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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.


Extracting integer and fractional parts.

IntegerPart[x] and FractionalPart[x] 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 non-integer 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+Iythe complex number x+iy
Re[z]the real part Re z
Im[z]the imaginary part Im z
Conjugate[z]the complex conjugate z* or
Abs[z]the absolute value z
Arg[z]the argument such that z=zei

Numerical functions of complex variables.