def test_DifferentialExtension_all_attrs():
# Test 'unimportant' attributes
DE = DifferentialExtension(exp(x) * log(x), x, handle_first="exp")
assert DE.f == exp(x) * log(x)
assert DE.newf == t0 * t1
assert DE.x == x
assert DE.cases == ["base", "exp", "primitive"]
assert DE.case == "primitive"
assert DE.level == -1
assert DE.t == t1 == DE.T[DE.level]
assert DE.d == Poly(1 / x, t1) == DE.D[DE.level]
raises(ValueError, lambda: DE.increment_level())
DE.decrement_level()
assert DE.level == -2
assert DE.t == t0 == DE.T[DE.level]
assert DE.d == Poly(t0, t0) == DE.D[DE.level]
assert DE.case == "exp"
DE.decrement_level()
assert DE.level == -3
assert DE.t == x == DE.T[DE.level] == DE.x
assert DE.d == Poly(1, x) == DE.D[DE.level]
assert DE.case == "base"
raises(ValueError, lambda: DE.decrement_level())
DE.increment_level()
DE.increment_level()
assert DE.level == -1
assert DE.t == t1 == DE.T[DE.level]
assert DE.d == Poly(1 / x, t1) == DE.D[DE.level]
assert DE.case == "primitive"
# Test methods
assert DE.indices("log") == [2]
assert DE.indices("exp") == [1]
def test_DifferentialExtension_all_attrs():
# Test 'unimportant' attributes
DE = DifferentialExtension(exp(x) * log(x), x, handle_first='exp')
assert DE.f == exp(x) * log(x)
assert DE.newf == t0 * t1
assert DE.x == x
assert DE.cases == ['base', 'exp', 'primitive']
assert DE.case == 'primitive'
assert DE.level == -1
assert DE.t == t1 == DE.T[DE.level]
assert DE.d == Poly(1 / x, t1) == DE.D[DE.level]
raises(ValueError, lambda: DE.increment_level())
DE.decrement_level()
assert DE.level == -2
assert DE.t == t0 == DE.T[DE.level]
assert DE.d == Poly(t0, t0) == DE.D[DE.level]
assert DE.case == 'exp'
DE.decrement_level()
assert DE.level == -3
assert DE.t == x == DE.T[DE.level] == DE.x
assert DE.d == Poly(1, x) == DE.D[DE.level]
assert DE.case == 'base'
raises(ValueError, lambda: DE.decrement_level())
DE.increment_level()
DE.increment_level()
assert DE.level == -1
assert DE.t == t1 == DE.T[DE.level]
assert DE.d == Poly(1 / x, t1) == DE.D[DE.level]
assert DE.case == 'primitive'
# Test methods
assert DE.indices('log') == [2]
assert DE.indices('exp') == [1]
def test_prde_special_denom():
a = Poly(t + 1, t)
ba = Poly(t**2, t)
bd = Poly(1, t)
G = [(Poly(t, t), Poly(1, t)), (Poly(t**2, t), Poly(1, t)),
(Poly(t**3, t), Poly(1, t))]
DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(t, t)]})
assert prde_special_denom(a, ba, bd, G, DE) == \
(Poly(t + 1, t), Poly(t**2, t), [(Poly(t, t), Poly(1, t)),
(Poly(t**2, t), Poly(1, t)), (Poly(t**3, t), Poly(1, t))], Poly(1, t))
G = [(Poly(t, t), Poly(1, t)), (Poly(1, t), Poly(t, t))]
assert prde_special_denom(Poly(1, t), Poly(t**2, t), Poly(1, t), G, DE) == \
(Poly(1, t), Poly(t**2 - 1, t), [(Poly(t**2, t), Poly(1, t)),
(Poly(1, t), Poly(1, t))], Poly(t, t))
DE = DifferentialExtension(
extension={'D': [Poly(1, x), Poly(-2 * x * t0, t0)]})
DE.decrement_level()
G = [(Poly(t, t), Poly(t**2, t)), (Poly(2 * t, t), Poly(t, t))]
assert prde_special_denom(Poly(5*x*t + 1, t), Poly(t**2 + 2*x**3*t, t), Poly(t**3 + 2, t), G, DE) == \
(Poly(5*x*t + 1, t), Poly(0, t), [(Poly(t, t), Poly(t**2, t)),
(Poly(2*t, t), Poly(t, t))], Poly(1, x))
DE = DifferentialExtension(
extension={'D': [Poly(1, x), Poly((t**2 + 1) * 2 * x, t)]})
G = [(Poly(t + x, t), Poly(t * x, t)), (Poly(2 * t, t), Poly(x**2, x))]
assert prde_special_denom(Poly(5*x*t + 1, t), Poly(t**2 + 2*x**3*t, t), Poly(t**3, t), G, DE) == \
(Poly(5*x*t + 1, t), Poly(0, t), [(Poly(t + x, t), Poly(x*t, t)),
(Poly(2*t, t, x), Poly(x**2, t, x))], Poly(1, t))
assert prde_special_denom(Poly(t + 1, t), Poly(t**2, t), Poly(t**3, t), G, DE) == \
(Poly(t + 1, t), Poly(0, t), [(Poly(t + x, t), Poly(x*t, t)), (Poly(2*t, t, x),
Poly(x**2, t, x))], Poly(1, t))
def test_rischDE():
# TODO: Add more tests for rischDE, including ones from the text
DE = DifferentialExtension(extension={'D':[Poly(1, x), Poly(t, t)]})
DE.decrement_level()
assert rischDE(Poly(-2*x, x), Poly(1, x), Poly(1 - 2*x - 2*x**2, x),
Poly(1, x), DE) == \
(Poly(x + 1, x), Poly(1, x))
def test_DifferentialExtension_all_attrs():
# Test 'unimportant' attributes
DE = DifferentialExtension(exp(x)*log(x), x, dummy=False, handle_first='exp')
assert DE.f == exp(x)*log(x)
assert DE.newf == t0*t1
assert DE.x == x
assert DE.cases == ['base', 'exp', 'primitive']
assert DE.case == 'primitive'
assert DE.level == -1
assert DE.t == t1 == DE.T[DE.level]
assert DE.d == Poly(1/x, t1) == DE.D[DE.level]
raises(ValueError, lambda: DE.increment_level())
DE.decrement_level()
assert DE.level == -2
assert DE.t == t0 == DE.T[DE.level]
assert DE.d == Poly(t0, t0) == DE.D[DE.level]
assert DE.case == 'exp'
DE.decrement_level()
assert DE.level == -3
assert DE.t == x == DE.T[DE.level] == DE.x
assert DE.d == Poly(1, x) == DE.D[DE.level]
assert DE.case == 'base'
raises(ValueError, lambda: DE.decrement_level())
DE.increment_level()
DE.increment_level()
assert DE.level == -1
assert DE.t == t1 == DE.T[DE.level]
assert DE.d == Poly(1/x, t1) == DE.D[DE.level]
assert DE.case == 'primitive'
def test_prde_special_denom():
a = Poly(t + 1, t)
ba = Poly(t**2, t)
bd = Poly(1, t)
G = [(Poly(t, t), Poly(1, t)), (Poly(t**2, t), Poly(1, t)), (Poly(t**3, t), Poly(1, t))]
DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(t, t)]})
assert prde_special_denom(a, ba, bd, G, DE) == \
(Poly(t + 1, t), Poly(t**2, t), [(Poly(t, t), Poly(1, t)),
(Poly(t**2, t), Poly(1, t)), (Poly(t**3, t), Poly(1, t))], Poly(1, t))
G = [(Poly(t, t), Poly(1, t)), (Poly(1, t), Poly(t, t))]
assert prde_special_denom(Poly(1, t), Poly(t**2, t), Poly(1, t), G, DE) == \
(Poly(1, t), Poly(t**2 - 1, t), [(Poly(t**2, t), Poly(1, t)),
(Poly(1, t), Poly(1, t))], Poly(t, t))
DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(-2*x*t0, t0)]})
DE.decrement_level()
G = [(Poly(t, t), Poly(t**2, t)), (Poly(2*t, t), Poly(t, t))]
assert prde_special_denom(Poly(5*x*t + 1, t), Poly(t**2 + 2*x**3*t, t), Poly(t**3 + 2, t), G, DE) == \
(Poly(5*x*t + 1, t), Poly(0, t), [(Poly(t, t), Poly(t**2, t)),
(Poly(2*t, t), Poly(t, t))], Poly(1, x))
DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly((t**2 + 1)*2*x, t)]})
G = [(Poly(t + x, t), Poly(t*x, t)), (Poly(2*t, t), Poly(x**2, x))]
assert prde_special_denom(Poly(5*x*t + 1, t), Poly(t**2 + 2*x**3*t, t), Poly(t**3, t), G, DE) == \
(Poly(5*x*t + 1, t), Poly(0, t), [(Poly(t + x, t), Poly(x*t, t)),
(Poly(2*t, t, x), Poly(x**2, t, x))], Poly(1, t))
assert prde_special_denom(Poly(t + 1, t), Poly(t**2, t), Poly(t**3, t), G, DE) == \
(Poly(t + 1, t), Poly(0, t), [(Poly(t + x, t), Poly(x*t, t)), (Poly(2*t, t, x),
Poly(x**2, t, x))], Poly(1, t))
def test_rischDE():
# TODO: Add more tests for rischDE, including ones from the text
DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(t, t)]})
DE.decrement_level()
assert rischDE(Poly(-2*x, x), Poly(1, x), Poly(1 - 2*x - 2*x**2, x),
Poly(1, x), DE) == \
(Poly(x + 1, x), Poly(1, x))
def test_special_denom():
# TODO: add more tests here
DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(t, t)]})
assert special_denom(Poly(1, t), Poly(t**2, t), Poly(1, t), Poly(t**2 - 1, t),
Poly(t, t), DE) == \
(Poly(1, t), Poly(t**2 - 1, t), Poly(t**2 - 1, t), Poly(t, t))
# assert special_denom(Poly(1, t), Poly(2*x, t), Poly((1 + 2*x)*t, t), DE) == 1
# issue 3940
# Note, this isn't a very good test, because the denominator is just 1,
# but at least it tests the exp cancellation case
DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(-2*x*t0, t0),
Poly(I*k*t1, t1)]})
DE.decrement_level()
assert special_denom(Poly(1, t0), Poly(I*k, t0), Poly(1, t0), Poly(t0, t0),
Poly(1, t0), DE) == \
(Poly(1, t0), Poly(I*k, t0), Poly(t0, t0), Poly(1, t0))
assert special_denom(Poly(1, t), Poly(t**2, t), Poly(1, t), Poly(t**2 - 1, t),
Poly(t, t), DE, case='tan') == \
(Poly(1, t, t0, domain='ZZ'), Poly(t**2, t0, t, domain='ZZ[x]'),
Poly(t, t, t0, domain='ZZ'), Poly(1, t0, domain='ZZ'))
raises(ValueError, lambda: special_denom(Poly(1, t), Poly(t**2, t), Poly(1, t), Poly(t**2 - 1, t),
Poly(t, t), DE, case='unrecognized_case'))
def test_special_denom():
# TODO: add more tests here
DE = DifferentialExtension(extension={'D':[Poly(1, x), Poly(t, t)]})
assert special_denom(Poly(1, t), Poly(t**2, t), Poly(1, t), Poly(t**2 - 1, t),
Poly(t, t), DE) == \
(Poly(1, t), Poly(t**2 - 1, t), Poly(t**2 - 1, t), Poly(t, t))
# assert special_denom(Poly(1, t), Poly(2*x, t), Poly((1 + 2*x)*t, t), DE) == 1
# Issue 841
# Note, this isn't a very good test, because the denominator is just 1,
# but at least it tests the exp cancellation case
DE = DifferentialExtension(extension={'D':[Poly(1, x), Poly(-2*x*t0, t0),
Poly(I*k*t1, t1)]})
DE.decrement_level()
assert special_denom(Poly(1, t0), Poly(I*k, t0), Poly(1, t0), Poly(t0, t0),
Poly(1, t0), DE) == \
(Poly(1, t0), Poly(I*k, t0), Poly(t0, t0), Poly(1, t0))
def test_special_denom():
# TODO: add more tests here
DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(t, t)]})
assert special_denom(Poly(1, t), Poly(t**2, t), Poly(1, t), Poly(t**2 - 1, t),
Poly(t, t), DE) == \
(Poly(1, t), Poly(t**2 - 1, t), Poly(t**2 - 1, t), Poly(t, t))
# assert special_denom(Poly(1, t), Poly(2*x, t), Poly((1 + 2*x)*t, t), DE) == 1
# issue 3940
# Note, this isn't a very good test, because the denominator is just 1,
# but at least it tests the exp cancellation case
DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(-2*x*t0, t0),
Poly(I*k*t1, t1)]})
DE.decrement_level()
assert special_denom(Poly(1, t0), Poly(I*k, t0), Poly(1, t0), Poly(t0, t0),
Poly(1, t0), DE) == \
(Poly(1, t0), Poly(I*k, t0), Poly(t0, t0), Poly(1, t0))
