def sample_messy_power(variable, entropy):
"""Returns unsimplified power expression like ((x**2)**3/x**4)**2/x**3."""
if entropy <= 0:
return variable
which = random.choice([1, 2, 3])
if which == 1:
exponent_entropy = min(2, entropy)
entropy -= exponent_entropy
exponent = number.integer_or_rational(exponent_entropy, signed=True)
left = sample_messy_power(variable, entropy)
return ops.Pow(left, exponent)
entropy_left = entropy / 2
if entropy_left < 1:
entropy_left = 0
entropy_right = entropy - entropy_left
if random.choice([False, True]):
entropy_left, entropy_right = entropy_right, entropy_left
left = sample_messy_power(variable, entropy_left)
right = sample_messy_power(variable, entropy_right)
if which == 2:
return ops.Mul(left, right)
else:
return ops.Div(left, right)
def _polynomial_coeffs_with_roots(roots, scale_entropy):
"""Returns a polynomial with the given roots.
The polynomial is generated by expanding product_{root in roots} (x - root),
and then (1) scaling by the coefficients so they are all integers with lcm 1,
and then (2) further scaling the coefficients by a random integer or rational
with `scale_entropy` digits.
Args:
roots: List of values.
scale_entropy: Float; entropy of the random coefficient scaling.
Returns:
List of coefficients `coeffs`, such that `coeffs[i]` is the coefficient of
variable ** i.
"""
variable = sympy.Symbol('x') # doesn't matter, only use coefficients
polynomial = sympy.Poly(sympy.prod([variable - root for root in roots]))
coeffs_reversed = polynomial.all_coeffs()
assert len(coeffs_reversed) == len(roots) + 1
coeffs = list(reversed(coeffs_reversed))
# Multiply terms to change rationals to integers, and then maybe reintroduce.
lcm = sympy.lcm([sympy.denom(coeff) for coeff in coeffs])
if scale_entropy > 0:
while True:
scale = number.integer_or_rational(scale_entropy, signed=True)
if scale != 0:
break
else:
scale = 1
return [coeff * scale * lcm for coeff in coeffs]
def testArithmeticLength(self):
"""Tests that the generated arithmetic expressions have given length."""
for _ in range(1000):
target = number.integer_or_rational(4, signed=True)
entropy = 8.0
length = random.randint(2, 10)
expression = arithmetic.arithmetic(target, entropy, length)
# Note: actual length is #ops = #numbers - 1.
actual_length = len(ops.number_constants(expression)) - 1
self.assertEqual(actual_length, length)
def _sub_op(value, sample_args, rationals_allowed):
"""Returns sampled args for `ops.Sub`."""
entropy, sample_args = sample_args.peel()
if rationals_allowed and sample_args.count >= 3:
x = number.integer_or_rational(entropy, True)
else:
x = number.integer(entropy, True)
if random.choice([False, True]):
op_args = [x, x - value]
else:
op_args = [value + x, x]
return ops.Sub, op_args, sample_args
def testArithmetic(self):
for _ in range(1000):
target = number.integer_or_rational(4, signed=True)
entropy = 8.0
expression = arithmetic.arithmetic(target, entropy)
self.assertEqual(sympy.sympify(expression), target)
def integer_or_rational_or_decimal(entropy):
if random.choice([False, True]):
return number.integer_or_decimal(entropy, signed=True)
else:
return number.integer_or_rational(entropy, signed=True)
#https://github.com/deepmind/mathematics_dataset/blob/master/mathematics_dataset/sample/arithmetic_test.py
from mathematics_dataset.sample import arithmetic
from mathematics_dataset.sample import number
for ix in range(100):
target = number.integer_or_rational(4, signed=True)
entropy = 9.0
expression = arithmetic.arithmetic(target, entropy)
print(expression)
def testIntegerOrRational(self, signed):
# Tests we can call it. Do it a few times so both code paths get executed.
for _ in range(10):
number.integer_or_rational(2, signed)
