June 2018 Update
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5278 changed files with 84726 additions and 14379 deletions
56
Task/AKS-test-for-primes/8th/aks-test-for-primes.8th
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56
Task/AKS-test-for-primes/8th/aks-test-for-primes.8th
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@ -0,0 +1,56 @@
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with: a
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: nextrow \ a -- a
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len
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[ ( drop [1] ),
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( drop [1,1] ),
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( ' n:+ y 1 slide 1 push ) ]
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swap 2 min caseof ;
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;with
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with: n
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: .x \ n --
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dup
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[ ( drop ),
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( drop "x" . ),
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( "x^" . . ) ]
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swap 2 min caseof space ;
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: .term \ coef exp -- ; omit coef for 1x^n when n > 0
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over 1 = over 0 > and if nip .x else swap . .x then ;
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: .sgn \ +/-1 --
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[ "-", null, "+" ]
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swap 1+ caseof . space ;
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: .lhs \ n --
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"(x-1)^" . . ;
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: .rhs \ a -- a
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a:len 1- >r
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1 swap ( third .sgn r@ rot - .term -1 * ) a:each
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nip rdrop ;
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: .eqn \ a -- a
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a:len 1- .lhs " = " . .rhs ;
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: .binomials \ --
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[] ( nextrow .eqn cr ) 8 times drop ;
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: primerow? \ a -- a ?
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a:len 3 < if false ;then
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1 a:@ >r \ 2nd position is the number to check for primality
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true swap ( nip dup 1 = swap r@ mod 0 = or and ) a:each swap
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rdrop ;
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: .primes-via-aks \ --
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[] ( nextrow primerow? if 1 a:@ . space then ) 50 times drop ;
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;with
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.binomials cr
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"The primes upto 50 are (via AKS): " . .primes-via-aks cr
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bye
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82
Task/AKS-test-for-primes/Elena/aks-test-for-primes.elena
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82
Task/AKS-test-for-primes/Elena/aks-test-for-primes.elena
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@ -0,0 +1,82 @@
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import extensions.
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singleton AksTest
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{
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static Array<long> c := V<long>(100).
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coef(int n)
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[
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int i := 0.
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int j := 0.
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if ((n < 0) || (n > 63)) [ AbortException new; raise ]. // gracefully deal with range issue
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c[i] := 1l.
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while(i < n)
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[
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j := i.
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c[1 + j] := 1l.
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while (j > 0)
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[
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c[j] := c[j - 1] - c[j].
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j -= 1
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].
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c[0] := c[0] negative.
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i += 1
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].
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var t := c.
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]
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bool is_prime(int n)
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[
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int i := n.
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self coef(n).
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(c[0]) += 1.
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(c[i]) -= 1.
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i -= 1.
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while ((i + 1 != 0) && (c[i+1] mod(n) == 0))
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[
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i -= 1
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].
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^ i < 0
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]
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show(int n)
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[
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int i := n.
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i += 1.
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while(i != 0)
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[
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i -= 1.
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console print("+",c[i],"x^",i).
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]
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]
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}
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public program =
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[
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0 till:10 do(:n)<int>
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[
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AksTest coef(n).
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console print("(x-1)^",n," = ").
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AksTest show(n).
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console printLine.
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].
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console print("Primes:").
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1 to(63) do(:n)<int>
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[
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if (AksTest is_prime(n))
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[
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console print(n," ").
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]
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].
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console printLine; readLine
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].
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@ -1,13 +1,20 @@
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: nextCoef(prev)
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| i |
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ListBuffer new dup add(0)
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prev size 1- loop: i [ dup add(prev at(i) prev at(i 1+) - ) ]
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dup add(0) ;
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import: mapping
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: coefs(n) [ 0, 1, 0 ] #nextCoef times(n) extract(2, n 2 + ) ;
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: isPrime(n) coefs(n) extract(2, n) conform(#[n mod 0 == ]) ;
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: nextCoef( prev -- [] )
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| i |
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Array new 0 over dup
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prev size 1- loop: i [ prev at(i) prev at(i 1+) - over add ]
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0 over add
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;
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: coefs( n -- [] )
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[ 0, 1, 0 ] #nextCoef times(n) extract(2, n 2 + ) ;
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: prime?( n -- b)
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coefs( n ) extract(2, n) conform?( #[n mod 0 == ] ) ;
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: aks
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| i |
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0 10 for: i [ System.Out "(x-1)^" << i << " = " << coefs(i) << cr ]
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50 seq filter(#isPrime) apply(#[ print " " print ]) printcr ;
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0 10 for: i [ System.Out "(x-1)^" << i << " = " << coefs( i ) << cr ]
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50 seq filter( #prime? ) apply(#.) printcr
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;
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31
Task/AKS-test-for-primes/Perl-6/aks-test-for-primes.pl6
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31
Task/AKS-test-for-primes/Perl-6/aks-test-for-primes.pl6
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constant expansions = [1], [1,-1], -> @prior { [|@prior,0 Z- 0,|@prior] } ... *;
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sub polyprime($p where 2..*) { so expansions[$p].[1 ..^ */2].all %% $p }
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# Showing the expansions:
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say ' p: (x-1)ᵖ';
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say '-----------';
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sub super ($n) {
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$n.trans: '0123456789'
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=> '⁰¹²³⁴⁵⁶⁷⁸⁹';
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}
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for ^13 -> $d {
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say $d.fmt('%2i: '), (
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expansions[$d].kv.map: -> $i, $n {
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my $p = $d - $i;
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[~] gather {
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take < + - >[$n < 0] ~ ' ' unless $p == $d;
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take $n.abs unless $p == $d > 0;
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take 'x' if $p > 0;
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take super $p - $i if $p > 1;
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}
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}
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)
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}
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# And testing the function:
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print "\nPrimes up to 100:\n { grep &polyprime, 2..100 }\n";
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9
Task/AKS-test-for-primes/R/aks-test-for-primes.r
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9
Task/AKS-test-for-primes/R/aks-test-for-primes.r
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@ -0,0 +1,9 @@
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AKS<-function(p){
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i<-2:p-1
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l<-unique(factorial(p) / (factorial(p-i) * factorial(i)))
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if(all(l%%p==0)){
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print(noquote("It is prime."))
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}else{
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print(noquote("It isn't prime."))
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}
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}
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@ -1,41 +1,42 @@
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/*REXX program calculates primes via the Agrawal─Kayal─Saxena (AKS) primality test.*/
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parse arg Z .; if Z=='' then Z=200 /*Z not specified? Then use default.*/
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OZ=Z; tell= Z<0; Z=abs(Z) /*Is Z negative? Then show expression.*/
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numeric digits max(9, Z%3) /*define a dynamic # of decimal digits.*/
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$.0='-'; $.1="+"; @.=1 /*$.x: sign char; default coefficients.*/
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#= /*define list of prime numbers (so far)*/
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do p=3 for Z; pm=p-1; pp=p+1 /*PM & PP: used as a coding convenience*/
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do m=2 for pp%2-1; mm=m-1 /*calculate coefficients for a power. */
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@.p.m=@.pm.mm + @.pm.m; h=pp-m /*calculate left side of coefficients*/
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@.p.h=@.p.m /* " right " " " */
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end /*m*/ /* [↑] The M DO loop creates both */
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end /*p*/ /* sides in the same loop, saving */
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/* a bunch of execution time. */
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if tell then say '(x-1)^0: 1' /*possibly display the first expression*/
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/* [↓] test for primality by division.*/
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do n=2 for Z; nh=n%2; d=n-1 /*create expressions; find the primes.*/
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do k=3 to nh while @.n.k//d==0 /*are coefficients divisible by N-1 ? */
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end /*k*/ /* [↑] skip the 1st & 2nd coefficients*/
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/* [↓] multiple THEN─IF faster than &s*/
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if k>nh then if d\==1 then if d\==4 then #=# d /*add a number to prime list.*/
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if \tell then iterate /*Don't tell? Don't show expressions.*/
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y='(x-1)^'d": " /*define the 1st part of the expression*/
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s=1 /*S: is the sign indicator (-1│+1).*/
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do j=n for n-1 by -1; jm=j-1 /*create the higher powers first. */
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if j==2 then xp='x' /*if power=1, then don't show the power*/
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else xp='x^'jm /* ··· else show power with ^ */
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if j==n then y=y xp /*no sign (+│-) for the 1st expression.*/
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else y=y $.s || @.n.j'∙'xp /*build the expression with sign (+|-).*/
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s=\s /*flip the sign for the next expression*/
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end /*j*/ /* [↑] the sign (now) is either 0 │ 1,*/
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/* and is displayed either - │ + */
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say y $.s || 1 /*just show the first N expressions, */
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end /*n*/ /* [↑] ··· but only for negative Z. */
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say /* [↓] Has Z a leading + ? Then show.*/
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if Z==word(. #, words(#)+1) then is= 'is' /*the number is a prime. */
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else is= "isn't" /* " " isn't " " */
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if left(OZ, 1)=='+' then say Z is 'prime.' /*display if OZ has a + (plus sign).*/
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else say 'primes:' # /*display the prime number list. */
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say /* [↓] the digit length of a big coef.*/
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say 'Found ' words(#) " primes and the largest coefficient has " length(@.pm.h),
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" decimal digits." /*stick a fork in it, we're all done. */
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parse arg Z .; if Z=='' | Z=="," then Z=200 /*Z not specified? Then use default.*/
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OZ=Z; tell= Z<0; Z=abs(Z) /*Is Z negative? Then show expression.*/
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numeric digits max(9, Z % 3) /*define a dynamic # of decimal digits.*/
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call AKS /*invoke the AKS funtion for coef. bld.*/
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if left(OZ,1)=='+' then do; say Z isAksp(); exit /*display if Z is or isn't a prime.*/
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end /* [↑] call isAKSp if Z has leading +.*/
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say; say "primes found:" # /*display the prime number list. */
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say; if \datatype(#, 'W') then exit /* [↓] the digit length of a big coef.*/
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say 'Found ' words(#) " primes and the largest coefficient has " length(@.pm.h) @dd
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exit /*stick a fork in it, we're all done. */
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/*──────────────────────────────────────────────────────────────────────────────────────*/
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isAKSp: if z==word(#,words(#)) then return ' is a prime.'; else return " isn't a prime."
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/*──────────────────────────────────────────────────────────────────────────────────────*/
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AKS: $.0= '-'; $.1= "+"; @.=1 /*$.x: sign char; default coefficients.*/
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q.=1; q.1=0; q.4=0 /*sparse array for faster comparisons. */
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#=; L= length(Z) /*define list of prime numbers (so far)*/
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do p=3 for Z; pm=p - 1; pp=p + 1 /*PM & PP: used as a coding convenience*/
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do m=2 for pp % 2 - 1; mm=m - 1 /*calculate coefficients for a power. */
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@.p.m= @.pm.mm + @.pm.m; h=pp - m /*calculate left side of coefficients*/
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@.p.h= @.p.m /* " right " " " */
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end /*m*/ /* [↑] The M DO loop creates both */
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end /*p*/ /* sides in the same loop. */
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if tell then say '(x-1)^'right(0, L)": 1" /*possibly display the first expression*/
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@dd= 'decimal digits.' /* [↓] test for primality by division.*/
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do n=2 for Z; nh=n % 2; d=n - 1 /*create expressions; find the primes.*/
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do k=3 to nh while @.n.k//d==0 /*are coefficients divisible by N-1 ? */
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end /*k*/ /* [↑] skip the 1st & 2nd coefficients*/
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if k>nh then if q.d then #=# d /*add a number to the prime list. */
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if \tell then iterate /*Don't tell? Don't show expressions.*/
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y='(x-1)^'right(d, L)": " /*define the 1st part of the expression*/
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s=1 /*S: is the sign indicator (-1│+1).*/
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do j=n for n-1 by -1 /*create the higher powers first. */
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if j==2 then xp= 'x' /*if power=1, then don't show the power*/
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else xp= 'x^' || (j-1) /* ··· else show power with ^ */
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if j==n then y=y xp /*no sign (+│-) for the 1st expression.*/
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else y=y $.s || @.n.j'∙'xp /*build the expression with sign (+|-).*/
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s= \s /*flip the sign for the next expression*/
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end /*j*/ /* [↑] the sign (now) is either 0 │ 1,*/
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say y $.s'1' /*just show the first N expressions, */
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end /*n*/ /* [↑] ··· but only for negative Z. */
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if #=='' then #='none'; return # /*if null, return "none"; else return #*/
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