abs

absolute value of a number

apply

apply homomorphism

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 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

ContentFreeFactor

factorization of multivariate polynomial into contentfree 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

nth 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 quasipolynomial 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 t1 is coprime with t2

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

IsMinusOne

test whether an object is 1

IsOne

test whether an object is one

IsPthPower

pth power test

IsRational

check if a RINGELEM is rational

IsSqFree

check if an INT or RINGELEM is squarefree

IsTerm

checks if the argument is a term

IsZero

test whether an object is zero

IsZeroDivisor

test whether a RINGELEM is a zerodivisor

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 powerproduct 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

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

product

the product of the elements of a list

PthRoot

Compute pth 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

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 floatingpoint string

SolomonTeraoIdeal

SolomonTerao 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 SwinnertonDyer polynomial with given roots

SylvesterMat

the Sylvester matrix of two polynomials

syz

syzygy modules

UnivariateIndetIndex

the index of the indeterminate of a univariate polynomial

wdeg

multidegree of a polynomial

ZPQ

change field for polynomials and ideals
