def lcim(numbers):
"""Returns the least common integral multiple of a list of numbers.
The numbers can be rational or irrational or a mixture of both.
`None` is returned for incommensurable numbers.
Examples
========
>>> from sympy import S, pi
>>> from sympy.calculus.util import lcim
>>> lcim([S(1)/2, S(3)/4, S(5)/6])
15/2
>>> lcim([2*pi, 3*pi, pi, pi/2])
6*pi
>>> lcim([S(1), 2*pi])
"""
result = None
if all(num.is_irrational for num in numbers):
factorized_nums = list(map(lambda num: num.factor(), numbers))
factors_num = list(
map(lambda num: num.as_coeff_Mul(),
factorized_nums))
term = factors_num[0][1]
if all(factor == term for coeff, factor in factors_num):
common_term = term
coeffs = [coeff for coeff, factor in factors_num]
result = lcm_list(coeffs) * common_term
elif all(num.is_rational for num in numbers):
result = lcm_list(numbers)
else:
pass
return result
def lcim(numbers):
"""Returns the least common integral multiple of a list of numbers.
The numbers can be rational or irrational or a mixture of both.
`None` is returned for incommensurable numbers.
Examples
========
>>> from sympy import S, pi
>>> from sympy.calculus.util import lcim
>>> lcim([S(1)/2, S(3)/4, S(5)/6])
15/2
>>> lcim([2*pi, 3*pi, pi, pi/2])
6*pi
>>> lcim([S(1), 2*pi])
"""
result = None
if all(num.is_irrational for num in numbers):
factorized_nums = list(map(lambda num: num.factor(), numbers))
factors_num = list(map(lambda num: num.as_coeff_Mul(), factorized_nums))
term = factors_num[0][1]
if all(factor == term for coeff, factor in factors_num):
common_term = term
coeffs = [coeff for coeff, factor in factors_num]
result = lcm_list(coeffs)*common_term
elif all(num.is_rational for num in numbers):
result = lcm_list(numbers)
else:
pass
return result
def d_from_primes_e(primes, e):
# Classic school book implementation
# d = modinv(e, (r1-1)*(r2-1)*(rn-1)...)
p_minus_1 = [p - 1 for p in primes]
d = long(modinv(e, sympy.lcm_list(p_minus_1)))
return d
test_values = {
x: 6,
y: 10,
z: 14,
}
# test Lcm
lhs = Lcm(x, y, z).subs(test_values)
rhs = Lcm(*(v for k,v in test_values.items()))
largs = list(lhs.args).sort()
rargs = list(rhs.args).sort()
assert largs == rargs
assert \
Lcm(x, y, z).subs(test_values).evalf() == \
lcm_list(tuple(v for k,v in test_values.items())).evalf()
assert \
Lcm(x, y, z).evalf(subs=test_values) == \
lcm_list(tuple(v for k,v in test_values.items())).evalf()
# test Gcd
lhs = Gcd(x, y, z).subs(test_values)
rhs = Gcd(*(v for k,v in test_values.items()))
largs = list(lhs.args).sort()
rargs = list(rhs.args).sort()
assert largs == rargs
assert \
Gcd(x, y, z).subs(test_values).evalf() == \
gcd_list(tuple(v for k,v in test_values.items())).evalf()
assert \
Gcd(x, y, z).evalf(subs=test_values) == \
