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))