os.clock () Returns an approximation of the amount in seconds of CPU time used by the program.

next (table [, index]) Allows a program to traverse all fields of a table. Its first argument is a table and its second argument is an index in this table. next returns the next index of the table and its associated value. When called with nil as its second argument, next returns an initial index and its associated value. When called with the last index, or with nil in an empty table, next returns nil. If the second argument is absent, then it is interpreted as nil. In particular, you can use

math.ult (m, n) Returns a boolean, true if and only if integer m is below integer n when they are compared as unsigned integers.

math.type (x) Returns "integer" if x is an integer, "float" if it is a float, or nil if x is not a number.

math.tointeger (x) If the value x is convertible to an integer, returns that integer. Otherwise, returns nil.

math.sqrt (x) Returns the square root of x. (You can also use the expression x^0.5 to compute this value.)

math.tan (x) Returns the tangent of x (assumed to be in radians).

math.sin (x) Returns the sine of x (assumed to be in radians).

math.randomseed (x) Sets x as the "seed" for the pseudo-random generator: equal seeds produce equal sequences of numbers.

math.random ([m [, n]]) When called without arguments, returns a pseudo-random float with uniform distribution in the range [0,1). When called with two integers m and n, math.random returns a pseudo-random integer with uniform distribution in the range [m, n]. (The value n-m cannot be negative and must fit in a Lua integer.) The call math.random(n) is equivalent to math.random(1,n). This function is an interface to the underling pseudo-random generator function provided by C.