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_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_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_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_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_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_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_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_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_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_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_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_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_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_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 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_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_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_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_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_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_eq14_autoresolution():
"""Is this Equation correctly auto-resolved?"""
eq = Equation((Sum([Monomial(('+', 3, 0)),
Monomial(('+', 10, 1))]), Monomial(('+', 10, 1))))
assert eq.auto_resolution() == wrap_nb('$(\\text{E}): $'
'\[3+10x=10x\]'
'\[10x-10x=-3\]'
'\[(10-10)x=-3\]'
'\[0x=-3\]'
'\[0=-3\]'
'This equation has no solution.'
'\\newline ')
def test_eq37_autoresolution():
"""Is this Equation correctly auto-resolved?"""
eq = Equation((Monomial((Fraction((Item(2), Item(3))), 1)),
Fraction((Item(4), Item(5)))))
assert eq.auto_resolution(dont_display_equations_name=True) == \
wrap_nb('\[\\frac{2}{3}x=\\frac{4}{5}\]'
'\[x=\\frac{4}{5}\div \\frac{2}{3}\]'
'\[x=\\frac{4}{5}\\times \\frac{3}{2}\]'
'\[x=\\frac{4\\times 3}{5\\times 2}\]'
'\[x=\\frac{\\bcancel{2}\\times 2\\times 3}'
'{5\\times \\bcancel{2}}\]'
'\[x=\\frac{6}{5}\]')
def test_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_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_eq21_autoresolution():
"""Is this Equation correctly auto-resolved?"""
eq = Equation((Sum([Monomial(('-', 1, 0)),
Monomial(('-', 4, 1))]), Monomial(('-', 9, 0))))
assert eq.auto_resolution() == wrap_nb('$(\\text{E}): $'
'\[-1-4x=-9\]'
'\[-4x=-9+1\]'
'\[-4x=-8\]'
'\[x=\\frac{-8}{-4}\]'
'\[x=\\frac{+\\bcancel{4}\\times 2}'
'{+\\bcancel{4}}\]'
'\[x=2\]')
def test_eq37_autoresolution():
"""Is this Equation correctly auto-resolved?"""
eq = Equation((Monomial((Fraction(
(Item(2), Item(3))), 1)), Fraction((Item(4), Item(5)))))
assert eq.auto_resolution(dont_display_equations_name=True) == \
wrap_nb('\[\\frac{2}{3}x=\\frac{4}{5}\]'
'\[x=\\frac{4}{5}\div \\frac{2}{3}\]'
'\[x=\\frac{4}{5}\\times \\frac{3}{2}\]'
'\[x=\\frac{4\\times 3}{5\\times 2}\]'
'\[x=\\frac{\\bcancel{2}\\times 2\\times 3}'
'{5\\times \\bcancel{2}}\]'
'\[x=\\frac{6}{5}\]')
def test_eq14_autoresolution():
"""Is this Equation correctly auto-resolved?"""
eq = Equation((Sum([Monomial(('+', 3, 0)), Monomial(('+', 10, 1))]),
Monomial(('+', 10, 1))))
assert eq.auto_resolution() == wrap_nb('$(\\text{E}): $'
'\[3+10x=10x\]'
'\[10x-10x=-3\]'
'\[(10-10)x=-3\]'
'\[0x=-3\]'
'\[0=-3\]'
'This equation has no solution.'
'\\newline ')
def test_eq21_autoresolution():
"""Is this Equation correctly auto-resolved?"""
eq = Equation((Sum([Monomial(('-', 1, 0)),
Monomial(('-', 4, 1))]),
Monomial(('-', 9, 0))))
assert eq.auto_resolution() == wrap_nb('$(\\text{E}): $'
'\[-1-4x=-9\]'
'\[-4x=-9+1\]'
'\[-4x=-8\]'
'\[x=\\frac{-8}{-4}\]'
'\[x=\\frac{+\\bcancel{4}\\times 2}'
'{+\\bcancel{4}}\]'
'\[x=2\]')
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_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_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 ')
class Q_Equation(Q_Structure):
# --------------------------------------------------------------------------
##
# @brief Constructor.
# @param **options Any options
# @return One instance of question.Q_Equation
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.equation = Equation((RANDOMLY, q_kind))
if 'expression_number' in options:
self.equation.set_number(options['expression_number'])
# --------------------------------------------------------------------------
##
# @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.equation,
display_name='OK'))
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
return M.write(self.equation.auto_resolution())
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_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_eq39_autoresolution():
"""Is this Equation correctly auto-resolved?"""
eq = Equation((Sum([
Monomial((Fraction((Item(2), Item(1))).simplified(), 1)),
Fraction((Item(1), Item(5)))
]), Fraction(('-', Item(4), Item(5)))))
assert eq.auto_resolution(dont_display_equations_name=True) == \
wrap_nb('\[2x+\\frac{1}{5}=-\\frac{4}{5}\]'
'\[2x=-\\frac{4}{5}-\\frac{1}{5}\]'
'\[2x=\\frac{-4-1}{5}\]'
'\[2x=-\\frac{5}{5}\]'
'\[2x=-\\frac{\\bcancel{5}}{\\bcancel{5}}\]'
'\[2x=-1\]'
'\[x=-\\frac{1}{2}\]')
def test_eq39_autoresolution():
"""Is this Equation correctly auto-resolved?"""
eq = Equation((Sum([Monomial((Fraction((Item(2),
Item(1))).simplified(), 1)),
Fraction((Item(1), Item(5)))]),
Fraction(('-', Item(4), Item(5)))))
assert eq.auto_resolution(dont_display_equations_name=True) == \
wrap_nb('\[2x+\\frac{1}{5}=-\\frac{4}{5}\]'
'\[2x=-\\frac{4}{5}-\\frac{1}{5}\]'
'\[2x=\\frac{-4-1}{5}\]'
'\[2x=-\\frac{5}{5}\]'
'\[2x=-\\frac{\\bcancel{5}}{\\bcancel{5}}\]'
'\[2x=-1\]'
'\[x=-\\frac{1}{2}\]')
class Q_Equation(Q_Structure):
# --------------------------------------------------------------------------
##
# @brief Constructor.
# @param **options Any options
# @return One instance of question.Q_Equation
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.equation = Equation((RANDOMLY, q_kind))
if 'expression_number' in options:
self.equation.set_number(options['expression_number'])
# --------------------------------------------------------------------------
##
# @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.equation, display_name='OK'))
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
return M.write(self.equation.auto_resolution())
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_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 test_t4_pyth_eq_autoresolution(t4):
"""
Check the auto-resolution of the pythagorean equation created from t4.
"""
eq_t4 = Equation(t4.pythagorean_substequality().substitute())
assert eq_t4.auto_resolution(dont_display_equations_name=True,
decimal_result=HUNDREDTH,
pythagorean_mode=True,
unit='cm') == \
wrap_nb('\[\\text{OP}^{2}=7^{2}-1.5^{2}\]'
'\[\\text{OP}^{2}=49-2.25\]'
'\[\\text{OP}^{2}=46.75\]'
'\[\\text{OP}=\\sqrt{\mathstrut 46.75}'
'\\text{ because \\text{OP} is positive.}\]'
'\[\\text{OP}\\simeq6.84\\text{ cm}\]')
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_eq20_autoresolution():
"""Is this Equation correctly auto-resolved?"""
eq = Equation((Sum([Monomial(('+', 5, 1))]),
Sum([Expandable((Item(1), Sum([Monomial(('+', 2, 0)),
Monomial(('-', 5, 1))]))),
Monomial(('-', 2, 0))])),
number=1)
assert eq.auto_resolution() == wrap_nb('$(\\text{E}_{1}): $'
'\[5x=(2-5x)-2\]'
'\[5x=2-5x-2\]'
'\[5x=2-2-5x\]'
'\[5x=-5x\]'
'\[5x+5x=0\]'
'\[(5+5)x=0\]'
'\[10x=0\]'
'\[x=0\]')
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 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_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 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_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_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_eq16_autoresolution():
"""Is this Equation correctly auto-resolved?"""
eq = Equation((Sum([Monomial(('+', 9, 1)),
Expandable((Monomial(('+', 9, 0)),
Sum([Monomial(('-', 4, 0)),
Monomial(('-', 1, 1))])))]),
Item(8)),
number=1)
assert eq.auto_resolution() == wrap_nb('$(\\text{E}_{1}): $'
'\[9x+9(-4-x)=8\]'
'\[9x+9\\times (-4)+9\\times '
'(-x)=8\]'
'\[9x-36-9x=8\]'
'\[(9-9)x-36=8\]'
'\[0x-36=8\]'
'\[-36=8\]'
'This equation has no solution.'
'\\newline ')
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_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_eq16_autoresolution():
"""Is this Equation correctly auto-resolved?"""
eq = Equation((Sum([
Monomial(('+', 9, 1)),
Expandable((Monomial(
('+', 9, 0)), Sum([Monomial(
('-', 4, 0)), Monomial(('-', 1, 1))])))
]), Item(8)),
number=1)
assert eq.auto_resolution() == wrap_nb('$(\\text{E}_{1}): $'
'\[9x+9(-4-x)=8\]'
'\[9x+9\\times (-4)+9\\times '
'(-x)=8\]'
'\[9x-36-9x=8\]'
'\[(9-9)x-36=8\]'
'\[0x-36=8\]'
'\[-36=8\]'
'This equation has no solution.'
'\\newline ')
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_eq38_autoresolution():
"""Is this Equation correctly auto-resolved?"""
eq = Equation((Sum([
Monomial((Fraction((Item(1), Item(4))), 1)),
Fraction((Item(1), Item(7)))
]), Fraction(('-', Item(3), Item(14)))))
assert eq.auto_resolution(dont_display_equations_name=True) == \
wrap_nb('\[\\frac{1}{4}x+\\frac{1}{7}=-\\frac{3}{14}\]'
'\[\\frac{1}{4}x=-\\frac{3}{14}-\\frac{1}{7}\]'
'\[\\frac{1}{4}x=-\\frac{3}{14}-\\frac{1\\times 2}'
'{7\\times 2}\]'
'\[\\frac{1}{4}x=-\\frac{3}{14}-\\frac{2}{14}\]'
'\[\\frac{1}{4}x=\\frac{-3-2}{14}\]'
'\[\\frac{1}{4}x=-\\frac{5}{14}\]'
'\[x=-\\frac{5}{14}\div \\frac{1}{4}\]'
'\[x=-\\frac{5}{14}\\times \\frac{4}{1}\]'
'\[x=-\\frac{5\\times 4}{14\\times 1}\]'
'\[x=-\\frac{5\\times \\bcancel{2}\\times 2}'
'{\\bcancel{2}\\times 7}\]'
'\[x=-\\frac{10}{7}\]')
def test_eq20_autoresolution():
"""Is this Equation correctly auto-resolved?"""
eq = Equation(
(Sum([Monomial(('+', 5, 1))]),
Sum([
Expandable(
(Item(1), Sum([Monomial(('+', 2, 0)),
Monomial(('-', 5, 1))]))),
Monomial(('-', 2, 0))
])),
number=1)
assert eq.auto_resolution() == wrap_nb('$(\\text{E}_{1}): $'
'\[5x=(2-5x)-2\]'
'\[5x=2-5x-2\]'
'\[5x=2-2-5x\]'
'\[5x=-5x\]'
'\[5x+5x=0\]'
'\[(5+5)x=0\]'
'\[10x=0\]'
'\[x=0\]')