exams.forge (version 1.0.10)

divisor_25: Number Properties

Description

• is_terminal checks whether x's can be expressed as a terminal fraction, basically divisor_25(denominator(x))

• divisor_25 checks whether all x's can be expressed as \(2^x 5^y\)

• prime_numbers returns all prime numbers up to a limit

• primes prime factorization of x, returns a matrix with the power of each prime number

• has_digits checks whether the x's have only digits after the decimal point, basically abs(x-round(x, digits))<tol

• all_integer checks whether all x's are integer, basically all(has_digits(x,0))

Usage

divisor_25(x)
denominator_25(x)
is_terminal(x)
round_25(x)
prime_numbers(n, sieve = FALSE)
primes(x, min = 2)
has_digits(
  x,
  digits = 2,
  tol = 10^{
     -digits - 6
 }
)
all_integer(x)
only_digits(
  x,
  digits = 2,
  tol = 10^{
     -digits - 6
 }
)
is_term(x)
denom_25(x)

Value

logical

Arguments

x

numeric: values to test/check

n

integer: find all prime numbers up to n

sieve

logical: should in any case the Sieve of Eratosthenes be used to compute prime numbers (default: FALSE)

min

integer: the minimum prime number used (default: 2)

digits

numeric: number of digits to check (default: 2)

tol

numeric: max. deviation from the rounded x (default: 1e-6)

Examples

is_terminal(2/3)   # 0.6666... non-terminal
is_terminal(1/5)   # 0.2       terminal
divisor_25(1:25)
prime_numbers(100) # all prime numbers less equal 100
primes(1:20)       # prime factorization of 1 to twenty