def test_expR_auto_er():
"""No extraneous parentheses or lines in exp. and red. of 2+(7.5-6.7)×6?"""
temp = Sum([Item(2), Product([Expandable((Item(1),
Sum([Decimal('7.5'),
-Decimal('6.7')]))),
Item(6)], compact_display=False)])
expR = Expression("R", temp)
assert expR.auto_expansion_and_reduction() == \
wrap_nb('$\\text{R}=2+(7.5-6.7)\\times 6$\\newline \n'
'$\\text{R}=2+0.8\\times 6$\\newline \n'
'$\\text{R}=2+4.8$\\newline \n'
'$\\text{R}=6.8$\\newline \n')
def test_expQ_auto_er():
"""No redundant lines in expansion and reduction of 9-(0.4+0.4)×5?"""
temp = Sum([9, Product([Expandable((Item(-1),
Sum([Decimal('0.4'),
Decimal('0.4')]))),
Item(5)], compact_display=False)])
expQ = Expression("Q", temp)
assert expQ.auto_expansion_and_reduction() == \
wrap_nb('$\\text{Q}=9-(0.4+0.4)\\times 5$\\newline \n'
'$\\text{Q}=9-0.8\\times 5$\\newline \n'
'$\\text{Q}=9-4$\\newline \n'
'$\\text{Q}=5$\\newline \n')
class sub_object(component.structure):
def __init__(self, build_data, **options):
super().setup("minimal", **options)
super().setup("numbers", nb=build_data, **options)
super().setup("nb_variants", nb=build_data, **options)
degrees1 = [0, 1]
degrees2 = [0, 1]
random.shuffle(degrees1)
random.shuffle(degrees2)
weighted_signs = [('+', 19), ('-', 1)]
weighted_signs = [val
for val, cnt in weighted_signs
for i in range(cnt)]
signs = ['+', '-']
self.expandable = Expandable((Polynomial([Monomial((random.choice(
weighted_signs),
self.nb1,
degrees1.pop())),
Monomial((random.choice(
signs),
self.nb3,
degrees1.pop()))]),
Polynomial([Monomial((random.choice(
weighted_signs),
self.nb2,
degrees2.pop())),
Monomial((random.choice(
signs),
self.nb4,
degrees2.pop()))])
))
self.expression = Expression(shared.number_of_the_question,
self.expandable)
self.expression_str = self.expression.printed
shared.number_of_the_question += 1
def q(self, **options):
return shared.machine.write_math_style2(self.expression_str)
def a(self, **options):
return shared.machine.write(
self.expression.auto_expansion_and_reduction(**options))
class sub_object(submodule.structure):
def __init__(self, numbers_to_use, **options):
super().setup("minimal", **options)
super().setup("numbers", nb=numbers_to_use, **options)
super().setup("nb_variants", nb=numbers_to_use, **options)
degrees1 = [0, 1]
degrees2 = [0, 1]
random.shuffle(degrees1)
random.shuffle(degrees2)
weighted_signs = [('+', 19), ('-', 1)]
weighted_signs = [
val for val, cnt in weighted_signs for i in range(cnt)
]
signs = ['+', '-']
self.expandable = Expandable(
(Polynomial([
Monomial(
(random.choice(weighted_signs), self.nb1, degrees1.pop())),
Monomial((random.choice(signs), self.nb3, degrees1.pop()))
]),
Polynomial([
Monomial((random.choice(weighted_signs), self.nb2,
degrees2.pop())),
Monomial((random.choice(signs), self.nb4, degrees2.pop()))
])))
self.expression = Expression(shared.number_of_the_question,
self.expandable)
self.expression_str = self.expression.printed
shared.number_of_the_question += 1
def q(self, **options):
return shared.machine.write_math_style2(self.expression_str)
def a(self, **options):
return shared.machine.write(
self.expression.auto_expansion_and_reduction(**options))
class Q_AlgebraExpressionExpansion(Q_Structure):
# --------------------------------------------------------------------------
##
# @brief Constructor
# @param **options Any options
# @return One instance of question.Q_AlgebraExpressionExpansion
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)
# --------------------------------------------------------------------------
##
# @brief Returns the text of the question as a str
def text_to_str(self):
M = shared.machine
result = ""
if self.q_kind in [
'numeric_sum_square', 'numeric_difference_square',
'numeric_squares_difference'
]:
# __
result += M.write_math_style2(M.type_string(self.numeric_aux))
else:
result += M.write_math_style2(M.type_string(self.expression))
result += M.write_new_line()
return result
# --------------------------------------------------------------------------
##
# @brief Returns the answer of the question as a str
def answer_to_str(self):
M = shared.machine
result = ""
if self.q_kind in [
'numeric_sum_square', 'numeric_difference_square',
'numeric_squares_difference'
]:
# __
result += M.write_math_style2(M.type_string(self.numeric_aux))
result += M.write_new_line()
result += M.write(self.expression.auto_expansion_and_reduction())
return result
class Q_AlgebraExpressionReduction(Q_Structure):
# --------------------------------------------------------------------------
##
# @brief Constructor.
# @param q_kind= the kind of question desired
# Available values are: 'product'
# 'sum'
# 'sum_of_products'
# @param **options Options detailed below:
# - short_test=bool
# 'yes'
# 'OK'
# any other value will be understood as 'no'
# - q_subkind=<string>
# 'minus_brackets_nb' (values: 1, 2, 3)
# 'plus_brackets_nb' (values: 1, 2, 3)
# @todo describe the different available options in this comment
# @return One instance of question.Q_AlgebraExpressionReduction
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)
# --------------------------------------------------------------------------
##
# @brief Returns the text of the question as a str
def text_to_str(self):
M = shared.machine
result = M.write_math_style2(M.type_string(self.expression))
result += M.write_new_line()
return result
# --------------------------------------------------------------------------
##
# @brief Returns the answer of the question as a str
def answer_to_str(self):
M = shared.machine
result = ""
if self.kind_of_answer == 'product_detailed':
result += M.write_math_style2(M.type_string(self.expression))
result += M.write_new_line()
if not is_.an_ordered_calculable_objects_list(self.objct.factor):
ordered_product = self.objct.order()
ordered_product.set_compact_display(False)
ordered_expression = Expression(self.expression.name,
ordered_product)
result += M.write_math_style2(
M.type_string(ordered_expression))
result += M.write_new_line()
final_product = self.objct.reduce_()
final_expression = Expression(self.expression.name, final_product)
result += M.write_math_style2(M.type_string(final_expression))
result += M.write_new_line()
elif ((self.kind_of_answer in ['sum', 'sum_not_reducible']) and
self.expression.right_hand_side.expand_and_reduce_next_step() is
None):
# __
result += M.write_math_style2(M.type_string(self.expression))
result += M.write_new_line()
result += M.write(_("This expression is not reducible."))
result += M.write_new_line()
else:
result += M.write(self.expression.auto_expansion_and_reduction())
return result
class Q_AlgebraExpressionReduction(Q_Structure):
# --------------------------------------------------------------------------
##
# @brief Constructor.
# @param q_kind= the kind of question desired
# Available values are: 'product'
# 'sum'
# 'sum_of_products'
# @param **options Options detailed below:
# - short_test=bool
# 'yes'
# 'OK'
# any other value will be understood as 'no'
# - q_subkind=<string>
# 'minus_brackets_nb' (values: 1, 2, 3)
# 'plus_brackets_nb' (values: 1, 2, 3)
# @todo describe the different available options in this comment
# @return One instance of question.Q_AlgebraExpressionReduction
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]
MIN_LENGTH = DEFAULT_MINIMUM_LENGTH_TABLE[q_kind]
MAX_LENGTH = DEFAULT_MAXIMUM_LENGTH_TABLE[q_kind]
LENGTH_SPAN = MAX_LENGTH - MIN_LENGTH + 1
# 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 = options.get('max_coeff', MAX_COEFF)
max_expon = options.get('max_expon', MAX_EXPONENT)
length = options.get('length',
random.choice([n + MIN_LENGTH
for n in range(LENGTH_SPAN)]))
# 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 = ['a', 'b', 'c', 'x', 'y', 'z']
self.kind_of_answer = 'product_detailed'
if 'use_reduced_alphabet' in options:
letters_package = ['a', 'b', 'c', 'd', 'g', 'h', 'k', 'p',
'q', 'r', 's', 't', 'u', 'v', 'w', 'x',
'y', 'z']
elif ('use_these_letters' in options
and type(options['use_these_letters']) is list
and all([type(elt) is str
for elt in 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))
# 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 = random.randint(1, max_literal_items_nb)
drawn_letters = list()
for j in range(nb_of_letters_to_draw):
drawn_letters.append(
random.choice(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 random.random() < 0.5:
occurences_nb = 2
else:
occurences_nb = \
random.randint(
min(2, same_letter_max_occurences),
same_letter_max_occurences)
else:
occurences_nb = \
random.randint(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 = random.randint(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 = random.choice(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 = random.choice(pre_items_list)
if next_item_kind == NUMERIC:
temp_item = Item((random.choices(['+', '-'],
cum_weights=[0.75,
1])[0],
random.randint(1, max_coeff),
1))
items_list.append(temp_item)
else:
item_value = next_item_kind
temp_item = Item((random.choices(['+', '-'],
cum_weights=[0.9,
1])[0],
item_value,
random.randint(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 random.random() > 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_integer(options['length'])
and options['length'] >= 2)):
# __
length = random.choices(
[n + MIN_LENGTH for n in range(LENGTH_SPAN)],
weights=[n for n in range(LENGTH_SPAN)])[0]
# 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'
length = options.get('length',
random.choice([n + MIN_LENGTH
for n in range(LENGTH_SPAN)]))
self.objct = Polynomial((RANDOMLY,
max_coeff,
max_expon,
length))
# 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)
# --------------------------------------------------------------------------
##
# @brief Returns the text of the question as a str
def text_to_str(self):
M = shared.machine
result = M.write_math_style2(M.type_string(self.expression))
result += M.write_new_line()
return result
# --------------------------------------------------------------------------
##
# @brief Returns the answer of the question as a str
def answer_to_str(self):
M = shared.machine
result = ""
if self.kind_of_answer == 'product_detailed':
result += M.write_math_style2(M.type_string(self.expression))
result += M.write_new_line()
if not all(self.objct.factor[i]
.alphabetical_order_cmp(self.objct.factor[i + 1]) > 0
for i in range(len(self.objct.factor) - 1)):
ordered_product = self.objct.order()
ordered_product.set_compact_display(False)
ordered_expression = Expression(self.expression.name,
ordered_product)
result += M.write_math_style2(
M.type_string(ordered_expression))
result += M.write_new_line()
final_product = self.objct.reduce_()
final_expression = Expression(self.expression.name,
final_product)
result += M.write_math_style2(M.type_string(final_expression))
result += M.write_new_line()
elif ((self.kind_of_answer in ['sum', 'sum_not_reducible'])
and self.expression.
right_hand_side.expand_and_reduce_next_step() is None):
# __
result += M.write_math_style2(M.type_string(self.expression))
result += M.write_new_line()
result += M.write(_("This expression is not reducible."))
result += M.write_new_line()
else:
result += M.write(self.expression.auto_expansion_and_reduction())
return result