Georg wrote :
while calculating the integer part of square roots I realized that
sqrt() returns wrong results for large inputs (although the sqrt()
command itself accepts "bignum" values).
example: int(sqrt(2^94533))
int isn't a "mathematical" Sage type, but Integer is a Sage type.
And Integer (sqrt(2^1234567)) fails
But floor over Integer seems fine :
n=10001 ; res=floor(sqrt(2^n)) ; sign(res^2-2^n) ; sign((res+1)^2-2^n)
I get -1 and 1.
but it fails around n=30000 or 40000.
You may also get a precise numerical approximation by the method
_____.n(digits=....).
By example : sqrt(2).n(digits=10000). But in this case you must compute
"by pen" the digit value.
A very similar exercice : Is the number of digits of 123^456^789 even or
odd ?
Of course you must read 123^(456^789), not (123^456)^789 !
I hope this help you...
F. (in France)
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