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# find primes from 3 up to max
max = 50
primes = []
for n in range(3, max):
composite = False
for d in range(2, n-1):
if n % d == 0:
composite = True
break
if not composite:
primes.append(n)
count = len(primes)
yes_marker = '[[Image:Yes check.svg|10px]]' # tick (U.S. "check") for residues
no_marker = '[[Image:Black x.svg|10px]]' # cross for non-residues
def colortag(n):
if n % 4 == 1:
return 'bgcolor=#e0ffff'
else:
return 'bgcolor=#ffe0e0'
# computes Legendre symbol (a/q)
# assumes a and q positive, q prime, (a, q) = 1
def legendre(a, q):
for n in range(1, q-1):
if (n * n) % q == a % q:
return 1;
return -1;
# print table header
print '{| class="wikitable"'
print '|-'
print '| || colspan=' + str(count+1), 'align="center" |', "''p''"
print '|-'
print '| rowspan=' + str(count+1), "| ''q'' || ",
for p in primes:
print '||', colortag(p), 'align="center" style="border-bottom:2px solid" |', "'''" + str(p) + "'''",
print
# now the main table
for q in primes:
# first column
print '|-'
print '|', colortag(q), 'align="right" style="border-right:2px solid" |', "''' " + str(q) + " '''",
# remaining columns
for p in primes:
print '||', colortag(1+(p-1)*(q-1)/2), '|',
if p == q:
print ' ',
else:
# symbol for (p/q)
if legendre(p, q) == 1:
print yes_marker,
else:
print no_marker,
if legendre(q, p) == 1:
print yes_marker,
else:
print no_marker,
print
print '|}'
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