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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
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
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
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
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
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
PreImage 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
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