big numbers in matlab / sym math tool

I have a problem using very big numbers in matlab. For example, i want to calculate 26^29.

Without Sym Math Tool i get 1.081999577417210e+41, or with Sym Maths Tool 108199957741720993031339765987128356372480. If i try to find its value in modulus 35, i get mod(26^29,35)=20.

When i use wolframalpha, i get 108199957741720996894562347292921981566976, and the modulus value 31, which is correct!

In matlab, if i subtract the wolfram's correct value from 26^29, the result is 0!

I am doing this as a simulation of Euler's totient theorem, and i banged my head around it for a while until it became obvious that there is an error in matlab.

Is there any way to bypass this error, and what can be the source of it?

Answer 1

[Sean de Wolski]

x = sym('26^29');
mod(x,35)
  ans = 
        31

I can only speculate how you were creating the sym before, but if you run:

sym(26^29)

It first evaluates

26^29

which is significantly larger than flintmax:

flintmax
ans =
 9.0072e+15

So the rounding error of converting to double has already occurred.

[Milan]

Thank you very much, Sean. I have made the exact mistake you mentioned by doing just sym(26^29).