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='Let {intermediate} = {composed}.',
handle=composition.FunctionHandle(intermediate_symbol),
intermediate=intermediate,
composed=expression)
def coefficient_named(value, sample_args, context=None):
"""E.g., "Express x^2 + 2x in the form h * x^2 + k * x + t and give h."."""
del value # not used
if context is None:
context = composition.Context()
variable = sympy.Symbol(context.pop())
entropy, sample_args = sample_args.peel()
degree = random.randint(1, 4)
if random.choice([False, True]):
coefficients = polynomials.sample_coefficients(
degree,
entropy / 2,
min_non_zero=random.randint(degree - 1, degree))
expanded = polynomials.expand_coefficients(coefficients, entropy / 2)
expression = polynomials.coefficients_to_polynomial(expanded, variable)
else:
expression = polynomials.sample_with_brackets(variable, degree,
entropy)
coefficients = list(reversed(sympy.Poly(expression).all_coeffs()))
named_coeffs = [sympy.Symbol(context.pop()) for _ in range(degree + 1)]
canonical = polynomials.coefficients_to_polynomial(named_coeffs, variable)
if random.random() < 0.2: # only small probability of non-zero power
power = random.randint(0, degree)
else:
non_zero_powers = [
i for i in range(degree + 1) if coefficients[i] != 0
]
power = random.choice(non_zero_powers)
value = coefficients[power]
named_coeff = named_coeffs[power]
template = random.choice([
'Ekspresikan {expression} sebagai {canonical} dan berikan {target}. '
'Atur ulang {expression} menjadi {canonical} dan berikan {target}.',
'Ekspresikan {expression} dalam bentuk {canonical} dan berikan {target}.',
'Atur ulang {expression} ke bentuk {canonical} dan berikan {target}.',
])
return example.Problem(question=example.question(context,
template,
expression=expression,
canonical=canonical,
target=named_coeff),
answer=value)
def _sample_integrand(coefficients, derivative_order, derivative_axis, entropy):
"""Integrates `coefficients` and adds sampled "constant" terms."""
coefficients = np.asarray(coefficients)
# Integrate (with zero for constant terms).
integrand = coefficients
for _ in range(derivative_order):
integrand = polynomials.integrate(integrand, derivative_axis)
# Add on sampled constant terms.
constant_degrees = np.array(integrand.shape) - 1
constant_degrees[derivative_axis] = derivative_order - 1
extra_coeffs = polynomials.sample_coefficients(constant_degrees, entropy)
pad_amount = coefficients.shape[derivative_axis]
pad = [(0, pad_amount if i == derivative_axis else 0)
for i in range(coefficients.ndim)]
extra_coeffs = np.pad(extra_coeffs, pad, 'constant', constant_values=0)
return integrand + extra_coeffs