Functions

To assign a function to the identifier NAME, with formal identifiers FORMAL_IDFIER, ..., FORMAL_IDFIER, use the syntax

NAME := function(FORMAL_IDFIER, ..., FORMAL_IDFIER)
    STATEMENTS
end function;

or, if the return expression is easily specified:

NAME := func< FORMAL_IDFIER, ..., FORMAL_IDFIER | EXPRESSION >

To call this function within a statement, use the expression

     NAME(ACTUAL, ..., ACTUAL)

When the function is called with actual values, Magma will return a value. In the func< ... > form, the value will be the value of EXPRESSION. In the function ... end function form, during the execution of the STATEMENTS Magma must encounter a statement

return EXPRESSION, ..., EXPRESSION;

so that a value or values can be returned from the function invocation, namely, the value of EXPRESSION(s).

Example

> Fibonacci := func< n | n le 2 select 1 else $$(n-1) + $$(n-2) >;
> f8 := Fibonacci(8); print f8;
21

Given positive integer N, this returns s and d such that N - 1 = 2^s * d.
> evenexp_odd := function(N)
function> s := 0; d := N;
function> q, r := Quotrem(d, 2);
function> while r eq 0 do
function|while> s +:= 1;
function|while> d := q;
function|while> q, r := Quotrem(d, 2);
function|while> end while;
function> return s, d;
function> end function;
> print evenexp_odd(2^8 * 35);
8 35

Subscreens

• Function Expressions
• Recursive functions