| 2.2.3 Commands and Functions returning INT |
| abs | absolute value of a number |
| AffHilbertFn | the affine Hilbert function |
| AsINT | convert into an INT |
| binomial | binomial coefficient |
| BinomialRepr, BinomialReprShift | binomial representation of integers |
| Bool01 | Convert a boolean to an integer |
| ceil | round rational up to integer |
| characteristic | the characteristic of a ring |
| ContFrac | continued fraction quotients |
| count | count the objects in a list |
| deg | the standard degree of a polynomial or moduleelem |
| den | denominator |
| depth | Depth of a module |
| dim | the dimension of a ring or quotient object |
| div | quotient for integers |
| EvalHilbertFn | evaluate the Hilbert function |
| factorial | factorial function |
| FactorMultiplicity | multiplicity of a factor of an integer |
| floor | round rational down to integer |
| FloorLog2, FloorLog10, FloorLogBase | integer part of the logarithm |
| FloorSqrt | (truncated) square root of an integer |
| gcd | greatest common divisor |
| GFanContainsPositiveVector | ... |
| GFanGetAmbientDimension | ... |
| GFanGetCodimension | ... |
| GFanGetDimension | ... |
| GFanGetDimensionOfLinealitySpace | ... |
| GradingDim | Number of components in weighted degree |
| HilbertFn | the Hilbert function |
| IndetIndex | index of an indeterminate |
| iroot | integer part of r-th root of an integer |
| lcm | least common multiple |
| len | the length of an object |
| LogCardinality | extension degree of a finite field |
| LPosn | the position of the leading power-product in a ModuleElem |
| MayerVietorisTreeN1 | N-1st Betti multidegrees of monomial ideals using Mayer-Vietoris trees |
| MinPowerInIdeal | the mininum power of a polynomial is an ideal |
| mod | remainder for integers |
| multiplicity | the multiplicity (degree) of a ring or quotient object |
| NextPrime | find the next largest prime number |
| NextProbPrime | find the next largest probable prime number |
| num | numerator |
| NumCols | number of columns in a matrix |
| NumCompts | the number of components |
| NumGens | number of generators |
| NumIndets | number of indeterminates |
| NumPartitions | number of partitions of an integer |
| NumRows | number of rows in a matrix |
| NumTerms | number of terms in a polynomial |
| PowerMod | compute a modular power efficiently |
| PrimitiveRoot | find a primitive root modulo a prime |
| random | random integer |
| randomized | randomize the coefficients of a given polynomial |
| reg | Castelnuovo-Mumford regularity of a module |
| RegularityIndex | regularity index of a Hilbert function or series |
| RingID | identification for ring |
| rk | rank of a matrix or module |
| RootBound | bound on roots of a polynomial over QQ |
| round | round to integer |
| seed | seed for random |
| sign | the sign of a number |
| TimeOfDay | the current time |
| UnivariateIndetIndex | the index of the indeterminate of a univariate polynomial |