def detect_prime_pairs_using_ster_broc_mat_format_with_fix_denomi(fix_denomi):
print '\n=== detect_prime_pairs_using_ster_broc_mat_format_with_fix_denomi = ', fix_denomi
# a is odd number
a_list = np.arange(3, fix_denomi, 2, dtype = int)
b = fix_denomi
# print a_list
# find co-prime of b
cnt, coprime_list = eul_totie(b)
# print coprime_list
display_option = False
# a1 will be p
for a1 in a_list:
# we only need to check a in 1st half of a_list
if(a1 > end_num/2):
break
# if a1 is a coprime of b
if a1 in coprime_list:
# get count_fract for the input fraction a/b
a1_cf_list = get_cont_fract(a1, b)
# get the matrix format for a1/b
a1_cf_mat_list, a1_ster_brot_mat, a1_b = ster_brot_mat_format_for_cont_fract(a1_cf_list, display_option)
# since we are only interested in p + q = N, which is a1 + a2 = b,
# therefore, a2 = b - a1
a2 = b - a1
# get count_fract for the input fraction a2/b
a2_cf_list = get_cont_fract(a2, b)
# get the matrix format for a2/b
a2_cf_mat_list, a2_ster_brot_mat, a2_b = ster_brot_mat_format_for_cont_fract(a2_cf_list, display_option)
# if a1 and a2 both are primes
if (a1 in prime_list) and (a2 in prime_list):
print a1_cf_list, ", ", ", num_of_turns: ", len(a1_cf_list), ", num_of_prod: ", np.sum(a1_cf_list), ", ", a1_b, " <==== GBC"
print a2_cf_list, ", ", ", num_of_turns: ", len(a2_cf_list), ", num_of_prod: ", np.sum(a2_cf_list), ", ", a2_b, " <==== GBC"
else:
print a1_cf_list, ", ", ", num_of_turns: ", len(a1_cf_list), ", num_of_prod: ", np.sum(a1_cf_list), ", ", a1_b
print a2_cf_list, ", ", ", num_of_turns: ", len(a2_cf_list), ", num_of_prod: ", np.sum(a2_cf_list), ", ", a2_b
print a1_ster_brot_mat
print a2_ster_brot_mat
def detect_primes_using_ster_broc_mat_format(start_num, end_num):
if(start_num%2 == 1):
print "--- detect_primes_using_ster_broc_mat_format(), start_num needs to be even ------------------------------------------"
# b is even number,
b_list = np.arange(start_num, end_num, 2, dtype = int)
print b_list
for b in b_list:
# print b
# we are only interested in the case tht a is odd number, and a is smaller than b
# so that we will get a/b
a_list = np.arange(3, b, 2, dtype = int)
# print a_list
# find coprimes of b
cnt, coprime_list = eul_totie(b)
# print coprime_list
for a in a_list:
if a in coprime_list:
# get count_fract for the input fraction a/b
cf_list = get_cont_fract(a, b)
# get the matrix format for a/b
cf_mat_list, ster_brot_mat, a_b = ster_brot_mat_format_for_cont_fract(cf_list)
# we can print out finding
# print cf_mat_list, ster_brot_mat, a_b
if a in prime_list:
sys.stdout.write("<================================== prime\n\n")
def get_all_cont_fracts_with_fix_denomi(fix_denomi):
b = fix_denomi
# a loop from 1 to b - 1
a_list = np.arange(1, fix_denomi, 1, dtype = int)
# print a_list
display_option = False
tmpstr_1 = 'b = %4d, length for i/b where 1 <= i < b are: '%(b)
sys.stdout.write(tmpstr_1)
sys.stdout.write(", format: [num_of_mat_prod, i/b], ")
# a1 will be p
max_num_prods = 0
for a1 in a_list:
# get count_fract for the input fraction a/b
a1_cf_list = get_cont_fract(a1, b)
# get the matrix format for a1/b
a1_cf_mat_list, a1_ster_brot_mat, a1_b = ster_brot_mat_format_for_cont_fract(a1_cf_list, display_option)
num_of_turns = len(a1_cf_list)
num_of_prod = np.sum(a1_cf_list)
tmpstr_1 = '[%d, %d/%d],'%(num_of_prod, a1_b[0], a1_b[1])
sys.stdout.write(tmpstr_1)
if(num_of_prod > max_num_prods):
max_num_prods = num_of_prod
print " max_num_prods: ", max_num_prods
display_option = False
end_level = 15
tree_as_breadth_1st_trav_list_upto_level = build_calk_wil_tree_upto_level(end_level)
print "============ To do the following test, end_level need larger than 15 ==================="
print "======if en_num is too small, it will not generate enough data for this test. ========"
max_diagonal = 60
diagonal_formula_coeff_list = detect_diagonal_pattern(tree_as_breadth_1st_trav_list_upto_level, max_diagonal)
a = 3
b = 13
has_found, found = find_entry_of_a_fract_in_tree(a, b, diagonal_formula_coeff_list)
assert(has_found == True)
cf_list = get_cont_fract(a, b)
cf_mat_list, ster_brot_mat, a_b = ster_brot_mat_format_for_cont_fract(cf_list)
a = 2
b = 9
has_found, found = find_entry_of_a_fract_in_tree(a, b, diagonal_formula_coeff_list)
assert(has_found == True)
cf_list = get_cont_fract(a, b)
cf_mat_list, ster_brot_mat, a_b = ster_brot_mat_format_for_cont_fract(cf_list)
a = 4
b =11
has_found, found = find_entry_of_a_fract_in_tree(a, b, diagonal_formula_coeff_list)
assert(has_found == True)
