Pisano period: Difference between revisions
Add PARI/GP implementation
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=={{header|PARI/GP}}==
{{trans|Mathematica}}
<syntaxhighlight lang="PARI/GP">
\\ Initialize an associative array equivalent
pisanos = Map();
\\ Function to calculate the Pisano period for a given prime p
pisano(p) = {
local(lastn, n, i);
if (p < 2, return(1));
if (mapisdefined(pisanos, p),
return(mapget(pisanos, p));
);
lastn = 0; n = 1;
for (i = 1, p^2,
[lastn, n] = [n, Mod(lastn + n, p)];
if (lastn == 0 && n == 1,
mapput(pisanos, p, i);
return(i);
);
);
return(1);
}
\\ Function to calculate Pisano period for a prime p and a power k
pisanoprime(p, k) = {
my(i = pisano(p));
if (!isprime(p), error("p must be prime"));
p^(k-1) * i;
}
\\ Function to calculate Pisano period for a composite number n
pisanotask(n) = {
my(factors = factor(n));
\\print("factors=" factors);
\\apply(x -> print("x=" x), factors);
lcm( vector(#factors~, i, pisanoprime(factors[i, 1], factors[i, 2])) );
}
{
\\ Print Pisano periods for prime numbers up to 15 with k=2
for (i = 1, 15,
if (isprime(i),
print("pisanoPrime[" i ", 2] = " pisanoprime(i, 2))
);
);
\\ Print Pisano periods for prime numbers up to 180 with k=1
for (i = 1, 180,
if (isprime(i),
print("pisanoPrime[" i ", 1] = " pisanoprime(i, 1))
);
);
\\ Print Pisano periods for numbers 2 to 180
print("\nPisano[n] for n from 2 to 180:");
print(vector(179, i, pisano(i+1)));
\\ Print Pisano periods using pisanotask for numbers 2 to 180
print("\nPisano[n] using pisanoPrime for n from 2 to 180:");
print(vector(179, i, pisanotask(i+1)));
}
</syntaxhighlight>
{{out}}
<pre>
pisanoPrime[2, 2] = 6
pisanoPrime[3, 2] = 24
pisanoPrime[5, 2] = 100
pisanoPrime[7, 2] = 112
pisanoPrime[11, 2] = 110
pisanoPrime[13, 2] = 364
pisanoPrime[2, 1] = 3
pisanoPrime[3, 1] = 8
pisanoPrime[5, 1] = 20
pisanoPrime[7, 1] = 16
pisanoPrime[11, 1] = 10
pisanoPrime[13, 1] = 28
pisanoPrime[17, 1] = 36
pisanoPrime[19, 1] = 18
pisanoPrime[23, 1] = 48
pisanoPrime[29, 1] = 14
pisanoPrime[31, 1] = 30
pisanoPrime[37, 1] = 76
pisanoPrime[41, 1] = 40
pisanoPrime[43, 1] = 88
pisanoPrime[47, 1] = 32
pisanoPrime[53, 1] = 108
pisanoPrime[59, 1] = 58
pisanoPrime[61, 1] = 60
pisanoPrime[67, 1] = 136
pisanoPrime[71, 1] = 70
pisanoPrime[73, 1] = 148
pisanoPrime[79, 1] = 78
pisanoPrime[83, 1] = 168
pisanoPrime[89, 1] = 44
pisanoPrime[97, 1] = 196
pisanoPrime[101, 1] = 50
pisanoPrime[103, 1] = 208
pisanoPrime[107, 1] = 72
pisanoPrime[109, 1] = 108
pisanoPrime[113, 1] = 76
pisanoPrime[127, 1] = 256
pisanoPrime[131, 1] = 130
pisanoPrime[137, 1] = 276
pisanoPrime[139, 1] = 46
pisanoPrime[149, 1] = 148
pisanoPrime[151, 1] = 50
pisanoPrime[157, 1] = 316
pisanoPrime[163, 1] = 328
pisanoPrime[167, 1] = 336
pisanoPrime[173, 1] = 348
pisanoPrime[179, 1] = 178
Pisano[n] for n from 2 to 180:
[3, 8, 6, 20, 24, 16, 12, 24, 60, 10, 24, 28, 48, 40, 24, 36, 24, 18, 60, 16, 30, 48, 24, 100, 84, 72, 48, 14, 120, 30, 48, 40, 36, 80, 24, 76, 18, 56, 60, 40, 48, 88, 30, 120, 48, 32, 24, 112, 300, 72, 84, 108, 72, 20, 48, 72, 42, 58, 120, 60, 30, 48, 96, 140, 120, 136, 36, 48, 240, 70, 24, 148, 228, 200, 18, 80, 168, 78, 120, 216, 120, 168, 48, 180, 264, 56, 60, 44, 120, 112, 48, 120, 96, 180, 48, 196, 336, 120, 300, 50, 72, 208, 84, 80, 108, 72, 72, 108, 60, 152, 48, 76, 72, 240, 42, 168, 174, 144, 120, 110, 60, 40, 30, 500, 48, 256, 192, 88, 420, 130, 120, 144, 408, 360, 36, 276, 48, 46, 240, 32, 210, 140, 24, 140, 444, 112, 228, 148, 600, 50, 36, 72, 240, 60, 168, 316, 78, 216, 240, 48, 216, 328, 120, 40, 168, 336, 48, 364, 180, 72, 264, 348, 168, 400, 120, 232, 132, 178, 120]
Pisano[n] using pisanoPrime for n from 2 to 180:
[3, 8, 6, 20, 24, 16, 12, 24, 60, 10, 24, 28, 48, 40, 24, 36, 24, 18, 60, 16, 30, 48, 24, 100, 84, 72, 48, 14, 120, 30, 48, 40, 36, 80, 24, 76, 18, 56, 60, 40, 48, 88, 30, 120, 48, 32, 24, 112, 300, 72, 84, 108, 72, 20, 48, 72, 42, 58, 120, 60, 30, 48, 96, 140, 120, 136, 36, 48, 240, 70, 24, 148, 228, 200, 18, 80, 168, 78, 120, 216, 120, 168, 48, 180, 264, 56, 60, 44, 120, 112, 48, 120, 96, 180, 48, 196, 336, 120, 300, 50, 72, 208, 84, 80, 108, 72, 72, 108, 60, 152, 48, 76, 72, 240, 42, 168, 174, 144, 120, 110, 60, 40, 30, 500, 48, 256, 192, 88, 420, 130, 120, 144, 408, 360, 36, 276, 48, 46, 240, 32, 210, 140, 24, 140, 444, 112, 228, 148, 600, 50, 36, 72, 240, 60, 168, 316, 78, 216, 240, 48, 216, 328, 120, 40, 168, 336, 48, 364, 180, 72, 264, 348, 168, 400, 120, 232, 132, 178, 120]
</pre>
=={{header|Perl}}==
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