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2.11.3 Commands and Functions for RINGELEM

abs	absolute value of a number
ApproxSolve	Approximate real solutions for polynomial system
ArrCone	cone of an arrangement of hyperplanes
ArrDeletion	deletes a hyperplane from a list of hyperplanes
ArrDerModule	set of generators of the module of logarithmic derivations of an arrangement of hyperplanes
ArrExponents	exponents of a free arrangement of hyperplanes
ArrRestriction	arrangement of hyperplanes A restricted to a hyperplane
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
ChebyshevPoly	Orthogonal Polynomials: Chebyshev, Hermite, Laguerre
ClearDenom	clear common denominator of a polynomial with rational coeffs
CoeffHeight	the maximum of the absolute values of the coefficients of a polynomial
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 an indet
CoeffListWRTSupport	list of coefficients of a polynomial wrt a power-product basis
CoeffOfTerm	coefficient of a term of a polynomial
CommonDenom	Common denominator of a polynomial with rational coefficients
ComputeElimFirst	ComputeElimFirst
ConstantCoeff	constant coefficient 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
CoprimeFactorBasis	determine coprime factor base for a set of integers or ring elements
CRTPoly	Chinese Remainder Theorem on polynomial coefficients
cyclotomic	n-th cyclotomic polynomial
CyclotomicFactors	find cyclotomic factors of a polynomial
CyclotomicIndex, CyclotomicTest	computes the index of a given 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
DicksonPoly	Dickson 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
FixedDivisor	compute (integer) fixed divisor for 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
GensJacobian	set of generators of the Jacobian ideal of a polynomial
GinJacobian	generic initial ideal of the Jacobian ideal of a polynomial
graeffe	graeffe transformation (squares the roots)
HermitePoly	Orthogonal Polynomials: Chebyshev, Hermite, Laguerre
homog	homogenize wrt an indeterminate
HomogCompt	homogeneous part of given degree
ideal	ideal generated by list
IndetIndex	index of an indeterminate
IndetName	the name of an indeterminate
IndetsProd	(product of) indeterminates actually in a polynomial
IndetSubscripts	the indices in the name of an indeterminate
interreduce	interreduce a list of polynomials
interreduced	interreduce a list of polynomials
IsArrFree	checks if the arrangement is free
IsConstant	checks if a ringelem is in the coefficient ring
IsCoprime	checks if two elements are coprime
IsDivisible	checks if A is divisible by B
IsElem	checks if A is an element of B
IsEvenPoly, IsOddPoly	test whether a polynomial is even or odd as a function
IsHomog	test whether given polynomials are homogeneous
IsIn	check if one object is contained in another
IsIndet	check if argument is an indeterminate
IsIndetPosPower	check if argument is a power of an indeterminate
IsInImage	check if a RINGELEM is in image of RINGHOM
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
IsLRSDegenerate	checks the given polynomial for LRS-degeneracy
IsLRSDegenerateOrder	checks the given polynomial for n-LRS-degeneracy
IsMinusOne	test whether an object is -1
IsOne	test whether an object is one
IsPalindromic	test whether a univariate polynomial is palindromic
IsPrimitivePoly	test if polynomial over finite field is primitive
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
JacobianMat	the Jacobian matrix of a list of polynomials
LaguerrePoly	Orthogonal Polynomials: Chebyshev, Hermite, Laguerre
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
LRSDegeneracyOrder	the LRS degeneracy order of a polynomial
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
MinGBoverZZ [PROTOTYPE]	[PROTOTYPE] minimal Groebner basis of polys over ZZ
MinPoly	minimal polynomial of a matrix
MinPolyQuot	minimal polynomial in quotient ring
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
MultiArrRestrictionZiegler	Ziegler multirestriction of the arrangement of hyperplanes wrt a hyperplane
MultiplicationMat	multiplication matrix of a ringelem
NewMatFilled	matrix filled with value
NF	normal form
NmzEhrhartRing	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
NumRealRoots	number of real roots of a polynomial
NumTerms	number of terms in a polynomial
operators, shortcuts	Special characters equivalent to commands
PerpIdealOfForm	Ideal of derivations annihilating a form
power	compute a power
preimage0	preimage of a RINGELEM
prim	primitive part of a polynomial
product	the product of the elements of a list
PthRoot	Compute p-th root
QZP	change field for polynomials and ideals
radical	radical of an ideal
RationalSolve	Rational solutions for 0-dim polynomial system
RationalSolveHomog	Rational solutions for 0-dim polynomial system
RatReconstructPoly	Rational reconstruction of polynomial coefficents
RealRoots	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
RootBoundTransform	transform of a polynomial, helpful for checking RootBound
SatSAGBI	SAGBI bases for subalgebra
ScientificStr	convert integer/rational to a floating-point string
SetEntry	set an entry into a matrix
SolomonTeraoIdeal	Solomon-Terao ideal of an arrangement of hyperplanes wrt a poly
SqFreeFactor	compute a squarefree factorization
SturmSeq	Sturm sequence of a univariate polynomial
subst	substitute values for indeterminates
sum	the sum of the elements of a list
support	the list of terms of a polynomial or moduleelem
SwinnertonDyerPoly	compute Swinnerton-Dyer polynomial with given roots
SylvesterMat	the Sylvester matrix of two polynomials
syz	syzygy modules
ThmProve [PROTOTYPE]	[PROTOTYPE] ThmProve
UnivariateIndetIndex	the index of the indeterminate of a univariate polynomial
wdeg	multi-degree of a polynomial
ZPQ	change field for polynomials and ideals