def test_mon_deg0_5_squared_printed():
"""Is this squared Monomial printed correctly?"""
m = Monomial(('+', 5, 0))
m.set_exponent(2)
assert m.printed == wrap_nb('5^{2}')
def level_03(q_subkind, **options):
a = randomly.integer(1, 10)
b = randomly.integer(1, 10)
steps = []
if q_subkind in [
'sum_square', 'sum_square_mixed', 'difference_square',
'difference_square_mixed'
]:
# __
first_term = Monomial(('+', Item(('+', a, 2)).evaluate(), 2))
second_term = Monomial(
('+', Item(('+', Product([2, a, b]).evaluate(), 1)).evaluate(), 1))
third_term = Monomial(('+', Item(('+', b, 2)).evaluate(), 0))
if q_subkind in ['difference_square', 'difference_square_mixed']:
second_term.set_sign('-')
if q_subkind in ['sum_square_mixed', 'difference_square_mixed']:
ordered_expression = Polynomial(
[first_term, second_term, third_term])
[first_term, second_term,
third_term] = randomly.mix([first_term, second_term, third_term])
steps.append(Polynomial([first_term, second_term, third_term]))
if q_subkind in ['sum_square_mixed', 'difference_square_mixed']:
steps.append(ordered_expression)
sq_a_monom = Monomial(('+', a, 1))
sq_b_monom = Monomial(('+', b, 0))
let_a_eq = Equality([Item('a'), sq_a_monom])
let_b_eq = Equality([Item('b'), sq_b_monom])
steps.append(
_("Let") + " " + let_a_eq.into_str(force_expression_markers=True) +
" " + _("and") + " " +
let_b_eq.into_str(force_expression_markers=True))
sq_a_monom.set_exponent(2)
sq_b_monom.set_exponent(2)
a_square_eq = Equality(
[Item(('+', 'a', 2)), sq_a_monom,
sq_a_monom.reduce_()])
b_square_eq = Equality(
[Item(('+', 'b', 2)), sq_b_monom,
sq_b_monom.reduce_()])
steps.append(
_("then") + " " +
a_square_eq.into_str(force_expression_markers=True))
steps.append(
_("and") + " " +
b_square_eq.into_str(force_expression_markers=True))
two_times_a_times_b_numeric = Product(
[Item(2), Monomial(('+', a, 1)),
Item(b)])
two_times_a_times_b_reduced = two_times_a_times_b_numeric.reduce_()
two_times_a_times_b_eq = Equality([
Product([Item(2), Item('a'), Item('b')]),
two_times_a_times_b_numeric, two_times_a_times_b_reduced
])
steps.append(
_("and") + " " +
two_times_a_times_b_eq.into_str(force_expression_markers=True))
steps.append(_("So it is possible to factorize:"))
if q_subkind in ['difference_square', 'difference_square_mixed']:
b = -b
factorized_expression = Sum([Monomial(('+', a, 1)), Item(b)])
factorized_expression.set_exponent(2)
steps.append(factorized_expression)
elif q_subkind in ['squares_difference', 'squares_difference_mixed']:
# To have some (ax)² - b² but also sometimes b² - (ax)²:
degrees = [2, 0, 1, 0]
if randomly.integer(1, 10) >= 8:
degrees = [0, 2, 0, 1]
first_term = Monomial(('+', Item(('+', a, 2)).evaluate(), degrees[0]))
second_term = Monomial(('-', Item(('+', b, 2)).evaluate(), degrees[1]))
sq_first_term = Monomial(('+', Item(
('+', a, 1)).evaluate(), degrees[2]))
sq_second_term = Monomial(('-', Item(
('+', b, 1)).evaluate(), degrees[3]))
# The 'mixed' cases are: -b² + (ax)² and -(ax)² + b²
if q_subkind == 'squares_difference_mixed':
[first_term, second_term] = randomly.mix([first_term, second_term])
[sq_first_term,
sq_second_term] = randomly.mix([sq_first_term, sq_second_term])
positive_sq_first = sq_first_term.clone()
positive_sq_first.set_sign('+')
positive_sq_second = sq_second_term.clone()
positive_sq_second.set_sign('+')
steps.append(Polynomial([first_term, second_term]))
first_inter = None
second_inter = None
if sq_second_term.is_negative():
first_inter = positive_sq_first.clone()
first_inter.set_exponent(2)
temp_second_inter = positive_sq_second.clone()
temp_second_inter.set_exponent(2)
second_inter = Product([-1, temp_second_inter])
else:
temp_first_inter = positive_sq_first.clone()
temp_first_inter.set_exponent(2)
first_inter = Product([-1, temp_first_inter])
second_inter = positive_sq_second.clone()
second_inter.set_exponent(2)
steps.append(Sum([first_inter, second_inter]))
if q_subkind == 'squares_difference_mixed':
steps.append(Sum([second_inter, first_inter]))
steps.append(_("So, this expression can be factorized:"))
sum1 = None
sum2 = None
if sq_second_term.is_negative():
sum1 = Sum([sq_first_term, sq_second_term])
sq_second_term.set_sign('+')
sum2 = Sum([sq_first_term, sq_second_term])
else:
sum1 = Sum([sq_second_term, sq_first_term])
sq_first_term.set_sign('+')
sum2 = Sum([sq_second_term, sq_first_term])
lil_box = [sum1, sum2]
steps.append(Product([randomly.pop(lil_box), randomly.pop(lil_box)]))
elif q_subkind in [
'fake_01', 'fake_01_mixed', 'fake_02', 'fake_02_mixed', 'fake_03',
'fake_03_mixed', 'fake_04_A', 'fake_04_A_mixed', 'fake_04_B',
'fake_04_B_mixed', 'fake_04_C', 'fake_04_C_mixed', 'fake_04_D',
'fake_04_D_mixed'
]:
# __
straight_cases = [
'fake_01', 'fake_02', 'fake_03', 'fake_04_A', 'fake_04_B',
'fake_04_C', 'fake_04_D'
]
match_pb_cases = [
'fake_01', 'fake_02', 'fake_01_mixed', 'fake_02_mixed'
]
sign_pb_cases = [
'fake_03', 'fake_03_mixed', 'fake_04_A', 'fake_04_B', 'fake_04_C',
'fake_04_D', 'fake_04_A_mixed', 'fake_04_B_mixed',
'fake_04_C_mixed', 'fake_04_D_mixed'
]
ax = Monomial(('+', a, 1))
b_ = Monomial(('+', b, 0))
ax_2 = ax.clone()
ax_2.set_exponent(2)
a2x2 = Monomial(('+', a * a, 2))
b_2 = Monomial(('+', b, 0))
b_2.set_exponent(2)
b2 = Monomial(('+', b * b, 0))
two_ax_b = Product([Item(2), Monomial(('+', a, 1)), Item(b)])
twoabx = Monomial(('+', 2 * a * b, 1))
fake_twoabx = Monomial(('+', a * b, 1))
if randomly.integer(1, 10) >= 8:
fake_twoabx = Monomial(
('+',
2 * a * b + randomly.pop([-1, 1]) * randomly.integer(1, 5),
1))
first_term = None
second_term = None
third_term = None
ordered_expression = None
mixed_expression = None
if q_subkind == 'fake_03' or q_subkind == 'fake_03_mixed':
first_term = a2x2.clone()
second_term = b2.clone()
ordered_expression = Polynomial([first_term, second_term])
mixed_expression = Polynomial([second_term, first_term])
else:
first_term = a2x2.clone()
third_term = b2.clone()
if q_subkind in [
'fake_01', 'fake_01_mixed', 'fake_02', 'fake_02_mixed'
]:
# __
second_term = fake_twoabx.clone()
else:
second_term = twoabx.clone()
if q_subkind == 'fake_02' or q_subkind == 'fake_02_mixed':
second_term.set_sign('-')
elif q_subkind == 'fake_04_A' or q_subkind == 'fake_04_A_mixed':
third_term.set_sign('-')
elif q_subkind == 'fake_04_B' or q_subkind == 'fake_04_B_mixed':
first_term.set_sign('-')
elif q_subkind == 'fake_04_C' or q_subkind == 'fake_04_C_mixed':
second_term.set_sign('-')
third_term.set_sign('-')
elif q_subkind == 'fake_04_D' or q_subkind == 'fake_04_D_mixed':
first_term.set_sign('-')
second_term.set_sign('-')
ordered_expression = Polynomial(
[first_term, second_term, third_term])
mixed_expression = Polynomial(
randomly.mix([first_term, second_term, third_term]))
if q_subkind in straight_cases:
steps.append(ordered_expression)
elif q_subkind == 'fake_03_mixed':
steps.append(mixed_expression)
else:
steps.append(mixed_expression)
steps.append(ordered_expression)
if q_subkind in match_pb_cases:
let_a_eq = Equality([Item('a'), ax])
let_b_eq = Equality([Item('b'), b_])
steps.append(
_("Let") + " " +
let_a_eq.into_str(force_expression_markers=True) + " " +
_("and") + " " +
let_b_eq.into_str(force_expression_markers=True))
a_square_eq = Equality([Item(('+', 'a', 2)), ax_2, a2x2])
b_square_eq = Equality([Item(('+', 'b', 2)), b_2, b2])
steps.append(
_("then") + " " +
a_square_eq.into_str(force_expression_markers=True))
steps.append(
_("and") + " " +
b_square_eq.into_str(force_expression_markers=True))
two_times_a_times_b_eq = Equality([
Product([Item(2), Item('a'), Item('b')]), two_ax_b, twoabx,
fake_twoabx
],
equal_signs=['=', '=', 'neq'])
steps.append(
_("but") + " " +
two_times_a_times_b_eq.into_str(force_expression_markers=True))
steps.append(_("So it does not match a binomial identity."))
steps.append(_("This expression cannot be factorized."))
elif q_subkind in sign_pb_cases:
steps.append(_("Because of the signs,"))
steps.append(_("it does not match a binomial identity."))
steps.append(_("This expression cannot be factorized."))
return steps
def test_3x_squared_printed():
"""Is this squared Monomial printed correctly?"""
m = Monomial(('+', 3, 1))
m.set_exponent(2)
assert m.printed == wrap_nb('(3x)^{2}')