Get the Prime Factorization.

Source: R/factorization.R

Get the Prime Factorization for a number with a particular coding.

ReducePrime(code, out.summary = FALSE, primes.div = NULL)

Arguments

code

A vector representing a number. See details.
out.summary

Is the result to be summarized? For example, (2, 3, 0, 0, 1) can be summarized as 2, 5; 3, 1. Default is FALSE.
primes.div

The vector of all prime numbers up to sqrt(length(code)). Default get them for you.

Value

Two rows representing prime numbers

Details

A code is the coding of a number as follows, $$number = \prod i^{code[i]},$$ or, which is equivalent, $$\log(number) = \sum code[i] * \log(i).$$ For example,

  • 5 is coded as (0, 0, 0, 0, 1),

  • 5! is coded as (1, 1, 1, 1, 1),

  • 8! is coded as (1, 1, 1, 1, 1, 1, 1, 1),

  • 8! / 5! is therefore coded as (0, 0, 0, 0, 0, 1, 1, 1),

  • 5! = 5 * 3 * 2^3 can be reduced to (0, 3, 1, 0, 1).

Note that the first element of a code has no effect.

Examples

code100 <- c(rep(0, 99), 1)
ReducePrime(c(rep(0, 99), 1), out.summary = TRUE)
#>        [,1] [,2]
#> primes    2    5
#> power     2    2
primes.div <- AllPrimesUpTo(floor(sqrt(length(code100))))
ReducePrime(c(rep(0, 99), 1), primes.div = primes.div)
#>   [1] 0 2 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
#>  [38] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
#>  [75] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0