def test_eq37_autoresolution():
"""Is this Equation correctly auto-resolved?"""
eq = Equation((Monomial((Fraction(
(Item(2), Item(3))), 1)), Fraction((Item(4), Item(5)))))
assert eq.auto_resolution(dont_display_equations_name=True) == \
wrap_nb('\[\\frac{2}{3}x=\\frac{4}{5}\]'
'\[x=\\frac{4}{5}\div \\frac{2}{3}\]'
'\[x=\\frac{4}{5}\\times \\frac{3}{2}\]'
'\[x=\\frac{4\\times 3}{5\\times 2}\]'
'\[x=\\frac{\\bcancel{2}\\times 2\\times 3}'
'{5\\times \\bcancel{2}}\]'
'\[x=\\frac{6}{5}\]')
def test_fractions_by_items_01_next_step():
"""Is this Product's calculation's next step correct?"""
p = Product([
Fraction((Item(3), Item(5))),
Item(8),
Fraction((Item(7), Item(11))),
Item(4),
Fraction((Item(13), Item(17)))
])
assert p.calculate_next_step().printed == \
wrap_nb('\\frac{3\\times 8\\times 7\\times 4\\times 13}{5\\times 11'
'\\times 17}')
def test_eq39_autoresolution():
"""Is this Equation correctly auto-resolved?"""
eq = Equation((Sum([
Monomial((Fraction((Item(2), Item(1))).simplified(), 1)),
Fraction((Item(1), Item(5)))
]), Fraction(('-', Item(4), Item(5)))))
assert eq.auto_resolution(dont_display_equations_name=True) == \
wrap_nb('\[2x+\\frac{1}{5}=-\\frac{4}{5}\]'
'\[2x=-\\frac{4}{5}-\\frac{1}{5}\]'
'\[2x=\\frac{-4-1}{5}\]'
'\[2x=-\\frac{5}{5}\]'
'\[2x=-\\frac{\\bcancel{5}}{\\bcancel{5}}\]'
'\[2x=-1\]'
'\[x=-\\frac{1}{2}\]')
def test_f6_simplification_line():
"""Is this Fraction's simplification line correct?"""
assert Fraction(('+',
Product([Item(10), Item(5)]),
Product([Item(5), Item(9)])))\
.simplification_line().printed == \
wrap_nb('\\frac{10\\times \\bcancel{5}}{\\bcancel{5}\\times 9}')
def test_eq29_autoresolution():
"""Is this Equation correctly auto-resolved?"""
eq = Equation(
(Monomial(('+', 1, 1)),
Sum([Fraction((Item(1), Item(4))),
Fraction((Item(1), Item(8)))])),
number=1)
assert eq.auto_resolution(decimal_result=2) == \
wrap_nb('$(\\text{E}_{1}): $'
'\[x=\\frac{1}{4}+\\frac{1}{8}\]'
'\[x=\\frac{1\\times 2}{4\\times 2}'
'+\\frac{1}{8}\]'
'\[x=\\frac{2}{8}+\\frac{1}{8}\]'
'\[x=\\frac{2+1}{8}\]'
'\[x=\\frac{3}{8}\]'
'\[x\\simeq0.38\]')
def test_f3_simplification_line():
"""Is this Fraction's simplification line correct?"""
assert Fraction(('+',
Product([Item(7), Item(6)]),
Product([Item(3), Item(3)])))\
.simplification_line().printed == \
wrap_nb('\\frac{7\\times \\bcancel{3}\\times 2}'
'{\\bcancel{3}\\times 3}')
def fig0b():
fig0b = InterceptTheoremConfiguration(sketch=False,
rotate_around_isobarycenter=40)
fig0b.set_lengths([6, 12, 9], Fraction((Item(4), Item(3))))
fig0b.setup_labels(['?', True, False, True, True, True, False, False],
segments_list=[fig0b.u, fig0b.side[1], fig0b.v] +
fig0b.small + fig0b.chunk)
return fig0b
def test_f5_simplification_line():
"""Is this Fraction's simplification line correct?"""
assert Fraction(('+',
Product([Item(8), Item(3)]),
Product([Item(5), Item(6)])))\
.simplification_line().printed == \
wrap_nb('\\frac{\\bcancel{2}\\times 4\\times \\bcancel{3}}{5\\times'
' \\bcancel{2}\\times \\bcancel{3}}')
def test_eq38_autoresolution():
"""Is this Equation correctly auto-resolved?"""
eq = Equation((Sum([
Monomial((Fraction((Item(1), Item(4))), 1)),
Fraction((Item(1), Item(7)))
]), Fraction(('-', Item(3), Item(14)))))
assert eq.auto_resolution(dont_display_equations_name=True) == \
wrap_nb('\[\\frac{1}{4}x+\\frac{1}{7}=-\\frac{3}{14}\]'
'\[\\frac{1}{4}x=-\\frac{3}{14}-\\frac{1}{7}\]'
'\[\\frac{1}{4}x=-\\frac{3}{14}-\\frac{1\\times 2}'
'{7\\times 2}\]'
'\[\\frac{1}{4}x=-\\frac{3}{14}-\\frac{2}{14}\]'
'\[\\frac{1}{4}x=\\frac{-3-2}{14}\]'
'\[\\frac{1}{4}x=-\\frac{5}{14}\]'
'\[x=-\\frac{5}{14}\div \\frac{1}{4}\]'
'\[x=-\\frac{5}{14}\\times \\frac{4}{1}\]'
'\[x=-\\frac{5\\times 4}{14\\times 1}\]'
'\[x=-\\frac{5\\times \\bcancel{2}\\times 2}'
'{\\bcancel{2}\\times 7}\]'
'\[x=-\\frac{10}{7}\]')
def __init__(self, q_kind='default_nothing', **options):
self.derived = True
# The call to the mother class __init__() method will set the
# fields matching optional arguments which are so far:
# self.q_kind, self.q_subkind
# plus self.options (modified)
Q_Structure.__init__(self, q_kind, AVAILABLE_Q_KIND_VALUES, **options)
# The purpose of this next line is to get the possibly modified
# value of **options
options = self.options
# That's the number of the question, not of the expressions it might
# contain !
self.number = ""
if 'number_of_questions' in options:
self.number = options['number_of_questions']
self.objct = None
# 1st OPTION
if q_kind == 'fraction_simplification':
root = randomly.integer(2,
19,
weighted_table=[
0.225, 0.225, 0, 0.2, 0, 0.2, 0, 0, 0,
0.07, 0, 0.0375, 0, 0, 0, 0.0375, 0,
0.005
])
factors_list = [j + 1 for j in range(10)]
ten_power_factor1 = 1
ten_power_factor2 = 1
if 'with_ten_powers' in options \
and is_.a_number(options['with_ten_powers']) \
and options['with_ten_powers'] <= 1 \
and options['with_ten_powers'] >= 0:
# __
if randomly.decimal_0_1() < options['with_ten_powers']:
ten_powers_list = [10, 10, 100, 100]
ten_power_factor1 = randomly.pop(ten_powers_list)
ten_power_factor2 = randomly.pop(ten_powers_list)
self.objct = Fraction(
('+', root * randomly.pop(factors_list) * ten_power_factor1,
root * randomly.pop(factors_list) * ten_power_factor2))
# 2d & 3d OPTIONS
# Fractions Products | Quotients
elif q_kind in ['fractions_product', 'fractions_quotient']:
# In some cases, the fractions will be generated
# totally randomly
if randomly.decimal_0_1() < 0:
lil_box = [n + 2 for n in range(18)]
a = randomly.pop(
lil_box,
weighted_table=FRACTION_PRODUCT_AND_QUOTIENT_TABLE)
b = randomly.pop(
lil_box,
weighted_table=FRACTION_PRODUCT_AND_QUOTIENT_TABLE)
lil_box = [n + 2 for n in range(18)]
c = randomly.pop(
lil_box,
weighted_table=FRACTION_PRODUCT_AND_QUOTIENT_TABLE)
d = randomly.pop(
lil_box,
weighted_table=FRACTION_PRODUCT_AND_QUOTIENT_TABLE)
f1 = Fraction((randomly.sign(plus_signs_ratio=0.75),
Item((randomly.sign(plus_signs_ratio=0.80), a)),
Item(
(randomly.sign(plus_signs_ratio=0.80), b))))
f2 = Fraction((randomly.sign(plus_signs_ratio=0.75),
Item((randomly.sign(plus_signs_ratio=0.80), c)),
Item(
(randomly.sign(plus_signs_ratio=0.80), d))))
# f1 = f1.simplified()
# f2 = f2.simplified()
# In all other cases (80%), we'll define a "seed" a plus two
# randomly numbers i and j to form the Product | Quotient:
# a×i / b × c / a × j
# Where b is a randomly number coprime to a×i
# and c is a randomly number coprime to a×j
else:
a = randomly.integer(2, 8)
lil_box = [i + 2 for i in range(7)]
i = randomly.pop(lil_box)
j = randomly.pop(lil_box)
b = randomly.coprime_to(a * i, [n + 2 for n in range(15)])
c = randomly.not_coprime_to(b, [n + 2 for n in range(30)],
excepted=a * j)
f1 = Fraction(
(randomly.sign(plus_signs_ratio=0.75),
Item((randomly.sign(plus_signs_ratio=0.80), a * i)),
Item((randomly.sign(plus_signs_ratio=0.80), b))))
f2 = Fraction(
(randomly.sign(plus_signs_ratio=0.75),
Item((randomly.sign(plus_signs_ratio=0.80), c)),
Item((randomly.sign(plus_signs_ratio=0.80), a * j))))
if randomly.heads_or_tails():
f3 = f1.clone()
f1 = f2.clone()
f2 = f3.clone()
if q_kind == 'fractions_quotient':
f2 = f2.invert()
if q_kind == 'fractions_product':
self.objct = Product([f1, f2])
elif q_kind == 'fractions_quotient':
self.objct = Quotient(('+', f1, f2, 1, 'use_divide_symbol'))
# 4th OPTION
# Fractions Sums
elif q_kind == 'fractions_sum':
randomly_position = randomly\
.integer(0, 16, weighted_table=FRACTIONS_SUMS_SCALE_TABLE)
chosen_seed_and_generator = FRACTIONS_SUMS_TABLE[randomly_position]
seed = randomly.integer(2, chosen_seed_and_generator[1])
# The following test is only intended to avoid having "high"
# results too often. We just check if the common denominator
# will be higher than 75 (arbitrary) and if yes, we redetermine
# it once. We don't do it twice since we don't want to totally
# forbid high denominators.
if seed * chosen_seed_and_generator[0][0] \
* chosen_seed_and_generator[0][1] >= 75:
# __
seed = randomly.integer(2, chosen_seed_and_generator[1])
lil_box = [0, 1]
gen1 = chosen_seed_and_generator[0][lil_box.pop()]
gen2 = chosen_seed_and_generator[0][lil_box.pop()]
den1 = Item(gen1 * seed)
den2 = Item(gen2 * seed)
temp1 = randomly.integer(1, 20)
temp2 = randomly.integer(1, 20)
num1 = Item(temp1 // gcd(temp1, gen1 * seed))
num2 = Item(temp2 // gcd(temp2, gen2 * seed))
f1 = Fraction((randomly.sign(plus_signs_ratio=0.7), num1, den1))
f2 = Fraction((randomly.sign(plus_signs_ratio=0.7), num2, den2))
self.objct = Sum([f1.simplified(), f2.simplified()])
# 5th
# still to imagine:o)
# Creation of the expression:
number = 0
if 'expression_number' in options \
and is_.a_natural_int(options['expression_number']):
# __
number = options['expression_number']
self.expression = Expression(number, self.objct)
def q1():
return Quotient(('+', Fraction(('+', 8, 9)), Fraction(
('+', 7, 2)), 1, 'use_divide_symbol'))
def q2():
return Quotient(('-', Fraction(('+', 1, 2)), Fraction(
('+', 1, 3)), 1, 'use_divide_symbol'))
def fs1():
return Sum([Fraction(('+', 1, 4)), Fraction(('+', 1, 8))])
def fs2():
return Sum([Fraction(('+', 1, 9)), Fraction(('+', 1, -12))])
def fs7():
return Sum([Item(4), Fraction((25, 10)), Item(-7), Fraction((1, 10))])
def fs0():
return Sum([Fraction(('+', 2, 3)), Fraction(('+', 3, 4))])
def fs5():
return Sum([Fraction(('+', 25, 10)), Fraction(('+', 1, 10))])
def fs6():
return Sum([Fraction(('-', 18, 5)), Fraction(('-', 2, 5))])
def fp1(): return Product([Fraction((14, 7)), Fraction((12, 12))]) @pytest.fixture
def test_f12_eval():
"""Is this Fraction correctly evaluated?"""
assert Fraction((Item(3), Item(7))).evaluate() == \
decimal.Decimal('0.4285714285714285714285714286')
def test_f12_eval2():
"""Is this Fraction correctly evaluated?"""
assert Fraction((Item(3), Item(7)))\
.evaluate(keep_not_decimal_nb_as_fractions=True).printed == \
wrap_nb('\\frac{3}{7}')
def f1():
return Fraction(('+', 92, 76))
def fig1():
fig1 = InterceptTheoremConfiguration(sketch=False,
butterfly=True,
rotate_around_isobarycenter=40)
fig1.set_lengths([6, 12, 9], Fraction((Item(4), Item(3))))
return fig1
def f2():
return Fraction(('+', Product([Item(10),
Item(6)]), Product([Item(7),
Item(2)])))
def test_f4_next_step():
"""Is this Fraction's calculation's next step correct?"""
assert Fraction(('+',
Product([Item(3), Item(7)]),
Product([Item(10), Item(4)])))\
.calculate_next_step().printed == wrap_nb('\\frac{21}{40}')
def generate_values(source_id):
if source_id == 'int_irreducible_frac':
return [(k, Fraction((n, k))) for k in [i + 2 for i in range(18)]
for n in coprime_generator(k)]
elif source_id == 'rank_words':
return [(elt,) for elt in RANKS]
elif source_id == 'decimal_and_10_100_1000_for_multi':
box_10_100_1000 = [10, 100, 1000]
result = set()
for n in range(20):
if not box_10_100_1000:
box_10_100_1000 = [10, 100, 1000]
chosen_10_100_1000 = box_10_100_1000.pop()
ranks_scale = list(RANKS[2:])
width = randomly.pop([1, 2, 3], weighted_table=[0.14, 0.63, 0.33])
start_rank = randomly.pop([n for n in range(len(ranks_scale))])
result |= {(chosen_10_100_1000,
generate_decimal(width, ranks_scale, start_rank))}
return list(result)
elif source_id == 'decimal_and_10_100_1000_for_divi':
box_10_100_1000 = [10, 100, 1000]
result = set()
for n in range(20):
if not box_10_100_1000:
box_10_100_1000 = [10, 100, 1000]
chosen_10_100_1000 = box_10_100_1000.pop()
ranks_scale = list(RANKS[2:])
width = randomly.pop([1, 2, 3], weighted_table=[0.14, 0.63, 0.33])
wt = {10: [0.2, 0.2, 0.2, 0.2, 0.2],
100: [0.25, 0.25, 0.25, 0.25, 0],
1000: [0.34, 0.33, 0.33, 0, 0]}
start_rank = randomly.pop([n for n in range(len(ranks_scale))],
weighted_table=wt[chosen_10_100_1000])
result |= {(chosen_10_100_1000,
generate_decimal(width, ranks_scale, start_rank))}
return list(result)
elif source_id == 'decimal_and_one_digit_for_multi':
box = [Decimal('0.1'), Decimal('0.01'), Decimal('0.001')]
result = set()
for n in range(20):
if not box:
box = [Decimal('0.1'), Decimal('0.01'), Decimal('0.001')]
chosen = box.pop()
ranks_scale = list()
if chosen == Decimal('0.1'):
ranks_scale = list(RANKS[:-1])
elif chosen == Decimal('0.01'):
ranks_scale = list(RANKS[:-2])
elif chosen == Decimal('0.001'):
ranks_scale = list(RANKS[:-3])
width = randomly.pop([1, 2, 3, 4],
weighted_table=[0.14, 0.43, 0.33, 0.2])
start_rank = randomly.pop([n for n in range(len(ranks_scale))])
result |= {(chosen,
generate_decimal(width, ranks_scale, start_rank))}
return list(result)
elif source_id == 'decimal_and_one_digit_for_divi':
box = [Decimal('0.1'), Decimal('0.01'), Decimal('0.001')]
result = set()
for n in range(20):
if not box:
box = [Decimal('0.1'), Decimal('0.01'), Decimal('0.001')]
chosen = box.pop()
ranks_scale = list()
if chosen == Decimal('0.1') or chosen == Decimal('0.01'):
ranks_scale = list(RANKS)
elif chosen == Decimal('0.001'):
ranks_scale = list(RANKS[1:])
width = randomly.pop([1, 2, 3, 4],
weighted_table=[0.14, 0.43, 0.33, 0.2])
start_rank = randomly.pop([n for n in range(len(ranks_scale))])
result |= {(chosen,
generate_decimal(width, ranks_scale, start_rank))}
return list(result)
elif source_id in ['nothing', 'bypass']:
return []
def fs3():
return Sum([Fraction(('+', -7, 10)), Fraction(('-', 11, -15))])
def fp0(): return Product([Fraction((5, 4)), Fraction((5, 5))]) @pytest.fixture
def fs4():
return Sum([Fraction(('+', 3, 4)), Item(-5)])
def fp2(): return Product([Fraction((9, -2)), Fraction((-8, 10))]) @pytest.fixture
def __init__(self, q_kind='default_nothing', **options):
self.derived = True
# The call to the mother class __init__() method will set the
# fields matching optional arguments which are so far:
# self.q_kind, self.q_subkind
# plus self.options (modified)
Q_Structure.__init__(self,
q_kind, AVAILABLE_Q_KIND_VALUES,
**options)
# The purpose of this next line is to get the possibly modified
# value of **options
options = self.options
# That's the number of the question, not of the expressions it might
# contain !
self.number = ""
if 'number_of_questions' in options:
self.number = options['number_of_questions']
self.objct = None
# 1st OPTION
if q_kind == 'fraction_simplification':
root = random.choices([n + 2 for n in range(19 - 2 + 1)],
weights=[0.225, 0.225, 0, 0.2,
0, 0.2, 0, 0, 0, 0.07,
0, 0.0375, 0, 0, 0,
0.0375, 0, 0.005])[0]
ten_power_factor1 = 1
ten_power_factor2 = 1
if 'with_ten_powers' in options \
and is_number(options['with_ten_powers']) \
and options['with_ten_powers'] <= 1 \
and options['with_ten_powers'] >= 0:
# __
if random.random() < options['with_ten_powers']:
ten_powers_list = [10, 10, 100, 100]
random.shuffle(ten_powers_list)
ten_power_factor1 = ten_powers_list.pop()
ten_power_factor2 = ten_powers_list.pop()
factors_list = [j + 1 for j in range(10)]
random.shuffle(factors_list)
self.objct = Fraction(('+',
root * factors_list.pop()
* ten_power_factor1,
root * factors_list.pop()
* ten_power_factor2))
# 2d & 3d OPTIONS
# Fractions Products | Quotients
elif q_kind in ['fractions_product', 'fractions_quotient']:
# In some cases, the fractions will be generated
# totally randomly
if random.random() < 0:
lil_box = [n + 2 for n in range(18)]
a = random.choices(
lil_box,
weights=FRACTION_PRODUCT_AND_QUOTIENT_TABLE)[0]
b = random.choices(
lil_box,
weights=FRACTION_PRODUCT_AND_QUOTIENT_TABLE)[0]
lil_box = [n + 2 for n in range(18)]
c = random.choices(
lil_box,
weights=FRACTION_PRODUCT_AND_QUOTIENT_TABLE)[0]
d = random.choices(
lil_box,
weights=FRACTION_PRODUCT_AND_QUOTIENT_TABLE)[0]
f1 = Fraction((random.choices(['+', '-'],
cum_weights=[0.75, 1])[0],
Item((random.choices(['+', '-'],
cum_weights=[0.80, 1])[0],
a)),
Item((random.choices(['+', '-'],
cum_weights=[0.80, 1])[0],
b))))
f2 = Fraction((random.choices(['+', '-'],
cum_weights=[0.75, 1])[0],
Item((random.choices(['+', '-'],
cum_weights=[0.80, 1])[0],
c)),
Item((random.choices(['+', '-'],
cum_weights=[0.80, 1])[0],
d))))
# f1 = f1.simplified()
# f2 = f2.simplified()
# In all other cases (80%), we'll define a "seed" a plus two
# randomly numbers i and j to form the Product | Quotient:
# a×i / b × c / a × j
# Where b is a randomly number coprime to a×i
# and c is a randomly number coprime to a×j
else:
a = random.randint(2, 8)
lil_box = [i + 2 for i in range(7)]
random.shuffle(lil_box)
i = lil_box.pop()
j = lil_box.pop()
b = random.choice(coprimes_to(a * i,
[n + 2 for n in range(15)]))
c = random.choice(not_coprimes_to(b,
[n + 2 for n in range(30)],
exclude=[a * j]))
f1 = Fraction((random.choices(['+', '-'],
cum_weights=[0.75, 1])[0],
Item((random.choices(['+', '-'],
cum_weights=[0.80, 1])[0],
a * i)),
Item((random.choices(['+', '-'],
cum_weights=[0.80, 1])[0],
b))))
f2 = Fraction((random.choices(['+', '-'],
cum_weights=[0.75, 1])[0],
Item((random.choices(['+', '-'],
cum_weights=[0.80, 1])[0],
c)),
Item((random.choices(['+', '-'],
cum_weights=[0.80, 1])[0],
a * j))))
if random.choice([True, False]):
f3 = f1.clone()
f1 = f2.clone()
f2 = f3.clone()
if q_kind == 'fractions_quotient':
f2 = f2.invert()
if q_kind == 'fractions_product':
self.objct = Product([f1, f2])
elif q_kind == 'fractions_quotient':
self.objct = Quotient(('+', f1, f2, 1,
'use_divide_symbol'))
# 4th OPTION
# Fractions Sums
elif q_kind == 'fractions_sum':
randomly_position = random\
.choices([n for n in range(17)],
weights=FRACTIONS_SUMS_SCALE_TABLE)[0]
chosen_seed_and_generator = FRACTIONS_SUMS_TABLE[randomly_position]
seed = random.randint(2, chosen_seed_and_generator[1])
# The following test is only intended to avoid having "high"
# results too often. We just check if the common denominator
# will be higher than 75 (arbitrary) and if yes, we redetermine
# it once. We don't do it twice since we don't want to totally
# forbid high denominators.
if seed * chosen_seed_and_generator[0][0] \
* chosen_seed_and_generator[0][1] >= 75:
# __
seed = random.randint(2, chosen_seed_and_generator[1])
lil_box = [0, 1]
gen1 = chosen_seed_and_generator[0][lil_box.pop()]
gen2 = chosen_seed_and_generator[0][lil_box.pop()]
den1 = Item(gen1 * seed)
den2 = Item(gen2 * seed)
temp1 = random.randint(1, 20)
temp2 = random.randint(1, 20)
num1 = Item(temp1 // gcd(temp1, gen1 * seed))
num2 = Item(temp2 // gcd(temp2, gen2 * seed))
f1 = Fraction((random.choices(['+', '-'], cum_weights=[0.7, 1])[0],
num1,
den1))
f2 = Fraction((random.choices(['+', '-'], cum_weights=[0.7, 1])[0],
num2,
den2))
self.objct = Sum([f1.simplified(),
f2.simplified()])
# 5th
# still to imagine:o)
# Creation of the expression:
number = 0
if 'expression_number' in options \
and is_natural(options['expression_number']):
# __
number = options['expression_number']
self.expression = Expression(number, self.objct)
