First - I love the library. There's so much functionality that it's going to take quite some time to explore it all
I'd love to see an `in-primes<http://pre.racket-lang.org/docs/html/math/number-theory.html>` function added to math/number-theory<http://pre.racket-lang.org/docs/html/math/number-theory.html>. Currently, I've come up with 3 easy ways of generating a sequence of primes all with varying degrees of performance. ;;method 1 - Bad performance, but I could see someone trying to define (sequence-map nth-prime (in-naturals)) ;;method 2 - Good performance, but still seems wasteful (sequence-filter prime? (in-naturals)) ;;method 3 - Good performance, but clunky to have to define yourself (define (in-primes [start 2]) (make-do-sequence (thunk (values values next-prime (next-prime (- start 1)) #f #f #f)))) Using a pseudo prime test (eg. Fermat, Miller-Rabin, etc.) however is not ideal when trying to enumerate a large swath of prime numbers starting at 2. Here's an example program that tries to sum all the primes under a million (time (for/sum ([i (in-primes)] #:break (<= 1000000 i)) i)) Which takes ~27 seconds on my machine using the current version of prime? Using a trial-division version like (define (prime2 n) (case n [(-2 2) #t] [(-1 1) #f] [else (and (odd? n) (for/and ([trial-divisor (in-range 3 (+ 1 (integer-sqrt n)) 2)]) (positive? (remainder n trial-divisor))))])) and redefining next-prime to use that, trims the time it takes to sum down to 0.25 seconds. It seems there are two typical use cases for dealing with primes. The first is dealing with big primes for the use of cryto etc. where you're typically interested in only 1 prime number at a time. This is where it makes sense to have these complicated primality tests with a low Big-O, and higher coefficient. The other use case is dealing with many smaller primes, where having a sieve or trial division makes more sense. Again, awesome library Marty On Sun, Dec 9, 2012 at 3:52 AM, Jens Axel Søgaard <jensa...@soegaard.net>wrote: > 2012/12/8 Danny Yoo <d...@hashcollision.org>: > >> Or maybe using a : or something to separate rows for 2D arrays? > >> (array 1 2 : 3 4) > > The matrix library uses arrays to represent the matrices. > An 2x3 matrix can be constructed as: > > (matrix/dim 2 3 > 1 2 3 > 4 5 6) > > (list->matrix '[[1 2 3] [4 5 6]]) > > (for/matrix: : Number 2 3 ([i (in-naturals)]) i) > > These expressions will all return the same 2D array. > > Given that the shape of a matrix is fixed, the problems > with square parentheses in constructor notation disappear. > That is, one could let matrix be a macro, and it could > accept both kinds of parentheses: > > (matrix [[1 2 3] [4 5 6]]) > (matrix ((1 2 3) (4 5 6))) > > See more matrix examples here: > > https://github.com/plt/racket/blob/master/collects/math/tests/matrix-tests.rkt > > -- > Jens Axel Søgaard > > ____________________ > Racket Users list: > http://lists.racket-lang.org/users >
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