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N4_generator.py
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N4_generator.py
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import math
import random
def generate(**kwargs):
force_listing = False
if kwargs['n3_n4_force_listing_method']:
force_listing = True
# Part (a): Listing method
rel_prime_dict = {
1: [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13],
2: [3, 5, 7, 9, 11, 13],
3: [2, 4, 5, 7, 8, 10, 11, 13],
4: [3, 5, 7, 9, 11, 13],
5: [2, 3, 4, 6, 7, 8, 9, 11, 12, 13],
6: [5, 7, 11, 13],
7: [2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13],
8: [3, 5, 7, 9, 11, 13],
9: [2, 4, 5, 7, 8, 10, 11, 13],
10: [3, 7, 9, 11, 13],
11: [2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13],
12: [5, 7, 11, 13],
13: [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]
}
step_a = random.choice(list(range(1, 11)))
step_b = random.choice([x for x in rel_prime_dict[step_a] if 3 <= x <= 8])
step_a, step_b = sorted([step_a, step_b])
gcd_cap = 75 // step_b + 1
gcd = random.choice(list(range(2, gcd_cap)))
listing_a = gcd * step_b
listing_b = gcd * step_a
listing_lcm = gcd * step_a * step_b
listing_list_a = ', '.join(map(str, list(range(listing_a, 2 * listing_lcm + listing_a + 1, listing_a)))) + '...'
listing_list_b = ', '.join(map(str, list(range(listing_b, 2 * listing_lcm + listing_b + 1, listing_b)))) + '...'
listing_prob = f'\\text{{LCM}}({listing_a},{listing_b})'
# Part (b): Factorization Method
primes = [2, 3, 5, 7, 11, 13]
primes_wts = [0.3, 0.25, 0.2, 0.15, 0.05, 0.05]
def get_factor(prime_cap=17):
available_primes = [x for x in primes if x < prime_cap]
available_primes_wts = primes_wts[:len(available_primes)]
factor = random.choices(available_primes, available_primes_wts, k=1)[0]
return factor
allow_one_prefactored = True
one_prefactored = False
factorization_type = 'b not prefactored'
if allow_one_prefactored is True:
one_prefactored = random.choice([True, False])
factorization_list_a = []
factorization_list_b = []
kernel = 1
kernel_size = random.choices([1, 2, 3], [0.2, 0.5, 0.3], k=1)[0]
kernel_prime_cap = 17 if kernel_size < 3 else 11
for i in range(kernel_size):
f = get_factor(prime_cap=kernel_prime_cap)
kernel = kernel * f
factorization_list_a.append(f)
factorization_list_b.append(f)
a = kernel
b = kernel
b_cap = 1000 if one_prefactored is True else 600
while True:
f = get_factor()
if a * f > 600:
break
else:
factorization_list_a.append(f)
a = a * f
while True:
f = get_factor()
if b * f == a:
if f == 2:
break
else:
f = get_factor(prime_cap=f)
if b * f > b_cap:
break
else:
factorization_list_b.append(f)
b = b * f
def list_lcm_union(list_a, list_b):
set_union = set(list_a).union(set(list_b))
list_union = []
for i in set_union:
num = max(list_a.count(i), list_b.count(i))
for j in range(num):
list_union.append(i)
return sorted(list_union)
factorization_mult_lcm = ' \\times '.join(
list(map(str, list_lcm_union(factorization_list_a, factorization_list_b))))
factorization_mult_a = ' \\times '.join(list(map(str, sorted(factorization_list_a))))
factorization_mult_b = ' \\times '.join(list(map(str, sorted(factorization_list_b))))
if one_prefactored is True:
factorization_type = 'b prefactored'
prefactored_b_list = []
for prime in primes:
prime_exp = factorization_list_b.count(prime)
if prime_exp == 1:
prefactored_b_list.append(f'{prime}')
if prime_exp > 1:
prefactored_b_list.append(f'{prime}^{prime_exp}')
factorization_a = a
factorization_b = ' \\times '.join(prefactored_b_list)
else:
if a > b:
factorization_a, factorization_b = b, a
factorization_mult_a, factorization_mult_b = factorization_mult_b, factorization_mult_a
else:
factorization_a, factorization_b = a, b
factorization_type += f', a_b kernel {kernel}'
factorization_prob = f'\\text{{LCM}}({factorization_a},{factorization_b})'
factorization_lcm = math.lcm(a, b)
if force_listing:
listing_prob_wording = "using the listing method (sometimes called the set intersection method). You must show correct lists and a final answer."
else:
listing_prob_wording = "using a method of your choice \\textbf{other than} the prime factorization method. You must show your work before giving the final answer."
return {
'listing_a': listing_a,
'listing_b': listing_b,
'listing_prob': listing_prob,
'listing_prob_wording': listing_prob_wording,
'listing_list_a': listing_list_a,
'listing_list_b': listing_list_b,
'listing_lcm': listing_lcm,
'factorization_a': factorization_a,
'factorization_b': factorization_b,
'factorization_prob': factorization_prob,
'factorization_mult_a': factorization_mult_a,
'factorization_mult_b': factorization_mult_b,
'factorization_mult_lcm': factorization_mult_lcm,
'factorization_lcm': factorization_lcm,
'factorization_type': factorization_type
}