| 2.5.4 Commands and Functions returning LIST |
| AllReducedGroebnerBases [OBSOLESCENT] | all reduced Groebner bases of an ideal |
| apply | apply homomorphism |
| ApproxSolve | Approximate real solutions for polynomial system |
| ascii | convert between characters and ascii code |
| BBasis5 | Border Basis of zero dimensional ideal |
| BinomialRepr, BinomialReprShift | binomial representation of integers |
| CartesianProduct, CartesianProductList | Cartesian product of lists |
| CFApproximants | continued fraction approximants |
| coefficients | list of coefficients of a polynomial |
| CoefficientsWRT | list of coeffs and PPs of a poly wrt indet or list of indets |
| CoeffListWRT | list of coefficients of a polynomial wrt and indet |
| compts | list of components of a ModuleElem |
| concat | concatenate lists |
| ConcatLists | concatenate a list of lists |
| ContFrac | continued fraction quotients |
| CurrentTypes | lists all data types |
| diff | returns the difference between two lists |
| distrib | the distribution of objects in a list |
| eigenfactors | eigenfactors of a matrix |
| eigenvectors | eigenvalues and eigenvectors of a matrix |
| EquiIsoDec | equidimensional isoradical decomposition |
| exponents | the list of exponents of the leading term of a polynomial |
| ExternalLibs | Linked external libraries |
| FGLM5 | perform a FGLM Groebner Basis conversion |
| fields | list the fields of a record |
| flatten | flatten a list |
| FrbAlexanderDual | Alexander Dual of monomial ideals |
| FrbAssociatedPrimes | Associated primes of monomial ideals |
| FrbIrreducibleDecomposition | Irreducible decomposition of monomial ideals |
| FrbMaximalStandardMonomials | Maximal standard monomials of monomial ideals |
| FrbPrimaryDecomposition | Primary decomposition of monomial ideals |
| GBasis | calculate a Groebner basis |
| GBasisTimeout | compute a Groebner basis with a timeout |
| GCDFreeBasis | determine (minimal) GCD free basis of a set of integers |
| GenericPoints | random projective points |
| GenRepr | representation in terms of generators |
| gens | list of generators of an ideal |
| Get | read characters from a device |
| GetCol | convert a column of a matrix into a list |
| GetCols | convert a matrix into a list of lists |
| GetRow | convert a row of a matrix into a list |
| GetRows | convert a matrix into a list of lists |
| GraverBasis | Graver basis |
| GroebnerFanIdeals | all reduced Groebner bases of an ideal |
| HilbertBasisKer | Hilbert basis for a monoid |
| homog | homogenize with respect to an indeterminate |
| HVector | the h-vector of a module or quotient object |
| in | list element selector in list constructor |
| indets | list of indetermiantes in a PolyRing |
| IndetSubscripts | the index of an indeterminate |
| interreduce, interreduced | interreduce a list of polynomials |
| intersection | intersect lists, ideals, or modules |
| IntersectList | intersect lists, ideals, or modules |
| InverseSystem | Inverse system of an ideal of derivations |
| JanetBasis | the Janet basis of an ideal |
| LinKerBasis | find the kernel of a matrix |
| MakeSet | remove duplicates from a list |
| MinGens | list of minimal generators |
| minors | list of minor determinants of a matrix |
| MinSubsetOfGens | list of minimal generators |
| monomials | the list of monomials of a polynomial |
| NewList | create a new list |
| NmzDiagInvariants | ring of invariants of a diagonalizable group action |
| NmzEhrhartRing | Computes the Ehrhart ring |
| NmzFiniteDiagInvariants | ring of invariants of a finite group action |
| NmzIntClosureMonIdeal | integral closure of a monomial ideal |
| NmzIntClosureToricRing | integral closure of a toric ring |
| NmzIntersectionValRings | intersection of ring of valuations |
| NmzNormalToricRing | normalization of a toric ring |
| NmzTorusInvariants | ring of invariants of torus action |
| NonZero | remove zeroes from a list |
| Packages | list of loaded packages |
| partitions | partitions of an integer |
| permutations | returns all permutations of the entries of a list |
| PrimaryDecomposition | primary decomposition of an ideal |
| PrimaryDecomposition0 | primary decomposition of a 0-dimensional ideal |
| PrimaryDecompositionGTZ0 | primary decomposition of a 0-dimensional ideal |
| QuotientBasis | vector space basis for zero-dimensional quotient rings |
| QZP | change field for polynomials and ideals |
| RandomSubset | random subset |
| RandomSubsetIndices | indices for random subset |
| RandomTuple | random tuple |
| RandomTupleIndices | indices for random tuples |
| RationalAffinePoints | Affine rational solutions |
| RationalProjectivePoints | Projective rational solutions |
| RationalSolve | Rational solutions for polynomial system |
| RealRoots | computes the real roots of a univariate polynomial |
| RealRootsApprox | approximations to the real roots of a univariate poly |
| ReducedGBasis | compute reduced Groebner basis |
| RefineGCDFreeBasis | refine an integer GCD free basis |
| res | free resolution |
| reverse, reversed | reverse a list |
| RingsOf | list of the rings of an object |
| SeparatorsOfPoints | separators for affine points |
| SeparatorsOfProjectivePoints | separators for projective points |
| shape | extended list of types involved in an expression |
| sorted | sort a list |
| SortedBy | sort a list |
| starting | list functions starting with a given string |
| StdBasis | Standard basis |
| subsets | returns all sublists of a list |
| support | the list of terms of a polynomial or moduleelem |
| SymbolRange | range of symbols for the indeterminates of a PolyRing |
| SymmetricPolys | list of symmetric polynomials |
| tail | remove the first element of a list |
| TopLevelFunctions | returns the functions available at top-level |
| tuples | N-tuples |
| UniversalGBasis | universal Groebner basis of the input ideal |
| wdeg | multi-degree of an polynomial |
| WithoutNth | removes the N-th component from a list |
| ZPQ | change field for polynomials and ideals |