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Jacobi symbol (view source)

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{{task}}
The '''[https://en.wikipedia.org/wiki/Jacobi_symbol Jacobi symbol]''' is a multiplicative function that generalizes the Legendre symbol. Specifically, the Jacobi symbol (a | n) equals the product of the Legendre symbols (a | p_i)^(k_i), where n = p_1^(k_1)*p_2^(k_2)*...*p_i^(k_i) and the Legendre symbol (a | p) denotes the value of a ^ ((p-1)/2) (mod p)
* (a | p) ≡   1     if a is a square (mod p)
* (a | p) ≡ -1     if a is not a square (mod p)
Line 12:
;Reference:
* [https://en.wikipedia.org/wiki/Jacobi_symbol Wikipedia article on Jacobi symbol].
 
=={{header|11l}}==
{{trans|Python}}
 
<syntaxhighlight lang="11l">F jacobi(=a, =n)
I n <= 0
X.throw ValueError(‘'n' must be a positive integer.’)
I n % 2 == 0
X.throw ValueError(‘'n' must be odd.’)
a %= n
V result = 1
L a != 0
L a % 2 == 0
a /= 2
V n_mod_8 = n % 8
I n_mod_8 C (3, 5)
result = -result
(a, n) = (n, a)
I a % 4 == 3 & n % 4 == 3
result = -result
a %= n
I n == 1
R result
E
R 0
 
print(‘n\k|’, end' ‘’)
V kmax = 20
L(k) 0..kmax
print(‘#3’.format(k), end' ‘’)
print("\n----", end' ‘’)
L(k) 0..kmax
print(end' ‘---’)
print()
L(n) (1..21).step(2)
print(‘#<2 |’.format(n), end' ‘’)
L(k) 0..kmax
print(‘#3’.format(jacobi(k, n)), end' ‘’)
print()</syntaxhighlight>
 
{{out}}
<pre>
n\k| 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
-------------------------------------------------------------------
1 | 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
3 | 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1
5 | 0 1 -1 -1 1 0 1 -1 -1 1 0 1 -1 -1 1 0 1 -1 -1 1 0
7 | 0 1 1 -1 1 -1 -1 0 1 1 -1 1 -1 -1 0 1 1 -1 1 -1 -1
9 | 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1
11 | 0 1 -1 1 1 1 -1 -1 -1 1 -1 0 1 -1 1 1 1 -1 -1 -1 1
13 | 0 1 -1 1 1 -1 -1 -1 -1 1 1 -1 1 0 1 -1 1 1 -1 -1 -1
15 | 0 1 1 0 1 0 0 -1 1 0 0 -1 0 -1 -1 0 1 1 0 1 0
17 | 0 1 1 -1 1 -1 -1 -1 1 1 -1 -1 -1 1 -1 1 1 0 1 1 -1
19 | 0 1 -1 -1 1 1 1 1 -1 1 -1 1 -1 -1 -1 -1 1 1 -1 0 1
21 | 0 1 -1 0 1 1 0 0 -1 0 -1 -1 0 -1 0 0 1 1 0 -1 1
</pre>
 
=={{header|Action!}}==
{{libheader|Action! Tool Kit}}
<syntaxhighlight lang="action!">INCLUDE "D2:PRINTF.ACT" ;from the Action! Tool Kit
 
INT FUNC Jacobi(INT a,n)
INT res,tmp
 
IF a>=n THEN
a=a MOD n
FI
res=1
WHILE a
DO
WHILE (a&1)=0
DO
a=a RSH 1
tmp=n&7
IF tmp=3 OR tmp=5 THEN
res=-res
FI
OD
tmp=a a=n n=tmp
IF (a%3)=3 AND (n%3)=3 THEN
res=-res
FI
a=a MOD n
OD
 
IF n=1 THEN
RETURN (res)
FI
RETURN (0)
 
PROC PrintTable(INT maxK,maxN)
INT res,n,k
CHAR ARRAY t(10)
 
Put('n) Put(7) Put('k) Put(124)
FOR k=0 TO maxK
DO
StrI(k,t) PrintF("%3S",t)
OD
PutE()
 
Put(18) Put(18) Put(18) Put(19)
FOR k=0 TO 3*maxK+2
DO
Put(18)
OD
PutE()
 
FOR n=1 TO maxN STEP 2
DO
StrI(n,t) PrintF("%3S",t)
Put(124)
FOR k=0 TO maxK
DO
res=Jacobi(k,n)
StrI(res,t) PrintF("%3S",t)
OD
PutE()
OD
RETURN
 
PROC Main()
Put(125) PutE() ;clear the screen
PrintTable(10,39)
RETURN</syntaxhighlight>
{{out}}
[https://gitlab.com/amarok8bit/action-rosetta-code/-/raw/master/images/Jacobi_symbol.png Screenshot from Atari 8-bit computer]
<pre>
n\k│ 0 1 2 3 4 5 6 7 8 9 10
───┼─────────────────────────────────
1│ 1 1 1 1 1 1 1 1 1 1 1
3│ 0 -1 1 0 -1 1 0 -1 1 0 -1
5│ 0 1 -1 1 1 0 1 -1 1 1 0
7│ 0 1 1 -1 1 -1 -1 0 1 1 -1
9│ 0 1 1 0 1 1 0 1 1 0 1
11│ 0 1 -1 1 1 1 -1 1 -1 1 -1
13│ 0 1 -1 -1 1 1 1 -1 -1 1 -1
15│ 0 1 1 0 1 0 0 1 1 0 0
17│ 0 1 1 1 1 -1 1 -1 1 1 -1
19│ 0 1 -1 -1 1 1 1 -1 -1 1 -1
21│ 0 1 -1 0 1 1 0 0 -1 0 -1
23│ 0 1 1 1 1 1 1 1 1 1 1
25│ 0 1 1 -1 1 0 -1 1 1 1 0
27│ 0 1 -1 0 1 -1 0 -1 -1 0 1
29│ 0 1 -1 1 1 1 -1 1 -1 1 -1
31│ 0 1 1 -1 1 1 -1 -1 1 1 1
33│ 0 1 1 0 1 1 0 -1 1 0 1
35│ 0 1 -1 1 1 0 -1 0 -1 1 0
37│ 0 1 -1 -1 1 -1 1 1 -1 1 1
39│ 0 1 1 0 1 1 0 1 1 0 1
</pre>
 
=={{header|ALGOL 68}}==
{{Trans|Wren}}
<syntaxhighlight lang="algol68">
BEGIN # Jacobi symbol - translation of the Wren sample #
 
PROC jacobi = ( INT a in, n in )INT:
IF n in <= 0 OR NOT ODD n in THEN
print( ( "The 'n' parameter of jacobi must be an odd positive integer.", newline ) );
stop
ELSE
INT a := a in MOD n in, n := n in;
INT result := 1;
WHILE a /= 0 DO
WHILE NOT ODD a DO
a OVERAB 2;
INT nm8 = n MOD 8;
IF nm8 = 3 OR nm8 = 5 THEN result := - result FI
OD;
INT t = a;
a := n;
n := t;
IF a MOD 4 = 3 AND n MOD 4 = 3 THEN result := - result FI;
a MODAB n
OD;
IF n = 1 THEN result ELSE 0 FI
FI # jacobi # ;
 
print( ( "Table of jacobi(a, n):", newline ) );
print( ( "n/a 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15", newline ) );
print( ( "---------------------------------------------------------------", newline ) );
FOR n BY 2 TO 29 DO
print( ( whole( n, -3 ) ) );
FOR a TO 15 DO print( ( whole( jacobi( a, n ), -4 ) ) ) OD;
print( ( newline ) )
OD
 
END
</syntaxhighlight>
{{out}}
<pre>
Table of jacobi(a, n):
n/a 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
---------------------------------------------------------------
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
3 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0
5 1 -1 -1 1 0 1 -1 -1 1 0 1 -1 -1 1 0
7 1 1 -1 1 -1 -1 0 1 1 -1 1 -1 -1 0 1
9 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0
11 1 -1 1 1 1 -1 -1 -1 1 -1 0 1 -1 1 1
13 1 -1 1 1 -1 -1 -1 -1 1 1 -1 1 0 1 -1
15 1 1 0 1 0 0 -1 1 0 0 -1 0 -1 -1 0
17 1 1 -1 1 -1 -1 -1 1 1 -1 -1 -1 1 -1 1
19 1 -1 -1 1 1 1 1 -1 1 -1 1 -1 -1 -1 -1
21 1 -1 0 1 1 0 0 -1 0 -1 -1 0 -1 0 0
23 1 1 1 1 -1 1 -1 1 1 -1 -1 1 1 -1 -1
25 1 1 1 1 0 1 1 1 1 0 1 1 1 1 0
27 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0
29 1 -1 -1 1 1 1 1 -1 1 -1 -1 -1 1 -1 -1
</pre>
 
=={{header|ALGOL W}}==
{{Trans|Wren}}
<syntaxhighlight lang="algolw">
begin % Jacobi symbol %
 
integer procedure jacobi( integer value aIn, nIn ) ;
if nIn <= 0 or not odd( nIn ) then begin
write( "The 'n' parameter of jacobi must be an odd positive integer." );
0
end
else begin
integer a, n, js;
a := aIn rem nIn; n := nIn; js := 1;
while a not = 0 do begin
while a rem 2 = 0 do begin
integer nm8;
a := a div 2;
nm8 := n rem 8;
if nm8 = 3 or nm8 = 5 then js := - js;
end while_a_rem_2_eq_0 ;
begin integer t; t := a; a := n; n := t end;
if a rem 4 = 3 and n rem 4 = 3 then js := - js;
a := a rem n
end;
if n = 1 then js else 0
end jacobi ;
 
write( "Table of jacobi(a, n):" );;
write( "n/a 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15" );
write( "---------------------------------------------------------------" );
for n := 1 step 2 until 29 do begin
write( i_w := 3, s_w := 0, n );
for a := 1 until 15 do writeon( i_w := 4, s_w := 0, jacobi( a, n ) );
end
 
end.
</syntaxhighlight>
{{out}}
<pre>
Table of jacobi(a, n):
n/a 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
---------------------------------------------------------------
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
3 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0
5 1 -1 -1 1 0 1 -1 -1 1 0 1 -1 -1 1 0
7 1 1 -1 1 -1 -1 0 1 1 -1 1 -1 -1 0 1
9 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0
11 1 -1 1 1 1 -1 -1 -1 1 -1 0 1 -1 1 1
13 1 -1 1 1 -1 -1 -1 -1 1 1 -1 1 0 1 -1
15 1 1 0 1 0 0 -1 1 0 0 -1 0 -1 -1 0
17 1 1 -1 1 -1 -1 -1 1 1 -1 -1 -1 1 -1 1
19 1 -1 -1 1 1 1 1 -1 1 -1 1 -1 -1 -1 -1
21 1 -1 0 1 1 0 0 -1 0 -1 -1 0 -1 0 0
23 1 1 1 1 -1 1 -1 1 1 -1 -1 1 1 -1 -1
25 1 1 1 1 0 1 1 1 1 0 1 1 1 1 0
27 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0
29 1 -1 -1 1 1 1 1 -1 1 -1 -1 -1 1 -1 -1
</pre>
 
=={{header|Arturo}}==
{{trans|Nim}}
<syntaxhighlight lang="rebol">jacobi: function [n,k][
N: n % k
K: k
 
result: 1
while [N <> 0][
while [even? N][
N: shr N 1
if contains? [3 5] and K 7 ->
result: neg result
]
[N,K]: @[K,N]
if and? 3=and N 3 3=and K 3 ->
result: neg result
N: N % K
]
if K <> 1 ->
result: 0
 
return result
]
 
print ["" "k/n" "|"] ++ map to [:string] 1..20 'item -> pad.left item 2
print repeat "=" 67
loop range.step:2 1 21 'k [
print [
"" pad to :string k 3 "|" join.with:" " map to [:string] map 1..20 'n -> jacobi n k
'item -> pad.left item 2
]
]</syntaxhighlight>
 
{{out}}
 
<pre> k/n | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
===================================================================
1 | 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
3 | 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1
5 | 1 -1 -1 1 0 1 -1 -1 1 0 1 -1 -1 1 0 1 -1 -1 1 0
7 | 1 1 -1 1 -1 -1 0 1 1 -1 1 -1 -1 0 1 1 -1 1 -1 -1
9 | 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1
11 | 1 -1 1 1 1 -1 -1 -1 1 -1 0 1 -1 1 1 1 -1 -1 -1 1
13 | 1 -1 1 1 -1 -1 -1 -1 1 1 -1 1 0 1 -1 1 1 -1 -1 -1
15 | 1 1 0 1 0 0 -1 1 0 0 -1 0 -1 -1 0 1 1 0 1 0
17 | 1 1 -1 1 -1 -1 -1 1 1 -1 -1 -1 1 -1 1 1 0 1 1 -1
19 | 1 -1 -1 1 1 1 1 -1 1 -1 1 -1 -1 -1 -1 1 1 -1 0 1
21 | 1 -1 0 1 1 0 0 -1 0 -1 -1 0 -1 0 0 1 1 0 -1 1
</pre>
 
=={{header|AutoHotkey}}==
<syntaxhighlight lang="autohotkey">result := "n/k|"
loop 20
result .= SubStr(" " A_Index, -1) " "
l := StrLen(result)
result .= "`n"
loop % l
result .= "-"
result .= "`n"
 
loop 21
{
if !Mod(n := A_Index, 2)
continue
result .= SubStr(" " n, -1) " |"
loop 20
result .= SubStr(" " jacobi(a := A_Index, n), -1) " "
result .= "`n"
}
MsgBox, 262144, , % result
return
 
jacobi(a, n) {
a := Mod(a, n), t := 1
while (a != 0) {
while !Mod(a, 2)
a := a >> 1, r := Mod(n, 8), t := (r=3 || r=5) ? -t : t
r := n, n := a, a := r
if (Mod(a, 4)=3 && Mod(n, 4)=3)
t := -t
a := Mod(a, n)
}
return (n=1) ? t : 0
}</syntaxhighlight>
{{out}}
<pre>n/k| 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
----------------------------------------------------------------
1 | 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
3 | 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1
5 | 1 -1 -1 1 0 1 -1 -1 1 0 1 -1 -1 1 0 1 -1 -1 1 0
7 | 1 1 -1 1 -1 -1 0 1 1 -1 1 -1 -1 0 1 1 -1 1 -1 -1
9 | 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1
11 | 1 -1 1 1 1 -1 -1 -1 1 -1 0 1 -1 1 1 1 -1 -1 -1 1
13 | 1 -1 1 1 -1 -1 -1 -1 1 1 -1 1 0 1 -1 1 1 -1 -1 -1
15 | 1 1 0 1 0 0 -1 1 0 0 -1 0 -1 -1 0 1 1 0 1 0
17 | 1 1 -1 1 -1 -1 -1 1 1 -1 -1 -1 1 -1 1 1 0 1 1 -1
19 | 1 -1 -1 1 1 1 1 -1 1 -1 1 -1 -1 -1 -1 1 1 -1 0 1
21 | 1 -1 0 1 1 0 0 -1 0 -1 -1 0 -1 0 0 1 1 0 -1 1 </pre>
 
=={{header|AWK}}==
{{trans|Go}}
<syntaxhighlight lang="awk">
<lang AWK>
# syntax: GAWK -f JACOBI_SYMBOL.AWK
BEGIN {
Line 62 ⟶ 431:
return(0)
}
</syntaxhighlight>
</lang>
{{out}}
<pre>
Line 82 ⟶ 451:
27 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0
29 1 -1 -1 1 1 1 1 -1 1 -1 -1 -1 1 -1 -1 1 -1 -1 -1 1 -1 1 1 1 1 -1 -1 1 0 1
</pre>
 
=={{header|C}}==
<syntaxhighlight lang="c">#include <stdlib.h>
#include <stdio.h>
 
#define SWAP(a, b) (((a) ^= (b)), ((b) ^= (a)), ((a) ^= (b)))
 
int jacobi(unsigned long a, unsigned long n) {
if (a >= n) a %= n;
int result = 1;
while (a) {
while ((a & 1) == 0) {
a >>= 1;
if ((n & 7) == 3 || (n & 7) == 5) result = -result;
}
SWAP(a, n);
if ((a & 3) == 3 && (n & 3) == 3) result = -result;
a %= n;
}
if (n == 1) return result;
return 0;
}
 
void print_table(unsigned kmax, unsigned nmax) {
printf("n\\k|");
for (int k = 0; k <= kmax; ++k) printf("%'3u", k);
printf("\n----");
for (int k = 0; k <= kmax; ++k) printf("---");
putchar('\n');
for (int n = 1; n <= nmax; n += 2) {
printf("%-2u |", n);
for (int k = 0; k <= kmax; ++k)
printf("%'3d", jacobi(k, n));
putchar('\n');
}
}
 
int main() {
print_table(20, 21);
return 0;
}</syntaxhighlight>
 
{{out}}
<pre>
n\k| 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
---+---------------------------------------------------------------
1 | 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
3 | 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1
5 | 0 1 -1 -1 1 0 1 -1 -1 1 0 1 -1 -1 1 0 1 -1 -1 1 0
7 | 0 1 1 -1 1 -1 -1 0 1 1 -1 1 -1 -1 0 1 1 -1 1 -1 -1
9 | 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1
11 | 0 1 -1 1 1 1 -1 -1 -1 1 -1 0 1 -1 1 1 1 -1 -1 -1 1
13 | 0 1 -1 1 1 -1 -1 -1 -1 1 1 -1 1 0 1 -1 1 1 -1 -1 -1
15 | 0 1 1 0 1 0 0 -1 1 0 0 -1 0 -1 -1 0 1 1 0 1 0
17 | 0 1 1 -1 1 -1 -1 -1 1 1 -1 -1 -1 1 -1 1 1 0 1 1 -1
19 | 0 1 -1 -1 1 1 1 1 -1 1 -1 1 -1 -1 -1 -1 1 1 -1 0 1
21 | 0 1 -1 0 1 1 0 0 -1 0 -1 -1 0 -1 0 0 1 1 0 -1 1
</pre>
 
 
=={{header|C++}}==
<syntaxhighlight lang="cpp">#include <algorithm>
#include <cassert>
#include <iomanip>
#include <iostream>
 
int jacobi(int n, int k) {
assert(k > 0 && k % 2 == 1);
n %= k;
int t = 1;
while (n != 0) {
while (n % 2 == 0) {
n /= 2;
int r = k % 8;
if (r == 3 || r == 5)
t = -t;
}
std::swap(n, k);
if (n % 4 == 3 && k % 4 == 3)
t = -t;
n %= k;
}
return k == 1 ? t : 0;
}
 
void print_table(std::ostream& out, int kmax, int nmax) {
out << "n\\k|";
for (int k = 0; k <= kmax; ++k)
out << ' ' << std::setw(2) << k;
out << "\n----";
for (int k = 0; k <= kmax; ++k)
out << "---";
out << '\n';
for (int n = 1; n <= nmax; n += 2) {
out << std::setw(2) << n << " |";
for (int k = 0; k <= kmax; ++k)
out << ' ' << std::setw(2) << jacobi(k, n);
out << '\n';
}
}
 
int main() {
print_table(std::cout, 20, 21);
return 0;
}</syntaxhighlight>
 
{{out}}
<pre>
n\k| 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
-------------------------------------------------------------------
1 | 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
3 | 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1
5 | 0 1 -1 -1 1 0 1 -1 -1 1 0 1 -1 -1 1 0 1 -1 -1 1 0
7 | 0 1 1 -1 1 -1 -1 0 1 1 -1 1 -1 -1 0 1 1 -1 1 -1 -1
9 | 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1
11 | 0 1 -1 1 1 1 -1 -1 -1 1 -1 0 1 -1 1 1 1 -1 -1 -1 1
13 | 0 1 -1 1 1 -1 -1 -1 -1 1 1 -1 1 0 1 -1 1 1 -1 -1 -1
15 | 0 1 1 0 1 0 0 -1 1 0 0 -1 0 -1 -1 0 1 1 0 1 0
17 | 0 1 1 -1 1 -1 -1 -1 1 1 -1 -1 -1 1 -1 1 1 0 1 1 -1
19 | 0 1 -1 -1 1 1 1 1 -1 1 -1 1 -1 -1 -1 -1 1 1 -1 0 1
21 | 0 1 -1 0 1 1 0 0 -1 0 -1 -1 0 -1 0 0 1 1 0 -1 1
</pre>
 
=={{header|Crystal}}==
{{trans|Swift}}
<langsyntaxhighlight lang="ruby">def jacobi(a, n)
raise ArgumentError.new "n must b positive and odd" if n < 1 || n.even?
res = 1
Line 107 ⟶ 598:
(0..10).each { |a| printf(" % 2d", jacobi(a, n)) }
puts
end</langsyntaxhighlight>
 
{{out}}
Line 126 ⟶ 617:
 
=={{header|Erlang}}==
<syntaxhighlight lang="erlang">
<lang Erlang>
jacobi(_, N) when N =< 0 -> 0jacobi_domain_error;
jacobi(_, N) when (N band 1) =:= 0 -> 0jacobi_domain_error; % N is even
jacobi(A, N) when A < 0 ->
J2 = ja(-A, N),
Line 154 ⟶ 645:
false -> J2
end.
</syntaxhighlight>
</lang>
 
=={{header|F_Sharp|F#}}==
<syntaxhighlight lang="fsharp">
//Jacobi Symbol. Nigel Galloway: July 14th., 2020
let J n m=let rec J n m g=match n with
0->if m=1 then g else 0
|n when n%2=0->J(n/2) m (if m%8=3 || m%8=5 then -g else g)
|n->J (m%n) n (if m%4=3 && n%4=3 then -g else g)
J (n%m) m 1
printfn "n\m 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30\n ----------------------------------------------------------------------------------------------------------------------"
[1..2..29]|>List.iter(fun m->printf "%3d" m; [1..30]|>List.iter(fun n->printf "%4d" (J n m)); printfn "")
</syntaxhighlight>
{{out}}
<pre style="font-size: 12px">
n\m 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
----------------------------------------------------------------------------------------------------------------------
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
3 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0
5 1 -1 -1 1 0 1 -1 -1 1 0 1 -1 -1 1 0 1 -1 -1 1 0 1 -1 -1 1 0 1 -1 -1 1 0
7 1 1 -1 1 -1 -1 0 1 1 -1 1 -1 -1 0 1 1 -1 1 -1 -1 0 1 1 -1 1 -1 -1 0 1 1
9 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0
11 1 -1 1 1 1 -1 -1 -1 1 -1 0 1 -1 1 1 1 -1 -1 -1 1 -1 0 1 -1 1 1 1 -1 -1 -1
13 1 -1 1 1 -1 -1 -1 -1 1 1 -1 1 0 1 -1 1 1 -1 -1 -1 -1 1 1 -1 1 0 1 -1 1 1
15 1 1 0 1 0 0 -1 1 0 0 -1 0 -1 -1 0 1 1 0 1 0 0 -1 1 0 0 -1 0 -1 -1 0
17 1 1 -1 1 -1 -1 -1 1 1 -1 -1 -1 1 -1 1 1 0 1 1 -1 1 -1 -1 -1 1 1 -1 -1 -1 1
19 1 -1 -1 1 1 1 1 -1 1 -1 1 -1 -1 -1 -1 1 1 -1 0 1 -1 -1 1 1 1 1 -1 1 -1 1
21 1 -1 0 1 1 0 0 -1 0 -1 -1 0 -1 0 0 1 1 0 -1 1 0 1 -1 0 1 1 0 0 -1 0
23 1 1 1 1 -1 1 -1 1 1 -1 -1 1 1 -1 -1 1 -1 1 -1 -1 -1 -1 0 1 1 1 1 -1 1 -1
25 1 1 1 1 0 1 1 1 1 0 1 1 1 1 0 1 1 1 1 0 1 1 1 1 0 1 1 1 1 0
27 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0
29 1 -1 -1 1 1 1 1 -1 1 -1 -1 -1 1 -1 -1 1 -1 -1 -1 1 -1 1 1 1 1 -1 -1 1 0 1
</pre>
 
=={{header|Factor}}==
The <code>jacobi</code> word already exists in the <code>math.extras</code> vocabulary. See the implementation [https://docs.factorcode.org/content/word-jacobi%2Cmath.extras.html here].
 
=={{header|FreeBASIC}}==
<syntaxhighlight lang="freebasic">function gcdp( a as uinteger, b as uinteger ) as uinteger
if b = 0 then return a
return gcdp( b, a mod b )
end function
 
function gcd(a as integer, b as integer) as uinteger
return gcdp( abs(a), abs(b) )
end function
 
function jacobi( a as uinteger, n as uinteger ) as integer
if gcd(a, n)<>1 then return 0
if a = 1 then return 1
if a>n then return jacobi( a mod n, n )
if a mod 2 = 0 then
if n mod 8 = 1 or n mod 8 = 7 then
return jacobi(a/2, n)
else
return -jacobi(a/2, n)
end if
end if
dim as integer q = (-1)^((a-1)/2 * (n-1)/2)
return q/jacobi(n, a)
end function
 
'print a table
 
function padto( i as ubyte, j as integer ) as string
return wspace(i-len(str(j)))+str(j)
end function
 
dim as uinteger pn, k, prime(0 to 16) = {3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61}
dim as string outstr = " k "
 
for k = 1 to 36
outstr = outstr + padto(2, k)+" "
next k
print outstr
print " n"
for pn=0 to 16
outstr= " "+padto( 2, prime(pn) )+" "
for k = 1 to 36
outstr = outstr + padto(2, jacobi(k, prime(pn))) + " "
next k
print outstr
next pn</syntaxhighlight>
{{out}}
<pre style="font-size: 11px"> k 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36
n
3 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0
5 1 -1 -1 1 0 1 -1 -1 1 0 1 -1 -1 1 0 1 -1 -1 1 0 1 -1 -1 1 0 1 -1 -1 1 0 1 -1 -1 1 0 1
7 1 1 -1 1 -1 -1 0 1 1 -1 1 -1 -1 0 1 1 -1 1 -1 -1 0 1 1 -1 1 -1 -1 0 1 1 -1 1 -1 -1 0 1
11 1 -1 1 1 1 -1 -1 -1 1 -1 0 1 -1 1 1 1 -1 -1 -1 1 -1 0 1 -1 1 1 1 -1 -1 -1 1 -1 0 1 -1 1
13 1 -1 1 1 -1 -1 -1 -1 1 1 -1 1 0 1 -1 1 1 -1 -1 -1 -1 1 1 -1 1 0 1 -1 1 1 -1 -1 -1 -1 1 1
17 1 1 -1 1 -1 -1 -1 1 1 -1 -1 -1 1 -1 1 1 0 1 1 -1 1 -1 -1 -1 1 1 -1 -1 -1 1 -1 1 1 0 1 1
19 1 -1 -1 1 1 1 1 -1 1 -1 1 -1 -1 -1 -1 1 1 -1 0 1 -1 -1 1 1 1 1 -1 1 -1 1 -1 -1 -1 -1 1 1
23 1 1 1 1 -1 1 -1 1 1 -1 -1 1 1 -1 -1 1 -1 1 -1 -1 -1 -1 0 1 1 1 1 -1 1 -1 1 1 -1 -1 1 1
29 1 -1 -1 1 1 1 1 -1 1 -1 -1 -1 1 -1 -1 1 -1 -1 -1 1 -1 1 1 1 1 -1 -1 1 0 1 -1 -1 1 1 1 1
31 1 1 -1 1 1 -1 1 1 1 1 -1 -1 -1 1 -1 1 -1 1 1 1 -1 -1 -1 -1 1 -1 -1 1 -1 -1 0 1 1 -1 1 1
37 1 -1 1 1 -1 -1 1 -1 1 1 1 1 -1 -1 -1 1 -1 -1 -1 -1 1 -1 -1 -1 1 1 1 1 -1 1 -1 -1 1 1 -1 1
41 1 1 -1 1 1 -1 -1 1 1 1 -1 -1 -1 -1 -1 1 -1 1 -1 1 1 -1 1 -1 1 -1 -1 -1 -1 -1 1 1 1 -1 -1 1
43 1 -1 -1 1 -1 1 -1 -1 1 1 1 -1 1 1 1 1 1 -1 -1 -1 1 -1 1 1 1 -1 -1 -1 -1 -1 1 -1 -1 -1 1 1
47 1 1 1 1 -1 1 1 1 1 -1 -1 1 -1 1 -1 1 1 1 -1 -1 1 -1 -1 1 1 -1 1 1 -1 -1 -1 1 -1 1 -1 1
53 1 -1 -1 1 -1 1 1 -1 1 1 1 -1 1 -1 1 1 1 -1 -1 -1 -1 -1 -1 1 1 -1 -1 1 1 -1 -1 -1 -1 -1 -1 1
59 1 -1 1 1 1 -1 1 -1 1 -1 -1 1 -1 -1 1 1 1 -1 1 1 1 1 -1 -1 1 1 1 1 1 -1 -1 -1 -1 -1 1 1
61 1 -1 1 1 1 -1 -1 -1 1 -1 -1 1 1 1 1 1 -1 -1 1 1 -1 1 -1 -1 1 -1 1 -1 -1 -1 -1 -1 -1 1 -1 1</pre>
 
=={{header|Go}}==
Line 163 ⟶ 753:
 
This translates the Lua code in the above referenced Wikipedia article to Go (for 8 byte integers) and checks that it gives the same answers for a small table of values - which it does.
<langsyntaxhighlight lang="go">package main
 
import (
Line 222 ⟶ 812:
fmt.Println()
}
}</langsyntaxhighlight>
 
{{out}}
Line 255 ⟶ 845:
=={{header|Haskell}}==
{{trans|Scheme}}
<langsyntaxhighlight lang="haskell">jacobi :: Integer -> Integer -> Integer
jacobi 0 1 = 1
jacobi 0 _ = 0
Line 268 ⟶ 858:
else if rem a_mod_n 4 == 3 && rem n 4 == 3
then negate $ jacobi n a_mod_n
else jacobi n a_mod_n</langsyntaxhighlight>
 
 
Or, expressing it slightly differently, and adding a tabulation:
<syntaxhighlight lang ="haskell">import Data.ListBool (replicate, transposebool)
import Data.List (replicate, transpose)
import Data.List.Split (chunksOf)
 
import Data.Bool (bool)
---------------------- JACOBI SYMBOL ---------------------
 
jacobi :: Int -> Int -> Int
jacobi = go
Line 282 ⟶ 874:
go 0 _ = 0
go x y
| even r = plusMinus (rem y 8 `elem` [3, 5]) (go (div r 2) y)
| otherwise = plusMinus (3 == rem r 4 && 3 == rem y 4) (go y r)
(rem y 8 `elem` [3, 5])
(go (div r 2) y)
| otherwise = plusMinus (p r && p y) (go y r)
where
plusMinus = bool id negate
p = (3 ==) . flip rem 4
r = rem x y
 
 
-------------------------- TEST ---------------------------
--------------------------- TEST -------------------------
main :: IO ()
main = putStrLn $ jacobiTable 11 9
 
------------------------- DISPLAY -------------------------
jacobiTable :: Int -> Int -> String
jacobiTable nCols nRows =
let nthrowLabels = [1, 3 .. (nRows2 * 2nRows)]
yscolLabels = [1,30 .. nthpred nCols]
in withColumnLabels ("" w: =fmap length (show nthcolLabels) $
cols = [0labelledRows ..(fmap predshow nCols]rowLabels) $
rjust = justifyRight w 'paddedCols ' . show$
chunksOf nRows $
showRow (x:xs) = unwords $ rjust x : "->" : map rjust xs
uncurry jacobi
rowLines =
showRow <$> ((,) <$> colLabels <*> rowLabels)
 
transpose
------------------- TABULATION FUNCTIONS -----------------
(ys :
paddedCols ::
chunksOf
Show a =>
nRows
[[a]] ->
(uncurry jacobi <$> ((<*>) . fmap (,)) cols [1,3 .. (nRows * 2)]))
[[String]]
in unlines $
paddedCols cols =
(justifyRight w ' ' [] ++ " " ++ unwords (rjust <$> cols)) :
let scols = fmap show <$> cols
replicate (length $ head rowLines) '-' : rowLines
w = maximum $ length <$> concat scols
in map (justifyRight w ' ') <$> scols
 
labelledRows :: [String] -> [[String]] -> [[String]]
labelledRows labels cols =
let w = maximum $ map length labels
in zipWith
(:)
((<> " ->") . justifyRight w ' ' <$> labels)
(transpose cols)
 
withColumnLabels :: [String] -> [[String]] -> String
withColumnLabels _ [] = ""
withColumnLabels labels rows@(x : _) =
let labelRow =
unwords $
zipWith
(`justifyRight` ' ')
(length <$> x)
labels
in unlines $
labelRow :
replicate (length labelRow) '-' : fmap unwords rows
 
justifyRight :: Int -> a -> [a] -> [a]
justifyRight n c = (drop . length) <*> (replicate n c ++<>)</langsyntaxhighlight>
{{Out}}
<pre> 0 1 2 3 4 5 6 7 8 9 10
Line 328 ⟶ 948:
 
=={{header|J}}==
<syntaxhighlight lang="j">
<lang J>
NB. directfunctionally equivalent translation of the Lua program found
NB. at https://en.wikipedia.org/wiki/Jacobi_symbol
NB. at the wikipedia entry incorporated here in comments.
jacobi=: {{
 
assert. (0<x) * 1=2|x
NB.function jacobi(n, k)
y=. x|y
jacobi=: dyad define every
t=. 1
 
while. y do.
k=. x NB. k is the left argument
e=. (|.#:y) i.1
n=. y NB. n is the right hand argument
y=. <.y%2^e
 
t=. t*_1^(*/3 = 4|x,y)+(2|e)*(8|x) e.3 5
NB.assert(k > 0 and k % 2 == 1)
assert. (k >'x 0) *y'=. 1 = 2y, y| kx
 
NB.n = n % k
n =. k | n
 
NB.t = 1
t =. 1
 
NB.while n ~= 0 do
while. n do.
 
NB. while n % 2 == 0 do
while. -. 2 | n do.
 
NB. n = n / 2
n =. <. n % 2
NB. r = k % 8
r =. 8 | k
 
NB. if r == 3 or r == 5 then
if. r e. 3 5 do.
 
NB. t = -t
t =. -t
 
NB. end
end.
 
NB. end
end.
 
NB. n, k = k, n
'n k' =. k , n
 
NB. if n % 4 == 3 and k % 4 == 3 then
if. (3 = 4 | n) *. (3 = 4 | k) do.
 
NB. t = -t
t =. -t
 
NB. end
end.
 
NB. n = n % k
n =. k | n
 
NB.end
end.
t*x=1
}}"0</syntaxhighlight>
 
NB.if k == 1 then
if. k = 1 do.
 
NB. return t
t
 
NB.else
else.
 
NB. return 0
0
 
NB.end
end.
 
NB.end
)
</lang>
<pre>
k=: 1 2 p. i. 30
Line 449 ⟶ 1,007:
 
=={{header|Java}}==
<langsyntaxhighlight lang="java">
 
public class JacobiSymbol {
Line 500 ⟶ 1,058:
 
}
</syntaxhighlight>
</lang>
{{out}}
<pre style="font-size: 13px">
<pre>
n\k 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
Line 520 ⟶ 1,078:
29 1 -1 -1 1 1 1 1 -1 1 -1 -1 -1 1 -1 -1 1 -1 -1 -1 1 -1 1 1 1 1 -1 -1 1 0 1
</pre>
 
=={{header|jq}}==
{{trans|Julia}}
<syntaxhighlight lang="jq">
def lpad($len): tostring | ($len - length) as $l | (" " * $l)[:$l] + .;
def rpad($len): tostring | ($len - length) as $l | . + (" " * $l)[:$l];
 
def jacobi(a; n):
{a: (a % n), n: n, result: 1}
| until(.a == 0;
until( .a % 2 != 0;
.a /= 2
| if (.n % 8) | IN(3, 5) then .result *= -1 else . end )
| {a: .n, n: .a, result} # swap .a and .n
| (.n % 4) as $nmod4
| if (.a % 4) == $nmod4 and $nmod4 == 3 then .result *= -1 else . end
| .a = .a % .n )
| if .n == 1 then .result else 0 end ;
" Table of jacobi(a; n)",
"n\\k 1 2 3 4 5 6 7 8 9 10 11 12",
"_____________________________________________________",
(range( 1; 32; 2) as $n
| "\($n|rpad(3))" + reduce range(1; 13) as $a (""; . + (jacobi($a; $n) | lpad(4) ))
)</syntaxhighlight>
{{out}}
<pre>
Table of jacobi(a, n)
n\k 1 2 3 4 5 6 7 8 9 10 11 12
_____________________________________________________
1 1 1 1 1 1 1 1 1 1 1 1 1
3 1 -1 0 1 -1 0 1 -1 0 1 -1 0
5 1 -1 -1 1 0 1 -1 -1 1 0 1 -1
7 1 1 -1 1 -1 -1 0 1 1 -1 1 -1
9 1 1 0 1 1 0 1 1 0 1 1 0
11 1 -1 1 1 1 -1 -1 -1 1 -1 0 1
13 1 -1 1 1 -1 -1 -1 -1 1 1 -1 1
15 1 1 0 1 0 0 -1 1 0 0 -1 0
17 1 1 -1 1 -1 -1 -1 1 1 -1 -1 -1
19 1 -1 -1 1 1 1 1 -1 1 -1 1 -1
21 1 -1 0 1 1 0 0 -1 0 -1 -1 0
23 1 1 1 1 -1 1 -1 1 1 -1 -1 1
25 1 1 1 1 0 1 1 1 1 0 1 1
27 1 -1 0 1 -1 0 1 -1 0 1 -1 0
29 1 -1 -1 1 1 1 1 -1 1 -1 -1 -1
31 1 1 -1 1 1 -1 1 1 1 1 -1 -1</pre>
 
=={{header|Julia}}==
{{trans|Python}}
<langsyntaxhighlight lang="julia">function jacobi(a, n)
a %= n
result = 1
Line 546 ⟶ 1,150:
end
end
</langsyntaxhighlight>{{out}}
<pre>
Table of jacobi(a, n) for a 1 to 12, n 1 to 31
Line 571 ⟶ 1,175:
 
=={{header|Kotlin}}==
<langsyntaxhighlight lang="scala">fun jacobi(A: Int, N: Int): Int {
assert(N > 0 && N and 1 == 1)
var a = A % N
Line 593 ⟶ 1,197:
}
return if (n == 1) result else 0
}</langsyntaxhighlight>
 
=={{header|Lua}}==
{{Trans|ALGOL 68}}
<syntaxhighlight lang="lua">
do -- Jacobi symbol - translation of the Algol 68 sample
 
 
local function jacobi( aIn, nIn )
if nIn <= 0 or nIn % 2 == 0 then
print( "The 'n' parameter of jacobi must be an odd positive integer." )
return 0
else
local a, n, result = aIn % nIn, nIn, 1
while a ~= 0 do
while a % 2 == 0 do
a = math.floor( a / 2 )
local nm8 = n % 8
if nm8 == 3 or nm8 == 5 then result = - result end
end
a, n = n, a;
if a % 4 == 3 and n % 4 == 3 then result = - result end
a = a % n
end
return n == 1 and result or 0
end
end
 
print( "Table of jacobi(a, n):" );
print( "n/a 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15" )
print( "---------------------------------------------------------------" )
for n = 1, 29, 2 do
io.write( string.format( "%3d", n ) )
for a = 1, 15 do io.write( string.format( "%4d", jacobi( a, n ) ) ) end
io.write( "\n" )
end
 
end
</syntaxhighlight>
{{out}}
<pre>
Table of jacobi(a, n):
n/a 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
---------------------------------------------------------------
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
3 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0
5 1 -1 -1 1 0 1 -1 -1 1 0 1 -1 -1 1 0
7 1 1 -1 1 -1 -1 0 1 1 -1 1 -1 -1 0 1
9 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0
11 1 -1 1 1 1 -1 -1 -1 1 -1 0 1 -1 1 1
13 1 -1 1 1 -1 -1 -1 -1 1 1 -1 1 0 1 -1
15 1 1 0 1 0 0 -1 1 0 0 -1 0 -1 -1 0
17 1 1 -1 1 -1 -1 -1 1 1 -1 -1 -1 1 -1 1
19 1 -1 -1 1 1 1 1 -1 1 -1 1 -1 -1 -1 -1
21 1 -1 0 1 1 0 0 -1 0 -1 -1 0 -1 0 0
23 1 1 1 1 -1 1 -1 1 1 -1 -1 1 1 -1 -1
25 1 1 1 1 0 1 1 1 1 0 1 1 1 1 0
27 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0
29 1 -1 -1 1 1 1 1 -1 1 -1 -1 -1 1 -1 -1
</pre>
 
=={{header|Mathematica}} / {{header|Wolfram Language}}==
<syntaxhighlight lang="mathematica">TableForm[Table[JacobiSymbol[n, k], {n, 1, 17, 2}, {k, 16}],
TableHeadings -> {ReplacePart[Range[1, 17, 2], 1 -> "n=1"],
ReplacePart[Range[16], 1 -> "k=1"]}]</syntaxhighlight>
{{out}}
Produces a nicely typeset table.
 
=={{header|Nim}}==
Translation of the Lua program from Wikipedia page.
<syntaxhighlight lang="nim">template isOdd(n: int): bool = (n and 1) != 0
template isEven(n: int): bool = (n and 1) == 0
 
 
func jacobi(n, k: int): range[-1..1] =
assert k > 0 and k.isOdd
var n = n mod k
var k = k
result = 1
while n != 0:
while n.isEven:
n = n shr 1
if (k and 7) in [3, 5]:
result = -result
swap n, k
if (n and 3) == 3 and (k and 3) == 3:
result = -result
n = n mod k
if k != 1: result = 0
 
when isMainModule:
 
import strutils
 
stdout.write "n/k|"
for n in 1..20:
stdout.write align($n, 3)
echo '\n' & repeat("—", 64)
 
for k in countup(1, 21, 2):
stdout.write align($k, 2), " |"
for n in 1..20:
stdout.write align($jacobi(n, k), 3)
echo ""</syntaxhighlight>
 
{{out}}
<pre>n/k| 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
————————————————————————————————————————————————————————————————
1 | 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
3 | 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1
5 | 1 -1 -1 1 0 1 -1 -1 1 0 1 -1 -1 1 0 1 -1 -1 1 0
7 | 1 1 -1 1 -1 -1 0 1 1 -1 1 -1 -1 0 1 1 -1 1 -1 -1
9 | 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1
11 | 1 -1 1 1 1 -1 -1 -1 1 -1 0 1 -1 1 1 1 -1 -1 -1 1
13 | 1 -1 1 1 -1 -1 -1 -1 1 1 -1 1 0 1 -1 1 1 -1 -1 -1
15 | 1 1 0 1 0 0 -1 1 0 0 -1 0 -1 -1 0 1 1 0 1 0
17 | 1 1 -1 1 -1 -1 -1 1 1 -1 -1 -1 1 -1 1 1 0 1 1 -1
19 | 1 -1 -1 1 1 1 1 -1 1 -1 1 -1 -1 -1 -1 1 1 -1 0 1
21 | 1 -1 0 1 1 0 0 -1 0 -1 -1 0 -1 0 0 1 1 0 -1 1</pre>
 
=={{header|Perl}}==
{{trans|Raku}}
<langsyntaxhighlight lang="perl">use strict;
use warnings;
 
Line 629 ⟶ 1,351:
printf '%4d', J($_, $n) for 1..$maxa;
print "\n"
}</langsyntaxhighlight>
{{out}}
<pre style="font-size: 13px">n\k 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
------------------------------------------------------------------------------------------------------------------------
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
Line 650 ⟶ 1,372:
 
=={{header|Phix}}==
<!--<syntaxhighlight lang="phix">(phixonline)-->
<lang Phix>function jacobi(integer a, n)
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
atom result = 1
<span style="color: #008080;">function</span> <span style="color: #000000;">jacobi</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
a = remainder(a,n)
<span style="color: #004080;">atom</span> <span style="color: #000000;">result</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span>
while a!=0 do
<span style="color: #000000;">a</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">remainder</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">,</span><span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
while remainder(a,2)==0 do
<span style="color: #008080;">while</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">!=</span><span style="color: #000000;">0</span> <span style="color: #008080;">do</span>
a /= 2
<span style="color: #008080;">while</span> <span style="color: #7060A8;">remainder</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)==</span><span style="color: #000000;">0</span> <span style="color: #008080;">do</span>
if find(remainder(n,8),{3,5}) then result *= -1 end if
<span style="color: #000000;">a</span> <span style="color: #0000FF;">/=</span> <span style="color: #000000;">2</span>
end while
<span style="color: #008080;">if</span> <span style="color: #7060A8;">find</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">remainder</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #000000;">8</span><span style="color: #0000FF;">),{</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">5</span><span style="color: #0000FF;">})</span> <span style="color: #008080;">then</span> <span style="color: #000000;">result</span> <span style="color: #0000FF;">*=</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">1</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
{a, n} = {n, a}
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
if remainder(a,4)==3 and remainder(n,4)==3 then result *= -1 end if
<span style="color: #0000FF;">{</span><span style="color: #000000;">a</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">}</span>
a = remainder(a,n)
<span style="color: #008080;">if</span> <span style="color: #7060A8;">remainder</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">,</span><span style="color: #000000;">4</span><span style="color: #0000FF;">)==</span><span style="color: #000000;">3</span> <span style="color: #008080;">and</span> <span style="color: #7060A8;">remainder</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #000000;">4</span><span style="color: #0000FF;">)==</span><span style="color: #000000;">3</span> <span style="color: #008080;">then</span> <span style="color: #000000;">result</span> <span style="color: #0000FF;">*=</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">1</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
end while
<span style="color: #000000;">a</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">remainder</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">,</span><span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
return iff(n==1 ? result : 0)
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
end function
<span style="color: #008080;">return</span> <span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">==</span><span style="color: #000000;">1</span> <span style="color: #0000FF;">?</span> <span style="color: #000000;">result</span> <span style="color: #0000FF;">:</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">)</span>
 
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
printf(1,"n\\a 0 1 2 3 4 5 6 7 8 9 10 11\n")
printf(1," ________________________________________________\n")
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"n\\a 0 1 2 3 4 5 6 7 8 9 10 11\n"</span><span style="color: #0000FF;">)</span>
for n=1 to 31 by 2 do
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">" ________________________________________________\n"</span><span style="color: #0000FF;">)</span>
printf(1,"%3d", n)
<span style="color: #008080;">for</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">31</span> <span style="color: #008080;">by</span> <span style="color: #000000;">2</span> <span style="color: #008080;">do</span>
for a=0 to 11 do
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%3d"</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
printf(1,"%4d",jacobi(a, n))
<span style="color: #008080;">for</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">to</span> <span style="color: #000000;">11</span> <span style="color: #008080;">do</span>
end for
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%4d"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">jacobi</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">))</span>
printf(1,"\n")
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
end for</lang>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"\n"</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<!--</syntaxhighlight>-->
{{out}}
<pre>
Line 694 ⟶ 1,419:
29 0 1 -1 -1 1 1 1 1 -1 1 -1 -1
31 0 1 1 -1 1 1 -1 1 1 1 1 -1
</pre>
 
=={{header|PL/M}}==
{{Trans|Wren}}...via Algol W.
{{works with|8080 PL/M Compiler}} ... under CP/M (or an emulator)
Note that although the 8080 PL/M compiler only supports unsigned integers, the unary minus operator produces a correct two's complement result, so for byte values, -1 = 255 and -255 = 1.
<syntaxhighlight lang="plm">
100H: /* JACOBI SYMBOL */
 
/* CP/M BDOS SYSTEM CALLS AND I/O ROUTINES */
BDOS: PROCEDURE( FN, ARG ); DECLARE FN BYTE, ARG ADDRESS; GOTO 5; END;
PR$CHAR: PROCEDURE( C ); DECLARE C BYTE; CALL BDOS( 2, C ); END;
PR$STRING: PROCEDURE( S ); DECLARE S ADDRESS; CALL BDOS( 9, S ); END;
PR$NL: PROCEDURE; CALL PR$STRING( .( 0DH, 0AH, '$' ) ); END;
PR$NUMBER: PROCEDURE( N ); /* PRINTS A NUMBER IN THE MINIMUN FIELD WIDTH */
DECLARE N ADDRESS;
DECLARE V ADDRESS, N$STR ( 6 )BYTE, W BYTE;
V = N;
W = LAST( N$STR );
N$STR( W ) = '$';
N$STR( W := W - 1 ) = '0' + ( V MOD 10 );
DO WHILE( ( V := V / 10 ) > 0 );
N$STR( W := W - 1 ) = '0' + ( V MOD 10 );
END;
CALL PR$STRING( .N$STR( W ) );
END PR$NUMBER;
 
/* TASK */
 
JACOBI: PROCEDURE( A$IN, N$IN )BYTE;
DECLARE ( A$IN, N$IN ) ADDRESS;
IF N$IN MOD 2 <> 1 THEN DO;
CALL PR$STRING( .'JACOBI PARAMETER NOT ODD$' );
RETURN 0;
END;
ELSE DO;
DECLARE ( A, N, NM8, T ) ADDRESS;
DECLARE JS BYTE;
A = A$IN MOD N$IN; N = N$IN; JS = 1;
DO WHILE A <> 0;
DO WHILE A MOD 2 = 0;
A = A / 2;
NM8 = N MOD 8;
IF NM8 = 3 OR NM8 = 5 THEN JS = - JS;
END;
T = A; A = N; N = T;
IF A MOD 4 = 3 AND N MOD 4 = 3 THEN JS = - JS;
A = A MOD N;
END;
IF N = 1 THEN RETURN JS;
ELSE RETURN 0;
END;
END JACOBI ;
 
DECLARE ( A, N )ADDRESS;
DECLARE JS BYTE;
 
CALL PR$STRING( .'TABLE OF JACOBI(A, N):$' );CALL PR$NL;
CALL PR$STRING( .'N/A 1 2 3 4 5 6 7$' );
CALL PR$STRING( .' 8 9 10 11 12 13 14 15$' );CALL PR$NL;
CALL PR$STRING( .'-------------------------------$' );
CALL PR$STRING( .'--------------------------------$' );CALL PR$NL;
DO N = 1 TO 29 BY 2;
CALL PR$CHAR( ' ' );
IF N < 10 THEN CALL PR$CHAR( ' ' );
CALL PR$NUMBER( N );
DO A = 1 TO 15;
JS = JACOBI( A, N );
IF JS = 0 THEN CALL PR$STRING( .' 0$' );
ELSE IF JS = 1 THEN CALL PR$STRING( .' 1$' );
ELSE CALL PR$STRING( .' -1$' );
END;
CALL PR$NL;
END;
 
EOF
</syntaxhighlight>
{{out}}
<pre>
TABLE OF JACOBI(A, N):
N/A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
---------------------------------------------------------------
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
3 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0
5 1 -1 -1 1 0 1 -1 -1 1 0 1 -1 -1 1 0
7 1 1 -1 1 -1 -1 0 1 1 -1 1 -1 -1 0 1
9 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0
11 1 -1 1 1 1 -1 -1 -1 1 -1 0 1 -1 1 1
13 1 -1 1 1 -1 -1 -1 -1 1 1 -1 1 0 1 -1
15 1 1 0 1 0 0 -1 1 0 0 -1 0 -1 -1 0
17 1 1 -1 1 -1 -1 -1 1 1 -1 -1 -1 1 -1 1
19 1 -1 -1 1 1 1 1 -1 1 -1 1 -1 -1 -1 -1
21 1 -1 0 1 1 0 0 -1 0 -1 -1 0 -1 0 0
23 1 1 1 1 -1 1 -1 1 1 -1 -1 1 1 -1 -1
25 1 1 1 1 0 1 1 1 1 0 1 1 1 1 0
27 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0
29 1 -1 -1 1 1 1 1 -1 1 -1 -1 -1 1 -1 -1
</pre>
 
=={{header|Python}}==
<langsyntaxhighlight lang="python">def jacobi(a, n):
if n <= 0:
raise ValueError("'n' must be a positive integer.")
Line 717 ⟶ 1,539:
return result
else:
return 0</langsyntaxhighlight>
 
=={{header|Raku}}==
Line 723 ⟶ 1,545:
{{works with|Rakudo|2019.11}}
 
<syntaxhighlight lang="raku" perl6line># Jacobi function
sub infix:<J> (Int $k is copy, Int $n is copy where * % 2) {
$k %= $n;
Line 752 ⟶ 1,574:
}
print "\n";
}</langsyntaxhighlight>
{{out}}
<pre style="font-size: 13px">n\k 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
------------------------------------------------------------------------------------------------------------------------
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
Line 776 ⟶ 1,598:
 
<br>A little extra code was added to make a prettier grid.
<langsyntaxhighlight lang="rexx">/*REXX pgm computes/displays the Jacobi symbol, the # of rows & columns can be specified*/
parse arg rows cols . /*obtain optional arguments from the CL*/
if rows='' | rows=="," then rows= 17 /*Not specified? Then use the default.*/
Line 809 ⟶ 1,631:
end /*while a\==0*/
if n==1 then return $
return 0</langsyntaxhighlight>
{{out|output|text=&nbsp; when using the default inputs:}}
<pre>
Line 828 ⟶ 1,650:
=={{header|Ruby}}==
{{trans|Crystal}}
<langsyntaxhighlight lang="ruby">def jacobi(a, n)
raise ArgumentError.new "n must b positive and odd" if n < 1 || n.even?
res = 1
Line 849 ⟶ 1,671:
(0..10).each { |a| printf(" % 2d", jacobi(a, n)) }
puts
end</langsyntaxhighlight>
 
{{out}}
Line 865 ⟶ 1,687:
15 0 1 1 0 1 0 0 -1 1 0 0
17 0 1 1 -1 1 -1 -1 -1 1 1 -1</pre>
 
=={{header|Rust}}==
{{trans|C++}}
<syntaxhighlight lang="rust">fn jacobi(mut n: i32, mut k: i32) -> i32 {
assert!(k > 0 && k % 2 == 1);
n %= k;
let mut t = 1;
while n != 0 {
while n % 2 == 0 {
n /= 2;
let r = k % 8;
if r == 3 || r == 5 {
t = -t;
}
}
std::mem::swap(&mut n, &mut k);
if n % 4 == 3 && k % 4 == 3 {
t = -t;
}
n %= k;
}
if k == 1 {
t
} else {
0
}
}
 
fn print_table(kmax: i32, nmax: i32) {
print!("n\\k|");
for k in 0..=kmax {
print!(" {:2}", k);
}
print!("\n----");
for _ in 0..=kmax {
print!("---");
}
println!();
for n in (1..=nmax).step_by(2) {
print!("{:2} |", n);
for k in 0..=kmax {
print!(" {:2}", jacobi(k, n));
}
println!();
}
}
 
fn main() {
print_table(20, 21);
}</syntaxhighlight>
 
{{out}}
<pre>
n\k| 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
-------------------------------------------------------------------
1 | 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
3 | 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1
5 | 0 1 -1 -1 1 0 1 -1 -1 1 0 1 -1 -1 1 0 1 -1 -1 1 0
7 | 0 1 1 -1 1 -1 -1 0 1 1 -1 1 -1 -1 0 1 1 -1 1 -1 -1
9 | 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1
11 | 0 1 -1 1 1 1 -1 -1 -1 1 -1 0 1 -1 1 1 1 -1 -1 -1 1
13 | 0 1 -1 1 1 -1 -1 -1 -1 1 1 -1 1 0 1 -1 1 1 -1 -1 -1
15 | 0 1 1 0 1 0 0 -1 1 0 0 -1 0 -1 -1 0 1 1 0 1 0
17 | 0 1 1 -1 1 -1 -1 -1 1 1 -1 -1 -1 1 -1 1 1 0 1 1 -1
19 | 0 1 -1 -1 1 1 1 1 -1 1 -1 1 -1 -1 -1 -1 1 1 -1 0 1
21 | 0 1 -1 0 1 1 0 0 -1 0 -1 -1 0 -1 0 0 1 1 0 -1 1
</pre>
 
=={{header|Scala}}==
<langsyntaxhighlight lang="scala">
def jacobi(a_p: Int, n_p: Int): Int =
{
Line 900 ⟶ 1,789:
} yield println("n = " + n + ", a = " + a + ": " + jacobi(a, n))
}
</syntaxhighlight>
</lang>
 
{{out|output}}
Line 1,016 ⟶ 1,905:
 
=={{header|Scheme}}==
<langsyntaxhighlight lang="scheme">(define jacobi (lambda (a n)
(let ((a-mod-n (modulo a n)))
(if (zero? a-mod-n)
Line 1,028 ⟶ 1,917:
(if (and (= (modulo a-mod-n 4) 3) (= (modulo n 4) 3))
(- (jacobi n a-mod-n))
(jacobi n a-mod-n)))))))</langsyntaxhighlight>
 
=={{header|Sidef}}==
Line 1,034 ⟶ 1,923:
Also built-in as '''kronecker(n,k)'''.
 
<langsyntaxhighlight lang="ruby">func jacobi(na, kn) {
 
assert(kn > 0, "#{kn} must be positive")
assert(kn.is_odd, "#{kn} must be odd")
 
var t = 1
while (na %= kn) {
varif v = n(a.valuation(2is_even) {
t *= (-1)**v if (k%8var ~~v [3,5]= a.valuation(2)
n >> t *= (-1)**v if (n%8 ~~ [3,5])
(n,k) a >>= (k,n)v
t = -t if ([n%4, k%4] == [3,3])}
(a,n) = (n,a)
t = -t if ([a%4, n%4] == [3,3])
}
 
kn==1 ? t : 0
}
 
for na in (0..50), kn in (0..50) {
assert_eq(jacobi(na, 2*kn + 1), kronecker(na, 2*kn + 1))
}</langsyntaxhighlight>
 
=={{header|Swift}}==
 
<langsyntaxhighlight lang="swift">import Foundation
 
func jacobi(a: Int, n: Int) -> Int {
Line 1,096 ⟶ 1,987:
 
print()
}</langsyntaxhighlight>
 
{{out}}
Line 1,111 ⟶ 2,002:
15 0 1 1 0 1 0 0 -1 1 0
17 0 1 1 -1 1 -1 -1 -1 1 1</pre>
 
=={{header|V (Vlang)}}==
{{trans|Go}}
<syntaxhighlight lang="v (vlang)">fn jacobi(aa u64, na u64) ?int {
mut a := aa
mut n := na
if n%2 == 0 {
return error("'n' must be a positive odd integer")
}
a %= n
mut result := 1
for a != 0 {
for a%2 == 0 {
a /= 2
nn := n % 8
if nn == 3 || nn == 5 {
result = -result
}
}
a, n = n, a
if a%4 == 3 && n%4 == 3 {
result = -result
}
a %= n
}
if n == 1 {
return result
}
return 0
}
fn main() {
println("Using hand-coded version:")
println("n/a 0 1 2 3 4 5 6 7 8 9")
println("---------------------------------")
for n := u64(1); n <= 17; n += 2 {
print("${n:2} ")
for a := u64(0); a <= 9; a++ {
t := jacobi(a, n)?
print(" ${t:2}")
}
println('')
}
}
</syntaxhighlight>
{{out}}
<pre>
n/a 0 1 2 3 4 5 6 7 8 9
---------------------------------
1 1 1 1 1 1 1 1 1 1 1
3 0 1 -1 0 1 -1 0 1 -1 0
5 0 1 -1 -1 1 0 1 -1 -1 1
7 0 1 1 -1 1 -1 -1 0 1 1
9 0 1 1 0 1 1 0 1 1 0
11 0 1 -1 1 1 1 -1 -1 -1 1
13 0 1 -1 1 1 -1 -1 -1 -1 1
15 0 1 1 0 1 0 0 -1 1 0
17 0 1 1 -1 1 -1 -1 -1 1 1
</pre>
 
=={{header|Wren}}==
{{trans|Python}}
{{libheader|Wren-fmt}}
<lang ecmascript>var jacobi = Fn.new { |a, n|
<syntaxhighlight lang="wren">import "./fmt" for Fmt
 
var jacobi = Fn.new { |a, n|
if (!n.isInteger || n <= 0 || n%2 == 0) {
Fiber.abort("The 'n' parameter must be an odd positive integer.")
Line 1,133 ⟶ 2,086:
}
return (n == 1) ? result : 0
}
 
var rset = Fn.new { |m, n|
var s = "%(n)"
var c = s.count
return (m > c) ? " " * (m - c) + s : s
}
 
Line 1,146 ⟶ 2,093:
var n = 1
while (n < 31) {
SystemFmt.write(rset.call(3"$3d", n))
for (a in 1..15) SystemFmt.write(rset.call(4"$4d", jacobi.call(a, n)))
System.print()
n = n + 2
}</langsyntaxhighlight>
 
{{out}}
Line 1,172 ⟶ 2,119:
27 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0
29 1 -1 -1 1 1 1 1 -1 1 -1 -1 -1 1 -1 -1
</pre>
 
=={{header|XPL0}}==
{{trans|C}}
<syntaxhighlight lang "XPL0">func Jacobi(A, N);
int A, N, Result, T;
[if A >= N then A:= rem(A/N);
Result:= 1;
while A do
[while (A&1) = 0 do
[A:= A >> 1;
if (N&7) = 3 or (N&7) = 5 then Result:= -Result;
];
T:= A; A:= N; N:= T;
if (A&3) = 3 and (N&3) = 3 then Result:= -Result;
A:= rem(A/N);
];
if N = 1 then return Result;
return 0;
];
 
proc PrintTable(KMax, NMax);
int KMax, NMax, K, N;
[Text(0, "N\K|");
Format(3, 0);
for K:= 0 to KMax do RlOut(0, float(K));
CrLf(0);
Text(0, "----");
for K:= 0 to KMax do Text(0, "---");
CrLf(0);
for N:= 1 to NMax do
[Format(2, 0);
RlOut(0, float(N));
Text(0, " |");
Format(3, 0);
for K:= 0 to KMax do
RlOut(0, float(Jacobi(K, N)));
CrLf(0);
N:= N+1;
];
];
 
PrintTable(20, 21);
</syntaxhighlight>
{{out}}
<pre>
N\K| 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
-------------------------------------------------------------------
1 | 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
3 | 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1
5 | 0 1 -1 -1 1 0 1 -1 -1 1 0 1 -1 -1 1 0 1 -1 -1 1 0
7 | 0 1 1 -1 1 -1 -1 0 1 1 -1 1 -1 -1 0 1 1 -1 1 -1 -1
9 | 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1
11 | 0 1 -1 1 1 1 -1 -1 -1 1 -1 0 1 -1 1 1 1 -1 -1 -1 1
13 | 0 1 -1 1 1 -1 -1 -1 -1 1 1 -1 1 0 1 -1 1 1 -1 -1 -1
15 | 0 1 1 0 1 0 0 -1 1 0 0 -1 0 -1 -1 0 1 1 0 1 0
17 | 0 1 1 -1 1 -1 -1 -1 1 1 -1 -1 -1 1 -1 1 1 0 1 1 -1
19 | 0 1 -1 -1 1 1 1 1 -1 1 -1 1 -1 -1 -1 -1 1 1 -1 0 1
21 | 0 1 -1 0 1 1 0 0 -1 0 -1 -1 0 -1 0 0 1 1 0 -1 1
</pre>
 
=={{header|zkl}}==
<langsyntaxhighlight lang="zkl">fcn jacobi(a,n){
if(n.isEven or n<1)
throw(Exception.ValueError("'n' must be a positive odd integer"));
Line 1,189 ⟶ 2,195:
}
if(n==1) result else 0
}</langsyntaxhighlight>
<langsyntaxhighlight lang="zkl">println("Using hand-coded version:");
println("n/a 0 1 2 3 4 5 6 7 8 9");
println("---------------------------------");
Line 1,197 ⟶ 2,203:
foreach a in (10){ print(" % d".fmt(jacobi(a,n))) }
println();
}</langsyntaxhighlight>
{{libheader|GMP}} GNU Multiple Precision Arithmetic Library
<langsyntaxhighlight lang="zkl">var [const] BI=Import.lib("zklBigNum"); // libGMP
println("\nUsing BigInt library function:");
println("n/a 0 1 2 3 4 5 6 7 8 9");
Line 1,207 ⟶ 2,213:
foreach a in (10){ print(" % d".fmt(BI(a).jacobi(n))) }
println();
}</langsyntaxhighlight>
{{out}}
<pre>
Alextretyak
1,480

edits

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