Package 'primefactr'

R package that uses Prime Factorization for computations.

Description

TODO

Arguments

n	A positive integer.

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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)

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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 NULL, there is only a numerator.
out.log	Is the logarithm of the result returned instead? Default is FALSE.

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)

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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

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

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)

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