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 powerproduct 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

nth cyclotomic polynomial

den

denominator

DensePoly

the sum of all powerproducts 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 quasipolynomial at an integer

FirstNonZero

the first nonzero entry in a MODULEELEM

FirstNonZeroPosn

the position of the first nonzero 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 powerproduct of a polynomial or ModuleElem

LT

the leading term of an object

MakeTerm

returns a monomial (powerproduct) 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 skewsymmetric 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 pth 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 SwinnertonDyer 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
