Sum digits after vpa(N,100) ?

Hi MatLab!

I've stumbled across a problem. I wish to take all the first hundred digits in the square root of 2 ---> sqrt(2) and sum them up.

I first use

N=sym('sqrt(2)'); vpa(N,100)

which gives me alot of digits. But when I try to num2str the answer it cant be done. How can I achieve this?

Answer 1

[Shashank Prasanna]

Here you go:

clear all

digits(100);

N=vpa(sym('sqrt(2)'));

sumA = 0;

for i = 1:100

    sumA = sumA + (floor(N*(10^(i-1))) - 10*floor(N*10^(i-2)));

end

disp(sumA)

Answer 2

[Jan]

Could you operate on the VPA number instead of converting it to a string? I do not have the Symbolic Toolbox, but I guess:

s = 0;
x = vpa(N, 100);
for ii = 1:100
  s = s + floor(x);
  x = rem(x, 1) * 10;
end

Does this work?

[EDITED]

N = sym('sqrt(2)'); 
x = vpa(N, 100);

s = 0;
for ii = 1:100
  f = floor(x);
  s = s + f;
  x = (x - f) * 10;
end

If rounding error appear, try it with 200 digits in the VPA command. Please use this as inspiration - as I said already, I do not have the corresponding toolboxes.

[Per]

No I dont think so, says it's an undifined function or method 'rem' for input arguments of type 'sym'.

Cant copy paste from Linux till Windows it seems, but my code is just as you wrote but starts first line with: N=sym('sqrt(2)')

[Jan]

Then at least floor worked? This would be fine, because rem() can be emulated using floor() .

[Per]

I've written it like this and it yields the answer 465. The correct answer is 475. So the code seems to be working but I dont know where my 10 little digits went :O

[Jan]

Then let's debug your algorithm:

x = 1.414213562373095...
-> iteration starts
  x = x*10-floor(x)*10
    = 14.14213... - 1 * 10
    = 4.14...;
  s = s + 4;

Does the 1 not matter? And why do the loop stop at 99, when you need 100 elements?

Another test:

S = ['1.41421356237309504880168872420969807856967187537694807', ...
     '3176679737990732478462107038850387534327641572735013846', ...
     '230912297024924836055850737212644121497099935831'];
D = S - '0';
sum(D(3:102))

[Jan]

Now I can run Matlab again. The [EDITED] version works and gives the correct result.