def _sub_question_or_entity(context, p, q, is_question):
"""Generates entity or question for subtraction p - q."""
value = p.value - q.value
if is_question:
templates = [
'{p} - {q}',
'Work out {p} - {q}.',
'What is {p} minus {q}?',
'What is {p} take away {q}?',
'What is {q} less than {p}?',
'Subtract {q} from {p}.',
'Calculate {p} - {q}.',
'What is {p} - {q}?',
]
if sympy.Ge(p.value, q.value):
# We calculate p - q, so the difference (|p - q|) is the correct answer.
for adjective in ['distance', 'difference']:
for pair in ['{p} and {q}', '{q} and {p}']:
templates.append('What is the {} between {}?'.format(adjective, pair))
template = random.choice(templates)
return example.Problem(
question=example.question(context, template, p=p, q=q, problem_type='sub'),
answer=value)
else:
return composition.Entity(
context=context,
value=value,
description='Let {self} = {p} - {q}.',
p=p, q=q,
problem_type='sub')
def _add_question_or_entity(context, p, q, is_question):
"""Generates entity or question for adding p + q."""
value = p.value + q.value
if is_question:
template = random.choice([
'{p} + {q}',
'{p}+{q}',
'Work out {p} + {q}.',
'Add {p} and {q}.',
'Put together {p} and {q}.',
'Sum {p} and {q}.',
'Total of {p} and {q}.',
'Add together {p} and {q}.',
'What is {p} plus {q}?',
'Calculate {p} + {q}.',
'What is {p} + {q}?',
])
return example.Problem(
question=example.question(context, template, p=p, q=q, problem_type='add'),
answer=value)
else:
return composition.Entity(
context=context,
value=value,
description='Let {self} = {p} + {q}.',
p=p, q=q,
problem_type='add')
def collect(value, sample_args, context=None):
"""Collect terms in an unsimplified polynomial."""
is_question = context is None
if context is None:
context = composition.Context()
entropy, sample_args = sample_args.peel()
if value is None:
entropy_value, entropy = entropy * np.random.dirichlet([2, 3])
degrees = [random.randint(1, 3)]
value = composition.Polynomial(
polynomials.sample_coefficients(degrees, entropy_value))
assert isinstance(value, composition.Polynomial)
coefficients = value.coefficients
all_coefficients_are_integer = True
for coeff in coefficients.flat:
if not number.is_integer(coeff):
all_coefficients_are_integer = False
break
if all_coefficients_are_integer:
coefficients = polynomials.expand_coefficients(coefficients, entropy)
else:
# put back the unused entropy
sample_args = composition.SampleArgs(sample_args.num_modules,
sample_args.entropy + entropy)
num_variables = coefficients.ndim
variables = [sympy.Symbol(context.pop()) for _ in range(num_variables)]
unsimplified = polynomials.coefficients_to_polynomial(
coefficients, variables)
simplified = unsimplified.sympy().expand()
# Bit of a hack: handle the very rare case where no number constants appearing
if not ops.number_constants(unsimplified):
unsimplified = ops.Add(unsimplified, ops.Constant(0))
context.sample_by_replacing_constants(sample_args, unsimplified)
if is_question:
template = 'Sederhanakan {unsimplified}.'
return example.Problem(question=example.question(
context, template, unsimplified=unsimplified),
answer=simplified)
else:
function_symbol = context.pop()
function = sympy.Function(function_symbol)(*variables)
return composition.Entity(
context=context,
value=value,
handle=composition.FunctionHandle(function_symbol),
expression=unsimplified,
polynomial_variables=variables,
description='Misalkan {function} = {unsimplified}.',
function=function,
unsimplified=unsimplified)
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 add(value, sample_args, context=None):
"""E.g., "Let f(x)=2x+1, g(x)=3x+2. What is 5*f(x) - 7*g(x)?"."""
is_question = context is None
if context is None:
context = composition.Context()
entropy, sample_args = sample_args.peel()
if value is None:
max_degree = 3
degree = random.randint(1, max_degree)
entropy -= math.log10(max_degree)
entropy_value = entropy / 2
entropy -= entropy_value
value = polynomials.sample_coefficients(degree,
entropy=entropy_value,
min_non_zero=random.randint(
1, 3))
value = composition.Polynomial(value)
c1, c2, coeffs1, coeffs2 = polynomials.coefficients_linear_split(
value.coefficients, entropy)
coeffs1 = polynomials.trim(coeffs1)
coeffs2 = polynomials.trim(coeffs2)
c1, c2, fn1, fn2 = context.sample(sample_args, [
c1, c2,
composition.Polynomial(coeffs1),
composition.Polynomial(coeffs2)
])
var = sympy.var(context.pop())
expression = (c1.handle * fn1.handle.apply(var) +
c2.handle * fn2.handle.apply(var))
if is_question:
answer = polynomials.coefficients_to_polynomial(
value.coefficients, var)
answer = answer.sympy()
template = random.choice(_TEMPLATES)
return example.Problem(question=example.question(context,
template,
composed=expression),
answer=answer)
else:
intermediate_symbol = context.pop()
intermediate = sympy.Function(intermediate_symbol)(var)
return composition.Entity(
context=context,
value=value,
description='Misalkan {intermediate} = {composed}.',
handle=composition.FunctionHandle(intermediate_symbol),
intermediate=intermediate,
composed=expression)
def evaluate(value, sample_args, context=None):
"""Entity for evaluating an integer-valued polynomial at a given point."""
is_question = context is None
if context is None:
context = composition.Context()
entropy, sample_args = sample_args.peel()
if value is None:
entropy_value = random.uniform(1, 1 + entropy / 3)
entropy = max(0, entropy - entropy_value)
value = number.integer(entropy_value, signed=True)
entropy_input = random.uniform(1, 1 + entropy / 3)
entropy = max(0, entropy - entropy_input)
input_ = number.integer(entropy_input, signed=True)
degree = random.randint(1, 3)
entropies = entropy * np.random.dirichlet(list(range(1, degree + 1)))
# Calculate coefficients in reverse order.
target = value
coeffs_reversed = []
for i, coeff_entropy in enumerate(entropies):
power = degree - i
coeff = number.integer(coeff_entropy, signed=True)
if input_ != 0:
coeff += int(round(target / input_**power))
if coeff == 0 and i == 0:
# Don't allow zero in leading coefficient.
coeff += random.choice([-1, 1])
coeffs_reversed.append(coeff)
target -= coeff * (input_**power)
coeffs_reversed.append(target)
coefficients = list(reversed(coeffs_reversed))
(polynomial_entity,
input_) = context.sample(sample_args,
[composition.Polynomial(coefficients), input_])
composed = polynomial_entity.handle.apply(input_.handle)
if is_question:
template = random.choice(_TEMPLATES)
return example.Problem(question=example.question(context,
template,
composed=composed),
answer=value)
else:
return composition.Entity(context=context,
value=value,
expression=composed,
description='Misalkan {self} be {composed}.',
composed=composed)
def gcd(value, sample_args, context=None):
"""Question for greatest common divisor of p and q."""
is_question = context is None
if context is None:
context = composition.Context()
entropy, sample_args = sample_args.peel()
if value is None:
value_entropy = 1 + random.uniform(0, entropy / 3)
entropy = max(1, entropy - value_entropy)
value = number.integer(value_entropy, False, min_abs=1)
p_mult, q_mult = _random_coprime_pair(entropy)
p = value * p_mult
q = value * q_mult
assert sympy.gcd(p, q) == value
p, q = context.sample(sample_args, [p, q])
adjective = (random.choice(['pembagi persekutuan', 'faktor umum']) +
random.choice([' terbesar', ' tertinggi']))
if is_question:
template = random.choice([
'Hitung {adjective} dari {p} dan {q}.',
'Apa {adjective} dari {p} dan {q}?',
])
return example.Problem(question=example.question(context,
template,
adjective=adjective,
p=p,
q=q),
answer=value)
else:
return composition.Entity(
context=context,
value=value,
description='Biarkan {self} menjadi {adjective} dari {p} dan {q}.',
adjective=adjective,
p=p,
q=q)
def gcd(value, sample_args, context=None):
"""Question for greatest common divisor of p and q."""
is_question = context is None
if context is None:
context = composition.Context()
entropy, sample_args = sample_args.peel()
if value is None:
value_entropy = 1 + random.uniform(0, entropy / 3)
entropy = max(1, entropy - value_entropy)
value = number.integer(value_entropy, False, min_abs=1)
p_mult, q_mult = _random_coprime_pair(entropy)
p = value * p_mult
q = value * q_mult
assert sympy.gcd(p, q) == value
p, q = context.sample(sample_args, [p, q])
adjective = (random.choice(['greatest', 'highest']) + ' common ' +
random.choice(['divisor', 'factor']))
if is_question:
template = random.choice([
'Calculate the {adjective} of {p} and {q}.',
'What is the {adjective} of {p} and {q}?',
])
return example.Problem(question=example.question(context,
template,
adjective=adjective,
p=p,
q=q),
answer=value)
else:
return composition.Entity(
context=context,
value=value,
description='Let {self} be the {adjective} of {p} and {q}.',
adjective=adjective,
p=p,
q=q)
def div_remainder(value, sample_args, context=None):
"""E.g., "What is the remainder when 27 is divided by 5?"."""
is_question = context is None
if context is None:
context = composition.Context()
entropy, sample_args = sample_args.peel()
if value is None:
entropy_value = 1 + random.uniform(0, entropy / 3)
entropy = max(0, entropy - entropy_value)
value = number.integer(entropy_value, signed=False)
entropy_a, entropy_q = entropy * np.random.dirichlet([1, 1])
a = number.integer(entropy_a, signed=False, min_abs=1)
q = value + number.integer(entropy_q, signed=False, min_abs=1)
p = a * q + value
assert p % q == value
p, q = context.sample(sample_args, [p, q])
if is_question:
template = random.choice([
'Hitung sisanya ketika {p} dibagi dengan {q}.',
'Berapa sisa jika {p} dibagi dengan {q}?',
])
return example.Problem(question=example.question(
context,
template,
p=p.expression_else_handle,
q=q.expression_else_handle),
answer=value)
else:
return composition.Entity(
context=context,
value=value,
description=
'Biarkan {self} menjadi sisa saat {p} dibagi dengan {q}.',
p=p,
q=q)
def div(value, sample_args, context=None):
"""Returns random question for dividing two numbers."""
del value # unused
is_question = context is None
if context is None:
context = composition.Context()
entropy, sample_args = sample_args.peel()
entropy_1, entropy_q = _entropy_for_pair(entropy)
q = number.integer(entropy_q, True, min_abs=1)
if random.choice([False, True]):
# Pick p/q with nice integer result.
answer = number.integer(entropy_1, True)
p = answer * q
else:
p = number.integer(entropy_1, True)
answer = p / q
p, q = context.sample(sample_args, [p, q])
if is_question:
template = random.choice([
'Divide {p} by {q}.',
'{p} divided by {q}',
'What is {p} divided by {q}?',
'Calculate {p} divided by {q}.',
])
return example.Problem(
question=example.question(context, template, p=p, q=q),
answer=answer
)
else:
return composition.Entity(
context=context,
value=answer,
description='Let {self} be {p} divided by {q}.',
p=p, q=q)
def _calculate(value, sample_args, context, add_sub, mul_div, length=None):
"""Questions for evaluating arithmetic expressions."""
is_question = context is None
if context is None:
context = composition.Context()
entropy, sample_args = sample_args.peel()
if value in [_INT, _INT_OR_RATIONAL]:
value_entropy = max(1.0, entropy / 4)
entropy = max(1.0, entropy - value_entropy)
sampler = _value_sampler(value)
value = sampler(value_entropy)
op = arithmetic.arithmetic(
value=value, entropy=entropy, add_sub=add_sub, mul_div=mul_div,
length=length)
context.sample_by_replacing_constants(sample_args, op)
if is_question:
template = random.choice([
'{op}',
'What is {op}?',
'Evaluate {op}.',
'Calculate {op}.',
'What is the value of {op}?',
])
return example.Problem(
question=example.question(context, template, op=op),
answer=value)
else:
return composition.Entity(
context=context,
value=value,
expression=op,
description='Let {self} be {op}.',
op=op)
def mul(value, sample_args, context=None):
"""Returns random question for multiplying two numbers."""
del value # unused
is_question = context is None
if context is None:
context = composition.Context()
entropy, sample_args = sample_args.peel()
entropy_p, entropy_q = _entropy_for_pair(entropy)
p = number.integer_or_decimal(entropy_p, True)
q = number.integer_or_decimal(entropy_q, True)
p, q = context.sample(sample_args, [p, q])
answer = p.value * q.value
if is_question:
templates = [
'{p}' + ops.MUL_SYMBOL + '{q}',
'{p} ' + ops.MUL_SYMBOL + ' {q}',
'Calculate {p}' + ops.MUL_SYMBOL + '{q}.',
'Work out {p} ' + ops.MUL_SYMBOL + ' {q}.',
'Multiply {p} and {q}.',
'Product of {p} and {q}.',
'What is the product of {p} and {q}?',
'{p} times {q}',
'What is {p} times {q}?',
]
template = random.choice(templates)
return example.Problem(
question=example.question(context, template, p=p, q=q),
answer=answer
)
else:
return composition.Entity(
context=context,
value=answer,
description='Let {self} = {p} * {q}.',
p=p, q=q)
def testInit_valueErrorIfSelfAndHandle(self):
with self.assertRaisesRegexp(ValueError, 'Cannot specify handle'):
composition.Entity(context=composition.Context(),
value=0,
description='Something with {self}. ',
handle='additional')
def _solve_linear_system(degree, value, sample_args, context=None):
"""Solve linear equations."""
is_question = context is None
if context is None:
context = composition.Context()
entropy, sample_args = sample_args.peel()
solutions = []
if value is not None:
solutions.append(value)
extra_solutions_needed = degree - len(solutions)
if extra_solutions_needed > 0:
entropies = (entropy / 4) * np.random.dirichlet(
np.ones(extra_solutions_needed))
entropies = np.maximum(1, entropies) # min per-solution entropy
entropy -= sum(entropies)
solutions += [
number.integer(solution_entropy, True)
for solution_entropy in entropies
]
entropy = max(1, entropy)
variables = [sympy.Symbol(context.pop()) for _ in range(degree)]
solution_index = 0
# If we're going to be creating a linear system with constants to replace by
# handles from other modules, then we need a linear system with constants
# occurring. Very occasionally this can fail to happen, e.g., "x = -x";
# normally this while loop will only see one iteration.
while True:
equations = linear_system.linear_system(variables=variables,
solutions=solutions,
entropy=entropy,
non_trivial_in=solution_index)
constants = ops.number_constants(equations)
if sample_args.num_modules <= 1 or constants:
break
context.sample_by_replacing_constants(sample_args, equations)
variable = variables[solution_index]
answer = solutions[solution_index]
equations = ', '.join([str(equation) for equation in equations])
if is_question:
template = random.choice([
'Selesaikan {equations} untuk {variable}.',
])
return example.Problem(
example.question(context,
template,
equations=equations,
variable=variable), answer)
else:
return composition.Entity(context=context,
value=answer,
description='Misalkan {equations}.',
handle=variable,
equations=equations)