def test_constant_multiple():
assert constant_renumber(constantsimp(C1*2 + 2, [C1]), 'C', 1, 1) == C1
assert constant_renumber(constantsimp(x*2/C1, [C1]), 'C', 1, 1) == C1*x
assert constant_renumber(constantsimp(C1**2*2 + 2, [C1]), 'C', 1, 1) == C1
assert constant_renumber(
constantsimp(sin(2*C1) + x + sqrt(2), [C1]), 'C', 1, 1) == C1 + x
assert constant_renumber(constantsimp(2*C1 + C2, [C1, C2]), 'C', 1, 2) == C1
def test_ode_solutions():
# only a few examples here, the rest will be tested in the actual dsolve tests
assert constant_renumber(constantsimp(C1*exp(2*x) + exp(x)*(C2 + C3), [C1, C2, C3]), 'C', 1, 3) == \
constant_renumber((C1*exp(x) + C2*exp(2*x)), 'C', 1, 2)
assert constant_renumber(
constantsimp(Eq(f(x), I*C1*sinh(x/3) + C2*cosh(x/3)), [C1, C2]),
'C', 1, 2) == constant_renumber(Eq(f(x), C1*sinh(x/3) + C2*cosh(x/3)), 'C', 1, 2)
assert constant_renumber(constantsimp(Eq(f(x), acos((-C1)/cos(x))), [C1]), 'C', 1, 1) == \
Eq(f(x), acos(C1/cos(x)))
assert constant_renumber(
constantsimp(Eq(log(f(x)/C1) + 2*exp(x/f(x)), 0), [C1]),
'C', 1, 1) == Eq(log(C1*f(x)) + 2*exp(x/f(x)), 0)
assert constant_renumber(constantsimp(Eq(log(x*sqrt(2)*sqrt(1/x)*sqrt(f(x))
/ C1) + x**2/(2*f(x)**2), 0), [C1]), 'C', 1, 1) == \
Eq(log(C1*sqrt(x)*sqrt(f(x))) + x**2/(2*f(x)**2), 0)
assert constant_renumber(constantsimp(Eq(-exp(-f(x)/x)*sin(f(x)/x)/2 + log(x/C1) -
cos(f(x)/x)*exp(-f(x)/x)/2, 0), [C1]), 'C', 1, 1) == \
Eq(-exp(-f(x)/x)*sin(f(x)/x)/2 + log(C1*x) - cos(f(x)/x) *
exp(-f(x)/x)/2, 0)
u2 = Symbol('u2')
_a = Symbol('_a')
assert constant_renumber(constantsimp(Eq(-Integral(-1/(sqrt(1 - u2**2)*u2),
(u2, _a, x/f(x))) + log(f(x)/C1), 0), [C1]), 'C', 1, 1) == \
Eq(-Integral(-1/(u2*sqrt(1 - u2**2)), (u2, _a, x/f(x))) +
log(C1*f(x)), 0)
assert [constantsimp(i, [C1]) for i in [Eq(f(x), sqrt(-C1*x + x**2)), Eq(f(x), -sqrt(-C1*x + x**2))]] == \
[Eq(f(x), sqrt(x*(C1 + x))), Eq(f(x), -sqrt(x*(C1 + x)))]
def test_constant_power_as_base():
assert constant_renumber(constantsimp(C1**C1, [C1]), 'C', 1, 1) == C1
assert constant_renumber(constantsimp(Pow(C1, C1), [C1]), 'C', 1, 1) == C1
assert constant_renumber(constantsimp(C1**C1, [C1]), 'C', 1, 1) == C1
assert constant_renumber(constantsimp(C1**C2, [C1, C2]), 'C', 1, 2) == C1
assert constant_renumber(constantsimp(C2**C1, [C1, C2]), 'C', 1, 2) == C1
assert constant_renumber(constantsimp(C2**C2, [C1, C2]), 'C', 1, 2) == C1
assert constant_renumber(constantsimp(C1**y, [C1, y]), 'C', 1, 1) == C1
assert constant_renumber(constantsimp(C1**x, [C1]), 'C', 1, 1) == C1**x
assert constant_renumber(constantsimp(C1**2, [C1]), 'C', 1, 1) == C1
assert constant_renumber(constantsimp(C1**(x * y), [C1]), 'C', 1,
1) == C1**(x * y)
def test_constant_power_as_base():
assert constant_renumber(constantsimp(C1**C1, [C1]), 'C', 1, 1) == C1
assert constant_renumber(constantsimp(Pow(C1, C1), [C1]), 'C', 1, 1) == C1
assert constant_renumber(constantsimp(C1**C1, [C1]), 'C', 1, 1) == C1
assert constant_renumber(constantsimp(C1**C2, [C1, C2]), 'C', 1, 2) == C1
assert constant_renumber(constantsimp(C2**C1, [C1, C2]), 'C', 1, 2) == C1
assert constant_renumber(constantsimp(C2**C2, [C1, C2]), 'C', 1, 2) == C1
assert constant_renumber(constantsimp(C1**y, [C1, y]), 'C', 1, 1) == C1
assert constant_renumber(constantsimp(C1**x, [C1]), 'C', 1, 1) == C1**x
assert constant_renumber(constantsimp(C1**2, [C1]), 'C', 1, 1) == C1
assert constant_renumber(
constantsimp(C1**(x*y), [C1]), 'C', 1, 1) == C1**(x*y)
def test_constant_function():
assert constant_renumber(constantsimp(sin(C1), [C1]), 'C', 1, 1) == C1
assert constant_renumber(constantsimp(f(C1), [C1]), 'C', 1, 1) == C1
assert constant_renumber(constantsimp(f(C1, C1), [C1]), 'C', 1, 1) == C1
assert constant_renumber(constantsimp(f(C1, C2), [C1, C2]), 'C', 1, 2) == C1
assert constant_renumber(constantsimp(f(C2, C1), [C1, C2]), 'C', 1, 2) == C1
assert constant_renumber(constantsimp(f(C2, C2), [C1, C2]), 'C', 1, 2) == C1
assert constant_renumber(
constantsimp(f(C1, x), [C1]), 'C', 1, 2) == f(C1, x)
assert constant_renumber(constantsimp(f(C1, y), [C1, y]), 'C', 1, 2) == C1
assert constant_renumber(constantsimp(f(y, C1), [C1, y]), 'C', 1, 2) == C1
assert constant_renumber(constantsimp(f(C1, y, C2), [C1, C2, y]), 'C', 1, 2) == C1
def test_constant_add():
assert constant_renumber(constantsimp(C1 + C1, [C1]), 'C', 1, 1) == C1
assert constant_renumber(constantsimp(C1 + 2, [C1]), 'C', 1, 1) == C1
assert constant_renumber(constantsimp(2 + C1, [C1]), 'C', 1, 1) == C1
assert constant_renumber(constantsimp(C1 + y, [C1, y]), 'C', 1, 1) == C1
assert constant_renumber(constantsimp(C1 + x, [C1]), 'C', 1, 1) == C1 + x
assert constant_renumber(constantsimp(C1 + C1, [C1]), 'C', 1, 1) == C1
assert constant_renumber(constantsimp(C1 + C2, [C1, C2]), 'C', 1, 2) == C1
assert constant_renumber(constantsimp(C2 + C1, [C1, C2]), 'C', 1, 2) == C1
assert constant_renumber(constantsimp(C1 + C2 + C1, [C1, C2]), 'C', 1, 2) == C1
def test_ode_solutions():
# only a few examples here, the rest will be tested in the actual dsolve tests
assert constant_renumber(constantsimp(C1*exp(2*x) + exp(x)*(C2 + C3), [C1, C2, C3]), 'C', 1, 3) == \
constant_renumber((C1*exp(x) + C2*exp(2*x)), 'C', 1, 2)
assert constant_renumber(
constantsimp(Eq(f(x),
I * C1 * sinh(x / 3) + C2 * cosh(x / 3)),
[C1, C2]), 'C', 1,
2) == constant_renumber(Eq(f(x),
C1 * sinh(x / 3) + C2 * cosh(x / 3)), 'C',
1, 2)
assert constant_renumber(constantsimp(Eq(f(x), acos((-C1)/cos(x))), [C1]), 'C', 1, 1) == \
Eq(f(x), acos(C1/cos(x)))
assert constant_renumber(
constantsimp(Eq(log(f(x) / C1) + 2 * exp(x / f(x)), 0), [C1]), 'C', 1,
1) == Eq(log(C1 * f(x)) + 2 * exp(x / f(x)), 0)
assert constant_renumber(constantsimp(Eq(log(x*sqrt(2)*sqrt(1/x)*sqrt(f(x))
/ C1) + x**2/(2*f(x)**2), 0), [C1]), 'C', 1, 1) == \
Eq(log(C1*sqrt(x)*sqrt(f(x))) + x**2/(2*f(x)**2), 0)
assert constant_renumber(constantsimp(Eq(-exp(-f(x)/x)*sin(f(x)/x)/2 + log(x/C1) -
cos(f(x)/x)*exp(-f(x)/x)/2, 0), [C1]), 'C', 1, 1) == \
Eq(-exp(-f(x)/x)*sin(f(x)/x)/2 + log(C1*x) - cos(f(x)/x) *
exp(-f(x)/x)/2, 0)
u2 = Symbol('u2')
_a = Symbol('_a')
assert constant_renumber(constantsimp(Eq(-Integral(-1/(sqrt(1 - u2**2)*u2),
(u2, _a, x/f(x))) + log(f(x)/C1), 0), [C1]), 'C', 1, 1) == \
Eq(-Integral(-1/(u2*sqrt(1 - u2**2)), (u2, _a, x/f(x))) +
log(C1*f(x)), 0)
assert [constantsimp(i, [C1]) for i in [Eq(f(x), sqrt(-C1*x + x**2)), Eq(f(x), -sqrt(-C1*x + x**2))]] == \
[Eq(f(x), sqrt(x*(C1 + x))), Eq(f(x), -sqrt(x*(C1 + x)))]
# issue sympy/sympy5770
k = Symbol('k', extended_real=True)
t = Symbol('t')
w = Function('w')
sol = dsolve(w(t).diff(t, 6) - k**6 * w(t), w(t))
assert len([s for s in sol.free_symbols if s.name.startswith('C')]) == 6
assert constantsimp((C1*cos(x) + C2*cos(x))*exp(x), {C1, C2}) == \
C1*cos(x)*exp(x)
assert constantsimp(C1*cos(x) + C2*cos(x) + C3*sin(x), {C1, C2, C3}) == \
C1*cos(x) + C3*sin(x)
assert constantsimp(exp(C1 + x), {C1}) == C1 * exp(x)
assert constantsimp(x + C1 + y, {C1, y}) == C1 + x
assert constantsimp(x + C1 + Integral(x, (x, 1, 2)), {C1}) == C1 + x
def test_constant_mul():
# We want C1 (Constant) below to absorb the y's, but not the x's
assert constant_renumber(constantsimp(y * C1, [C1]), 'C', 1, 1) == C1 * y
assert constant_renumber(constantsimp(C1 * y, [C1]), 'C', 1, 1) == C1 * y
assert constant_renumber(constantsimp(x * C1, [C1]), 'C', 1, 1) == x * C1
assert constant_renumber(constantsimp(C1 * x, [C1]), 'C', 1, 1) == x * C1
assert constant_renumber(constantsimp(2 * C1, [C1]), 'C', 1, 1) == C1
assert constant_renumber(constantsimp(C1 * 2, [C1]), 'C', 1, 1) == C1
assert constant_renumber(constantsimp(y * C1 * x, [C1, y]), 'C', 1,
1) == C1 * x
assert constant_renumber(constantsimp(x * y * C1, [C1, y]), 'C', 1,
1) == x * C1
assert constant_renumber(constantsimp(y * x * C1, [C1, y]), 'C', 1,
1) == x * C1
assert constant_renumber(constantsimp(C1 * x * y, [C1, y]), 'C', 1,
1) == C1 * x
assert constant_renumber(constantsimp(x * C1 * y, [C1, y]), 'C', 1,
1) == x * C1
assert constant_renumber(constantsimp(C1 * y * (y + 1), [C1]), 'C', 1,
1) == C1 * y * (y + 1)
assert constant_renumber(constantsimp(y * C1 * (y + 1), [C1]), 'C', 1,
1) == C1 * y * (y + 1)
assert constant_renumber(constantsimp(x * (y * C1), [C1]), 'C', 1,
1) == x * y * C1
assert constant_renumber(constantsimp(x * (C1 * y), [C1]), 'C', 1,
1) == x * y * C1
assert constant_renumber(constantsimp(C1 * (x * y), [C1, y]), 'C', 1,
1) == C1 * x
assert constant_renumber(constantsimp((x * y) * C1, [C1, y]), 'C', 1,
1) == x * C1
assert constant_renumber(constantsimp((y * x) * C1, [C1, y]), 'C', 1,
1) == x * C1
assert constant_renumber(constantsimp(y * (y + 1) * C1, [C1, y]), 'C', 1,
1) == C1
assert constant_renumber(constantsimp((C1 * x) * y, [C1, y]), 'C', 1,
1) == C1 * x
assert constant_renumber(constantsimp(y * (x * C1), [C1, y]), 'C', 1,
1) == x * C1
assert constant_renumber(constantsimp((x * C1) * y, [C1, y]), 'C', 1,
1) == x * C1
assert constant_renumber(constantsimp(C1 * x * y * x * y * 2, [C1, y]),
'C', 1, 1) == C1 * x**2
assert constant_renumber(constantsimp(C1 * x * y * z, [C1, y, z]), 'C', 1,
1) == C1 * x
assert constant_renumber(constantsimp(C1 * x * y**2 * sin(z), [C1, y, z]),
'C', 1, 1) == C1 * x
assert constant_renumber(constantsimp(C1 * C1, [C1]), 'C', 1, 1) == C1
assert constant_renumber(constantsimp(C1 * C2, [C1, C2]), 'C', 1, 2) == C1
assert constant_renumber(constantsimp(C2 * C2, [C1, C2]), 'C', 1, 2) == C1
assert constant_renumber(constantsimp(C1 * C1 * C2, [C1, C2]), 'C', 1,
2) == C1
assert constant_renumber(constantsimp(C1 * x * 2**x, [C1]), 'C', 1,
1) == C1 * x * 2**x
def test_constant_repeated():
assert C1 + C1 * x == constant_renumber(C1 + C1 * x, 'C', 1, 3)
def test_constant_function_multiple():
# The rules to not renumber in this case would be too complicated, and
# dsolve is not likely to ever encounter anything remotely like this.
assert constant_renumber(constantsimp(f(C1, C1, x), [C1]), 'C', 1,
1) == f(C1, C1, x)
def test_constant_power_as_exp():
assert constant_renumber(constantsimp(x**C1, [C1]), 'C', 1, 1) == x**C1
assert constant_renumber(constantsimp(y**C1, [C1, y]), 'C', 1, 1) == C1
assert constant_renumber(constantsimp(x**y**C1, [C1, y]), 'C', 1,
1) == x**C1
assert constant_renumber(constantsimp((x**y)**C1, [C1]), 'C', 1,
1) == (x**y)**C1
assert constant_renumber(constantsimp(x**(y**C1), [C1, y]), 'C', 1,
1) == x**C1
assert constant_renumber(constantsimp(x**C1**y, [C1, y]), 'C', 1,
1) == x**C1
assert constant_renumber(constantsimp(x**(C1**y), [C1, y]), 'C', 1,
1) == x**C1
assert constant_renumber(constantsimp((x**C1)**y, [C1]), 'C', 1,
1) == (x**C1)**y
assert constant_renumber(constantsimp(2**C1, [C1]), 'C', 1, 1) == C1
assert constant_renumber(constantsimp(Integer(2)**C1, [C1]), 'C', 1,
1) == C1
assert constant_renumber(constantsimp(exp(C1), [C1]), 'C', 1, 1) == C1
assert constant_renumber(constantsimp(exp(C1 + x), [C1]), 'C', 1,
1) == C1 * exp(x)
assert constant_renumber(constantsimp(Pow(2, C1), [C1]), 'C', 1, 1) == C1
def test_constant_power_as_exp():
assert constant_renumber(constantsimp(x**C1, [C1]), 'C', 1, 1) == x**C1
assert constant_renumber(constantsimp(y**C1, [C1, y]), 'C', 1, 1) == C1
assert constant_renumber(constantsimp(x**y**C1, [C1, y]), 'C', 1, 1) == x**C1
assert constant_renumber(
constantsimp((x**y)**C1, [C1]), 'C', 1, 1) == (x**y)**C1
assert constant_renumber(
constantsimp(x**(y**C1), [C1, y]), 'C', 1, 1) == x**C1
assert constant_renumber(constantsimp(x**C1**y, [C1, y]), 'C', 1, 1) == x**C1
assert constant_renumber(
constantsimp(x**(C1**y), [C1, y]), 'C', 1, 1) == x**C1
assert constant_renumber(
constantsimp((x**C1)**y, [C1]), 'C', 1, 1) == (x**C1)**y
assert constant_renumber(constantsimp(2**C1, [C1]), 'C', 1, 1) == C1
assert constant_renumber(constantsimp(Integer(2)**C1, [C1]), 'C', 1, 1) == C1
assert constant_renumber(constantsimp(exp(C1), [C1]), 'C', 1, 1) == C1
assert constant_renumber(
constantsimp(exp(C1 + x), [C1]), 'C', 1, 1) == C1*exp(x)
assert constant_renumber(constantsimp(Pow(2, C1), [C1]), 'C', 1, 1) == C1
def test_constant_mul():
# We want C1 (Constant) below to absorb the y's, but not the x's
assert constant_renumber(constantsimp(y*C1, [C1]), 'C', 1, 1) == C1*y
assert constant_renumber(constantsimp(C1*y, [C1]), 'C', 1, 1) == C1*y
assert constant_renumber(constantsimp(x*C1, [C1]), 'C', 1, 1) == x*C1
assert constant_renumber(constantsimp(C1*x, [C1]), 'C', 1, 1) == x*C1
assert constant_renumber(constantsimp(2*C1, [C1]), 'C', 1, 1) == C1
assert constant_renumber(constantsimp(C1*2, [C1]), 'C', 1, 1) == C1
assert constant_renumber(constantsimp(y*C1*x, [C1, y]), 'C', 1, 1) == C1*x
assert constant_renumber(constantsimp(x*y*C1, [C1, y]), 'C', 1, 1) == x*C1
assert constant_renumber(constantsimp(y*x*C1, [C1, y]), 'C', 1, 1) == x*C1
assert constant_renumber(constantsimp(C1*x*y, [C1, y]), 'C', 1, 1) == C1*x
assert constant_renumber(constantsimp(x*C1*y, [C1, y]), 'C', 1, 1) == x*C1
assert constant_renumber(constantsimp(C1*y*(y + 1), [C1]), 'C', 1, 1) == C1*y*(y+1)
assert constant_renumber(constantsimp(y*C1*(y + 1), [C1]), 'C', 1, 1) == C1*y*(y+1)
assert constant_renumber(constantsimp(x*(y*C1), [C1]), 'C', 1, 1) == x*y*C1
assert constant_renumber(constantsimp(x*(C1*y), [C1]), 'C', 1, 1) == x*y*C1
assert constant_renumber(constantsimp(C1*(x*y), [C1, y]), 'C', 1, 1) == C1*x
assert constant_renumber(constantsimp((x*y)*C1, [C1, y]), 'C', 1, 1) == x*C1
assert constant_renumber(constantsimp((y*x)*C1, [C1, y]), 'C', 1, 1) == x*C1
assert constant_renumber(constantsimp(y*(y + 1)*C1, [C1, y]), 'C', 1, 1) == C1
assert constant_renumber(constantsimp((C1*x)*y, [C1, y]), 'C', 1, 1) == C1*x
assert constant_renumber(constantsimp(y*(x*C1), [C1, y]), 'C', 1, 1) == x*C1
assert constant_renumber(constantsimp((x*C1)*y, [C1, y]), 'C', 1, 1) == x*C1
assert constant_renumber(
constantsimp(C1*x*y*x*y*2, [C1, y]), 'C', 1, 1) == C1*x**2
assert constant_renumber(constantsimp(C1*x*y*z, [C1, y, z]), 'C', 1, 1) == C1*x
assert constant_renumber(
constantsimp(C1*x*y**2*sin(z), [C1, y, z]), 'C', 1, 1) == C1*x
assert constant_renumber(constantsimp(C1*C1, [C1]), 'C', 1, 1) == C1
assert constant_renumber(constantsimp(C1*C2, [C1, C2]), 'C', 1, 2) == C1
assert constant_renumber(constantsimp(C2*C2, [C1, C2]), 'C', 1, 2) == C1
assert constant_renumber(constantsimp(C1*C1*C2, [C1, C2]), 'C', 1, 2) == C1
assert constant_renumber(
constantsimp(C1*x*2**x, [C1]), 'C', 1, 1) == C1*x*2**x
def test_constant_repeated():
assert C1 + C1*x == constant_renumber( C1 + C1*x, 'C', 1, 3)
def test_constant_function_multiple():
# The rules to not renumber in this case would be too complicated, and
# dsolve is not likely to ever encounter anything remotely like this.
assert constant_renumber(
constantsimp(f(C1, C1, x), [C1]), 'C', 1, 1) == f(C1, C1, x)
