def _differentiate_polynomial(value, sample_args, context, num_variables):
"""Generates a question for differentiating a polynomial."""
is_question = context is None
if context is None:
context = composition.Context()
if value is not None:
num_variables = value.coefficients.ndim
entropy, sample_args = sample_args.peel()
max_derivative_order = 3
derivative_order = random.randint(1, max_derivative_order)
entropy = max(0, entropy - math.log10(max_derivative_order))
derivative_axis = random.randint(0, num_variables - 1)
if value is None:
coefficients = _generate_polynomial(
num_variables, entropy, derivative_order, derivative_axis)
else:
coefficients = _sample_integrand(
value.coefficients, derivative_order, derivative_axis, entropy)
(entity,) = context.sample(
sample_args, [composition.Polynomial(coefficients)])
value = coefficients
for _ in range(derivative_order):
value = polynomials.differentiate(value, axis=derivative_axis)
nth = display.StringOrdinal(derivative_order)
if entity.has_expression():
polynomial = entity.expression
variables = entity.polynomial_variables
else:
variables = [sympy.Symbol(context.pop()) for _ in range(num_variables)]
polynomial = entity.handle.apply(*variables)
variable = variables[derivative_axis]
if is_question:
template = _template(context.module_count, derivative_order, len(variables))
answer = polynomials.coefficients_to_polynomial(value, variables).sympy()
return example.Problem(
question=example.question(
context, template, eq=polynomial, var=variable, nth=nth),
answer=answer)
else:
fn_symbol = context.pop()
variables_string = ', '.join(str(variable) for variable in variables)
assert len(variables) == 1 # since below we don't specify var we diff wrt
return composition.Entity(
context=context,
value=composition.Polynomial(value),
description='Misalkan {fn} ({variables}) menjadi turunan ke-{nth} dari {eq}.',
handle=composition.FunctionHandle(fn_symbol),
fn=fn_symbol, variables=variables_string, nth=nth, eq=polynomial)
def nearest_integer_root(sample_args):
"""E.g., "Calculate the cube root of 35 to the nearest integer."."""
context = composition.Context()
# With at least 50% probability, pick square or cube root (these are most
# important roots!).
if random.choice([False, True]):
one_over_exponent = random.randint(2, 3)
else:
one_over_exponent = random.randint(2, 10)
entropy, sample_args = sample_args.peel()
value = number.integer(entropy, signed=False)
answer = int(round(value ** (1 / one_over_exponent)))
templates = [
'What is {value} to the power of 1/{one_over_exponent}, to the nearest'
' integer?',
]
if one_over_exponent != 2: # "What is the second root of 4?" never used.
ordinal = str()
templates += [
'What is the {ordinal} root of {value} to the nearest integer?',
]
if one_over_exponent == 2:
templates += [
'What is the square root of {value} to the nearest integer?',
]
elif one_over_exponent == 3:
templates += [
'What is the cube root of {value} to the nearest integer?',
]
template = random.choice(templates)
ordinal = display.StringOrdinal(one_over_exponent)
return example.Problem(
question=example.question(
context, template, value=value, ordinal=ordinal,
one_over_exponent=one_over_exponent),
answer=answer)
def kth_biggest(sample_args, count=None):
"""Asks for the kth biggest value in a list."""
sample_args = sample_args()
context = composition.Context()
entropy, sample_args = sample_args.peel()
values = _unique_values(entropy, count=count)
count = len(values)
display_multichoice = random.choice([False, True])
if display_multichoice:
_mark_choice_letters_used(count, context)
entities = context.sample(sample_args, values)
sorted_entities = sorted(entities, key=_entity_sort_key)
ordinal = random.randint(1, count)
if random.choice([False, True]):
# Do from biggest.
answer = sorted_entities[-ordinal]
adjective = 'terbesar'
else:
# Do from smallest.
answer = sorted_entities[ordinal - 1]
adjective = 'terkecil'
if ordinal > 1:
adjective = str(display.StringOrdinal(ordinal)) + ' ' + adjective
if display_multichoice:
return _kth_biggest_multichoice_question(context=context,
entities=entities,
adjective=adjective,
answer=answer)
else:
return _kth_biggest_list_question(context=context,
entities=entities,
adjective=adjective,
answer=answer)
def testCreate_errorIfNegative(self):
with self.assertRaisesRegexp(ValueError, 'Unsupported ordinal'):
display.StringOrdinal(-1)
def testBasic(self): ordinal = display.StringOrdinal(0) self.assertEqual(str(ordinal), 'zeroth') ordinal = display.StringOrdinal(10) self.assertEqual(str(ordinal), 'tenth')