3.2.2 Numerical Functions

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

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

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 , -1 for
UnitStep[x]	1 for , 0 for
Abs[x]	absolute value of x
Clip[x]	clipped to be between -1 and + 1
Rescale[x, {, }]	rescaled to run from 0 to 1
Max[, , ... ] or Max[{, , ... }, ... ]
	the maximum of , , ...
Min[, , ... ] or Min[{, , ... }, ... ]
	the minimum of , , ...

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