def base_types(value, base):
if isinstance(value, Fraction) and isinstance(base, Fraction):
result = int(str(int(value)), int(base)) # value must be string
return Fraction(result, 1)
elif isinstance(value, Fraction) and isinstance(base, str):
return [Fraction(int(str(int(value)), toOrd(c))) for c in base]
elif isinstance(value, str) and isinstance(base, Fraction):
result = int(value, int(base))
return Fraction(result, 1)
elif isinstance(value, str) and isinstance(base, str):
if len(base) == 1:
return base_types(value, Fraction(toOrd(base)))
else:
return [base_types(value, Fraction(toOrd(b))) for b in base]
elif isinstance(value, Fraction) and isinstance(base, list):
return [base_types(value, b) for b in base]
elif isinstance(value, list) and isinstance(base, Fraction):
return [base_types(v, base) for v in value]
elif isinstance(value, str) and isinstance(base, list):
return [base_types(value, b) for b in base]
elif isinstance(value, list) and isinstance(base, str):
return [base_types(v, base) for v in value]
# base can be a char, use codepage value to convert
elif isinstance(value, list) and isinstance(base, list):
if len(value) > len(base):
return [base_types(i, j) for (i, j) in zip(value, cycle(base))]
else:
return [base_types(i, j) for (i, j) in zip(cycle(value), base)]
def addition_types(x, y):
if isinstance(x, Fraction) and isinstance(y, Fraction):
return x + y
elif isinstance(x, Fraction) and isinstance(y, str):
return ''.join([toChr(toOrd(c) + int(x)) for c in y])
elif isinstance(x, str) and isinstance(y, Fraction):
return ''.join([toChr(toOrd(c) + int(y)) for c in x])
elif isinstance(x, str) and isinstance(y, str):
return x + y
elif isinstance(x, Fraction) and isinstance(y, list):
return [addition_types(x, i) for i in y]
elif isinstance(x, list) and isinstance(y, Fraction):
return [addition_types(i, y) for i in x]
elif isinstance(x, str) and isinstance(y, list):
return [addition_types(x, i) for i in y]
elif isinstance(x, list) and isinstance(y, str):
return [addition_types(i, y) for i in x]
elif isinstance(x, list) and isinstance(y, list):
if len(x) > len(y):
return [addition_types(i, j) for (i, j) in zip(x, cycle(y))]
else:
return [addition_types(i, j) for (i, j) in zip(cycle(x), y)]
def make_ord_types(x):
if isinstance(x, Fraction):
return [Fraction(toOrd(c)) for c in str(x)]
elif isinstance(x, str):
return [Fraction(toOrd(c)) for c in x]
elif isinstance(x, list):
return [make_ord_types(i) for i in x]
def toInt(x):
if isinstance(x, Fraction):
return int(x)
elif isinstance(x, str):
return toOrd(x)
elif isinstance(x, list):
return len(x)
def index_types(x, y):
if isinstance(x, Fraction) and isinstance(y, Fraction):
return x.numerator if isTrue(y) else x.denominator
elif isinstance(x, Fraction) and isinstance(y, str):
return [x.numerator if isTrue(c) else x.denominator for c in y]
elif isinstance(x, str) and isinstance(y, Fraction):
return x[int(y) % len(x)]
elif isinstance(x, str) and isinstance(y, str):
return [x[toOrd(c) % len(x)] for c in y]
elif isinstance(x, Fraction) and isinstance(y, list):
return [index_types(x, i) for i in y]
elif isinstance(x, list) and isinstance(y, Fraction):
return x[int(y)]
elif isinstance(x, str) and isinstance(y, list):
return [[index_types(x, i)] for i in y]
elif isinstance(x, list) and isinstance(y, str):
return [[index_types(i, y)] for i in x]
elif isinstance(x, list) and isinstance(y, list):
if len(x) > len(y):
return [index_types(i, j) for (i, j) in zip(x, cycle(y))]
else:
return [index_types(i, j) for (i, j) in zip(cycle(x), y)]
def apply_not_types(x):
if isinstance(x, Fraction):
return Fraction(1) if x == 0 else Fraction(0)
elif isinstance(x, str):
return [apply_not_types(Fraction(toOrd(c))) for c in x]
elif isinstance(x, list):
return [apply_not_types(i) for i in x]
def dec_types(x):
if isinstance(x, Fraction):
return x - 1
elif isinstance(x, str):
return ''.join([toChr(toOrd(c) - 1) for c in x])
elif isinstance(x, list):
return [dec_types(i) for i in x]
def prime_types(x):
if isinstance(x, Fraction):
result = nth_prime_number(int(x))
return Fraction(result)
elif isinstance(x, str):
result = nth_prime_number(toOrd(x))
return Fraction(result)
elif isinstance(x, list):
return [prime_types(i) for i in x]
def sci_format_types(x):
if isinstance(x, Fraction):
if x == int(x):
return Fraction(10**x).limit_denominator(10**abs(int(x)))
else:
return Fraction(10**x).limit_denominator(10**abs(int(x)) * 1000)
elif isinstance(x, str):
return [sci_format_types(Fraction(toOrd(c))) for c in x]
elif isinstance(x, list):
return [sci_format_types(i) for i in x]
def factorial_types(x):
if isinstance(x, Fraction):
fact = Fraction(1)
for i in range(1, 1 + int(x)):
fact = fact * i
return fact
elif isinstance(x, str):
return [factorial_types(Fraction(toOrd(c))) for c in x]
elif isinstance(x, list):
return [factorial_types(i) for i in x]
def make_sum_types(x):
if isinstance(x, Fraction):
digits = str(int(x))
result = 0
for d in digits:
result += int(d)
return Fraction(result)
elif isinstance(x, str):
return Fraction(sum([int(toOrd(c)) for c in x]))
elif isinstance(x, list):
return Fraction(sum([make_sum_types(i) for i in x]))
def power_types(x, y):
if isinstance(x, Fraction) and isinstance(y, Fraction):
return x**y
elif isinstance(x, Fraction) and isinstance(y, str):
return [Fraction(x**toOrd(c)) for c in y]
elif isinstance(x, str) and isinstance(y, Fraction):
return [Fraction(toOrd(c)**y) for c in x]
elif isinstance(x, str) and isinstance(y, str):
if len(x) > len(y):
return [
Fraction(toOrd(i)**toOrd(j)) for (i, j) in zip(x, cycle(y))
]
else:
return [
Fraction(toOrd(i)**toOrd(j)) for (i, j) in zip(cycle(x), y)
]
elif isinstance(x, Fraction) and isinstance(y, list):
return [power_types(x, i) for i in y]
elif isinstance(x, list) and isinstance(y, Fraction):
return [power_types(i, y) for i in x]
elif isinstance(x, str) and isinstance(y, list):
return [[power_types(x, i)] for i in y]
elif isinstance(x, list) and isinstance(y, str):
return [[power_types(i, y)] for i in x]
elif isinstance(x, list) and isinstance(y, list):
if len(x) > len(y):
return [power_types(i, j) for (i, j) in zip(x, cycle(y))]
else:
return [power_types(i, j) for (i, j) in zip(cycle(x), y)]
def fraction_types(x, y):
if isinstance(x, Fraction) and isinstance(y, Fraction):
return Fraction(x, y).limit_denominator()
elif isinstance(x, Fraction) and isinstance(y, str):
return [Fraction(x, toOrd(c)) for c in y]
elif isinstance(x, str) and isinstance(y, Fraction):
return [Fraction(toOrd(c), y) for c in x]
elif isinstance(x, str) and isinstance(y, str):
if len(x) > len(y):
return [
Fraction(toOrd(i), toOrd(j)) for (i, j) in zip(x, cycle(y))
]
else:
return [
Fraction(toOrd(i), toOrd(j)) for (i, j) in zip(cycle(x), y)
]
elif isinstance(x, Fraction) and isinstance(y, list):
return [fraction_types(x, i) for i in y]
elif isinstance(x, list) and isinstance(y, Fraction):
return [fraction_types(i, y) for i in x]
elif isinstance(x, str) and isinstance(y, list):
return [[fraction_types(x, i)] for i in y]
elif isinstance(x, list) and isinstance(y, str):
return [[fraction_types(i, y)] for i in x]
elif isinstance(x, list) and isinstance(y, list):
if len(x) > len(y):
return [fraction_types(i, j) for (i, j) in zip(x, cycle(y))]
else:
return [fraction_types(i, j) for (i, j) in zip(cycle(x), y)]
def module_types(x, y):
if isinstance(x, Fraction) and isinstance(y, Fraction):
return x % y
elif isinstance(x, Fraction) and isinstance(y, str):
return [Fraction(x % toOrd(c)) for c in y]
elif isinstance(x, str) and isinstance(y, Fraction):
return [Fraction(toOrd(c) % y) for c in x]
elif isinstance(x, str) and isinstance(y, str):
if len(x) > len(y):
return [
Fraction(toOrd(i) % toOrd(j)) for (i, j) in zip(x, cycle(y))
]
else:
return [
Fraction(toOrd(i) % toOrd(j)) for (i, j) in zip(cycle(x), y)
]
elif isinstance(x, Fraction) and isinstance(y, list):
return [module_types(x, i) for i in y]
elif isinstance(x, list) and isinstance(y, Fraction):
return [module_types(i, y) for i in x]
elif isinstance(x, str) and isinstance(y, list):
return [[module_types(x, i)] for i in y]
elif isinstance(x, list) and isinstance(y, str):
return [[module_types(i, y)] for i in x]
elif isinstance(x, list) and isinstance(y, list):
if len(x) > len(y):
return [module_types(i, j) for (i, j) in zip(x, cycle(y))]
else:
return [module_types(i, j) for (i, j) in zip(cycle(x), y)]
def quocient_types(x, y):
if isinstance(x, Fraction) and isinstance(y, Fraction):
return Fraction(x // y)
elif isinstance(x, Fraction) and isinstance(y, str):
return [Fraction(x // toOrd(c)) for c in y]
elif isinstance(x, str) and isinstance(y, Fraction):
return [Fraction(toOrd(c) // y) for c in x]
elif isinstance(x, str) and isinstance(y, str):
if len(x) > len(y):
return [
Fraction(toOrd(i) // toOrd(j)) for (i, j) in zip(x, cycle(y))
]
else:
return [
Fraction(toOrd(i) // toOrd(j)) for (i, j) in zip(cycle(x), y)
]
elif isinstance(x, Fraction) and isinstance(y, list):
return [quocient_types(x, i) for i in y]
elif isinstance(x, list) and isinstance(y, Fraction):
return [quocient_types(i, y) for i in x]
elif isinstance(x, str) and isinstance(y, list):
return [[quocient_types(x, i)] for i in y]
elif isinstance(x, list) and isinstance(y, str):
return [[quocient_types(i, y)] for i in x]
elif isinstance(x, list) and isinstance(y, list):
if len(x) > len(y):
return [quocient_types(i, j) for (i, j) in zip(x, cycle(y))]
else:
return [quocient_types(i, j) for (i, j) in zip(cycle(x), y)]
def less_than_types(x, y):
if isinstance(x, Fraction) and isinstance(y, Fraction):
return Fraction(1) if x < y else Fraction(0)
elif isinstance(x, Fraction) and isinstance(y, str):
return [Fraction(1) if x < toOrd(c) else Fraction(0) for c in y]
elif isinstance(x, str) and isinstance(y, Fraction):
return [Fraction(1) if toOrd(c) < y else Fraction(0) for c in x]
elif isinstance(x, str) and isinstance(y, str):
if len(x) > len(y):
return [
Fraction(1) if i < j else Fraction(0)
for (i, j) in zip(x, cycle(y))
]
else:
return [
Fraction(1) if i < j else Fraction(0)
for (i, j) in zip(cycle(x), y)
]
elif isinstance(x, Fraction) and isinstance(y, list):
return [less_than_types(x, i) for i in y]
elif isinstance(x, list) and isinstance(y, Fraction):
return [less_than_types(i, y) for i in x]
elif isinstance(x, str) and isinstance(y, list):
return [[less_than_types(x, i)] for i in y]
elif isinstance(x, list) and isinstance(y, str):
return [[less_than_types(i, y)] for i in x]
elif isinstance(x, list) and isinstance(y, list):
if len(x) > len(y):
return [less_than_types(i, j) for (i, j) in zip(x, cycle(y))]
else:
return [less_than_types(i, j) for (i, j) in zip(cycle(x), y)]
def different_types(x, y):
if isinstance(x, Fraction) and isinstance(y, Fraction):
return Fraction(1) if x != y else Fraction(0)
elif isinstance(x, Fraction) and isinstance(y, str):
return [Fraction(1) if x != toOrd(c) else Fraction(0) for c in y]
elif isinstance(x, str) and isinstance(y, Fraction):
return [Fraction(1) if toOrd(c) != y else Fraction(0) for c in x]
elif isinstance(x, str) and isinstance(y, str):
if len(x) > len(y):
return [
Fraction(1) if i != j else Fraction(0)
for (i, j) in zip(x, cycle(y))
]
else:
return [
Fraction(1) if i != j else Fraction(0)
for (i, j) in zip(cycle(x), y)
]
elif isinstance(x, Fraction) and isinstance(y, list):
return [different_types(x, i) for i in y]
elif isinstance(x, list) and isinstance(y, Fraction):
return [different_types(i, y) for i in x]
elif isinstance(x, str) and isinstance(y, list):
return [[different_types(x, i)] for i in y]
elif isinstance(x, list) and isinstance(y, str):
return [[different_types(i, y)] for i in x]
elif isinstance(x, list) and isinstance(y, list):
if len(x) > len(y):
return [different_types(i, j) for (i, j) in zip(x, cycle(y))]
else:
return [different_types(i, j) for (i, j) in zip(cycle(x), y)]
def greater_eq_than_types(x, y):
if isinstance(x, Fraction) and isinstance(y, Fraction):
return Fraction(1) if x >= y else Fraction(0)
elif isinstance(x, Fraction) and isinstance(y, str):
return [Fraction(1) if x >= toOrd(c) else Fraction(0) for c in y]
elif isinstance(x, str) and isinstance(y, Fraction):
return [Fraction(1) if toOrd(c) >= y else Fraction(0) for c in x]
elif isinstance(x, str) and isinstance(y, str):
if len(x) > len(y):
return [
Fraction(1) if i >= j else Fraction(0)
for (i, j) in zip(x, cycle(y))
]
else:
return [
Fraction(1) if i >= j else Fraction(0)
for (i, j) in zip(cycle(x), y)
]
elif isinstance(x, Fraction) and isinstance(y, list):
return [greater_eq_than_types(x, i) for i in y]
elif isinstance(x, list) and isinstance(y, Fraction):
return [greater_eq_than_types(i, y) for i in x]
elif isinstance(x, str) and isinstance(y, list):
return [[greater_eq_than_types(x, i)] for i in y]
elif isinstance(x, list) and isinstance(y, str):
return [[greater_eq_than_types(i, y)] for i in x]
elif isinstance(x, list) and isinstance(y, list):
if len(x) > len(y):
return [greater_eq_than_types(i, j) for (i, j) in zip(x, cycle(y))]
else:
return [greater_eq_than_types(i, j) for (i, j) in zip(cycle(x), y)]
def equal_types(x, y):
if isinstance(x, Fraction) and isinstance(y, Fraction):
return Fraction(1) if x == y else Fraction(0)
elif isinstance(x, Fraction) and isinstance(y, str):
return [Fraction(1) if x == toOrd(c) else Fraction(0) for c in y]
elif isinstance(x, str) and isinstance(y, Fraction):
return [Fraction(1) if toOrd(c) == y else Fraction(0) for c in x]
elif isinstance(x, str) and isinstance(y, str):
if len(x) > len(y):
return [
Fraction(1) if i == j else Fraction(0)
for (i, j) in zip(x, cycle(y))
]
else:
return [
Fraction(1) if i == j else Fraction(0)
for (i, j) in zip(cycle(x), y)
]
elif isinstance(x, Fraction) and isinstance(y, list):
return [equal_types(x, i) for i in y]
elif isinstance(x, list) and isinstance(y, Fraction):
return [equal_types(i, y) for i in x]
elif isinstance(x, str) and isinstance(y, list):
return [[equal_types(x, i)] for i in y]
elif isinstance(x, list) and isinstance(y, str):
return [[equal_types(i, y)] for i in x]
elif isinstance(x, list) and isinstance(y, list):
if len(x) > len(y):
return [equal_types(i, j) for (i, j) in zip(x, cycle(y))]
else:
return [equal_types(i, j) for (i, j) in zip(cycle(x), y)]
def make_any_types(x):
if isinstance(x, Fraction):
return Fraction(1) if x != 0 else Fraction(0)
elif isinstance(x, str):
ords = [int(toOrd(c)) for c in x]
result = 0
for d in ords:
result += d
return Fraction(1) if result > 0 else Fraction(0)
elif isinstance(x, list):
prods = [make_any_types(i) for i in x]
result = 0
for d in prods:
result += d
return Fraction(1) if result > 0 else Fraction(0)
def make_prod_types(x):
if isinstance(x, Fraction):
digits = str(int(x))
result = 1
for d in digits:
result *= int(d)
return Fraction(result)
elif isinstance(x, str):
ords = [int(toOrd(c)) for c in x]
result = 1
for d in ords:
result *= d
return Fraction(result)
elif isinstance(x, list):
prods = [make_prod_types(i) for i in x]
result = 1
for d in prods:
result *= d
return Fraction(result)
def makeRange1_types(x):
if isinstance(x, Fraction):
return [Fraction(i) for i in range(1, int(x) + 1)]
elif isinstance(x, str):
if x.islower():
id_a = toOrd('a')
id_x = toOrd(x)
return list(codepage[id_a:id_x + 1])
elif x.isupper():
id_A = toOrd('A')
id_x = toOrd(x)
return list(codepage[id_A:id_x + 1])
elif x.isdigit():
id_0 = toOrd('1')
id_x = toOrd(x)
return list(codepage[id_0:id_x + 1])
else:
return '' # otherwise do nothing
elif isinstance(x, list):
return [makeRange1_types(i) for i in x]
def apply_and_types(x, y):
if isinstance(x, Fraction) and isinstance(y, Fraction):
return Fraction(1) if x != 0 and y != 0 else Fraction(0)
elif isinstance(x, Fraction) and isinstance(y, str):
return [
Fraction(1) if x != 0 and toOrd(c) != 0 else Fraction(0) for c in y
]
elif isinstance(x, str) and isinstance(y, Fraction):
return [
Fraction(1) if toOrd(c) != 0 and y != 0 else Fraction(0) for c in x
]
elif isinstance(x, str) and isinstance(y, str):
if len(x) > len(y):
return [
Fraction(1) if toOrd(i) != 0 and toOrd(j) != 0 else Fraction(0)
for (i, j) in zip(x, cycle(y))
]
else:
return [
Fraction(1) if toOrd(i) != 0 and toOrd(j) != 0 else Fraction(0)
for (i, j) in zip(cycle(x), y)
]
elif isinstance(x, Fraction) and isinstance(y, list):
return [apply_and_types(x, i) for i in y]
elif isinstance(x, list) and isinstance(y, Fraction):
return [apply_and_types(i, y) for i in x]
elif isinstance(x, str) and isinstance(y, list):
return [[apply_and_types(x, i)] for i in y]
elif isinstance(x, list) and isinstance(y, str):
return [[apply_and_types(i, y)] for i in x]
elif isinstance(x, list) and isinstance(y, list):
if len(x) > len(y):
return [apply_and_types(i, j) for (i, j) in zip(x, cycle(y))]
else:
return [apply_and_types(i, j) for (i, j) in zip(cycle(x), y)]
