| Encoding: | UTF-8 |
| Type: | Package |
| Title: | Use Prime Factorization for Computations |
| Version: | 0.1.1 |
| Date: | 2018-05-17 |
| Description: | Use Prime Factorization for simplifying computations, for instance for ratios of large factorials. |
| License: | GPL-3 |
| LazyData: | TRUE |
| Depends: | R (≥ 3.2.3) |
| RoxygenNote: | 6.0.1 |
| Suggests: | testthat, covr |
| URL: | https://github.com/privefl/primefactr |
| BugReports: | https://github.com/privefl/primefactr/issues |
| NeedsCompilation: | no |
| Packaged: | 2018-05-19 09:04:50 UTC; privef |
| Author: | Florian Privé [aut, cre] |
| Maintainer: | Florian Privé <florian.prive.21@gmail.com> |
| Repository: | CRAN |
| Date/Publication: | 2018-05-19 09:19:16 UTC |
R package that uses Prime Factorization for computations.
Description
TODO
Arguments
n |
A positive integer. |
Get all prime numbers.
Description
Get all prime numbers up to n.
Usage
AllPrimesUpTo(n)
Arguments
n |
A positive integer. |
Value
A integer vector of all prime numbers up to n.
Examples
AllPrimesUpTo(10)
AllPrimesUpTo(100)
AllPrimesUpTo(1e6)
Compute the ratio of factorials.
Description
Compute the ratio of factorials
using Prime Factorization.
For example, ComputeDivFact(c(a, b), c(d, e, f)) computes
\frac{a! b!}{d! e! f!}.
Usage
ComputeDivFact(num, deno = NULL, out.log = FALSE)
Arguments
num |
The vector of all numbers which have their factorials in the numerator. |
deno |
The vector of all numbers which have their factorials
in the denominator. Default is |
out.log |
Is the logarithm of the result returned instead?
Default is |
Value
The result of the ratio or its logarithm
if out.log = TRUE.
See Also
choose
Examples
choose(100, 20)
ComputeDivFact(100, c(20, 80))
lchoose(100, 20)
ComputeDivFact(100, c(20, 80), out.log = TRUE)
factorial(100)
ComputeDivFact(100)
lfactorial(100)
ComputeDivFact(100, out.log = TRUE)
Is a prime number?
Description
Is n a prime number? You can see what is a prime number there.
Usage
IsPrime(n)
Arguments
n |
A positive integer. |
Value
A boolean.
Examples
IsPrime(1) # FALSE
IsPrime(5) # TRUE
IsPrime(59999999) # TRUE
Get the Prime Factorization.
Description
Get the Prime Factorization for a number with a particular coding.
Usage
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 |
primes.div |
The vector of all prime numbers
up to |
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.
Value
Two rows representing prime numbers
Examples
code100 <- c(rep(0, 99), 1)
ReducePrime(c(rep(0, 99), 1), out.summary = TRUE)
primes.div <- AllPrimesUpTo(floor(sqrt(length(code100))))
ReducePrime(c(rep(0, 99), 1), primes.div = primes.div)