for example

Axel Vogt — Sat, 07 Jan 2012 18:53:42 Z

L:=[seq(x(i), i=0 .. 20)]:
map('t -> type(t, integer)', L);
convert(%, set); # to see, which values occure

                                {true}

Early termination

epostma — Tue, 10 Jan 2012 02:45:16 Z

Hi Pete3431,

I'd like to try to set things up in such a way that once a non-integer value is produced, it doesn't need to continue searching and stops immediately. If you prefer the method of defining a procedure with remember table, then we can keep the definition of x as is (including assigning to x(0), x(1), x(2)). After that, I would do:

testIntegers := proc(seqname :: appliable,
                     {rng :: range(integer) := 0 .. 20},
                     $)
local i;
    for i from lhs(rng) to rhs(rng) do
        if not type(seqname(i), 'integer') then
            return false;
        end if;
    end do;

    return true;
end proc;

Then you can ask for testIntegers(x), or if the first 21 numbers are maybe not enough, testIntegers(x, 'rng' = 0 .. 30) to test the first 31 numbers. It will return true in both cases, because these entries are all integers. Both of these are relatively quick. More importantly, if we run forget(x) in order to clear the set values of x and use new initial conditions 1, 2, 3, then computation of x(5) will already trigger stopping the loop.

In this way you get the best of both worlds: it's reasonably fast if indeed the sequence consists of only integers (because the in-memory size of the integers involved is a lot smaller than the size of fractions), and typically even faster if there are non-integer values.

If you'd be OK with tracking integer or non-integer status only until the values get too large to fit into an 8-byte signed integer (about 10^18), we could look at optimizing the code further to be able to use the Compiler.

Hope this helps,

Erik Postma
Maplesoft.

MaplePrimes - answers and comments on Question, Tidying up a messy set of Proc and loops. (Recurrece relations)

for example

Early termination