Re: Surprising behaviour of sqrt() on squares of integers

[Jack Brennen <jfb@brennen.net>]

By the way, if you want a function that returns an integer when possible
and a real when not possible, you can roll your own in one line (assumes
the input is a non-negative INT or a REAL):

? mysqrt(x) = if(issquare(x),sqrtint(x),sqrt(x))
? for(x=0,10,print([x,mysqrt(x)]))
[0, 0]
[1, 1]
[2, 1.4142135623730950488016887242096980786]
[3, 1.7320508075688772935274463415058723670]
[4, 2]
[5, 2.2360679774997896964091736687312762354]
[6, 2.4494897427831780981972840747058913920]
[7, 2.6457513110645905905016157536392604257]
[8, 2.8284271247461900976033774484193961571]
[9, 3]
[10, 3.1622776601683793319988935444327185337]


On 4/23/2013 4:37 PM, Jack Brennen wrote:
> I thought that the behavior was that sqrt() of a non-negative integer or
> real returns a real, and sqrtint() of a non-negative integer
> returns an integer.  Both of your examples work fine with sqrtint():
>
> ? Mod(5,sqrtint(9))
> Mod(2, 3)
> ? sqrtint(2^256)
> 340282366920938463463374607431768211456
> ? 2^128
> 340282366920938463463374607431768211456
>
>
>
> On 4/23/2013 4:31 PM, Richard in Reading wrote:
> > This is just a toy example but there are other real situation where
> > it's annoying that PARI doesn't recognize when you want to take a
> > square root of the square of an integer and return an integer.
> >
> > Is there some justification for this or is it worth me reporting it as
> > a bug.
> >
> >   ? Mod(5,sqrt(9))
> >    ***   at top-level: Mod(5,sqrt(denominat
> >    ***                 ^--------------------
> >    *** Mod: forbidden division t_INT % t_REAL.
> >    ***   Break loop: type 'break' to go back to GP
> >
> > ? sqrt(2^256)
> > %17 = 3.4028236692093846346337460743176821146 E38
> > ? 2^128
> > %18 = 340282366920938463463374607431768211456
> >
> > The above should return the same value in my opinion.
> >
> > Richard Heylen