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 __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_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 rubbish_polynomial():
return Polynomial([
Monomial(('+', 1, 2)),
Monomial(('+', 7, 1)),
Monomial(('-', 10, 2)),
Monomial(('-', 9, 1)),
Monomial(('+', 9, 2))
])
def expP():
t = Sum([Expandable((Monomial(('+', 7, 0)),
Sum([Monomial(('-', 6, 1)),
Monomial((6, 0))]))),
BinomialIdentity((Monomial(('-', 10, 1)),
Monomial(('-', 3, 0))),
difference_square='OK')])
return Expression("P", t)
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_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_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_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_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_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_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 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 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 expN():
t = Sum([Expandable((Monomial(('-', 1, 0)),
Expandable((Sum([Monomial((2, 1)),
Monomial((9, 0))]),
Sum([Monomial((-3, 1)),
Monomial((-7, 0))]))))),
Expandable((Monomial((4, 0)),
Sum([Monomial((-3, 1)),
Monomial((9, 0))]))),
Monomial((13, 0))])
return Expression("N", t)
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_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_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_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_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_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_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_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_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_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_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('\[5^{2}=4^{2}+x\]'
'\[25=16+x\]'
'\[x=25-16\]'
'\[x=9\]')
