# [R] Ryacas and fractions with simultaenously very large numerators and denominators

Gabor Grothendieck ggrothendieck at gmail.com
Thu Nov 23 20:23:26 CET 2006

```There is likely some limitation in the Ryacas interface that needs to
be addressed by the Ryacas developers.  yacas itself can support very large
numbers so just use yacas directly.

Aside from that I, as mentioned previously in this thread,  yacas returns a
"yacas" object and that is a complex structure for which it makes no sense
to try to use "paste".

This works:

> x <- Sym("3/2")
> for(i in 2:5) x <- as.Sym(yacas(x*x))
> x
expression(43046721/65536)

but quickly comes up against some limits in Ryacas (not in yacas)
if you go past 5.

This also works and is even easier but may quickly generate enormous strings
that might overflow the interface:

> x <- Sym("3/2")
> for(i in 2:5) x <- x*x
> dput(x)
structure("( ( ( ( 3/2 * 3/2 ) * ( 3/2 * 3/2 ) ) * ( ( 3/2 * 3/2 ) * (
3/2 * 3/2 ) ) ) * ( ( ( 3/2 * 3/2 ) * ( 3/2 * 3/2 ) ) * ( ( 3/2 * 3/2
) * ( 3/2 * 3/2 ) ) ) )", class = c("Sym",
"character"))
> x
expression(43046721/65536)

Using yacas directly:

yacas
...
In> x := 3/2
Out> 3/2
In> x := 3/2
Out> 3/2
In> x := x*x
Out> 9/4
In> x := x*x
Out> 81/16
In> x := x*x
Out> 6561/256
In> x := x*x
Out> 43046721/65536
In> x := x*x
Out> 1853020188851841/4294967296
In> x := x*x
Out> 3433683820292512484657849089281/18446744073709551616
In> x := x*x
Out> 11790184577738583171520872861412518665678211592275841109096961/340282366920
938463463374607431768211456
In> x := x*x
Out> 139008452377144732764939786789661303114218850808529137991604824430036072629
766435941001769154109609521811665540548899435521/1157920892373161954235709850086
87907853269984665640564039457584007913129639936

On 11/23/06, Paul Smith <phhs80 at gmail.com> wrote:
> Dear All
>
> I am doing the following:
>
> > x <- yacas("3/2")
> > for (i in 2:400)
> +    x <- yacas(paste(x,"*",x))
> > x
> expression(Inf^1.260864167e+117/Inf^6.304320836e+116)
> > Eval(x)
> [1] NaN
>
> No luck this way. However, I am successful with
>
> > y <- yacas("(3/2)^400")
> > y
> expression(7.05507910865533e+190/2.58224987808691e+120)
> > Eval(y)
> [1] 2.732144e+70
>
> If Ryacas/Yacas cannot multiply fractions with simultaenously very
> large numerators and denominators, what else should I use?
>
>
> Paul
>
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