| 2.11.3 Commands and Functions for RINGELEM |
| abs | absolute value of a number |
| apply | apply homomorphism |
| ApproxSolve | Approximate real solutions for polynomial system |
| AsINT | convert into an INT |
| AsRAT | convert into a RAT |
| 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 |
| 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 |
| CoeffOfTerm | coefficient of a term of a polynomial |
| content | content of a polynomial |
| ContentFreeFactor | factorization of multivariate polynomial into content-free factors |
| ContentWRT | content of a polynomial wrt and indet or a list of indets |
| CRTPoly | Chinese Remainder Theorem on polynomial coefficients |
| cyclotomic | n-th cyclotomic polynomial |
| DecimalStr | convert rational number to decimal string |
| deg | the standard degree of a polynomial or moduleelem |
| den | denominator |
| deriv | the derivative of a polynomial or rational function |
| DerivationAction | Action of a derivation |
| DF | the degree form of a polynomial |
| discriminant | the discriminant of a polynomial |
| DivAlg | division algorithm |
| eigenfactors | eigenfactors of a matrix |
| eigenvectors | eigenvalues and eigenvectors of a matrix |
| elim | eliminate variables |
| eval | substitute numbers or polynomials for indeterminates |
| EvalQuasiPoly | Evaluate a quasi-polynomial at an integer |
| exponents | the list of exponents of the leading term of a polynomial |
| factor | factor a polynomial |
| FloatApprox | approx. of rational number of the form M*2^E |
| FloatStr | convert rational number to a decimal string |
| FrbAlexanderDual | Alexander Dual of monomial ideals |
| gcd | greatest common divisor |
| GenRepr | representation in terms of generators |
| homog | homogenize with respect to an indeterminate |
| ideal | ideal generated by list |
| IndetIndex | index of an indeterminate |
| IndetName | the name of an indeterminate |
| IndetSubscripts | the index of an indeterminate |
| interreduce, interreduced | interreduce a list of polynomials |
| IsConstant | checks if a ringelem is in the coefficient ring |
| IsDivisible | checks if A is divisible by B |
| IsElem | checks if A is an element of B |
| IsHomog | test whether given polynomials are homogeneous |
| IsIn | check if one object is contained in another |
| IsIndet | checks argument is an indetermiante |
| IsInRadical | check if a polynomial (or ideal) is in a radical |
| IsInteger | check if a RINGELEM is integer |
| IsInvertible | check if a RINGELEM is invertible |
| IsIrred | check if a RINGELEM is irreducible |
| IsOne | test whether an object is one |
| IsPthPower | p-th power test |
| IsRational | check if a RINGELEM is rational |
| IsSqFree | check if an INT or RINGELEM is square-free |
| IsTerm | checks if the argument is a term |
| IsZero | test whether an object is zero |
| IsZeroDivisor | test whether a RINGELEM is a zero-divisor |
| jacobian | the Jacobian of a list of polynomials |
| LC | the leading coefficient of a polynomial or ModuleElem |
| lcm | least common multiple |
| LF | the leading form of a polynomial or an ideal |
| LinearSimplify | simplifying linear substitution for a univariate poly over QQ |
| 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 |
| MantissaAndExponent2 | convert rational number to a binary float |
| max | a maximum element of a sequence or list |
| min | a minimum element of a sequence or list |
| MinPoly | minimal polynomial of a matrix |
| MinPolyModular | minimal polynomial with modular method |
| MinPolyQuotDef, MinPolyQuotElim, MinPolyQuotMat | compute a minimal polynomial |
| MinPowerInIdeal | the mininum power of a polynomial is an ideal |
| monic | divide polynomials by their leading coefficients |
| monomials | the list of monomials of a polynomial |
| MultiplicationMat | the multiplication matrix of a ringelem |
| NewMatFilled | matrix filled with value |
| NF | normal form |
| NmzEhrhartRing | Computes the Ehrhart ring |
| NmzIntClosureMonIdeal | integral closure of a monomial ideal |
| NmzIntClosureToricRing | integral closure of a toric ring |
| NmzNormalToricRing | normalization of a toric ring |
| NR | normal reduction |
| num | numerator |
| NumTerms | number of terms in a polynomial |
| PerpIdealOfForm | Ideal of derivations annihilating a form |
| PreImage | preimage of a RINGELEM |
| product | the product of the elements of a list |
| 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 |
| RealRoots | computes the real roots of a univariate polynomial |
| RealRootsApprox | approximations to the real roots of a univariate poly |
| resultant | the resultant of two polynomials |
| RingElem | convert an expression into a RINGELEM |
| RingOf | the ring of the object |
| RingsOf | list of the rings of an object |
| RootBound | bound on roots of a polynomial over QQ |
| ScientificStr | convert integer/rational to a floating-point string |
| SqFreeFactor | compute a squarefree factorization |
| StarPrint, StarSprint | print polynomial with *'s for multiplications |
| SubalgebraRepr | representation of a polynomial as a subalgebra element |
| subst | substitute values for indeterminates |
| sum | the sum of the elements of a list |
| support | the list of terms of a polynomial or moduleelem |
| sylvester | the Sylvester matrix of two polynomials |
| syz | syzygy modules |
| UnivariateIndetIndex | the index of the indeterminate of a univariate polynomial |
| wdeg | multi-degree of an polynomial |
| ZPQ | change field for polynomials and ideals |