NAME min - minimum, or minimum of defined minima SYNOPSIS min(x_1, x_2, ...) TYPES x_1, x_2, ... any return any DESCRIPTION If an argument x_i is a list with elements e_1, e_2, ..., e_n, it is treated as if x_i were replaced by e_1, e_2, ..., e_n; this may continue recurively if any of the e_j is a list. If an argument x_i is an object of type xx, then x_i is replaced by xx_min(x_i) if the function xx_min() has been defined. If the type xx has been defined by: obj xx = {x, y, z}, an appropriate definition of xx_min(a) is sometimes min(a.x, a.y, a.z). min(a) then returns the minimum of the elements of a. If x_i has the null value, it is ignored. Thus, sum(a, , b, , c) If x_i has the null value, it is ignored. Thus, min(a, , b, , c) will return the same as min(a, b, c). Assuming the above replacements, and that the x_1, x_2, ..., are of sufficently simple ordered types (e.g. real numbers or strings), or, if some are objects, the relevant xx_rel(a,b) has been defined and returns a real-number value for any comparison that has to be made, min(x_1, x_2, ...) returns the value determined by min(x_1) = x_1, and succesively for later arguments, by the use of the equivalent of min(a,b) = (a < b) ? a : b. If the ordering determined by < is total, min(x_1, ...) will be the minimum value among the arguments. For a preorder relation it may be one of several minimal values. For other relations, it may be difficult to predict the result. EXAMPLE > print min(2), min(5, 3, 7, 2, 9), min(3.2, -0.5, 8.7, -1.2, 2.5) 2 2 -1.2 > print min(list(3,5), 7, list(6, list(7,8), 2)) 2 > print min("one", "two", "three", "four") four > obj point {x, y} > define point_rel(a,b) = sgn(a.x - b.x) > obj point A = {1, 5} > obj point B = {1, 4} > obj point C = {3, 3} > print min(A, B, C) obj point {1, 5} > define point_min(a) = a.x > print min(A, B, C) 1 LIMITS The number of arguments is not to exceed 100. LIBRARY NUMBER *qmin(NUMBER *x1, NUMBER *x2) SEE ALSO max, obj