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Fouriest transform of Integers

John May 2816 Maple 16
February 01 2013
9

Today's SMBC strip by Zach Weinersmith is a silly math joke but it was pretty much begging for implementation.

So, here is a simple brute force Maple program to compute the Fouriest transform of an integer.

fouriest := proc(n::posint, ob::posint:=10)
local b,f,cap,i,rdx,fc;
    b := ob:
    f := nops(select(`=`, convert(n, base, ob),4));

    if f > 0 then
        cap := ceil( exp(ln(n)/f) );
    else
        cap := n-1;
    end if;

    for i from 5 to n-1 while i < cap do
        rdx := convert(n, base, i);
        fc := nops(select(`=`, rdx, 4));
  
        if fc > f then
            f := fc;
            b := i;
            # new cap is largest base where n has more than f digits
            cap := ceil( exp(ln(n)/f) );
        end if;
    end do:

    return cat(`#msub(mo(`,cat(`"`,ListTools:-Reverse(convert(n, base, b))[],`"`),`),mo("`,b,`"))`);
end proc:

Try it on his example: fouriest(624);

or on random examples: n := rand(); fouriest(n);

Enjoy.

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