How to obtain the representation of an arbitrary fraction in a particular base? For example, the representation of 1/3 in base 2 should be
[[0], [0, 1, 0, 1, 0, 1, ...]
But when I type digits(1/3, 2) in GP shell and press Enter, all I see is the following error:
? digits(1/3, 2)
*** at top-level: digits(1/3,2)
*** ^-------------
*** digits: incorrect type in digits (t_FRAC).
How to solve the problem?
The value 1/3 is 1/3 and doesn't have a base. If you want to output that in some base to some precision you can multiply by base^precision:
digits(floor(1/3 * 2^50), 2)
Edited: A more complete solution:
Vec(digits(floor(frac(1/3) * 2^50), 2), -50)
The above only deals with the fractional part. The integer part can be obtained with (1/3)\1. The number of fractional digits is in this case 50 and appears twice. This could be packaged as a function:
fracdigits(f,b,n)=[digits(f\1, b), Vec(digits(floor(frac(f) * b^n), b), -n)]
fracdigits(1/3, 2, 50)
fracdigits(1/8, 2, 50)