fns2 http://www.openmath.org/cd/fns2.ocd 2003-04-01 2001-03-12 2 0 official arith1 fns1 list1 quant1 relation1 set1 logic1 relation1 alg1 This CD holds further functions concerning functions themselves. A particularly interesting function is apply_to_list which applies an nary function to all the elements in a specified list. For example, such a function can be used to form sums and products in conjunction with plus and times respectively. kernel This symbol denotes the kernel of a given function. This may be defined as the subset of the range of the given function which maps to the identity element of the image of the given function, however no semantics are assumed. The kernel of a function is also known as the null space of the function. x in the kernal of f implies that f(x) = 0 apply_to_list This symbol is used to denote the repeated application of an n-ary function on the elements of a given list. For example when used with plus or times this can represent sums and products. The symbol takes two arguments; the first of which is the n-ary function, the second a list. For all n 1 + 2 + ... + n = n(n+1)/2. 1 1 2 One may form a set in the following way. This gives the set {1^2, 2^2, ... , 10^2 } 1 10 2 right_compose This symbol represents a function forming the right-composition of its two functional arguments. right_compose(f,g)(x) = g(f(x))