180 lines
8.5 KiB
Python
180 lines
8.5 KiB
Python
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"""
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If the arbitrary constant class from issue 4435 is ever implemented, this
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should serve as a set of test cases.
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"""
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from sympy.core.function import Function
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from sympy.core.numbers import I
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from sympy.core.power import Pow
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from sympy.core.relational import Eq
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from sympy.core.singleton import S
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from sympy.core.symbol import Symbol
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from sympy.functions.elementary.exponential import (exp, log)
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from sympy.functions.elementary.hyperbolic import (cosh, sinh)
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from sympy.functions.elementary.miscellaneous import sqrt
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from sympy.functions.elementary.trigonometric import (acos, cos, sin)
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from sympy.integrals.integrals import Integral
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from sympy.solvers.ode.ode import constantsimp, constant_renumber
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from sympy.testing.pytest import XFAIL
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x = Symbol('x')
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y = Symbol('y')
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z = Symbol('z')
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u2 = Symbol('u2')
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_a = Symbol('_a')
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C1 = Symbol('C1')
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C2 = Symbol('C2')
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C3 = Symbol('C3')
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f = Function('f')
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def test_constant_mul():
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# We want C1 (Constant) below to absorb the y's, but not the x's
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assert constant_renumber(constantsimp(y*C1, [C1])) == C1*y
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assert constant_renumber(constantsimp(C1*y, [C1])) == C1*y
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assert constant_renumber(constantsimp(x*C1, [C1])) == x*C1
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assert constant_renumber(constantsimp(C1*x, [C1])) == x*C1
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assert constant_renumber(constantsimp(2*C1, [C1])) == C1
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assert constant_renumber(constantsimp(C1*2, [C1])) == C1
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assert constant_renumber(constantsimp(y*C1*x, [C1, y])) == C1*x
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assert constant_renumber(constantsimp(x*y*C1, [C1, y])) == x*C1
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assert constant_renumber(constantsimp(y*x*C1, [C1, y])) == x*C1
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assert constant_renumber(constantsimp(C1*x*y, [C1, y])) == C1*x
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assert constant_renumber(constantsimp(x*C1*y, [C1, y])) == x*C1
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assert constant_renumber(constantsimp(C1*y*(y + 1), [C1])) == C1*y*(y+1)
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assert constant_renumber(constantsimp(y*C1*(y + 1), [C1])) == C1*y*(y+1)
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assert constant_renumber(constantsimp(x*(y*C1), [C1])) == x*y*C1
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assert constant_renumber(constantsimp(x*(C1*y), [C1])) == x*y*C1
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assert constant_renumber(constantsimp(C1*(x*y), [C1, y])) == C1*x
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assert constant_renumber(constantsimp((x*y)*C1, [C1, y])) == x*C1
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assert constant_renumber(constantsimp((y*x)*C1, [C1, y])) == x*C1
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assert constant_renumber(constantsimp(y*(y + 1)*C1, [C1, y])) == C1
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assert constant_renumber(constantsimp((C1*x)*y, [C1, y])) == C1*x
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assert constant_renumber(constantsimp(y*(x*C1), [C1, y])) == x*C1
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assert constant_renumber(constantsimp((x*C1)*y, [C1, y])) == x*C1
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assert constant_renumber(constantsimp(C1*x*y*x*y*2, [C1, y])) == C1*x**2
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assert constant_renumber(constantsimp(C1*x*y*z, [C1, y, z])) == C1*x
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assert constant_renumber(constantsimp(C1*x*y**2*sin(z), [C1, y, z])) == C1*x
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assert constant_renumber(constantsimp(C1*C1, [C1])) == C1
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assert constant_renumber(constantsimp(C1*C2, [C1, C2])) == C1
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assert constant_renumber(constantsimp(C2*C2, [C1, C2])) == C1
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assert constant_renumber(constantsimp(C1*C1*C2, [C1, C2])) == C1
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assert constant_renumber(constantsimp(C1*x*2**x, [C1])) == C1*x*2**x
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def test_constant_add():
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assert constant_renumber(constantsimp(C1 + C1, [C1])) == C1
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assert constant_renumber(constantsimp(C1 + 2, [C1])) == C1
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assert constant_renumber(constantsimp(2 + C1, [C1])) == C1
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assert constant_renumber(constantsimp(C1 + y, [C1, y])) == C1
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assert constant_renumber(constantsimp(C1 + x, [C1])) == C1 + x
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assert constant_renumber(constantsimp(C1 + C1, [C1])) == C1
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assert constant_renumber(constantsimp(C1 + C2, [C1, C2])) == C1
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assert constant_renumber(constantsimp(C2 + C1, [C1, C2])) == C1
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assert constant_renumber(constantsimp(C1 + C2 + C1, [C1, C2])) == C1
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def test_constant_power_as_base():
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assert constant_renumber(constantsimp(C1**C1, [C1])) == C1
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assert constant_renumber(constantsimp(Pow(C1, C1), [C1])) == C1
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assert constant_renumber(constantsimp(C1**C1, [C1])) == C1
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assert constant_renumber(constantsimp(C1**C2, [C1, C2])) == C1
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assert constant_renumber(constantsimp(C2**C1, [C1, C2])) == C1
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assert constant_renumber(constantsimp(C2**C2, [C1, C2])) == C1
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assert constant_renumber(constantsimp(C1**y, [C1, y])) == C1
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assert constant_renumber(constantsimp(C1**x, [C1])) == C1**x
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assert constant_renumber(constantsimp(C1**2, [C1])) == C1
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assert constant_renumber(
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constantsimp(C1**(x*y), [C1])) == C1**(x*y)
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def test_constant_power_as_exp():
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assert constant_renumber(constantsimp(x**C1, [C1])) == x**C1
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assert constant_renumber(constantsimp(y**C1, [C1, y])) == C1
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assert constant_renumber(constantsimp(x**y**C1, [C1, y])) == x**C1
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assert constant_renumber(
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constantsimp((x**y)**C1, [C1])) == (x**y)**C1
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assert constant_renumber(
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constantsimp(x**(y**C1), [C1, y])) == x**C1
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assert constant_renumber(constantsimp(x**C1**y, [C1, y])) == x**C1
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assert constant_renumber(
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constantsimp(x**(C1**y), [C1, y])) == x**C1
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assert constant_renumber(
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constantsimp((x**C1)**y, [C1])) == (x**C1)**y
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assert constant_renumber(constantsimp(2**C1, [C1])) == C1
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assert constant_renumber(constantsimp(S(2)**C1, [C1])) == C1
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assert constant_renumber(constantsimp(exp(C1), [C1])) == C1
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assert constant_renumber(
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constantsimp(exp(C1 + x), [C1])) == C1*exp(x)
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assert constant_renumber(constantsimp(Pow(2, C1), [C1])) == C1
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def test_constant_function():
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assert constant_renumber(constantsimp(sin(C1), [C1])) == C1
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assert constant_renumber(constantsimp(f(C1), [C1])) == C1
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assert constant_renumber(constantsimp(f(C1, C1), [C1])) == C1
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assert constant_renumber(constantsimp(f(C1, C2), [C1, C2])) == C1
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assert constant_renumber(constantsimp(f(C2, C1), [C1, C2])) == C1
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assert constant_renumber(constantsimp(f(C2, C2), [C1, C2])) == C1
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assert constant_renumber(
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constantsimp(f(C1, x), [C1])) == f(C1, x)
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assert constant_renumber(constantsimp(f(C1, y), [C1, y])) == C1
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assert constant_renumber(constantsimp(f(y, C1), [C1, y])) == C1
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assert constant_renumber(constantsimp(f(C1, y, C2), [C1, C2, y])) == C1
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def test_constant_function_multiple():
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# The rules to not renumber in this case would be too complicated, and
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# dsolve is not likely to ever encounter anything remotely like this.
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assert constant_renumber(
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constantsimp(f(C1, C1, x), [C1])) == f(C1, C1, x)
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def test_constant_multiple():
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assert constant_renumber(constantsimp(C1*2 + 2, [C1])) == C1
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assert constant_renumber(constantsimp(x*2/C1, [C1])) == C1*x
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assert constant_renumber(constantsimp(C1**2*2 + 2, [C1])) == C1
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assert constant_renumber(
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constantsimp(sin(2*C1) + x + sqrt(2), [C1])) == C1 + x
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assert constant_renumber(constantsimp(2*C1 + C2, [C1, C2])) == C1
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def test_constant_repeated():
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assert C1 + C1*x == constant_renumber( C1 + C1*x)
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def test_ode_solutions():
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# only a few examples here, the rest will be tested in the actual dsolve tests
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assert constant_renumber(constantsimp(C1*exp(2*x) + exp(x)*(C2 + C3), [C1, C2, C3])) == \
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constant_renumber(C1*exp(x) + C2*exp(2*x))
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assert constant_renumber(
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constantsimp(Eq(f(x), I*C1*sinh(x/3) + C2*cosh(x/3)), [C1, C2])
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) == constant_renumber(Eq(f(x), C1*sinh(x/3) + C2*cosh(x/3)))
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assert constant_renumber(constantsimp(Eq(f(x), acos((-C1)/cos(x))), [C1])) == \
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Eq(f(x), acos(C1/cos(x)))
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assert constant_renumber(
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constantsimp(Eq(log(f(x)/C1) + 2*exp(x/f(x)), 0), [C1])
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) == Eq(log(C1*f(x)) + 2*exp(x/f(x)), 0)
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assert constant_renumber(constantsimp(Eq(log(x*sqrt(2)*sqrt(1/x)*sqrt(f(x))
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/C1) + x**2/(2*f(x)**2), 0), [C1])) == \
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Eq(log(C1*sqrt(x)*sqrt(f(x))) + x**2/(2*f(x)**2), 0)
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assert constant_renumber(constantsimp(Eq(-exp(-f(x)/x)*sin(f(x)/x)/2 + log(x/C1) -
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cos(f(x)/x)*exp(-f(x)/x)/2, 0), [C1])) == \
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Eq(-exp(-f(x)/x)*sin(f(x)/x)/2 + log(C1*x) - cos(f(x)/x)*
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exp(-f(x)/x)/2, 0)
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assert constant_renumber(constantsimp(Eq(-Integral(-1/(sqrt(1 - u2**2)*u2),
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(u2, _a, x/f(x))) + log(f(x)/C1), 0), [C1])) == \
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Eq(-Integral(-1/(u2*sqrt(1 - u2**2)), (u2, _a, x/f(x))) +
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log(C1*f(x)), 0)
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assert [constantsimp(i, [C1]) for i in [Eq(f(x), sqrt(-C1*x + x**2)), Eq(f(x), -sqrt(-C1*x + x**2))]] == \
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[Eq(f(x), sqrt(x*(C1 + x))), Eq(f(x), -sqrt(x*(C1 + x)))]
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@XFAIL
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def test_nonlocal_simplification():
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assert constantsimp(C1 + C2+x*C2, [C1, C2]) == C1 + C2*x
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def test_constant_Eq():
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# C1 on the rhs is well-tested, but the lhs is only tested here
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assert constantsimp(Eq(C1, 3 + f(x)*x), [C1]) == Eq(x*f(x), C1)
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assert constantsimp(Eq(C1, 3 * f(x)*x), [C1]) == Eq(f(x)*x, C1)
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