abs

absolute value of a number

AffHilbertFn

the affine Hilbert function

ascii

convert between characters and ascii code

AsINT

convert into an INT

AsRAT

convert into a RAT

binomial

binomial coefficient

BinomialRepr, BinomialReprShift

binomial representation of integers

ContFracToRat

convert continued fraction to rational

CRT

Chinese Remainder Theorem

CRTPoly

Chinese Remainder Theorem on polynomial coefficients

cyclotomic

nth cyclotomic polynomial

date

the date

DecimalStr

convert rational number to decimal string

den

denominator

DensePoly

the sum of all powerproducts of a given degree

div

quotient for integers

ElimMat

matrix for elimination ordering

EvalHilbertFn

evaluate the Hilbert function

exponents

the list of exponents of the leading term of a polynomial

Ext

presentation Ext modules as quotients of free modules

factorial

factorial function

FactorMultiplicity

multiplicity of a factor of an integer

first

the first N elements of a list

flatten

flatten a list

FloatApprox

approx. of rational number of the form M*2^E

FloatStr

convert rational number to a decimal string

FloorLog2, FloorLog10, FloorLogBase

integer part of the logarithm

FloorSqrt

(truncated) square root of an integer

format

convert object to formatted string

GBasisTimeout

compute a Groebner basis with a timeout

gcd

greatest common divisor

GCDFreeBasis

determine (minimal) GCD free basis of a set of integers

GenericPoints

random projective points

Get

read characters from a device

GetCol

convert a column of a matrix into a list

GetRow

convert a row of a matrix into a list

HilbertFn

the Hilbert function

IdentityMat

the identity matrix

incr, decr

increment/decrement a counter

indent

prints in a more readable way

indet

individual indeterminates

insert [OBSOLESCENT]

[OBSOLESCENT] insert an object in a list

InverseSystem

Inverse system of an ideal of derivations

IO.SprintTrunc

convert to a string and truncate

iroot

integer part of rth root of an integer

IsEven, IsOdd

test whether an integer is even or odd

IsInteger

check if a RINGELEM is integer

IsOne

test whether an object is one

IsPositiveGrading

check if a matrix defines a positive grading

IsPrime

prime integer test

IsProbPrime

checks if an integer is a probable prime

IsSqFree

check if an INT or RINGELEM is squarefree

IsZero

test whether an object is zero

IsZeroCol, IsZeroRow

test whether a column(row) is zero

last

the last N elements of a list

lcm

least common multiple

LexMat

matrices for std. termorderings

MakeMatByRows, MakeMatByCols

convert a list into a matrix

MakeTerm

returns a monomial (powerproduct) with given exponents

MakeTermOrd

Make a term order matrix from a given matrix

MantissaAndExponent10

convert rational number to a float

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

minors

list of minor determinants of a matrix

mod

remainder for integers

NewFreeModule

create a new FreeModule

NewList

create a new list

NewMat

Zero matrix

NewMatFilled

matrix filled with value

NewPolyRing

create a new PolyRing

NewRingFp

create a new finite field

NewRingTwinFloat

create a new twinfloat ring

NextPrime

find the next largest prime number

NextProbPrime

find the next largest probable prime number

num

numerator

NumPartitions

number of partitions of an integer

operators, shortcuts

Special characters equivalent to commands

partitions

partitions of an integer

PowerMod

compute a modular power efficiently

PrimitiveRoot

find a primitive root modulo a prime

product

the product of the elements of a list

random

random integer

randomized

randomize the coefficients of a given polynomial

RandomSubset

random subset

RandomSubsetIndices

indices for random subset

RandomTuple

random tuple

RandomTupleIndices

indices for random tuples

RandomUnimodularMat

random unimodular matrix

RatReconstructByContFrac, RatReconstructByLattice

rational reconstruction from modular image

RatReconstructPoly

Rational reconstruction of polynomial coefficents

RatReconstructWithBounds

deterministic rational reconstruction from modular image

RefineGCDFreeBasis

refine an integer GCD free basis

remove

remove an object in a list

RevLexMat

matrices for std. termorderings

RingElem

convert an expression into a RINGELEM

RingQQt

predefined polynomial rings

ScientificStr

convert integer/rational to a floatingpoint string

seed

seed for
random

SetRow

set a list as a row into a matrix

SetStackSize

secret ;)

sign

the sign of a number

SmoothFactor

find small prime factors of an integer

SourceRegion

read commands from a region in a file

spaces

return a string of spaces

StarPrint, StarSprint

print polynomial with *'s for multiplications

StdDegLexMat

matrices for std. termorderings

StdDegRevLexMat

matrices for std. termorderings

submat

submatrix

subsets

returns all sublists of a list

sum

the sum of the elements of a list

SwapRows

swap two rows in a matrix

SymbolRange

range of symbols for the indeterminates of a PolyRing

syz

syzygy modules

tuples

Ntuples

WithoutNth

removes the Nth component from a list

XelMat

matrices for std. termorderings

ZeroMat

matrix filled with 0
