| Index Entry | Section |
|---|
|
| O | | |
|---|
| Oaku-Takayama algorithm | 7.5.4 dmod_lib |
| Objects | 3.5.4 Objects |
| olga.lib | 7.5.21 olga_lib |
| olga_lib | 7.5.21 olga_lib |
| oneDimBelongSemigroup | D.4.4.3 oneDimBelongSemigroup |
| oneNcfrac | 7.5.15.0. oneNcfrac |
| onesVector | D.13.2.59 onesVector |
| online help | 3.1.3 The online help system |
| open | 5.1.110 open |
| opentex | D.9.2.2 opentex |
| operatorAlgebra | 7.10.2.1 operatorAlgebra |
| operatorBM | 7.5.4.0. operatorBM |
| operatorModulo | 7.5.4.0. operatorModulo |
| oppose | 7.3.19 oppose |
| opposite | 7.3.20 opposite |
| opposite polynomial | 5.1.155 system |
| opposite ring | 5.1.155 system |
| option | 5.1.111 option |
| option Imap | 5.1.111 option |
| option(warn) | 3.9.7 option(warn) |
| optionIsSet | D.2.12.16 optionIsSet |
| or | 4.7.6 boolean operations |
| or | 6.3.2 Evaluation of logical expressions |
| orbit | D.5.10 orbitparam_lib |
| orbit | D.5.10.1 tangentGens |
| orbit | D.5.10.4 parametrizeOrbit |
| orbit | D.5.10.5 maxZeros |
| orbit_variety | D.7.1.33 orbit_variety |
| orbitConeOrbits | D.13.3.14 orbitConeOrbits |
| orbitCones | D.13.3.5 orbitCones |
| orbitparam.lib | D.5.10 orbitparam_lib |
| orbitparam_lib | D.5.10 orbitparam_lib |
| ord | 5.1.112 ord |
| ord_test | D.2.12.11 ord_test |
| order ideal, border basis | D.4.31.1 borderBasis |
| order ideal, border basis | D.4.31.2 modBorder |
| ordering | D.15.2.5 diffAlgebraChangeOrd |
| ordering | D.15.2.21 difformIsBigger |
| ordering | D.15.2.22 difformIsSmaller |
| orderings | B.2.2 General definitions for orderings |
| orderings introduction | B.2.1 Introduction to orderings |
| orderings, a | B.2.8 Extra weight vector |
| orderings, global | B.2.3 Global orderings |
| orderings, L | B.2.9 Pseudo ordering L |
| orderings, local | B.2.4 Local orderings |
| orderings, M | B.2.6 Matrix orderings |
| orderings, product | B.2.7 Product orderings |
| ordstr | 5.1.113 ordstr |
| origin | D.13.2.2 origin |
| Orlik-Solomon | D.14.1.29 arrOrlikSolomon |
| orthogonalize | D.3.2.5 orthogonalize |
| outer | D.3.1.8 outer |
| output | 3.6 Input and output |
| Output | D.4.15.35 netMatrix |
| Output | D.14.5.1 catNets |
| Output | D.14.5.3 netBigIntMat |
| Output | D.14.5.4 netBigIntMatShort |
| Output | D.14.5.5 netCoefficientRing |
| Output | D.14.5.6 netIdeal |
| Output | D.14.5.7 netInt |
| Output | D.14.5.8 netBigInt |
| Output | D.14.5.9 netIntMat |
| Output | D.14.5.10 netIntMatShort |
| Output | D.14.5.11 netIntVector |
| Output | D.14.5.12 netIntVectorShort |
| Output | D.14.5.13 netNumber |
| Output | D.14.5.14 netList |
| Output | D.14.5.15 netMap |
| Output | D.14.5.16 netMap2 |
| Output | D.14.5.17 netmatrix |
| Output | D.14.5.18 netmatrixShort |
| Output | D.14.5.19 netPoly |
| Output | D.14.5.20 netPrimePower |
| Output | D.14.5.21 netRing |
| Output | D.14.5.22 netString |
| Output | D.14.5.23 netvector |
| Output | D.14.5.24 netvectorShort |
| Output | D.14.5.25 stackNets |
| Output, formatting of | A.1.6 Formatting output |
| outputting monomials | 5.3.7 short |
|
| P | | |
|---|
| p-adic numbers | p-adic numbers |
| package | 4.16 package |
| package declarations | 4.16.1 package declarations |
| package related functions | 4.16.2 package related functions |
| pairset | D.12.4.11 pairset |
| par | 5.1.114 par |
| par2varRing | D.1.2 par2varRing |
| paraConic | D.5.11.9 paraConic |
| parallel computing | D.15.23 systhreads_lib |
| parallel skeletons | D.2.7 parallel_lib |
| parallel.lib | D.2.7 parallel_lib |
| parallel_lib | D.2.7 parallel_lib |
| parallelization | D.2.7 parallel_lib |
| Parallelization | A.1.8 Parallelization with ssi links |
| parallelization | D.2.11 resources_lib |
| Parallelization | D.2.6 modular_lib |
| parallelization | D.2.13 tasks_lib |
| parallelTestAND | D.2.7.4 parallelTestAND |
| parallelTestOR | D.2.7.5 parallelTestOR |
| parallelWaitAll | D.2.7.3 parallelWaitAll |
| parallelWaitFirst | D.2.7.2 parallelWaitFirst |
| parallelWaitN | D.2.7.1 parallelWaitN |
| param | D.6.15.4 param |
| Parameter list | 3.7.2 Parameter list |
| parameter, as numbers | 4.15 number |
| parameter, default | 3.7.2 Parameter list |
| parameter, optional | 3.7.2 Parameter list |
| Parameters | A.1.5 Parameters |
| parameterSubstitute | D.13.6.31 parameterSubstitute |
| parametric annihilator | 7.5.4 dmod_lib |
| parametric annihilator for variety | 7.5.7 dmodvar_lib |
| parametric ideal | D.2.4.1 grobcov |
| parametric ideal | D.2.4.8 extendpoly |
| parametric ideal | D.2.4.8 extendpoly |
| parametric ideal | D.2.4.9 extendGC |
| parametrization | D.5.10 orbitparam_lib |
| Parametrization | D.5.11 paraplanecurves_lib |
| parametrization | D.5.10.4 parametrizeOrbit |
| parametrization | D.6.15.4 param |
| Parametrization, image. | D.5.11.10 testParametrization |
| parametrizeOrbit | D.5.10.4 parametrizeOrbit |
| paraPlaneCurve | D.5.11.3 paraPlaneCurve |
| paraplanecurves.lib | D.5.11 paraplanecurves_lib |
| paraplanecurves_lib | D.5.11 paraplanecurves_lib |
| pardeg | 5.1.115 pardeg |
| parstr | 5.1.116 parstr |
| part | D.5.2.52 part |
| PartC | D.5.2.54 PartC |
| partial fraction | D.15.13 pfd_lib |
| partial_molien | D.7.1.11 partial_molien |
| partitions | D.4.8.8 partitions |
| partitions | D.4.8.8 partitions |
| PartitionVar | D.15.4.18 PartitionVar |
| ParToVar | D.15.4.21 ParToVar |
| partOver | D.5.2.55 partOver |
| partUnder | D.5.2.56 partUnder |
| path | E.5 Used environment variables |
| path integral | D.4.8 ellipticcovers_lib |
| Path names | Path names |
| paths | E.5 Used environment variables |
| pause | D.2.5.9 pause |
| PBW | 7.5.3 central_lib |
| PBW basis | Definition (PBW basis) |
| PBW_eqDeg | 7.5.3.0. PBW_eqDeg |
| PBW_maxDeg | 7.5.3.0. PBW_maxDeg |
| PBW_maxMonom | 7.5.3.0. PBW_maxMonom |
| pdivi | D.2.4.3 pdivi |
| pdivi | D.2.4.4 pnormalf |
| pdivi2 | D.2.9.4 pdivi2 |
| PerfectPowerTest | D.12.1.3 PerfectPowerTest |
| permcol | D.3.1.20 permcol |
| permrow | D.3.1.21 permrow |
| permutationFromIntvec | D.13.3.20 permutationFromIntvec |
| permutations | D.4.8.9 permute |
| permutations, sum, max, min | D.14.2 combinat_lib |
| permutationToIntvec | D.13.3.21 permutationToIntvec |
| permute | D.4.8.9 permute |
| permute_L | D.10.1.13 permute_L |
| perron | 7.5.22.0. perron |
| perron.lib | 7.5.22 perron_lib |
| perron_lib | 7.5.22 perron_lib |
| Perturbation walk | D.4.10.5 pwalk |
| PEsolve | D.8.1.2 PEsolve |
| pFactor | D.12.2.22 pFactor |
| pfd | D.15.13.1 pfd |
| pfd.lib | D.15.13 pfd_lib |
| pfd_lib | D.15.13 pfd_lib |
| pfdMat | D.15.13.9 pfdMat |
| Pfister, Gerhard | Acknowledgements |
| PH_ais | D.14.6.3 PH_ais |
| PH_nais | D.14.6.4 PH_nais |
| phindex.lib | D.14.6 phindex_lib |
| phindex_lib | D.14.6 phindex_lib |
| picksFormula | D.13.4.9 picksFormula |
| pid | 5.1.155 system |
| pIntersect | 7.5.2.0. pIntersect |
| pIntersectSyz | 7.5.2.0. pIntersectSyz |
| Pipe links | 4.10.6 Pipe links |
| plainInvariants | D.6.10.10 plainInvariants |
| planeCur | D.6.6.5 planeCur |
| plot | D.9.3.1 plot |
| plotRot | D.9.4.2 plotRot |
| plotRotated | D.9.4.1 plotRotated |
| plotRotatedDirect | D.9.4.4 plotRotatedDirect |
| plotRotatedList | D.9.4.3 plotRotatedList |
| plotRotatedListFromSpecifyList | D.9.4.5 plotRotatedListFromSpecifyList |
| plural | D.2.12.18 hasCommutativeVars |
| PLURAL | 7.1 PLURAL |
| PLURAL libraries | 7.5 PLURAL libraries |
| PLURAL LIBs | 7.5 PLURAL libraries |
| pmat | D.2.5.3 pmat |
| pnormalf | D.2.4.4 pnormalf |
| pnormalform | D.2.9.7 pnormalform |
| PocklingtonLehmer | D.12.2.20 PocklingtonLehmer |
| Poincare polynomial | D.14.1.41 arrPoincare |
| pointid.lib | D.4.25 pointid_lib |
| pointid_lib | D.4.25 pointid_lib |
| points | D.15.3.1 points |
| Polar curves | A.4.3 Polar curves |
| PollardRho | D.12.2.21 PollardRho |
| pollTask | D.2.13.10 pollTask |
| polSol | 7.5.14.0. polSol |
| polSolFiniteRank | 7.5.14.0. polSolFiniteRank |
| poly | 4.17 poly |
| poly (plural) | 7.2.4 poly (plural) |
| poly declarations | 4.17.1 poly declarations |
| poly declarations (plural) | 7.2.4.1 poly declarations (plural) |
| poly expressions | 4.17.2 poly expressions |
| poly expressions (plural) | 7.2.4.2 poly expressions (plural) |
| poly operations | 4.17.3 poly operations |
| poly operations (plural) | 7.2.4.3 poly operations (plural) |
| poly related functions | 4.17.4 poly related functions |
| poly related functions (plural) | 7.2.4.4 poly related functions (plural) |
| poly2list | 7.5.5.0. poly2list |
| poly2zdd | D.14.7.16 poly2zdd |
| polybori | D.14.7 polybori_lib |
| Polybori, Boolean Groebner Basis | D.14.7.18 disp_zdd |
| PolyBoRi, Boolean Groebner Basis | D.14.7.1 boolean_std |
| PolyBoRi, Boolean Groebner Basis | D.14.7.3 boolean_constant |
| PolyBoRi, Boolean Groebner Basis | D.14.7.4 boolean_poly |
| PolyBoRi, Boolean Groebner Basis | D.14.7.5 direct_boolean_poly |
| PolyBoRi, Boolean Groebner Basis | D.14.7.6 recursive_boolean_poly |
| PolyBoRi, Boolean Groebner Basis | D.14.7.7 boolean_ideal |
| PolyBoRi, Boolean Groebner Basis | D.14.7.8 boolean_set |
| PolyBoRi, Boolean Groebner Basis | D.14.7.9 from_boolean_constant |
| PolyBoRi, Boolean Groebner Basis | D.14.7.10 from_boolean_poly |
| PolyBoRi, Boolean Groebner Basis | D.14.7.11 direct_from_boolean_poly |
| PolyBoRi, Boolean Groebner Basis | D.14.7.12 recursive_from_boolean_poly |
| PolyBoRi, Boolean Groebner Basis | D.14.7.13 from_boolean_ideal |
| PolyBoRi, Boolean Groebner Basis | D.14.7.14 from_boolean_set |
| PolyBoRi, Boolean Groebner Basis | D.14.7.15 bvar |
| PolyBoRi, Boolean Groebner Basis | D.14.7.17 zdd2poly |
| PolyBoRi, zero-supressed decision diagram | D.14.7.16 poly2zdd |
| polybori.lib | D.14.7 polybori_lib |
| polybori.lib | D.14.7 polybori_lib |
| polybori_lib | D.14.7 polybori_lib |
| polyclass.lib | D.15.14 polyclass_lib |
| polyclass_lib | D.15.14 polyclass_lib |
| polyDK | D.4.12.2 polyDK |
| polyInterpolation | D.4.9.2 polyInterpolation |
| polylib.lib | D.2.8 polylib_lib |
| polylib_lib | D.2.8 polylib_lib |
| polymake.lib | D.13.4 polymake_lib |
| polymake_lib | D.13.4 polymake_lib |
| polynomial | D.15.2.32 derivationFromPoly |
| Polynomial data | B. Polynomial data |
| polynomial functions | D.15.16 ringgb_lib |
| polynomial solutions | 7.5.14 dmodloc_lib |
| polynomial, opposite | 5.1.155 system |
| polynomials | D.15.14 polyclass_lib |
| polytope | 4.27 polytope |
| polytope | D.13.4 polymake_lib |
| polytopeViaInequalities | D.13.2.32 polytopeViaInequalities |
| polytopeViaPoints | D.13.2.33 polytopeViaPoints |
| polyVars | 7.5.14.0. polyVars |
| pos_def | D.3.2.16 pos_def |
| poset | D.14.1.38 arrLattice |
| positiveOrthant | D.13.2.3 positiveOrthant |
| posweight | D.6.21.8 posweight |
| Pottier algorithm | C.6.2.2 The algorithm of Pottier |
| power | D.3.1.9 power |
| power set | D.14.2.2 sublists |
| power_products | D.7.1.25 power_products |
| powerN | D.12.2.6 powerN |
| powerpolyX | D.12.1.7 powerpolyX |
| powersums | D.12.6.12 powersums |
| powerX | D.12.2.15 powerX |
| powSumSym | D.5.2.9 powSumSym |
| PPolyH | D.5.5.2 PPolyH |
| PPolyN | D.5.5.10 PPolyN |
| PPolyQp | D.5.5.5 PPolyQp |
| PPolyS | D.5.5.8 PPolyS |
| preComp | D.4.18.11 preComp |
| Preface | 1. Preface |
| preim | D.15.25.2 preim |
| preimage | 5.1.117 preimage |
| preimage | 7.5.19 ncpreim_lib |
| preimage | D.15.25.2 preim |
| preimage (plural) | 7.3.21 preimage (plural) |
| preimage under a map between local rings, map between local rings, map between local and global rings | D.2.12.14 preimageLoc |
| preimageLattice | D.15.12.20 preimageLattice |
| preimageLoc | D.2.12.14 preimageLoc |
| preimageNC | 7.5.19.0. preimageNC |
| Prep | D.2.4.6 Prep |
| prepareAss | D.4.26.15 prepareAss |
| prepEmbDiv | D.5.16.6 prepEmbDiv |
| prepMat | D.7.5.1 prepMat |
| prepRealclassify | D.6.4.17 prepRealclassify |
| prepSV | D.10.1.8 prepSV |
| presentation | D.4.15.36 presentation |
| presentTree | D.5.15.6 presentTree |
| presolve.lib | D.8.3 presolve_lib |
| presolve_lib | D.8.3 presolve_lib |
| Primary decomposition | A.3.9 Primary decomposition |
| primary decomposition | D.4.26 primdec_lib |
| primary decomposition | D.4.27 primdecint_lib |
| primary decomposition of modules | D.4.18 mprimdec_lib |
| primary decomposition, numerical | D.5.9 numerDecom_lib |
| primary_char0 | D.7.1.15 primary_char0 |
| primary_char0_no_molien | D.7.1.17 primary_char0_no_molien |
| primary_char0_no_molien_random | D.7.1.22 primary_char0_no_molien_random |
| primary_char0_random | D.7.1.20 primary_char0_random |
| primary_charp | D.7.1.16 primary_charp |
| primary_charp_no_molien | D.7.1.18 primary_charp_no_molien |
| primary_charp_no_molien_random | D.7.1.23 primary_charp_no_molien_random |
| primary_charp_random | D.7.1.21 primary_charp_random |
| primary_charp_without | D.7.1.19 primary_charp_without |
| primary_charp_without_random | D.7.1.24 primary_charp_without_random |
| primary_invariants | D.7.1.3 primary_invariants |
| primary_invariants_random | D.7.1.4 primary_invariants_random |
| primdec.lib | D.4.26 primdec_lib |
| primdec_lib | D.4.26 primdec_lib |
| PrimdecA | D.4.18.2 PrimdecA |
| PrimdecB | D.4.18.3 PrimdecB |
| primdecGTZ | D.4.26.2 primdecGTZ |
| primdecGTZE | D.4.26.3 primdecGTZE |
| primdecint.lib | D.4.27 primdecint_lib |
| primdecint_lib | D.4.27 primdecint_lib |
| primdecMon | D.4.17.16 primdecMon |
| primdecSY | D.4.26.4 primdecSY |
| primdecSYE | D.4.26.5 primdecSYE |
| primdecZ | D.4.27.1 primdecZ |
| primdecZM | D.4.27.2 primdecZM |
| prime | 5.1.118 prime |
| primeClosure | D.4.23.8 primeClosure |
| primecoeffs | D.2.3.18 primecoeffs |
| primefactors | 5.1.119 primefactors |
| primes | D.2.3.13 primes |
| primitiv.lib | D.4.28 primitiv_lib |
| primitiv_lib | D.4.28 primitiv_lib |
| primitive | D.4.28.1 primitive |
| primitive element | D.4.28.1 primitive |
| primitive_extra | D.4.28.2 primitive_extra |
| primitiveSpan | D.15.12.27 primitiveSpan |
| primL | D.12.2.10 primL |
| primList | D.12.2.9 primList |
| primparam | D.6.10.5 primparam |
| primRoot | D.4.34.3 primRoot |
| primTest | D.4.18.10 primTest |
| principal intersection | 7.5.2 bfun_lib |
| print | 5.1.120 print |
| print | D.14.1.5 arrPrintMatrix |
| print | D.15.2.9 difformGenToString |
| print | D.15.2.11 difformToString |
| print | D.15.2.12 difformPrint |
| print | D.15.2.34 derivationToString |
| print | D.15.2.35 derivationPrint |
| printBetti | D.4.15.17 printBetti |
| printf | 5.1.121 printf |
| printFreeModule | D.4.15.9 printFreeModule |
| printGraph | D.4.8.2 printGraph |
| printGraphG | D.5.17.22 printGraphG |
| printGroup | D.15.12.8 printGroup |
| printHom | D.4.15.12 printHom |
| printlevel | 5.3.6 printlevel |
| printMatrix | D.4.15.8 printMatrix |
| printModule | D.4.15.11 printModule |
| printMoebius | D.14.1.44 printMoebius |
| printNormalFormEquation | D.15.14.3 printNormalFormEquation |
| printPoly | D.15.14.2 printPoly |
| printPuiseux | D.15.15.4 printPuiseux |
| printResolution | D.4.15.10 printResolution |
| printSheaf | D.5.17.10 printSheaf |
| printStack | D.5.17.24 printStack |
| printTask | D.2.13.5 printTask |
| printVariety | D.5.17.2 printVariety |
| proc | 4.18 proc |
| proc declaration | 4.18.1 proc declaration |
| proc expression | 4.18.2 proc expression |
| Procedure definition | 3.7.1 Procedure definition |
| procedure, ASCII help | 3.8.7.1 mdouble |
| procedure, ASCII/Texinfo help | 3.8.7.3 msum |
| procedure, texinfo help | 3.8.7.2 mtriple |
| Procedure-specific commands | 3.7.5 Procedure-specific commands |
| Procedures | 3.7 Procedures |
| Procedures and libraries | 2.3.3 Procedures and libraries |
| Procedures and libraries | A.1.2 Writing procedures and libraries |
| Procedures in a library | 3.8.6 Procedures in a library |
| procedures, help string | 3.7.3 Help string |
| procedures, static | 3.7.1 Procedure definition |
| procs with different argument types | 4.18.3 procs with different argument types |
| prodcrit | D.12.4.9 prodcrit |
| product | D.2.3.14 product |
| product | D.15.2.17 difformMul |
| product | D.15.2.39 derivationMul |
| Product orderings | B.2.7 Product orderings |
| product variety, abstract variety | D.5.17.3 productVariety |
| productgroup | D.15.12.29 productgroup |
| productOfProjectiveSpaces | D.15.24.1 productOfProjectiveSpaces |
| productVariety | D.5.17.3 productVariety |
| Programming | A.1 Programming |
| progress watch | 5.1.111 option |
| projective bundle, abstract variety, sheaf, enumeration of conics | D.5.17.7 projectiveBundle |
| projective dimension | 7.5.23 purityfiltration_lib |
| projective limes | p-adic numbers |
| projective space, abstract variety | D.5.17.6 projectiveSpace |
| projectiveBundle | D.5.17.7 projectiveBundle |
| projectiveDimension | 7.5.23.0. projectiveDimension |
| projectiveSpace | D.5.17.6 projectiveSpace |
| projectLattice | D.15.12.21 projectLattice |
| projPoints | D.15.3.2 projPoints |
| prompt | 3.1.2 The SINGULAR prompt |
| prompt, option | 5.1.111 option |
| propagator | D.4.8 ellipticcovers_lib |
| propagator | D.4.8.3 propagator |
| propagator | D.15.25 tropicalEllipticCovers_lib |
| propagator of a graph | D.15.25.9 PropagatorFunction |
| PropagatorFunction | D.15.25.9 PropagatorFunction |
| prot, option | 5.1.111 option |
| protocol of computations | 5.1.111 option |
| proximitymatrix | D.6.1.5 proximitymatrix |
| prune | 5.1.122 prune |
| prune_map | 5.1.123 prune_map |
| pruneModule | D.4.15.43 pruneModule |
| prwalk | D.15.17.1 prwalk |
| Pseudo ordering L | B.2.9 Pseudo ordering L |
| psigncnd | D.8.9.2 psigncnd |
| PtoCrep | D.2.4.7 PtoCrep |
| puiseux | D.15.15.5 puiseux |
| Puiseux expansion | D.6.1 alexpoly_lib |
| Puiseux expansion | D.6.15 hnoether_lib |
| Puiseux expansions | D.15.15.1 puiseuxList |
| Puiseux pairs | A.4.6 Invariants of plane curve singularities |
| Puiseux pairs | D.6.15.6 invariants |
| puiseux2generators | D.6.15.16 puiseux2generators |
| puiseuxExpansion | D.13.6.3 puiseuxExpansion |
| puiseuxexpansions.lib | D.15.15 puiseuxexpansions_lib |
| puiseuxexpansions_lib | D.15.15 puiseuxexpansions_lib |
| puiseuxList | D.15.15.1 puiseuxList |
| pure tensor | 7.5.1 bimodules_lib |
| purelist | 7.5.23.0. purelist |
| purity | 7.5.23 purityfiltration_lib |
| purityFiltration | 7.5.23.0. purityFiltration |
| purityfiltration.lib | 7.5.23 purityfiltration_lib |
| purityfiltration_lib | 7.5.23 purityfiltration_lib |
| purityTriang | 7.5.23.0. purityTriang |
| pushForward | D.15.12.46 pushForward |
| pwalk | D.4.10.5 pwalk |
| pyobject | 4.28 pyobject |
| pyobject | D.14.7 polybori_lib |
| pyobject declarations | 4.28.1 pyobject declarations |
| pyobject expressions | 4.28.2 pyobject expressions |
| pyobject operations | 4.28.3 pyobject operations |
| pyobject related functions | 4.28.4 pyobject related functions |
| pyramid | D.15.4.12 pyramid |
| python_eval | 4.28.5 python_eval |
| python_import | 4.28.6 python_import |
| python_run | 4.28.7 python_run |
|
