def test_div_zero(self):
with self.assertRaises(ZeroDivisionError):
RealAlgebraicNumber(1) / 0
with self.assertRaises(ZeroDivisionError):
RealAlgebraicNumber(-1) / 0
with self.assertRaises(ZeroDivisionError):
RealAlgebraicNumber(0) / 0
def test_floor(self):
self.assertEqual(math.floor(RealAlgebraicNumber(123)), 123)
self.assertEqual(math.floor(RealAlgebraicNumber(123) / 10), 12)
self.assertEqual(math.floor(RealAlgebraicNumber(128) / 10), 12)
self.assertEqual(math.floor(RealAlgebraicNumber(123)
** (RealAlgebraicNumber(1) / 2)), 11)
self.assertEqual(math.floor(RealAlgebraicNumber(-123)), -123)
self.assertEqual(math.floor(RealAlgebraicNumber(-123) / 10), -13)
self.assertEqual(math.floor(RealAlgebraicNumber(-128) / 10), -13)
self.assertEqual(math.floor(-(RealAlgebraicNumber(123)
** (RealAlgebraicNumber(1) / 2))), -12)
def test_trunc(self):
self.assertEqual(math.trunc(RealAlgebraicNumber(123)), 123)
self.assertEqual(math.trunc(RealAlgebraicNumber(123) / 10), 12)
self.assertEqual(math.trunc(RealAlgebraicNumber(128) / 10), 12)
self.assertEqual(math.trunc(RealAlgebraicNumber(123)
** (RealAlgebraicNumber(1) / 2)), 11)
self.assertEqual(math.trunc(RealAlgebraicNumber(-123)), -123)
self.assertEqual(math.trunc(RealAlgebraicNumber(-123) / 10), -12)
self.assertEqual(math.trunc(RealAlgebraicNumber(-128) / 10), -12)
self.assertEqual(math.trunc(-(RealAlgebraicNumber(123)
** (RealAlgebraicNumber(1) / 2))), -11)
def test_ceil(self):
self.assertEqual(math.ceil(RealAlgebraicNumber(123)), 123)
self.assertEqual(math.ceil(RealAlgebraicNumber(123) / 10), 13)
self.assertEqual(math.ceil(RealAlgebraicNumber(128) / 10), 13)
self.assertEqual(math.ceil(RealAlgebraicNumber(123)
** (RealAlgebraicNumber(1) / 2)), 12)
self.assertEqual(math.ceil(RealAlgebraicNumber(-123)), -123)
self.assertEqual(math.ceil(RealAlgebraicNumber(-123) / 10), -12)
self.assertEqual(math.ceil(RealAlgebraicNumber(-128) / 10), -12)
self.assertEqual(math.ceil(-(RealAlgebraicNumber(123)
** (RealAlgebraicNumber(1) / 2))), -11)
def test_to_integer(self):
self.assertEqual(RealAlgebraicNumber(123).to_integer(), 123)
self.assertEqual((RealAlgebraicNumber(123) / 10).to_integer(), None)
self.assertEqual((RealAlgebraicNumber(128) / 10).to_integer(), None)
self.assertEqual((RealAlgebraicNumber(123)
** (RealAlgebraicNumber(1) / 2)).to_integer(), None)
self.assertEqual(RealAlgebraicNumber(-123).to_integer(), -123)
self.assertEqual((RealAlgebraicNumber(-123) / 10).to_integer(), None)
self.assertEqual((RealAlgebraicNumber(-128) / 10).to_integer(), None)
self.assertEqual((-(RealAlgebraicNumber(123)
** (RealAlgebraicNumber(1) / 2))
).to_integer(), None)
def test_is_integer(self):
self.assertEqual(RealAlgebraicNumber(123).is_integer(), True)
self.assertEqual((RealAlgebraicNumber(123) / 10).is_integer(), False)
self.assertEqual((RealAlgebraicNumber(128) / 10).is_integer(), False)
self.assertEqual((RealAlgebraicNumber(123)
** (RealAlgebraicNumber(1) / 2)).is_integer(), False)
self.assertEqual(RealAlgebraicNumber(-123).is_integer(), True)
self.assertEqual((RealAlgebraicNumber(-123) / 10).is_integer(), False)
self.assertEqual((RealAlgebraicNumber(-128) / 10).is_integer(), False)
self.assertEqual((-(RealAlgebraicNumber(123)
** (RealAlgebraicNumber(1) / 2))
).is_integer(), False)
def test_recip(self):
self.assertEqual(RealAlgebraicNumber(123).recip().minimal_polynomial,
[-1, 123])
self.assertEqual((RealAlgebraicNumber(123) / 10
).recip().minimal_polynomial,
[-10, 123])
self.assertEqual((RealAlgebraicNumber(128) / 10
).recip().minimal_polynomial,
[-5, 64])
self.assertEqual((-(RealAlgebraicNumber(123)
** (RealAlgebraicNumber(1) / 2))
).recip().minimal_polynomial,
[1, 0, -123])
def test_to_rational(self):
self.assertEqual(RealAlgebraicNumber(123).to_rational(), (123, 1))
self.assertEqual((RealAlgebraicNumber(123) / 10).to_rational(),
(123, 10))
self.assertEqual((RealAlgebraicNumber(128) / 10).to_rational(),
(64, 5))
self.assertEqual((RealAlgebraicNumber(123)
** (RealAlgebraicNumber(1) / 2)).to_rational(), None)
self.assertEqual(RealAlgebraicNumber(-123).to_rational(), (-123, 1))
self.assertEqual((RealAlgebraicNumber(-123) / 10).to_rational(),
(-123, 10))
self.assertEqual((RealAlgebraicNumber(-128) / 10).to_rational(),
(-64, 5))
self.assertEqual((-(RealAlgebraicNumber(123)
** (RealAlgebraicNumber(1) / 2))
).to_rational(), None)
def test_div(self):
self.assertEqual(RealAlgebraicNumber(1) / 2,
RealAlgebraicNumber(1) / 2)
self.assertEqual(1 / RealAlgebraicNumber(2),
RealAlgebraicNumber(1) / 2)
self.assertEqual(RealAlgebraicNumber(1) / RealAlgebraicNumber(2),
RealAlgebraicNumber(1) / 2)
def test_minimal_polynomial(self):
self.assertEqual(RealAlgebraicNumber(123).minimal_polynomial,
[-123, 1])
self.assertEqual((RealAlgebraicNumber(123) / 10).minimal_polynomial,
[-123, 10])
self.assertEqual((RealAlgebraicNumber(128) / 10).minimal_polynomial,
[-64, 5])
self.assertEqual((RealAlgebraicNumber(123)
** (RealAlgebraicNumber(1) / 2)).minimal_polynomial,
[-123, 0, 1])
self.assertEqual(RealAlgebraicNumber(-123).minimal_polynomial,
[123, 1])
self.assertEqual((RealAlgebraicNumber(-123) / 10).minimal_polynomial,
[123, 10])
self.assertEqual((RealAlgebraicNumber(-128) / 10).minimal_polynomial,
[64, 5])
self.assertEqual((-(RealAlgebraicNumber(123)
** (RealAlgebraicNumber(1) / 2))
).minimal_polynomial,
[-123, 0, 1])
def test_construct(self):
self.assertEqual(repr(RealAlgebraicNumber()),
"<RealAlgebraicNumber { minimal_polynomial: 0 + 1*X, "
"interval: DyadicFractionInterval { "
"lower_bound_numer: 0, upper_bound_numer: 0, "
"log2_denom: 0 } }>")
self.assertEqual(repr(RealAlgebraicNumber(42)),
"<RealAlgebraicNumber { "
"minimal_polynomial: -42 + 1*X, "
"interval: DyadicFractionInterval { "
"lower_bound_numer: 42, upper_bound_numer: 42, "
"log2_denom: 0 } }>")
self.assertEqual(repr(RealAlgebraicNumber(-5)),
"<RealAlgebraicNumber { "
"minimal_polynomial: 5 + 1*X, "
"interval: DyadicFractionInterval { "
"lower_bound_numer: -5, upper_bound_numer: -5, "
"log2_denom: 0 } }>")
self.assertEqual(repr(RealAlgebraicNumber(RealAlgebraicNumber(-5))),
"<RealAlgebraicNumber { "
"minimal_polynomial: 5 + 1*X, "
"interval: DyadicFractionInterval { "
"lower_bound_numer: -5, upper_bound_numer: -5, "
"log2_denom: 0 } }>")
def test_recip_zero(self):
with self.assertRaises(ZeroDivisionError):
RealAlgebraicNumber(0).recip()
def test_pow(self):
self.assertEqual(RealAlgebraicNumber(1) ** 2, 1)
self.assertEqual(1 ** RealAlgebraicNumber(2), 1)
self.assertEqual(RealAlgebraicNumber(1) ** RealAlgebraicNumber(2), 1)
def test_sub(self):
self.assertEqual(RealAlgebraicNumber(1) - 2, -1)
self.assertEqual(1 - RealAlgebraicNumber(2), -1)
self.assertEqual(RealAlgebraicNumber(1) - RealAlgebraicNumber(2), -1)
def test_add(self):
self.assertEqual(RealAlgebraicNumber(1) + 2, 3)
self.assertEqual(1 + RealAlgebraicNumber(2), 3)
self.assertEqual(RealAlgebraicNumber(1) + RealAlgebraicNumber(2), 3)
def test_mul(self):
self.assertEqual(RealAlgebraicNumber(1) * 2, 2)
self.assertEqual(1 * RealAlgebraicNumber(2), 2)
self.assertEqual(RealAlgebraicNumber(1) * RealAlgebraicNumber(2), 2)
def test_degree(self):
self.assertEqual(RealAlgebraicNumber(123).degree, 1)
self.assertEqual((RealAlgebraicNumber(123) / 10).degree, 1)
self.assertEqual((RealAlgebraicNumber(128) / 10).degree, 1)
self.assertEqual((RealAlgebraicNumber(123)
** (RealAlgebraicNumber(1) / 2)).degree, 2)
self.assertEqual(RealAlgebraicNumber(-123).degree, 1)
self.assertEqual((RealAlgebraicNumber(-123) / 10).degree, 1)
self.assertEqual((RealAlgebraicNumber(-128) / 10).degree, 1)
self.assertEqual((-(RealAlgebraicNumber(123)
** (RealAlgebraicNumber(1) / 2))
).degree, 2)
self.assertEqual((-(RealAlgebraicNumber(123)
** (RealAlgebraicNumber(1) / 3))
).degree, 3)
self.assertEqual((-(RealAlgebraicNumber(123)
** (RealAlgebraicNumber(1) / 4))
).degree, 4)
def test_floor_ceil_log2(self):
with self.assertRaises(ValueError):
RealAlgebraicNumber(0).floor_log2()
with self.assertRaises(ValueError):
RealAlgebraicNumber(0).ceil_log2()
with self.assertRaises(ValueError):
RealAlgebraicNumber(-1).floor_log2()
with self.assertRaises(ValueError):
RealAlgebraicNumber(-1).ceil_log2()
self.assertEqual(RealAlgebraicNumber(1).floor_log2(), 0)
self.assertEqual(RealAlgebraicNumber(1).ceil_log2(), 0)
self.assertEqual(RealAlgebraicNumber(2).floor_log2(), 1)
self.assertEqual(RealAlgebraicNumber(2).ceil_log2(), 1)
self.assertEqual(RealAlgebraicNumber(3).floor_log2(), 1)
self.assertEqual(RealAlgebraicNumber(3).ceil_log2(), 2)
self.assertEqual(RealAlgebraicNumber(4).floor_log2(), 2)
self.assertEqual(RealAlgebraicNumber(4).ceil_log2(), 2)
self.assertEqual((RealAlgebraicNumber(1) / 4).floor_log2(), -2)
self.assertEqual((RealAlgebraicNumber(1) / 4).ceil_log2(), -2)
self.assertEqual((RealAlgebraicNumber(1) / 3).floor_log2(), -2)
self.assertEqual((RealAlgebraicNumber(1) / 3).ceil_log2(), -1)
def test_abs(self):
self.assertEqual(abs(RealAlgebraicNumber(1)), 1)
self.assertEqual(abs(RealAlgebraicNumber(-2)), 2)
def test_neg(self):
self.assertEqual(-RealAlgebraicNumber(1), -1)
self.assertEqual(-RealAlgebraicNumber(-2), 2)