def test_poly_multiplication(t1, t2, t3):
assert Poly(Term(1, Factor("t1", 1))) * Poly(Term(2, Factor("t2", 1))) == Poly(
Term(2, Factor("t1", 1), Factor("t2", 1))
)
assert t1 * 1 is t1
assert 1 * t1 is t1
assert t1 * 2 == t1 * const(2)
assert 2 * t1 == t1 * const(2)
def test_poly_addition(t1, t2, t3):
assert Poly(Term(1, Factor("t1", 1))) + Poly(Term(1, Factor("t2", 1))) == Poly(
Term(1, Factor("t1", 1)), Term(1, Factor("t2", 1))
)
assert t1 + 0 is t1
assert 0 + t1 is t1
assert t1 + 1 == t1 + const(1)
assert 1 + t1 == t1 + const(1)
assert -t1 == Poly(Term(-1, Factor("t1", 1)))
def test_term_multiplication():
result = Term(1, Factor("t1", 1)) * Term(2, Factor("t2", 2))
expected = Term(2, Factor("t1", 1), Factor("t2", 2))
assert result == expected
t = Term(1, Factor("t", 1))
assert t * 1 is t
assert 1 * t is t
with pytest.raises(RuntimeError):
t * 2
def test_merge_common_factors():
result = set(
_merge_common_factors(
Factor("t1", 1),
Factor("t2", 2),
Factor("t3", 3),
Factor("t2", 4),
Factor("t1", 5),
)
)
expected = {Factor("t1", 6), Factor("t2", 6), Factor("t3", 3)}
assert result == expected
def test_factor_multiply():
assert Factor("t", 1) * Factor("t", 2) == Factor("t", 3)
f = Factor("t", 1)
assert 1 * f is f
assert f * 1 is f
with pytest.raises(RuntimeError):
Factor("t1", 1) * Factor("t2", 1)
with pytest.raises(RuntimeError):
Factor("t", 1) * 2
def test_merge_common_terms():
result = set(
_merge_common_terms(
Term(1, Factor("t1", 1)),
Term(2, Factor("t2", 1)),
Term(3, Factor("t3", 1)),
Term(4, Factor("t2", 1)),
Term(5, Factor("t1", 1)),
)
)
assert result == {
Term(6, Factor("t1", 1)),
Term(6, Factor("t2", 1)),
Term(3, Factor("t3", 1)),
}
def test_term_addition():
assert Term(1, Factor("t", 2)) + Term(2, Factor("t", 2)) == Term(3, Factor("t", 2))
t = Term(1, Factor("t", 1))
assert t + 0 is t
assert 0 + t is t
with pytest.raises(RuntimeError):
Term(1, Factor("t1", 1)) + Term(1, Factor("t2", 1))
with pytest.raises(RuntimeError):
t + 1
def test_factor_equality(f):
assert f(Factor("t", 2)) == f(Factor("t", 2))
assert f(Factor("t", 2)) != f(Factor("t2", 2))
assert f(Factor("t", 1)) != f(Factor("t", 2))
def test_factor_eval():
assert Factor("t", 2).eval(t=2) == 4
def test_factor_str():
f = Factor("t", 2)
assert str(f) == "t^2"
assert str(f) == repr(f)
def test_factor_constructor():
assert Factor("t") == Factor("t", 1)
with pytest.raises(ValueError):
Factor("t", 0)
def test_term_eval():
assert Term(2, Factor("t", 3)).eval(t=4) == 2 * 4**3
def test_poly_subtraction(t1, t2):
assert t1 - t1 == Poly(Term(0))
assert 1 - t1 == Poly(Term(1), Term(-1, Factor("t1", 1)))
assert t1 - 1 == Poly(Term(-1), Term(1, Factor("t1", 1)))
def test_term_str():
t = Term(2, Factor("t2", 2), Factor("t1", 1))
assert str(t) == "2 * t1^1 t2^2"
assert str(t) == repr(t)
assert str(Term(1)) == "1"
def test_poly_constructor():
assert Poly(
Term(1, Factor("t1", 1)), Term(2, Factor("t1", 1)), Term(2, Factor("t2", 2))
) == Poly(Term(3, Factor("t1", 1)), Term(2, Factor("t2", 2)))
def test_poly_collect_for(t1, t2, t3):
result = (t1**2 * t2 * t3**3 + 2 * t1**2).collect_for(Factor("t1", 2))
expected = 2 + t2 * t3**3
assert result == expected
def test_term_is_function_of():
t = Term(2, Factor("t1", 1), Factor("t2", 1))
assert t.is_function_of("t1")
assert t.is_function_of("t2")
assert not t.is_function_of("t3")
def test_term_highest_power():
t = Term(2, Factor("t1", 2), Factor("t2", 3))
assert t.highest_power("t1") == 2
assert t.highest_power("t2") == 3
assert t.highest_power("t3") == 0
def test_term_equality(f):
x = Term(2, Factor("t1", 1), Factor("t2", 2))
y = Term(2, Factor("t2", 2), Factor("t1", 1))
assert f(x) == f(y)
x = Term(2, Factor("t1", 1), Factor("t2", 2))
y = Term(2, Factor("t1", 2), Factor("t2", 2))
assert f(x) != f(y)
x = Term(1, Factor("t1", 1), Factor("t2", 2))
y = Term(2, Factor("t1", 1), Factor("t2", 2))
assert f(x) != f(y)
def test_term_collect_for():
t = Term(2, Factor("t1", 1), Factor("t2", 2))
assert t.collect_for(Factor("t1", 1)) == Term(2, Factor("t2", 2))
assert t.collect_for(Factor("t2", 2)) == Term(2, Factor("t1", 1))
with pytest.raises(RuntimeError):
t.collect_for(Factor("t3", 2))
def test_term_is_constant():
assert Term(2).is_constant()
assert not Term(2, Factor("t", 1)).is_constant()
def test_term_constructor():
assert Term(Factor("t", 2)) == Term(1, Factor("t", 2))
assert Term(Factor("t", 2), Factor("t", 3)) == Term(Factor("t", 5))
assert Term(0, Factor("t", 2)) == Term(0)
def test_term_substitute(t1, t2):
result = Term(2, Factor("t1", 1), Factor("t2", 2)).substitute("t2", t1 - t2)
expected = 2 * t1**3 - 4 * t1**2 * t2 + 2 * t1 * t2**2
assert result == expected