def test_f6_simplification_line():
"""Is this Fraction's simplification line correct?"""
assert Fraction(('+',
Product([Item(10), Item(5)]),
Product([Item(5), Item(9)])))\
.simplification_line().printed == \
wrap_nb('\\frac{10\\times \\bcancel{5}}{\\bcancel{5}\\times 9}')
def test_product_sum_2_3x_times_sum_minus4_6x_is_not_reducible():
"""Is this Product not reducible?"""
p = Product([
Sum([Item(2), Monomial(('+', 3, 1))]),
Sum([Item(-4), Monomial(('+', 6, 1))])
])
assert not p.is_reducible()
def test_eq15_autoresolution():
"""Is this Equation correctly auto-resolved?"""
eq = Equation((Item(1), Item(2)), number=1)
assert eq.auto_resolution() == wrap_nb('$(\\text{E}_{1}): $'
'\[1=2\]'
'This equation has no solution.'
'\\newline ')
def test_product_9_times_minus2_times_7ab_printed():
"""Is this Product correctly printed?"""
assert Product([Item(9),
Product([Item(-2),
Item(7),
Item('a'),
Item('b')])])\
.printed == wrap_nb('9\\times (-2)\\times 7ab')
def fig0b():
fig0b = InterceptTheoremConfiguration(sketch=False,
rotate_around_isobarycenter=40)
fig0b.set_lengths([6, 12, 9], Fraction((Item(4), Item(3))))
fig0b.setup_labels(['?', True, False, True, True, True, False, False],
segments_list=[fig0b.u, fig0b.side[1], fig0b.v] +
fig0b.small + fig0b.chunk)
return fig0b
def test_f5_simplification_line():
"""Is this Fraction's simplification line correct?"""
assert Fraction(('+',
Product([Item(8), Item(3)]),
Product([Item(5), Item(6)])))\
.simplification_line().printed == \
wrap_nb('\\frac{\\bcancel{2}\\times 4\\times \\bcancel{3}}{5\\times'
' \\bcancel{2}\\times \\bcancel{3}}')
def test_f3_simplification_line():
"""Is this Fraction's simplification line correct?"""
assert Fraction(('+',
Product([Item(7), Item(6)]),
Product([Item(3), Item(3)])))\
.simplification_line().printed == \
wrap_nb('\\frac{7\\times \\bcancel{3}\\times 2}'
'{\\bcancel{3}\\times 3}')
def test_cpeq1_autoresolution():
"""Is this Equation correctly auto-resolved?"""
eq = CrossProductEquation((Item(6), Item(1.4), Item(1.5), Item("AB")))
assert eq.auto_resolution(dont_display_equations_name=True,
skip_fraction_simplification=True,
decimal_result=2) == \
wrap_nb('\[\\frac{6}{1.5}=\\frac{1.4}{\\text{AB}}\]'
'\[\\text{AB}=\\frac{1.4\\times 1.5}{6}\]'
'\[\\text{AB}=0.35\]')
def test_eq25_autoresolution():
"""Is this Equation correctly auto-resolved?"""
eq = Equation((Item(
('+', 5, 2)), Sum([Item(
('+', 4, 2)), Monomial(('+', 1, 1))])),
number=1)
assert eq.auto_resolution(dont_display_equations_name=True) == \
wrap_nb('\[5^{2}=4^{2}+x\]'
'\[25=16+x\]'
'\[x=25-16\]'
'\[x=9\]')
def test_eq37_autoresolution():
"""Is this Equation correctly auto-resolved?"""
eq = Equation((Monomial((Fraction(
(Item(2), Item(3))), 1)), Fraction((Item(4), Item(5)))))
assert eq.auto_resolution(dont_display_equations_name=True) == \
wrap_nb('\[\\frac{2}{3}x=\\frac{4}{5}\]'
'\[x=\\frac{4}{5}\div \\frac{2}{3}\]'
'\[x=\\frac{4}{5}\\times \\frac{3}{2}\]'
'\[x=\\frac{4\\times 3}{5\\times 2}\]'
'\[x=\\frac{\\bcancel{2}\\times 2\\times 3}'
'{5\\times \\bcancel{2}}\]'
'\[x=\\frac{6}{5}\]')
def big_product():
s = Sum(['x', 3])
s.set_exponent(3)
p = Product(Monomial((1, 2)))
p.set_exponent(3)
p1 = Product([2, 3])
p1.set_exponent(3)
return Product([
Monomial((2, 1)),
Monomial((-4, 2)), s,
Item(5), p,
Item(('+', -1, 2)), p1
])
def complicated_sum_to_reduce():
return Sum([
Monomial(('+', 3, 1)),
Item(4),
Sum([
Monomial(('+', 3, 1)),
Monomial(('+', 5, 2)),
Product([Item(-7), Item('a'), Item('b')])
]),
Product([Item('-a'), Item('b')]),
Monomial(('+', 5, 2)),
Item(2),
Monomial(('-', 2, 1)),
Product([Item(2), Item('a'), Item('b')])
])
def test_eq32_autoresolution():
"""Is this Equation correctly auto-resolved?"""
eq = Equation((Monomial(('+', 1, 1)), SquareRoot(Item(16))))
assert eq.auto_resolution(dont_display_equations_name=True,
decimal_result=2) == \
wrap_nb('\[x=\\sqrt{\mathstrut 16}\]'
'\[x=4\]')
def test_eq29_autoresolution():
"""Is this Equation correctly auto-resolved?"""
eq = Equation(
(Monomial(('+', 1, 1)),
Sum([Fraction((Item(1), Item(4))),
Fraction((Item(1), Item(8)))])),
number=1)
assert eq.auto_resolution(decimal_result=2) == \
wrap_nb('$(\\text{E}_{1}): $'
'\[x=\\frac{1}{4}+\\frac{1}{8}\]'
'\[x=\\frac{1\\times 2}{4\\times 2}'
'+\\frac{1}{8}\]'
'\[x=\\frac{2}{8}+\\frac{1}{8}\]'
'\[x=\\frac{2+1}{8}\]'
'\[x=\\frac{3}{8}\]'
'\[x\\simeq0.38\]')
def test_eq28_autoresolution():
"""Is this Equation correctly auto-resolved?"""
eq = Equation((Monomial(('+', 8, 1)), Item(6)), number=1)
assert eq.auto_resolution(decimal_result=2) == \
wrap_nb('$(\\text{E}_{1}): $'
'\[8x=6\]'
'\[x=\\frac{6}{8}\]'
'\[x=0.75\]')
def test_eq23_autoresolution():
"""Is this Equation correctly auto-resolved?"""
eq = Equation(
(Item(5),
Sum([
Expandable(
(Item(1), Sum([Monomial(('+', 1, 1)),
Monomial(('-', 2, 0))]))),
Item(7)
])),
number=1)
assert eq.auto_resolution() == wrap_nb('$(\\text{E}_{1}): $'
'\[5=(x-2)+7\]'
'\[5=x-2+7\]'
'\[5=x+5\]'
'\[x=5-5\]'
'\[x=0\]')
def test_eq27_autoresolution():
"""Is this Equation correctly auto-resolved?"""
eq = Equation((Monomial(('+', 3, 1)), Item(1)), number=1)
assert eq.auto_resolution(decimal_result=2) == \
wrap_nb('$(\\text{E}_{1}): $'
'\[3x=1\]'
'\[x=\\frac{1}{3}\]'
'\[x\\simeq0.33\]')
def test_eq5_autoresolution():
"""Is this Equation correctly auto-resolved?"""
eq = Equation((Monomial(('+', 12, 1)), Item(8)), number=1)
assert eq.auto_resolution() == wrap_nb('$(\\text{E}_{1}): $'
'\[12x=8\]'
'\[x=\\frac{8}{12}\]'
'\[x=\\frac{\\bcancel{4}\\times 2}'
'{\\bcancel{4}\\times 3}\]'
'\[x=\\frac{2}{3}\]')
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_eq36_autoresolution():
"""Is this Equation correctly auto-resolved?"""
eq = Equation((Item(
('+', "EF", 2)), Sum([Item(
('+', 60, 2)), Item(('+', 91, 2))])),
number=1,
variable_letter_name="AB")
assert eq.auto_resolution(dont_display_equations_name=True,
pythagorean_mode=True,
unit='cm') == \
wrap_nb('\[\\text{EF}^{2}=60^{2}+91^{2}\]'
'\[\\text{EF}^{2}=3600+8281\]'
'\[\\text{EF}^{2}=11881\]'
'\[\\text{EF}='
'\\sqrt{\mathstrut 11881}'
'\\text{ because \\text{EF} '
'is positive.}\]'
'\[\\text{EF}=109\\text{ cm}\]')
def test_fractions_by_items_01_next_step():
"""Is this Product's calculation's next step correct?"""
p = Product([
Fraction((Item(3), Item(5))),
Item(8),
Fraction((Item(7), Item(11))),
Item(4),
Fraction((Item(13), Item(17)))
])
assert p.calculate_next_step().printed == \
wrap_nb('\\frac{3\\times 8\\times 7\\times 4\\times 13}{5\\times 11'
'\\times 17}')
def test_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 test_eq35_autoresolution():
"""Is this Equation correctly auto-resolved?"""
eq = Equation((Item(
('+', 73, 2)), Sum([Item(
('+', 48, 2)), Item(('+', "AB", 2))])),
number=1,
variable_letter_name="AB")
assert eq.auto_resolution(dont_display_equations_name=True,
decimal_result=2,
pythagorean_mode=True) == \
wrap_nb('\[73^{2}=48^{2}+\\text{AB}^{2}\]'
'\[5329=2304+\\text{AB}^{2}\]'
'\[\\text{AB}^{2}=5329-2304\]'
'\[\\text{AB}^{2}=3025\]'
'\[\\text{AB}='
'\\sqrt{\mathstrut 3025}'
'\\text{ because \\text{AB} '
'is positive.}\]'
'\[\\text{AB}=55\]')
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_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_eq17_autoresolution():
"""Is this Equation correctly auto-resolved?"""
eq = Equation(
(Expandable((Item(-1), Sum([Monomial(
(-11, 1)), Item(-10)]))),
Sum([
Expandable((Item(1), Sum([Item(-15), Monomial((12, 1))]))),
Item(-1)
])),
number=1)
assert eq.auto_resolution() == wrap_nb('$(\\text{E}_{1}): $'
'\[-(-11x-10)=(-15+12x)-1\]'
'\[11x+10=-15+12x-1\]'
'\[11x+10=-15-1+12x\]'
'\[11x+10=-16+12x\]'
'\[11x-12x=-16-10\]'
'\[(11-12)x=-26\]'
'\[-x=-26\]'
'\[x=26\]')
def test_eq18_autoresolution():
"""Is this Equation correctly auto-resolved?"""
eq = Equation((Sum([
Monomial(('-', 8, 0)),
Monomial(('+', 9, 0)),
Monomial(('-', 1, 0))
]), Expandable((Item(10), Sum([Item(-2), Monomial((-12, 1))])))),
number=1)
assert eq.auto_resolution() == \
wrap_nb('$(\\text{E}_{1}): $'
'\[-8+9-1=10(-2-12x)\]'
'\[0=10\\times (-2)+10\\times (-12x)\]'
'\[0=-20-120x\]'
'\[120x=-20\]'
'\[x=-\\frac{20}{120}\]'
'\[x=-\\frac{\\bcancel{10}\\times'
' 2}{\\bcancel{10}\\times 12}\]'
'\[x=-\\frac{\\bcancel{2}}'
'{\\bcancel{2}\\times 6}\]'
'\[x=-\\frac{1}{6}\]')
def __init__(self, numbers_to_use, **options):
nb_list = list(numbers_to_use)
hole = Item(Value('...'))
self.hidden_one = None
visible_one = None
self.product = Item(Product([nb_list[0], nb_list[1]]).evaluate())
if isinstance(nb_list[1], Fraction):
self.hidden_one = nb_list[1]
visible_one = nb_list[0]
else:
nb1 = randomly.pop(nb_list)
nb2 = randomly.pop(nb_list)
nb_list = [nb1, nb2]
self.hidden_one = Item(randomly.pop(nb_list))
visible_one = randomly.pop(nb_list)
factors = [visible_one, hole]
self.holed_product = Product([randomly.pop(factors),
randomly.pop(factors)])
self.holed_product.set_compact_display(False)
def test_eq22_autoresolution():
"""Is this Equation correctly auto-resolved?"""
eq = Equation((Sum([
Expandable(
(Item(3), Sum([Monomial(
('-', 9, 0)), Monomial(('+', 6, 1))]))),
Item(-8)
]), Sum([Item(9)])),
number=1)
assert eq.auto_resolution() == wrap_nb('$(\\text{E}_{1}): $'
'\[3(-9+6x)-8=9\]'
'\[3\\times (-9)+3\\times 6x-8=9\]'
'\[-27+18x-8=9\]'
'\[-27-8+18x=9\]'
'\[-35+18x=9\]'
'\[18x=9+35\]'
'\[18x=44\]'
'\[x=\\frac{44}{18}\]'
'\[x=\\frac{\\bcancel{2}\\times 22}'
'{\\bcancel{2}\\times 9}\]'
'\[x=\\frac{22}{9}\]')