Determinant

Please keep discussion son the list.

Yes, I am asking whether that integer can be exactly represented on a computer.

Yes, but it requires significant effort to do so because you need arbitrary-precision algorithms.

I use 64 bit.

I have changed 64 up to 1024 but nothing changed.

I don't think we are talking about the same thing here.

I have tried also to use Rmpfr package, but I haven't solved my problem?

You have not clearly stated what the problem is you are trying to solve. Clearly you don't need to know whether the number is an integer - you already know it is. You also know that a number of that size cannot be exactly represented natively in your computer. So asking whether it turns out to be a whole number or not is asking a question about the machine precision and the algorithm, not about the number.

How do you think I can use the Rmpfr package?
2^63-1

[1] 9.223372e+18

print(2^63 - 1, digits=19)

[1] 9223372036854775808       # wrong!

library(Rmpfr)
a <- mpfr(2, 64)
print(a^63 - 1, digits=19)
1 'mpfr' number of precision  64   bits 
[1] 9223372036854775807       # correct!

... but you will need to change the code that does the calculation so that it uses mpfr-class number with enough precision to safely avoid rounding errors for the size of all intermediate values in your calculation. Probably this means you will write your own determinant algorithm - and if this is just for one matrix it doesn't need to be fast so why not. Google tells me there are division-free algorithms for calculating determinants that are O(n^4). But as I wrote above, I can't imagine why this makes sense.


B.

Vasilis