[R] Determinant

[David Winsemius]

On May 14, 2015, at 12:50 PM, David Winsemius wrote:

> 
> On May 14, 2015, at 1:44 AM, chasiotisv at math.auth.gr wrote:
> 
>> Hello,
>> 
>> I am Vasilis Chasiotis and I am a candidate Ph.D. student in Aristotle University of Thessaloniki in Greece.
>> 
>> I have the following problem.
>> 
>> I want to check if the square of a number ( for example the square of 1.677722e+29 ) is an integer.
>> 
> 
> The square of 1.677722e+29 is almost certainly an integer since the power of 10  (+29)  exceeds the number of digits. That implies that the number in non-scientific notation has many 0's on the righthand side.
> 
> I'm guessing that you may be asking whether the square-root is an integer.
> 
>> The problem is that this number is the calculation of the determinant (so the number should be an integer) of a matrix 22x22, which means it has an approximation ( the "real" number is 1.6777216e+29 but R gives to me  1.6777215999999849e+29 ), because R use LU-decomposition to calculate the determinant.
>> 
>> That means that the radical of the number 1.6777215999999849e+29 is not an integer, but it should be.
> 
> Again guessing that by 'radical' you mean the square-root. I am also confused about  what test you were applying to that result to determine that it was not an integer. 
> 
> At any rate, I'm guessing that the limitation of R's numerical accuracy may get in the way of determining whether the square-root is an integer. If it were integer then it should equal floor(n) :
> 
> (1.6777215999999849e+29)^(1/2) - floor((1.6777215999999849e+29)^(1/2)) 
> #[1] 0.125
> 
> (1.6777216e+29)^(1/2) - floor( (1.6777216e+29)^(1/2) )
> #[1] 0
> 
> That's because that number was the product of two perfect squares:
> 
>> 16777216^(1/2) - floor( 1.6777216^(1/2) )
> [1] 4095


Sorry: Meant to copy this to the response:

> 16777216^(1/2) - floor( 16777216^(1/2) )
[1] 0
> 16777216^(1/2) 
[1] 4096


> 
> And 10^22 = 10^11*10^11
> 
> 
> If you know how big the  original was you could round it to the correct precision but that seems too much to hope for.
> 
> print( round(1.6777215999999849e+29, digits=10) , digits=10)
> #[1] 1.6777216e+29
> 
> identical( (1.6777216e+29)^(1/2) , floor( (1.6777216e+29)^(1/2) ) )
> #[1] TRUE
> 
>> 
>> How can we overcome this problem? 
> 
> There are a couple of packages that support exact math on really large numbers. You need to clarify what is being requested. You definitely need to review R-FAQ 7.31 and make sure you understand it and also review ?double and ?integer
> 
> -- 
> 
> David Winsemius
> Alameda, CA, USA
> 
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David Winsemius
Alameda, CA, USA