makelist

Format: makelist( f(x), x, x1, x2, step )

Arguments: [any] f(x) Function or expression

(node) x Name of the input variable in f(x)

(num) x1 Lower limit

(num) x2 Upper limit

(num) step Optional step size; default = 1

Returns: [any] A list of f(x) where x is equal to all numbers from x1 to x2 inclusive, in increments of step

Description: Makelist creates a temporary variable named x and then constructs a list by setting x equal to all numbers from x1 to x2 and repeatedly evaluating f(x). That is, makelist(f(x),x,x1,x2) = [f(x),f(x+1),...,f(x2)]

If a node named x already exists, it is replaced for all evaluations of f(x) and is then restored to its original state.

Note: If the expression f(x) is a tree node rather than a function based on x, the reset primitive must be used to cause the tree to recalculate on each iteration. Constants retain their value from the first evaluation and return this value on all subsequent evaluations. To cause the constant to be reevaluated, use an expression similar to

makelist({reset,f},x,x1,x2)

rather than

makelist(f,x,x1,x2)

Examples: makelist(n,n,3,7) = [3,4,5,6,7]

makelist(n^2,n,1,4) = [1,4,9,16]

makelist(rand,n,1,10) = list of 10 random numbers

See Also: Range, each, both, sigma