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2.11.4 Commands and Functions returning RINGELEM
abs absolute value of a number
apply apply homomorphism
ArrCharPoly characteristic polynomial of an arrangement of hyperplanes
ArrPoincarePoly Poincare polynomial of an arrangement of hyperplanes
ArrTuttePoly Tutte polynomial of an arrangement of hyperplanes
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
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
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
DenSigma den of ideal, wrt to ordering sigma
deriv the derivative of a polynomial or rational function
det the determinant of a matrix
DF the degree form of a polynomial
DicksonPoly Dickson 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 position of the first non-zero entry in a MODULEELEM
FixedDivisor compute (integer) fixed divisor for polynomial
gcd greatest common divisor
graeffe graeffe transformation (squares the roots)
GraverBasis Graver basis
HermitePoly Orthogonal Polynomials: Chebyshev, Hermite, Laguerre
HilbertPoly the Hilbert polynomial
homog homogenize wrt an indeterminate
HomogCompt homogeneous part of given degree
ImplicitHypersurface implicitization of hypersurface
indet individual indeterminates
IndetsProd (product of) indeterminates actually in a polynomial
Interpolate interpolating polynomial
interreduced interreduce a list of polynomials
InverseSystem Inverse system of an ideal of derivations
JanetBasis the Janet basis of an ideal
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
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
MinPolyQuot minimal polynomial in quotient ring
monic divide polynomials by their leading coefficients
NF normal form
NmzDiagInvariants ring of invariants of a diagonalizable group action
NmzEhrhartRing 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
operators, shortcuts Special characters equivalent to commands
pfaffian the Pfaffian of a skew-symmetric matrix
PosetCharPoly characteristic polynomial of a poset from the relations of the poset
PosetPoincarePoly Poincare polynomial of a poset from the relations of the poset
power compute a power
PthRoot Compute p-th root
QZP change field for polynomials and ideals
radical radical of an ideal
RandomLinearForm random linear form in polynomial ring
RationalAffinePoints Affine rational solutions
RationalProjectivePoints Projective rational solutions
RationalSolve Rational solutions for polynomial system
RatReconstructPoly Rational reconstruction of polynomial coefficents
ReducedGBasis reduced Groebner basis
resultant the resultant of two polynomials
RingElem convert an expression into a RINGELEM
RingElems convert an expression into a RINGELEM
ScalarProduct scalar product
SwinnertonDyerPoly compute Swinnerton-Dyer polynomial with given roots
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