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
init_caller = INIT_CALLER[q_kind]
self.expandable_objct = None
self.numeric_aux = None
if q_kind == 'any_basic_expd':
randomly_drawn = randomly.decimal_0_1()
if randomly_drawn <= 0.25:
self.expandable_objct = Expandable((RANDOMLY, 'monom0_polyn1'),
randomly_reversed=0.5)
elif randomly_drawn <= 0.50:
self.expandable_objct = Expandable((RANDOMLY, 'monom1_polyn1'),
randomly_reversed=0.5)
else:
self.expandable_objct = Expandable((RANDOMLY, 'polyn1_polyn1'))
elif q_kind in ['monom0_polyn1', 'monom1_polyn1']:
self.expandable_objct = Expandable((RANDOMLY, q_kind),
randomly_reversed=0.5)
elif q_kind == 'monom01_polyn1':
self.expandable_objct = Expandable(
(RANDOMLY, randomly.pop(['monom0_polyn1', 'monom1_polyn1'])),
randomly_reversed=0.5)
elif q_kind == 'polyn1_polyn1':
self.expandable_objct = Expandable((RANDOMLY, 'polyn1_polyn1'))
elif q_kind == 'sum_of_any_basic_expd':
if self.q_subkind in ['harder', 'with_a_binomial']:
# __
choices = ['monom0_polyn1', 'monom1_polyn1']
drawn_types = list()
drawn_types.append(randomly.pop(choices))
if self.q_subkind == 'with_a_binomial':
drawn_types.append('any_binomial')
else:
drawn_types.append('minus_polyn1_polyn1')
aux_expd_list = list()
for t in drawn_types:
if t == 'any_binomial':
aux_expd_list.append(
BinomialIdentity((RANDOMLY, 'any'), **options))
else:
aux_expd_list.append(Expandable((RANDOMLY, t)))
final_list = list()
for i in range(len(aux_expd_list)):
final_list.append(randomly.pop(aux_expd_list))
self.expandable_objct = Sum(final_list)
elif self.q_subkind == 'easy':
choices = ['monom0_polyn1', 'monom1_polyn1']
aux_expd_list = list()
aux_expd_list.append(
Expandable((RANDOMLY, randomly.pop(choices))))
if randomly.heads_or_tails():
aux_expd_list.append(Expandable((RANDOMLY, 'sign_exp')))
else:
aux_expd_list.append(
Monomial((RANDOMLY, 15, randomly.integer(0, 2))))
final_list = list()
for i in range(len(aux_expd_list)):
final_list.append(randomly.pop(aux_expd_list))
self.expandable_objct = Sum(final_list)
else:
choices = [
'monom0_polyn1', 'monom0_polyn1', 'monom1_polyn1',
'monom1_polyn1', 'polyn1_polyn1', 'minus_polyn1_polyn1'
]
drawn_types = list()
drawn_types.append(randomly.pop(choices))
drawn_types.append(randomly.pop(choices))
aux_expd_list = list()
for element in drawn_types:
aux_expd_list.append(Expandable((RANDOMLY, element)))
aux_expd_list.append(Monomial((RANDOMLY, 15, 2)))
final_list = list()
for i in range(len(aux_expd_list)):
final_list.append(randomly.pop(aux_expd_list))
self.expandable_objct = Sum(final_list)
elif q_kind in ['sign_expansion', 'sign_expansion_short_test']:
sign_exp_kind = options.get('sign_exp_kind', 0)
if q_kind == 'sign_expansion_short_test':
sign_exp_kind = 1
if sign_exp_kind == 0:
sign_exp_kind = randomly.integer(1, 5)
# Creation of the terms
aux_terms_list = list()
aux_expd_1 = Expandable((Monomial(
(randomly.sign(), 1, 0)), Polynomial((RANDOMLY, 15, 2, 2))))
aux_expd_2 = Expandable((Monomial(
(randomly.sign(), 1, 0)), Polynomial((RANDOMLY, 15, 2, 2))))
aux_expd_3 = Expandable((Monomial(
(randomly.sign(), 1, 0)), Polynomial((RANDOMLY, 15, 2, 2))))
long_aux_expd = Expandable((Monomial(
(randomly.sign(), 1, 0)), Polynomial((RANDOMLY, 15, 2, 3))))
if q_kind == 'sign_expansion_short_test':
long_aux_expd = Expandable((Monomial(
('-', 1, 0)), Polynomial((RANDOMLY, 15, 2, 3))))
aux_monomial = Monomial((RANDOMLY, 15, 2))
# 1st kind: a Monomial and ± (long Polynomial)
# (like in a short test)
if sign_exp_kind == 1:
aux_terms_list.append(long_aux_expd)
aux_terms_list.append(aux_monomial)
# 2d kind: ± (x+3) ± (4x - 7)
elif sign_exp_kind == 2:
aux_terms_list.append(aux_expd_1)
aux_terms_list.append(aux_expd_2)
# 3d kind: ± (x+3) ± (4x - 7) ± (x² - 5x)
elif sign_exp_kind == 3:
aux_terms_list.append(aux_expd_1)
aux_terms_list.append(aux_expd_2)
aux_terms_list.append(aux_expd_3)
# 4th kind: ± (x+3) ± (4x - 7) ± Monomial
elif sign_exp_kind == 4:
aux_terms_list.append(aux_expd_1)
aux_terms_list.append(aux_expd_2)
aux_terms_list.append(aux_monomial)
# 5th kind: ± (x+3) ± Monomial ± (long Polynomial)
elif sign_exp_kind == 5:
aux_terms_list.append(aux_expd_2)
aux_terms_list.append(aux_monomial)
aux_terms_list.append(long_aux_expd)
# add as many possibilities as wanted,
# don't forget to increase the last number here:
# sign_exp_kind = randomly.integer(1, 5) (what's a bit above)
# Now let's distribute the terms randomly
final_terms_list = list()
for i in range(len(aux_terms_list)):
final_terms_list.append(randomly.pop(aux_terms_list))
self.expandable_objct = Sum(final_terms_list)
elif q_kind in [
'numeric_sum_square', 'numeric_difference_square',
'numeric_squares_difference'
]:
# __
self.expandable_objct = init_caller(
(options['couple'][0], options['couple'][1]), **options)
if q_kind in ['numeric_sum_square', 'numeric_difference_square']:
self.numeric_aux = Sum(
[options['couple'][0], options['couple'][1]]).reduce_()
self.numeric_aux.set_exponent(2)
else: # squares_difference's case
aux1 = Sum([options['couple'][0],
options['couple'][1]]).reduce_()
temp = options['couple'][1].clone()
temp.set_sign('-')
aux2 = Sum([options['couple'][0], temp]).reduce_()
self.numeric_aux = Product([aux1, aux2])
else:
if q_kind == 'any_binomial':
q_kind = 'any'
self.expandable_objct = init_caller((RANDOMLY, q_kind), **options)
# 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.expandable_objct)
if self.numeric_aux is not None:
self.numeric_aux = Expression(number, self.numeric_aux)
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 level_01(q_subkind, **options):
if q_subkind == 'default' \
or q_subkind == 'three_terms' \
or q_subkind == 'ax + b' \
or q_subkind == 'ax² + b' \
or q_subkind == 'ax² + bx':
# __
# the idea is to build the final factorized result first and to
# expand it to get the question (and the solution's steps
# in the same time)
if q_subkind == 'default':
common_factor = Monomial((RANDOMLY, 6, 1))
# In order to reduce the number of cases where x² appears,
# let the common factor be of degree 0 most of the time.
common_factor.set_degree(
randomly.integer(0, 1, weighted_table=[0.85, 0.15]))
elif q_subkind in ['three_terms', 'ax + b', 'ax² + b']:
common_factor = Monomial((RANDOMLY, 6, 0))
elif q_subkind == 'ax² + bx':
common_factor = Monomial((RANDOMLY, 6, 1))
common_factor.set_degree(1)
# to avoid having a situation like 1×(2x + 3) which isn't
# factorizable:
if common_factor.get_degree() == 0:
common_factor.set_coeff(randomly.integer(2, 6))
# signs are randomly chosen ; the only case that is to be avoided
# is all signs are negative (then it wouldn't factorize well...
# I mean then the '-' should be factorized and not left in the final
# result)
signs_box = [['+', '+'], ['+', '-']]
signs = randomly.pop(signs_box)
# this next test is to avoid -2x + 6 being factorized -2(x - 3)
# which is not wrong but not "natural" to pupils
# this test should be changed when a third term is being used.
if signs == ['+', '-']:
common_factor.set_sign('+')
coeff_1 = randomly.integer(2, 10)
coeff_2 = randomly.coprime_to(coeff_1, [i + 1 for i in range(10)])
coeff_3 = None
if q_subkind == 'three_terms':
coeff_3 = randomly.coprime_to(coeff_1 * coeff_2,
[i + 1 for i in range(9)])
third_sign = randomly.sign()
if third_sign == '-':
common_factor.set_sign('+')
signs.append(third_sign)
lil_box = []
lil_box.append(Monomial(('+', 1, 0)))
if q_subkind == 'ax² + b':
lil_box.append(Monomial(('+', 1, 2)))
else:
lil_box.append(Monomial(('+', 1, 1)))
if ((common_factor.get_degree() == 0 and randomly.integer(1, 20) > 17
and q_subkind == 'default') or q_subkind == 'three_terms'):
# __
lil_box.append(Monomial(('+', 1, 2)))
first_term = randomly.pop(lil_box)
second_term = randomly.pop(lil_box)
third_term = None
first_term.set_coeff(coeff_1)
first_term.set_sign(randomly.pop(signs))
second_term.set_coeff(coeff_2)
second_term.set_sign(randomly.pop(signs))
if q_subkind == 'three_terms':
third_term = randomly.pop(lil_box)
third_term.set_coeff(coeff_3)
third_term.set_sign(randomly.pop(signs))
if first_term.is_positive() and second_term.is_positive()\
and third_term.is_positive():
# __
common_factor.set_sign(randomly.sign())
if not (q_subkind == 'three_terms'):
if common_factor.get_degree() == 0 \
and first_term.get_degree() >= 1 \
and second_term.get_degree() >= 1:
# __
if randomly.heads_or_tails():
first_term.set_degree(0)
else:
second_term.set_degree(0)
if q_subkind == 'three_terms':
solution = Expandable(
(common_factor, Sum([first_term, second_term, third_term])))
else:
solution = Expandable(
(common_factor, Sum([first_term, second_term])))
# now create the expanded step and the reduced step (which will
# be given as a question)
temp_steps = []
current_step = solution.clone()
while current_step is not None:
temp_steps.append(current_step)
current_step = current_step.expand_and_reduce_next_step()
# now we put the steps in the right order
steps = []
for i in range(len(temp_steps)):
steps.append(temp_steps[len(temp_steps) - 1 - i])
return steps
elif q_subkind == 'not_factorizable':
signs_box = [['+', '+'], ['+', '-']]
signs = randomly.pop(signs_box)
coeff_1 = randomly.integer(2, 10)
coeff_2 = randomly.coprime_to(coeff_1, [i + 1 for i in range(10)])
lil_box = []
lil_box.append(Monomial(('+', 1, 0)))
lil_box.append(Monomial(('+', 1, 1)))
lil_box.append(Monomial(('+', 1, 2)))
first_term = randomly.pop(lil_box)
second_term = randomly.pop(lil_box)
first_term.set_coeff(coeff_1)
first_term.set_sign(randomly.pop(signs))
second_term.set_coeff(coeff_2)
second_term.set_sign(randomly.pop(signs))
if first_term.get_degree() >= 1 \
and second_term.get_degree() >= 1:
# __
if randomly.heads_or_tails():
first_term.set_degree(0)
else:
second_term.set_degree(0)
steps = []
solution = _("So far, we don't know if this expression can be "
"factorized.")
steps.append(Sum([first_term, second_term]))
steps.append(solution)
return steps
def level_02(q_subkind, **options):
max_coeff = 20
if 'max_coeff' in options and is_.an_integer(options['max_coeff']):
max_coeff = options['max_coeff']
attribute_a_minus_sign = 'randomly'
if 'minus_sign' in options and options['minus_sign']:
attribute_a_minus_sign = 'yes'
elif 'minus_sign' in options and not options['minus_sign']:
attribute_a_minus_sign = 'no'
# Creation of the objects
# The three Monomials: ax², bx and c
# Maybe we don't need to keep the integer values...
a_val = randomly.integer(1, max_coeff)
b_val = randomly.integer(1, max_coeff)
c_val = randomly.integer(1, max_coeff)
if q_subkind in [
'type_1_A0', 'type_1_B0', 'type_1_C0', 'type_1_A1', 'type_1_B1',
'type_1_C1'
]:
# __
c_val = randomly.integer(2, max_coeff)
ax2 = Monomial((randomly.sign(), a_val, 2))
bx = Monomial((randomly.sign(), b_val, 1))
c = Monomial((randomly.sign(), c_val, 0))
# deg1: mx + p
# and we need two of them
deg1 = []
for i in range(2):
deg1_mx = Monomial((randomly.sign(), randomly.integer(1,
max_coeff), 1))
deg1_p = None
if q_subkind in [
'type_1_A0', 'type_1_B0', 'type_1_C0', 'type_1_D0',
'type_1_E0', 'type_1_F0', 'type_1_G0', 'type_1_H0',
'type_1_I0', 'type_1_A1', 'type_1_B1', 'type_1_D1',
'type_1_E1', 'type_1_G1', 'type_1_H1', 'type_4_A0'
]:
# __
deg1_p = Monomial(
(randomly.sign(), randomly.integer(1, max_coeff), 0))
else:
deg1_p = Monomial(
(randomly.sign(), randomly.integer(0, max_coeff), 0))
if not deg1_p.is_null():
lil_box = [deg1_mx, deg1_p]
deg1.append(
Polynomial([randomly.pop(lil_box),
randomly.pop(lil_box)]))
else:
deg1.append(deg1_mx)
# deg2: mx² + px + r
# and we also need two of them
deg2 = []
for i in range(2):
deg2_mx2 = Monomial((randomly.sign(), randomly.integer(1,
max_coeff), 2))
deg2_px = None
deg2_r = None
if q_subkind in [
'type_1_A0', 'type_1_B0', 'type_1_C0', 'type_1_D0',
'type_1_E0', 'type_1_F0', 'type_1_G0', 'type_1_H0',
'type_1_I0', 'type_1_A1', 'type_1_B1', 'type_1_D1',
'type_1_E1', 'type_1_G1', 'type_1_H1'
]:
# __
if randomly.heads_or_tails():
deg2_px = Monomial(
(randomly.sign(), randomly.integer(1, max_coeff), 1))
deg2_r = Monomial(
(randomly.sign(), randomly.integer(0, max_coeff), 0))
else:
deg2_px = Monomial(
(randomly.sign(), randomly.integer(0, max_coeff), 1))
deg2_r = Monomial(
(randomly.sign(), randomly.integer(1, max_coeff), 0))
else:
deg2_px = Monomial(
(randomly.sign(), randomly.integer(0, max_coeff), 1))
deg2_r = Monomial(
(randomly.sign(), randomly.integer(0, max_coeff), 0))
lil_box = [deg2_mx2]
if not deg2_px.is_null():
lil_box.append(deg2_px)
if not deg2_r.is_null():
lil_box.append(deg2_r)
monomials_list_for_deg2 = []
for i in range(len(lil_box)):
monomials_list_for_deg2.append(randomly.pop(lil_box))
deg2.append(Polynomial(monomials_list_for_deg2))
# Let's attribute the common factor C according to the required type
# (NB: expression ± C×F1 ± C×F2)
C = None
if q_subkind in [
'type_1_A0', 'type_1_B0', 'type_1_C0', 'type_1_A1', 'type_1_B1'
]:
# __
C = c
elif q_subkind in [
'type_1_D0', 'type_1_E0', 'type_1_F0', 'type_1_D1', 'type_1_E1'
]:
# __
C = bx
elif q_subkind in [
'type_1_G0', 'type_1_H0', 'type_1_I0', 'type_1_G1', 'type_1_H1'
]:
# __
C = ax2
elif q_subkind in [
'type_2_A0', 'type_2_B0', 'type_2_C0', 'type_2_A1', 'type_2_B1',
'type_4_A0'
]:
# __
C = Polynomial([bx, c])
elif q_subkind in [
'type_2_D0', 'type_2_E0', 'type_2_F0', 'type_2_D1', 'type_2_E1'
]:
# __
C = Polynomial([ax2, c])
elif q_subkind in [
'type_3_A0', 'type_3_B0', 'type_3_C0', 'type_3_A1', 'type_3_B1'
]:
# __
C = Polynomial([ax2, bx, c])
# Let's attribute F1 and F2 according to the required type
# (NB: expression ± C×F1 ± C×F2)
F1 = None
F2 = None
if q_subkind in [
'type_1_A0', 'type_1_A1', 'type_1_D0', 'type_1_D1', 'type_1_G0',
'type_1_G1', 'type_2_A0', 'type_2_A1', 'type_2_D0', 'type_2_D1',
'type_3_A0', 'type_3_A1'
]:
# __
F1 = deg1[0]
F2 = deg1[1]
elif q_subkind in [
'type_1_B0', 'type_1_B1', 'type_1_E0', 'type_1_E1', 'type_1_H0',
'type_1_H1', 'type_2_B0', 'type_2_B1', 'type_2_E0', 'type_2_E1',
'type_3_B0', 'type_3_B1'
]:
# __
F1 = deg2[0]
F2 = deg2[1]
elif q_subkind in [
'type_1_C0', 'type_1_F0', 'type_1_I0', 'type_2_C0', 'type_2_F0',
'type_3_C0'
]:
# __
F1 = deg1[0]
F2 = deg2[0]
# The special case type_4_A0: (ax+b)² + (ax+b)×deg1'
# aka C² + C×F1
elif q_subkind == 'type_4_A0':
F1 = C.clone()
F2 = deg1[0]
# Let's put a "1" somewhere in the type_*_*1
if q_subkind in [
'type_1_A1', 'type_1_D1', 'type_1_G1', 'type_2_A1', 'type_2_D1',
'type_3_A1', 'type_1_B1', 'type_1_E1'
'type_1_H1', 'type_2_B1', 'type_2_E1', 'type_3_B1'
]:
# __
if randomly.heads_or_tails():
F1 = Item(1)
else:
F2 = Item(1)
# Let's possibly attribute a minus_sign
# (NB: expression ± C×F1 ± C×F2)
minus_sign = None
# this will contain the name of the factor having
# a supplementary minus sign in such cases:
# C×F1 - C×F2# - C×F1 + C×F2
# in all the following cases, it doesn't bring anything to attribute
# a minus sign
if ((q_subkind
in ['type_1_A0', 'type_1_B0', 'type_1_C0', 'type_1_A1', 'type_1_B1']
and c_val < 0) or
((q_subkind
in ['type_1_D0', 'type_1_E0', 'type_1_F0', 'type_1_D1', 'type_1_E1'])
and b_val < 0) or
((q_subkind
in ['type_1_G0', 'type_1_H0', 'type_1_I0', 'type_1_G1', 'type_1_H1'])
and a_val < 0)):
# __
pass # here we let minus_sign equal to None
# otherwise, let's attribute one randomly,
# depending on attribute_a_minus_sign
else:
if attribute_a_minus_sign in ['yes', 'randomly']:
# __
if (attribute_a_minus_sign == 'yes' or randomly.heads_or_tails()):
# __
if randomly.heads_or_tails():
minus_sign = "F1"
else:
minus_sign = "F2"
else:
pass # here we let minus_sign equal to None
# Now let's build the expression !
expression = None
box_product1 = [C, F1]
box_product2 = [C, F2]
if q_subkind == 'type_4_A0':
CF1 = Product([C])
CF1.set_exponent(Value(2))
else:
CF1 = Product([randomly.pop(box_product1), randomly.pop(box_product1)])
CF2 = Product([randomly.pop(box_product2), randomly.pop(box_product2)])
if minus_sign == "F1":
if len(F1) >= 2:
CF1 = Expandable((Item(-1), CF1))
else:
CF1 = Product([Item(-1), CF1])
elif minus_sign == "F2":
if len(F2) >= 2:
CF2 = Expandable((Item(-1), CF2))
else:
CF2 = Product([Item(-1), CF2])
expression = Sum([CF1, CF2])
# Now let's build the factorization steps !
steps = []
steps.append(expression)
F1F2_sum = None
if minus_sign is None:
F1F2_sum = Sum([F1, F2])
elif minus_sign == "F1":
if len(F1) >= 2:
F1F2_sum = Sum([Expandable((Item(-1), F1)), F2])
else:
F1F2_sum = Sum([Product([Item(-1), F1]), F2])
elif minus_sign == "F2":
if len(F2) >= 2:
F1F2_sum = Sum([F1, Expandable((Item(-1), F2))])
else:
F1F2_sum = Sum([F1, Product([Item(-1), F2])])
temp = Product([C, F1F2_sum])
temp.set_compact_display(False)
steps.append(temp)
F1F2_sum = F1F2_sum.expand_and_reduce_next_step()
while F1F2_sum is not None:
steps.append(Product([C, F1F2_sum]))
F1F2_sum = F1F2_sum.expand_and_reduce_next_step()
# This doesn't fit the need, because too much Products are
# wrongly recognized as reducible !
if steps[len(steps) - 1].is_reducible():
steps.append(steps[len(steps) - 1].reduce_())
return steps
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
MAX_COEFF = MAX_COEFF_TABLE[q_kind]
MAX_EXPONENT = MAX_EXPONENT_TABLE[q_kind]
DEFAULT_MINIMUM_LENGTH = DEFAULT_MINIMUM_LENGTH_TABLE[q_kind]
DEFAULT_MAXIMUM_LENGTH = DEFAULT_MAXIMUM_LENGTH_TABLE[q_kind]
# This field is to be used in the answer_to_strs() method
# to determine a possibly different algorithm for particular cases
self.kind_of_answer = ""
# Max coefficient & degree values...
max_coeff = MAX_COEFF
max_expon = MAX_EXPONENT
if 'max_coeff' in options and options['max_coeff'] >= 1:
max_coeff = options['max_coeff']
if 'max_expon' in options and options['max_expon'] >= 1:
max_expon = options['max_expon']
length = randomly.integer(DEFAULT_MINIMUM_LENGTH,
DEFAULT_MAXIMUM_LENGTH,
weighted_table=[0.15, 0.25, 0.6])
if ('length' in options and is_.an_integer(options['length'])
and options['length'] >= 2):
# __
length = options['length']
# 1st CASE:
# PRODUCT REDUCTION
if q_kind == 'product':
# First let's determine a pack of letters where to draw
# The default one will be [a, b, c, x, y, z]
# but the reduced or entire alphabets can be used as well
letters_package = alphabet.abc + alphabet.xyz
if 'short_test' in options and options['short_test']:
# __
self.objct = Product(
[Monomial((RANDOMLY, 12, 1)),
Monomial((RANDOMLY, 12, 1))])
self.objct.factor[0].set_degree(1)
self.objct.factor[1].set_degree(1)
else:
# In the case of an exercise about reducing products
# in a training sheet, the answers will be more detailed
self.kind_of_answer = 'product_detailed'
if 'use_reduced_alphabet' in options:
letters_package = alphabet.reduced
elif 'use_the_entire_alphabet' in options:
letters_package = alphabet.lowercase
elif 'use_these_letters' in options \
and is_.a_string_list(options['use_these_letters']):
# __
letters_package = options['use_these_letters']
# Maximum Items number. (We make sure at the same time that
# we won't
# risk to draw a greater number of letters than the available
# letters
# in letters_package)
max_literal_items_nb = min(PR_MAX_LITERAL_ITEMS_NB,
len(letters_package))
if ('max_literal_items_nb' in options
and 2 <= options['max_literal_items_nb'] <= 6):
# __
max_literal_items_nb = min(options['max_literal_items_nb'],
len(letters_package))
# Maximum number of occurences of the same letter in
# the initial expression
same_letter_max_occurences = PR_SAME_LETTER_MAX_OCCURENCES_NB
if ('nb_occurences_of_the_same_letter' in options
and options['nb_occurences_of_the_same_letter'] >= 1):
# __
same_letter_max_occurences = options['nb_occurences_of'
'_the_same_letter']
# CREATION OF THE EXPRESSION
# We draw randomly the letters that will appear
# in the expression
current_letters_package = list(letters_package)
nb_of_letters_to_draw = randomly.integer(
1, max_literal_items_nb)
drawn_letters = list()
for j in range(nb_of_letters_to_draw):
drawn_letters.append(randomly.pop(current_letters_package))
# Let's determine how many times will appear each letter
# and then create a list containing each of these letters
# the number of times they will appear
pre_items_list = list()
items_list = list()
for j in range(len(drawn_letters)):
if j == 0:
# We make sure that at least one letter occurs twice
# so that the exercise remains interesting !
# But the number of cases this letter occurs 3 three
# times should be limited to keep sufficient
# simple cases for the pupils to begin with.
# It is really easy to make it much more complicated
# simply giving:
# nb_occurences_of_the_same_letter=<enough_high_nb>
# as an argument.
if randomly.decimal_0_1() < 0.5:
occurences_nb = 2
else:
occurences_nb = randomly\
.integer(2, same_letter_max_occurences)
else:
occurences_nb = randomly\
.integer(1, same_letter_max_occurences)
if occurences_nb >= 1:
for k in range(occurences_nb):
pre_items_list.append(drawn_letters[j])
# draw the number of numeric Items
nb_item_num = randomly.integer(1, PR_NUMERIC_ITEMS_MAX_NB)
# put them in the pre items' list
for j in range(nb_item_num):
pre_items_list.append(NUMERIC)
# prepare the items' list that will be given to the Product's
# constructor
loop_nb = len(pre_items_list)
for j in range(loop_nb):
next_item_kind = randomly.pop(pre_items_list)
# It's not really useful nor really possible to limit the
# number
# of occurences of the same letter being drawn twice in
# a row because it belongs to the exercise and there
# are many cases when
# the same letter is in the list in 3 over 4 elements.
# if j >= 1 and next_item_kind == items_list[j - 1]
# .raw_value:
# pre_items_list.append(next_item_kind)
# next_item_kind = randomly.pop(pre_items_list)
if next_item_kind == NUMERIC:
temp_item = Item((randomly.sign(plus_signs_ratio=0.75),
randomly.integer(1, max_coeff), 1))
items_list.append(temp_item)
else:
item_value = next_item_kind
temp_item = Item(
(randomly.sign(plus_signs_ratio=0.9), item_value,
randomly.integer(1, max_expon)))
items_list.append(temp_item)
# so now that the items_list is complete,
# let's build the Product !
self.objct = Product(items_list)
self.objct.set_compact_display(False)
# Let's take some × symbols off the Product to match a more
# usual situation
for i in range(len(self.objct) - 1):
if ((self.objct.factor[i].is_numeric()
and self.objct.factor[i + 1].is_literal())
or (self.objct.factor[i].is_literal()
and self.objct.factor[i + 1].is_literal()
and self.objct.factor[i].raw_value !=
self.objct.factor[i + 1].raw_value
and randomly.decimal_0_1() > 0.5)):
# __
self.objct.info[i] = False
# 2d CASE:
# SUM OF PRODUCTS REDUCTION
if q_kind == 'sum_of_products':
if (not ('length' in options and is_.an_integer(options['length'])
and options['length'] >= 2)):
# __
length = randomly.integer(DEFAULT_MINIMUM_LENGTH,
DEFAULT_MAXIMUM_LENGTH,
weighted_table=[0.15, 0.25, 0.6])
# Creation of the list to give later to the Sum constructor
products_list = list()
for i in range(length):
monomial1 = Monomial((RANDOMLY, max_coeff, max_expon))
monomial2 = Monomial((RANDOMLY, max_coeff, max_expon))
products_list.append(Product([monomial1, monomial2]))
# Creation of the Sum
self.objct = Sum(products_list)
# 3d CASE:
# SUM REDUCTION
if q_kind == 'sum':
self.kind_of_answer = 'sum'
# Let's determine the length of the Sum to create
if not ('length' in options and is_.an_integer(options['length'])
and options['length'] >= 1):
# __
length = randomly\
.integer(DEFAULT_MINIMUM_LENGTH,
DEFAULT_MAXIMUM_LENGTH,
weighted_table=[0.1, 0.25, 0.5, 0.1, 0.05])
else:
length = options['length']
# Creation of the Polynomial...
if 'short_test' in options:
self.objct = Polynomial((RANDOMLY, max_coeff, 2, length - 1))
temp_sum = self.objct.term
degree_1_monomial_here = False
for i in range(len(temp_sum)):
if temp_sum[i].degree == 1:
degree_1_monomial_here = True
if degree_1_monomial_here == 1:
temp_sum.append(Monomial((randomly.sign(), 1, 1)))
else:
# this should be 2d deg Polynomial w/out any 1st deg term
temp_sum.append(Monomial((randomly.sign(), 1, 2)))
self.objct.reset_element()
for i in range(length):
self.objct.term.append(randomly.pop(temp_sum))
self.objct.info.append(False)
else:
self.objct = Polynomial(
(RANDOMLY, max_coeff, max_expon, length))
if q_kind == 'long_sum':
m = []
for i in range(length):
m.append(Monomial(RANDOMLY, max_coeff, max_expon))
self.objct = Polynomial(m)
if q_kind == 'long_sum_including_a_coeff_1':
m = []
for i in range(length - 1):
m.append(Monomial(RANDOMLY, max_coeff, max_expon))
m.append(Monomial(RANDOMLY, 1, max_expon))
terms_list = []
for i in range(len(m)):
terms_list.append(randomly.pop(m))
self.objct = Polynomial(terms_list)
if q_kind == 'sum_not_reducible':
self.kind_of_answer = 'sum_not_reducible'
m1 = Monomial((RANDOMLY, max_coeff, 0))
m2 = Monomial((RANDOMLY, max_coeff, 1))
m3 = Monomial((RANDOMLY, max_coeff, 2))
lil_box = [m1, m2, m3]
self.objct = Polynomial([randomly.pop(lil_box)])
for i in range(len(lil_box) - 1):
self.objct.append(randomly.pop(lil_box))
if q_kind == 'sum_with_minus-brackets':
minus_brackets = []
for i in range(3):
minus_brackets.append(
Expandable((Monomial(('-', 1, 0)),
Polynomial(
(RANDOMLY, 15, 2, randomly.integer(2,
3))))))
m1 = Monomial((RANDOMLY, max_coeff, 0))
m2 = Monomial((RANDOMLY, max_coeff, 1))
m3 = Monomial((RANDOMLY, max_coeff, 2))
m4 = Monomial((RANDOMLY, max_coeff, randomly.integer(0, 2)))
lil_box = [m1, m2, m3, m4]
plus_brackets = []
for i in range(3):
plus_brackets.append(
Expandable((Monomial(('+', 1, 0)),
Polynomial(
(RANDOMLY, 15, 2, randomly.integer(2,
3))))))
big_box = []
big_box.append(minus_brackets[0])
if ('minus_brackets_nb' in options
and 2 <= options['minus_brackets_nb'] <= 3):
# __
big_box.append(minus_brackets[1])
if options['minus_brackets_nb'] == 3:
big_box.append(minus_brackets[2])
for i in range(randomly.integer(1, 4)):
big_box.append(randomly.pop(lil_box))
if ('plus_brackets_nb' in options
and 1 <= options['plus_brackets_nb'] <= 3):
# __
for i in range(options['plus_brackets_nb']):
big_box.append(plus_brackets[i])
final_terms = []
for i in range(len(big_box)):
final_terms.append(randomly.pop(big_box))
self.objct = Sum(final_terms)
# 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)