Vocabulary/qco
>> << Down to: Dyad Back to: Vocabulary Thru to: Dictionary
q: y Prime Factors
Rank Infinity -- operates on x and y as a whole -- WHY IS THIS IMPORTANT?
The prime factorization of integer y, listed in ascending order.
The same as (3 p: y). See Primes (p:).
q: 2^31 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 q: 1+ 2^31 3 715827883 q: 2+ 2^31 2 5 5 13 41 61 1321
Common uses
Mathematical investigations.
Related Primitives
Primes (p:)
x q: y Prime Exponents
Rank 0 0 -- operates on individual atoms of x and y, producing a result that may require fill -- WHY IS THIS IMPORTANT?
Selected primes and their exponents in the factorization of y.
An exponent of 0 means that the corresponding prime is not a factor of y.
p: i.10 NB. the first 10 primes 2 3 5 7 11 13 17 19 23 29 q: 700 NB. prime factors of 700 2 2 5 5 7 _ q: 700 NB. 700 = (2^2) * (3^0) * (5^2) * (7^1) 2 0 2 1 __ q: 700 2 5 7 2 2 1
The rank of the result, and the values listed, depend on x.
x Result
Rank
Meaning of Results Number of Primes Zero exponents included? positive 1 The leading exponents of the prime factorization (keeping primes in ascending order) x (x=_ means "up through the last nonzero exponent") yes negative 2 Second row: The trailing exponents of the prime factorization (keeping primes in ascending order) |x (x=__ means "all nonzero exponents") no First row: the corresponding primes
Common uses
1. Calculate the number of divisors of a number
*/ >: _ q: 17 2 */ >: _ q: 60 12
More Information
1. When x is negative:
- the table t =. primes,:exponents is calculated, including primes with 0 exponents, ending with the largest prime with a nonzero exponent;
- The last (|x)<.({:$t) columns of t are selected (i. e. the last |x columns, but no more columns than exist in t);
- Columns with 0 exponents are then deleted.
Because the zero exponents are deleted at the last step, the result of x q: y is not the same as that of x {. __ q: y .
_3 q: 2*3*5*17 17 1
2. __ q: y is equivalent to 2 p: y .
Related Primitives
Primes (p:)
Details
1. The result has integer or extended-integer precision, depending on the size of the largest prime factor.