| 2.11.4 Commands and Functions returning RINGELEM |
| abs | absolute value of a number |
| apply | apply homomorphism |
| binomial | binomial coefficient |
| CanonicalRepr | representative of a class in a quotient ring |
| CharPoly | characteristic polynomial of a matrix |
| ClearDenom | clear common denominator of a polynomial with rational coeffs |
| CoeffListWRT | list of coefficients of a polynomial wrt and indet |
| CoeffOfTerm | coefficient of a term of a polynomial |
| ComputeElimFirst | ComputeElimFirst |
| content | content of a polynomial |
| ContentWRT | content of a polynomial wrt and indet or a list of indets |
| cyclotomic | n-th cyclotomic polynomial |
| den | denominator |
| DensePoly | the sum of all power-products of a given degree |
| deriv | the derivative of a polynomial or rational function |
| det | the determinant of a matrix |
| DF | the degree form of a polynomial |
| discriminant | the discriminant of a polynomial |
| eigenfactors | eigenfactors of a matrix |
| EvalQuasiPoly | Evaluate a quasi-polynomial at an integer |
| FirstNonZero | the first non-zero entry in a MODULEELEM |
| FirstNonZeroPosn | the first non-zero entry in a MODULEELEM |
| gcd | greatest common divisor |
| GraverBasis | Graver basis |
| HilbertPoly | the Hilbert polynomial |
| homog | homogenize with respect to an indeterminate |
| ImplicitHypersurface | implicitization of hypersurface |
| indet | individual indeterminates |
| Interpolate | interpolating polynomial |
| interreduce, interreduced | interreduce a list of polynomials |
| InverseSystem | Inverse system of an ideal of derivations |
| JanetBasis | the Janet basis of an ideal |
| LC | the leading coefficient of a polynomial or ModuleElem |
| lcm | least common multiple |
| LF | the leading form of a polynomial or an ideal |
| LinKerBasis | find the kernel of a matrix |
| LM | the leading monomial of a polynomial or ModuleElem |
| LPP | the leading power-product of a polynomial or ModuleElem |
| LT | the leading term of an object |
| MakeTerm | returns a monomial (power-product) with given exponents |
| MinPoly | minimal polynomial of a matrix |
| MinPolyModular | minimal polynomial with modular method |
| MinPolyQuotDef, MinPolyQuotElim, MinPolyQuotMat | compute a minimal polynomial |
| monic | divide polynomials by their leading coefficients |
| NF | normal form |
| 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 |
| NR | normal reduction |
| num | numerator |
| one | one of a ring |
| pfaffian | the Pfaffian of a skew-symmetric matrix |
| PthRoot | Compute p-th root |
| QZP | change field for polynomials and ideals |
| randomize | randomize the coefficients of a given polynomial |
| randomized | randomize the coefficients of a given polynomial |
| RationalAffinePoints | Affine rational solutions |
| RationalProjectivePoints | Projective rational solutions |
| RationalSolve | Rational solutions for polynomial system |
| RatReconstructPoly | Rational reconstruction of polynomial coefficents |
| ReadExpr | Read RINGELEM expression from string |
| ReducedGBasis | compute reduced Groebner basis |
| resultant | the resultant of two polynomials |
| RingElem | convert an expression into a RINGELEM |
| SymbolRange | range of symbols for the indeterminates of a PolyRing |
| SymmetricPolys | list of symmetric polynomials |
| UniversalGBasis | universal Groebner basis of the input ideal |
| zero | zero of a ring |
| ZPQ | change field for polynomials and ideals |