Numerical Functions

Throughout the Wolfram Language there is support not only for approximate real numbers, but also for exact numbers represented in algebraic or symbolic form. Functions like (RefLink[Floor, paclet:ref/Floor]), (RefLink[IntegerPart, paclet:ref/IntegerPart]), and (RefLink[Max, paclet:ref/Max]) are all in effect set up to "prove theorems"—often using original algorithms developed at Wolfram Research—to give values with exact inputs.

(RefLink[MixedFractionParts, paclet:ref/MixedFractionParts]) — integer and fractional parts of a mixed fraction

(RefLink[Min, paclet:ref/Min]), (RefLink[Max, paclet:ref/Max]) — minimum, maximum of numbers or lists

(RefLink[RealAbs, paclet:ref/RealAbs]) — absolute value of real numbers

(RefLink[RealSign, paclet:ref/RealSign]) — sign of real numbers (-1, 0, +1)

(RefLink[Abs, paclet:ref/Abs]) — absolute value of complex numbers

(RefLink[Sign, paclet:ref/Sign]) — sign of complex numbers

(RefLink[Clip, paclet:ref/Clip]) — clip to between -1 and +1 or other limits

(RefLink[Rescale, paclet:ref/Rescale]) — rescale to run between 0 and 1

(RefLink[Chop, paclet:ref/Chop]) — chop small values to 0

(RefLink[Threshold, paclet:ref/Threshold]) — set values in a list below a threshold to 0.

(RefLink[LogisticSigmoid, paclet:ref/LogisticSigmoid]) — sigmoid function

(RefLink[Unitize, paclet:ref/Unitize]) — 0 for x==0, and 1 otherwise

(RefLink[UnitStep, paclet:ref/UnitStep]) — 0 for x<0, and 1 for x≥0

(RefLink[Ramp, paclet:ref/Ramp]) — 0 for x<0, and x for x≥0

(RefLink[Piecewise, paclet:ref/Piecewise]) — general piecewise function

(RefLink[Boole, paclet:ref/Boole]) — 1 for (RefLink[True, paclet:ref/True]), 0 for (RefLink[False, paclet:ref/False])

(RefLink[DiscreteIndicator, paclet:ref/DiscreteIndicator]) — indicator function for a discrete set

(RefLink[NumericalOrder, paclet:ref/NumericalOrder]) — give -1, 0, +1 for less, equal, greater

(OrangeLink[Integer Functions », paclet:guide/IntegerFunctions])

(RefLink[IntegerQ, paclet:ref/IntegerQ]) — test whether an expression is an integer