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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
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 and indet
CoeffOfTerm	coefficient of a term of a polynomial
CommonDenom	Common denominator of a polynomial with rational coefficients
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
FactorAlgExt	factorization algebraic extensions
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
graeffe	graeffe transformation (squares the roots)
HermitePoly	Orthogonal Polynomials: Chebyshev, Hermite, Laguerre
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
IsCoprime	checks if t1 is coprime with t2
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
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
IsMinusOne	test whether an object is -1
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
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
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
MinPolyQuot, 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
preimage0	preimage of a RINGELEM
PrimaryDecompositionCore0	primary decomposition of a 0-dimensional ideal
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
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
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