Function: sqr
Section: transcendental
C-Name: gsqr
Prototype: G
Help: sqr(x): square of x. NOT identical to x*x.
Description:
 (int):int        sqri($1)
 (mp):mp          gsqr($1)
 (gen):gen        gsqr($1)
Doc: square of $x$. This operation is not completely
 straightforward, i.e.~identical to $x * x$, since it can usually be
 computed more efficiently (roughly one-half of the elementary
 multiplications can be saved). Also, squaring a $2$-adic number increases
 its precision. For example,
 \bprog
 ? (1 + O(2^4))^2
 %1 = 1 + O(2^5)
 ? (1 + O(2^4)) * (1 + O(2^4))
 %2 = 1 + O(2^4)
 @eprog\noindent
 Note that this function is also called whenever one multiplies two objects
 which are known to be \emph{identical}, e.g.~they are the value of the same
 variable, or we are computing a power.
 \bprog
 ? x = (1 + O(2^4)); x * x
 %3 = 1 + O(2^5)
 ? (1 + O(2^4))^4
 %4 = 1 + O(2^6)
 @eprog\noindent
 (note the difference between \kbd{\%2} and \kbd{\%3} above).
