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 test_eq11_autoresolution():
"""Is this Equation correctly auto-resolved?"""
eq = Equation((Polynomial([Monomial(
('+', 5, 0)), Monomial(
('-', 1, 1))]), Polynomial([Monomial(('+', 5, 1))])),
number=1)
assert eq.auto_resolution() == wrap_nb('$(\\text{E}_{1}): $'
'\[5-x=5x\]'
'\[-x-5x=-5\]'
'\[(-1-5)x=-5\]'
'\[-6x=-5\]'
'\[x=\\frac{-5}{-6}\]'
'\[x=\\frac{5}{6}\]')
def test_eq8_autoresolution():
"""Is this Equation correctly auto-resolved?"""
eq = Equation(
(Polynomial([Monomial(
('+', 4, 1)), Monomial(('+', 2, 0))]),
Polynomial([Monomial(
('-', 3, 0)), Monomial(('+', 2, 1))])),
number=1)
assert eq.auto_resolution() == wrap_nb('$(\\text{E}_{1}): $'
'\[4x+2=-3+2x\]'
'\[4x-2x=-3-2\]'
'\[(4-2)x=-5\]'
'\[2x=-5\]'
'\[x=-\\frac{5}{2}\]')
def test_eq9_autoresolution():
"""Is this Equation correctly auto-resolved?"""
eq = Equation(
(Polynomial([Monomial(
('-', 2, 1)), Monomial(('+', 5, 0))]),
Polynomial([Monomial(
('+', 3, 1)), Monomial(('-', 4, 0))])),
number=1)
assert eq.auto_resolution() == wrap_nb('$(\\text{E}_{1}): $'
'\[-2x+5=3x-4\]'
'\[-2x-3x=-4-5\]'
'\[(-2-3)x=-9\]'
'\[-5x=-9\]'
'\[x=\\frac{-9}{-5}\]'
'\[x=\\frac{9}{5}\]')
def test_eq13_autoresolution():
"""Is this Equation correctly auto-resolved?"""
eq = Equation(
(Polynomial([Monomial(
('+', 1, 1)), Monomial(('+', 5, 0))]),
Polynomial([Monomial(
('+', 1, 1)), Monomial(('+', 2, 0))])),
number=1)
assert eq.auto_resolution() == wrap_nb('$(\\text{E}_{1}): $'
'\[x+5=x+2\]'
'\[x-x=2-5\]'
'\[(1-1)x=-3\]'
'\[0x=-3\]'
'\[0=-3\]'
'This equation has no solution.'
'\\newline ')
def expI():
t = Sum([Monomial(('+', 4, 1)),
Expandable((Monomial(('+', 1, 0)),
Polynomial([Monomial(('-', 15, 1)),
Monomial(('+', 8, 0)),
Monomial(('-', 5, 1))])))])
return Expression("I", t)
def test_eq10_autoresolution():
"""Is this Equation correctly auto-resolved?"""
eq = Equation(
(Polynomial([Monomial(
('+', 5, 0)), Monomial(('+', 4, 1))]),
Polynomial([Monomial(
('-', 20, 1)), Monomial(('+', 3, 0))])),
number=1)
assert eq.auto_resolution() == wrap_nb('$(\\text{E}_{1}): $'
'\[5+4x=-20x+3\]'
'\[4x+20x=3-5\]'
'\[(4+20)x=-2\]'
'\[24x=-2\]'
'\[x=-\\frac{2}{24}\]'
'\[x=-\\frac{\\bcancel{2}}'
'{\\bcancel{2}\\times 12}\]'
'\[x=-\\frac{1}{12}\]')
def rubbish_polynomial():
return Polynomial([
Monomial(('+', 1, 2)),
Monomial(('+', 7, 1)),
Monomial(('-', 10, 2)),
Monomial(('-', 9, 1)),
Monomial(('+', 9, 2))
])
def test_complicated_sum_02():
"""Is this Sum correctly printed as (6+x)^{2}+12(2+11x)?"""
assert Sum([
BinomialIdentity((Monomial(('+', 6, 0)), Monomial(('+', 1, 1)))),
Expandable(
(Monomial(('+', 12, 0)),
Sum([Polynomial([Monomial(('+', 2, 0)),
Monomial(('+', 11, 1))])])))
]).printed == wrap_nb('(6+x)^{2}+12(2+11x)')
def test_eq0_autoresolution():
"""Is this Equation correctly auto-resolved?"""
eq = Equation((Polynomial([Monomial(
('+', 1, 1)), Monomial(('+', 7, 0))]), Item(3)),
number=1)
assert eq.auto_resolution() == wrap_nb('$(\\text{E}_{1}): $'
'\[x+7=3\]'
'\[x=3-7\]'
'\[x=-4\]')
def test_eq1_autoresolution():
"""Is this Equation correctly auto-resolved?"""
eq = Equation((Polynomial([Monomial(
('-', 8, 0)), Monomial(('+', 1, 1))]), Item(-2)),
number=1)
assert eq.auto_resolution() == wrap_nb('$(\\text{E}_{1}): $'
'\[-8+x=-2\]'
'\[x=-2+8\]'
'\[x=6\]')
def test_eq2_autoresolution():
"""Is this Equation correctly auto-resolved?"""
eq = Equation(
(Item(-5), Polynomial([Monomial(
('+', 1, 1)), Monomial(('+', 3, 0))])),
number=1)
assert eq.auto_resolution() == wrap_nb('$(\\text{E}_{1}): $'
'\[-5=x+3\]'
'\[x=-5-3\]'
'\[x=-8\]')
def test_eq6_autoresolution():
"""Is this Equation correctly auto-resolved?"""
eq = Equation((Polynomial([Monomial(
('+', 2, 1)), Monomial(('+', 3, 0))]), Item(8)),
number=1)
assert eq.auto_resolution() == wrap_nb('$(\\text{E}_{1}): $'
'\[2x+3=8\]'
'\[2x=8-3\]'
'\[2x=5\]'
'\[x=\\frac{5}{2}\]')
def test_eq7_autoresolution():
"""Is this Equation correctly auto-resolved?"""
eq = Equation((Polynomial([Monomial(
('+', 19, 0)), Monomial(('+', 3, 1))]), Monomial(('+', 2, 1))),
number=1)
assert eq.auto_resolution() == wrap_nb('$(\\text{E}_{1}): $'
'\[19+3x=2x\]'
'\[3x-2x=-19\]'
'\[(3-2)x=-19\]'
'\[x=-19\]')
def test_eq12_autoresolution():
"""Is this Equation correctly auto-resolved?"""
eq = Equation((Polynomial([Monomial(
('+', 2, 1)), Monomial(('+', 1, 0))]), Item(1)),
number=1)
assert eq.auto_resolution() == wrap_nb('$(\\text{E}_{1}): $'
'\[2x+1=1\]'
'\[2x=1-1\]'
'\[2x=0\]'
'\[x=0\]')
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 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_complicated_sum_01():
"""Is this Sum correctly printed as 2-10x^{2}+9?"""
assert Sum([Item(2),
Product([Polynomial([Monomial(('-', 10, 2)),
Monomial(('+', 9, 0))])])]).printed == \
wrap_nb('2-10x^{2}+9')
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)
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)
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