J has a few different ways of representing numbers, including:
- Machine integers (limited to 64 or 32 bit); this is what you get if you type
a number like 123
- Machine floating-point numbers (limited precision, but can have decimal
points in them); this is what you get if you type a number like 3.45 or 1p1
- Extended-precision numbers (unlimited precision, but can only represent
integers and rational numbers); this is what you get if you type a number like
123x or 3r4
You would like an unlimited-precision representation of pi, I assume. But the
present implementation of j is incapable of this; the only things it can
represent with unlimited precision are integers and rational numbers, and pi
is irrational.
Machine representation of irrational numbers is a very interesting topic, but
it is fraught with tradeoffs and complexities, and the present implementation
of j does not attempt it. As far as I know, all implementations of apl have
the same limitation; there, too, ○1 is a floating-point approximation. And I
do not think most apl implementations even have extended-precision integers or
rational numbers.
You might like to look into computer algebra systems (cas), such as mathematica.
On Sun, 15 May 2022, yt wrote:
Dear All,
i come back to start in J
in jijx>tour>overview
3p5 NB. Pi (3 * Pi ^ 5)
918.059
may be it is not the better way to find Pi :
1p1 NB. Pi (1 * Pi ^ 1)
1p1
3.14159
1p1x
|ill-formed number
| 1p1x
| ^
but this is ok for :
^/ 2 3 4
2.41785e24
^/ 2 3 4x
2417851639229258349412352
3^4
81
2^81
2.41785e24
2^81x
2417851639229258349412352
why 1p1 is not good ?
i have not this problem in APL
Sorry for the inconvenience
Regards,
Yves
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