_lib | 
|  | lift (letterplace) | 7.8.2 lift (letterplace) | 
|  | lift (plural) | 7.3.11 lift (plural) | 
|  | lift_kbase | D.6.7.3 lift_kbase | 
|  | lift_rel_kb | D.6.7.4 lift_rel_kb | 
|  | liftenvelope | 7.5.1.0. liftenvelope | 
|  | liftstd | 5.1.81 liftstd | 
|  | liftstd (letterplace) | 7.8.3 liftstd (letterplace) | 
|  | liftstd (plural) | 7.3.12 liftstd (plural) | 
|  | Limitations | 6.1 Limitations | 
|  | linalg.lib | D.3.2 linalg_lib | 
|  | linalg_lib | D.3.2 linalg_lib | 
|  | linealityDimension | D.13.1.29 linealityDimension | 
|  | linealitySpace | D.13.1.30 linealitySpace | 
|  | Linear algebra | D.3 Linear algebra | 
|  | linear algebra | 5.1.3 bareiss | 
|  | linear algebra | 5.1.84 ludecomp | 
|  | linear algebra | 5.1.85 luinverse | 
|  | linear algebra | 5.1.86 lusolve | 
|  | Linear code | D.10.2 decodegb_lib | 
|  | linear code, dual | D.10.1.11 dual_code | 
|  | linear code, systematic | D.10.1.12 sys_code | 
|  | linear interreduction | 7.5.2 bfun_lib | 
|  | linear_relations | D.3.1.24 linear_relations | 
|  | LinearActionQ | D.7.3.8 LinearActionQ | 
|  | LinearCombinationQ | D.7.3.9 LinearCombinationQ | 
|  | linearCombinations | 7.5.3.0. linearCombinations | 
|  | LinearizeAction | D.7.3.7 LinearizeAction | 
|  | linearlyEquivalent | D.15.13.9 linearlyEquivalent | 
|  | linearMapKernel | 7.5.3.0. linearMapKernel | 
|  | linearpart | D.8.2.8 linearpart | 
|  | linesHypersurface | D.15.33.30 linesHypersurface | 
|  | link | 4.9 link | 
|  | link | A.1.8 Parallelization with ssi links | 
|  | link declarations | 4.9.1 link declarations | 
|  | link expressions | 4.9.2 link expressions | 
|  | link related functions | 4.9.3 link related functions | 
|  | linReduce | 7.5.2.0. linReduce | 
|  | linReduceIdeal | 7.5.2.0. linReduceIdeal | 
|  | linSyzSolve | 7.5.2.0. linSyzSolve | 
|  | list | 4.10 list | 
|  | list | D.15.12.26 difformListCont | 
|  | list | D.15.12.27 difformListSort | 
|  | list declarations | 4.10.1 list declarations | 
|  | list expressions | 4.10.2 list expressions | 
|  | list operations | 4.10.3 list operations | 
|  | list related functions | 4.10.4 list related functions | 
|  | lists | D.15.9.1 intersectLists | 
|  | lists, elements | D.15.9.3 member | 
|  | listvar | 5.1.82 listvar | 
|  | lll | D.15.25.51 lll | 
|  | LLL | 5.1.153 system | 
|  | load | 5.2.12 load | 
|  | Loading a library | 3.8.11 Loading a library | 
|  | loadLib, option | 5.1.110 option | 
|  | loadProc, option | 5.1.110 option | 
|  | local methods | D.4.11 locnormal_lib | 
|  | local methods | D.4.11.1 locNormal | 
|  | local names | 3.7.4 Names in procedures | 
|  | Local orderings | B.2.4 Local orderings | 
|  | local rings, computing in | A.1.3 Rings associated to monomial orderings | 
|  | local weighted lexicographical ordering | B.2.4 Local orderings | 
|  | local weighted reverse lexicographical ordering | B.2.4 Local orderings | 
|  | localInvar | D.7.2.6 localInvar | 
|  | localization | A.1.3 Rings associated to monomial orderings | 
|  | localization | D.14.1.18 arrLocalize | 
|  | localization of D-module | 7.5.5 dmodapp_lib | 
|  | localization of D-module | 7.5.13 dmodloc_lib | 
|  | locally closed set | D.2.4.5 Crep | 
|  | locally closed set | D.2.4.6 Prep | 
|  | locally closed set | D.2.4.7 PtoCrep | 
|  | locally closed set | D.2.4.8 extendpoly | 
|  | locally closed set | D.2.4.22 ConsLevels | 
|  | locally closed set | D.2.4.24 Grob1Levels | 
|  | localstd | D.12.5.14 localstd | 
|  | locAtZero | D.4.19.10 locAtZero | 
|  | locNormal | D.4.11.1 locNormal | 
|  | locnormal.lib | D.4.11 locnormal_lib | 
|  | locnormal_lib | D.4.11 locnormal_lib | 
|  | locStatus | 7.5.20.0. locStatus | 
|  | locstd | D.6.15.9 locstd | 
|  | locus | D.2.4.10 locus | 
|  | locus | D.2.4.10 locus | 
|  | locus | D.2.4.11 locusdg | 
|  | locus | D.2.4.12 envelop | 
|  | locus | D.2.4.13 locusto | 
|  | locus | D.2.4.14 stdlocus | 
|  | locus | D.2.4.15 AssocTanToEnv | 
|  | locus | D.2.4.16 FamElemsAtEnvCompPoints | 
|  | locusdg | D.2.4.11 locusdg | 
|  | locusto | D.2.4.13 locusto | 
|  | Log for matrices | D.5.3.3 matrixLog | 
|  | log2 | D.12.1.2 log2 | 
|  | logarithmic annihilator ideal | 7.5.4 dmod_lib | 
|  | logarithmic annihilator ideal | 7.5.6 dmodideal_lib | 
|  | logg | D.15.33.35 logg | 
|  | Long coefficients | A.1.4 Long coefficients | 
|  | LOT algorithm | 7.5.4 dmod_lib | 
|  | lp, global ordering | B.2.3 Global orderings | 
|  | lpCalcSubstDegBound | 7.10.3.6 lpCalcSubstDegBound | 
|  | lpDegBound | 7.10.4.2 lpDegBound | 
|  | lpDivision | 7.10.4.5 lpDivision | 
|  | lpGBPres2Poly | 7.10.4.6 lpGBPres2Poly | 
|  | lpGlDimBound | 7.10.3.4 lpGlDimBound | 
|  | lpHilbert | 7.10.1.4 lpHilbert | 
|  | lpIsPrime | 7.10.3.3 lpIsPrime | 
|  | lpIsSemiPrime | 7.10.3.2 lpIsSemiPrime | 
|  | lpKDim | 7.10.1.2 lpKDim | 
|  | lpKDimCheck | 7.10.1.1 lpKDimCheck | 
|  | lpMonomialBasis | 7.10.1.3 lpMonomialBasis | 
|  | lpNcgenCount | 7.10.4.4 lpNcgenCount | 
|  | lpNoetherian | 7.10.3.1 lpNoetherian | 
|  | lprint | D.2.5.2 lprint | 
|  | lpSickleDim | 7.10.1.5 lpSickleDim | 
|  | lpSubstitute | 7.10.3.5 lpSubstitute | 
|  | lpVarBlockSize | 7.10.4.3 lpVarBlockSize | 
|  | lres | 5.1.83 lres | 
|  | ls, local ordering | B.2.4 Local orderings | 
|  | lsum | D.4.6.10 lsum | 
|  | LU-decomposition of a matrix of numbers | 5.1.84 ludecomp | 
|  | ludecomp | 5.1.84 ludecomp | 
|  | luinverse | 5.1.85 luinverse | 
|  | lusolve | 5.1.86 lusolve | 
| 
 |