# Numerical Functions

 IntegerPart[x] integer part of x FractionalPart[x] fractional part of x Round[x] integer 〈x〉 closest to x Floor[x] greatest integer ⌊x⌋ not larger than x Ceiling[x] least integer ⌈x⌉ not smaller than x Rationalize[x] rational number approximation to x Rationalize[x,dx] rational approximation within tolerance dx

Functions relating real numbers and integers.

 x IntegerPart[x] FractionalPart[x] Round[x] Floor[x] Ceiling[x] 2.4 2 0.4 2 2 3 2.5 2 0.5 2 2 3 2.6 2 0.6 3 2 3 -2.4 -2 -0.4 -2 -3 -2 -2.5 -2 -0.5 -2 -3 -2 -2.6 -2 -0.6 -3 -3 -2

Extracting integer and fractional parts.

IntegerPart[x] and can be thought of as extracting digits to the left and right of the decimal point. Round[x] is often used for forcing numbers that are close to integers to be exactly integers. Floor[x] and Ceiling[x] often arise in working out how many elements there will be in sequences of numbers with noninteger spacings.

 Sign[x] 1 for x>0, -1 for x<0 UnitStep[x] 1 for x≥0, 0 for x<0 Abs[x] absolute value x of x Clip[x] x clipped to be between ‐1 and +1 Rescale[x,{xmin,xmax}] x rescaled to run from 0 to 1 Max[x1,x2,…] or Max[{x1,x2,…},…] the maximum of x1, x2, … Min[x1,x2,…] or Min[{x1,x2,…},…] the minimum of x1, x2, …

Numerical functions of real variables.

 x+I y the complex number Null Re[z] the real part Null Im[z] the imaginary part Null Conjugate[z] the complex conjugate Null or Null Abs[z] the absolute value z Arg[z] the argument Null such that Null

Numerical functions of complex variables.