fracDo {Rfractran}

The FRACTRAN Interpreter Function

Description

This implements the FRACTRAN process, to wit For the first fraction f in the list for which nf is an integer, replace n by nf. Repeat this rule until no fraction in the list produces an integer when multiplied by n, then halt.

Usage

fracDo(input, fractions = NULL, nums, denoms, tries = 100,
 stopFun = NULL, liveUpdate = TRUE, ...)

Arguments

input

The starting integer for the given FRACTRAN code (fraction sequence)

fractions

The sequence of fractions. Must be in bigq form. If NULL, then nums and denoms must be supplied.

nums

Vector of integers (or bigz values ) representing the numerators of the FRACTRAN fractions. If fractions is supplied, this is ignored.

denoms

Vector of integers (or bigz values ) representing the denominators of the FRACTRAN fractions. If fractions is supplied, this is ignored.

tries

A 'safety' limiter on the number of times to process the next integer generated. This avoids possible infinite runs or other time-wasters.

stopFun

Optional user-supplied function that can be used to terminate a FRACTRAN run early, or to take mid-run actions such as sending information to the console. See Details for more information.

liveUpdate

If set to TRUE, a few dots and words are sent to the console to indicate that the algorithm is still running.

...

Possible additional arguments for stopFun or future use.

Details

Some FRACTRAN programs do not terminate, most famously the prime generators. If a specific value is being looked for, an appropriate stopFun can be supplied to check for that value. stopFun must return a single logical value (R, as always will convert numerics to logical if necessary) indicating success as TRUE. The first argument to stopFun must accept a single bigq value. If there are more arguments, they must be entered after all named arguments. Note that this function does not have to send TRUE; it could be used solely to execute other commands mid-run. See stopPrime for one such example.

Value

A vector of all the bigq values generated. These all have denominator == 1, as they are the integers found in each iteration of the FRACTRAN algorithm.

Author(s)

Carl Witthoft <[e-mail]

References

https://esolangs.org/wiki/Fractran https://oeis.org/wiki/List_of_FRACTRAN_programs_to_compute_core_sequences

See Also

fracMake

Examples

# addition:  { 3/2   } .  enter 2^a*3^b and get 3^(a+b) answer when terminated
addit <- fracDo(2^5*3^8,nums = 3, denoms = 2)
# Last value returned is what we want. But can't take log(bigq) 
log(numerator(addit[length(addit)]),3)