Vehicle-cpp/hkpc/software/sympy/solvers/tests/test_constantsimp.py

"""
If the arbitrary constant class from issue 4435 is ever implemented, this
should serve as a set of test cases.
"""

from sympy.core.function import Function
from sympy.core.numbers import I
from sympy.core.power import Pow
from sympy.core.relational import Eq
from sympy.core.singleton import S
from sympy.core.symbol import Symbol
from sympy.functions.elementary.exponential import (exp, log)
from sympy.functions.elementary.hyperbolic import (cosh, sinh)
from sympy.functions.elementary.miscellaneous import sqrt
from sympy.functions.elementary.trigonometric import (acos, cos, sin)
from sympy.integrals.integrals import Integral
from sympy.solvers.ode.ode import constantsimp, constant_renumber
from sympy.testing.pytest import XFAIL


x = Symbol('x')
y = Symbol('y')
z = Symbol('z')
u2 = Symbol('u2')
_a = Symbol('_a')
C1 = Symbol('C1')
C2 = Symbol('C2')
C3 = Symbol('C3')
f = Function('f')


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])) == C1*y
    assert constant_renumber(constantsimp(C1*y, [C1])) == C1*y
    assert constant_renumber(constantsimp(x*C1, [C1])) == x*C1
    assert constant_renumber(constantsimp(C1*x, [C1])) == x*C1
    assert constant_renumber(constantsimp(2*C1, [C1])) == C1
    assert constant_renumber(constantsimp(C1*2, [C1])) == C1
    assert constant_renumber(constantsimp(y*C1*x, [C1, y])) == C1*x
    assert constant_renumber(constantsimp(x*y*C1, [C1, y])) == x*C1
    assert constant_renumber(constantsimp(y*x*C1, [C1, y])) == x*C1
    assert constant_renumber(constantsimp(C1*x*y, [C1, y])) == C1*x
    assert constant_renumber(constantsimp(x*C1*y, [C1, y])) == x*C1
    assert constant_renumber(constantsimp(C1*y*(y + 1), [C1])) == C1*y*(y+1)
    assert constant_renumber(constantsimp(y*C1*(y + 1), [C1])) == C1*y*(y+1)
    assert constant_renumber(constantsimp(x*(y*C1), [C1])) == x*y*C1
    assert constant_renumber(constantsimp(x*(C1*y), [C1])) == x*y*C1
    assert constant_renumber(constantsimp(C1*(x*y), [C1, y])) == C1*x
    assert constant_renumber(constantsimp((x*y)*C1, [C1, y])) == x*C1
    assert constant_renumber(constantsimp((y*x)*C1, [C1, y])) == x*C1
    assert constant_renumber(constantsimp(y*(y + 1)*C1, [C1, y])) == C1
    assert constant_renumber(constantsimp((C1*x)*y, [C1, y])) == C1*x
    assert constant_renumber(constantsimp(y*(x*C1), [C1, y])) == x*C1
    assert constant_renumber(constantsimp((x*C1)*y, [C1, y])) == x*C1
    assert constant_renumber(constantsimp(C1*x*y*x*y*2, [C1, y])) == C1*x**2
    assert constant_renumber(constantsimp(C1*x*y*z, [C1, y, z])) == C1*x
    assert constant_renumber(constantsimp(C1*x*y**2*sin(z), [C1, y, z])) == C1*x
    assert constant_renumber(constantsimp(C1*C1, [C1])) == C1
    assert constant_renumber(constantsimp(C1*C2, [C1, C2])) == C1
    assert constant_renumber(constantsimp(C2*C2, [C1, C2])) == C1
    assert constant_renumber(constantsimp(C1*C1*C2, [C1, C2])) == C1
    assert constant_renumber(constantsimp(C1*x*2**x, [C1])) == C1*x*2**x

def test_constant_add():
    assert constant_renumber(constantsimp(C1 + C1, [C1])) == C1
    assert constant_renumber(constantsimp(C1 + 2, [C1])) == C1
    assert constant_renumber(constantsimp(2 + C1, [C1])) == C1
    assert constant_renumber(constantsimp(C1 + y, [C1, y])) == C1
    assert constant_renumber(constantsimp(C1 + x, [C1])) == C1 + x
    assert constant_renumber(constantsimp(C1 + C1, [C1])) == C1
    assert constant_renumber(constantsimp(C1 + C2, [C1, C2])) == C1
    assert constant_renumber(constantsimp(C2 + C1, [C1, C2])) == C1
    assert constant_renumber(constantsimp(C1 + C2 + C1, [C1, C2])) == C1


def test_constant_power_as_base():
    assert constant_renumber(constantsimp(C1**C1, [C1])) == C1
    assert constant_renumber(constantsimp(Pow(C1, C1), [C1])) == C1
    assert constant_renumber(constantsimp(C1**C1, [C1])) == C1
    assert constant_renumber(constantsimp(C1**C2, [C1, C2])) == C1
    assert constant_renumber(constantsimp(C2**C1, [C1, C2])) == C1
    assert constant_renumber(constantsimp(C2**C2, [C1, C2])) == C1
    assert constant_renumber(constantsimp(C1**y, [C1, y])) == C1
    assert constant_renumber(constantsimp(C1**x, [C1])) == C1**x
    assert constant_renumber(constantsimp(C1**2, [C1])) == C1
    assert constant_renumber(
        constantsimp(C1**(x*y), [C1])) == C1**(x*y)


def test_constant_power_as_exp():
    assert constant_renumber(constantsimp(x**C1, [C1])) == x**C1
    assert constant_renumber(constantsimp(y**C1, [C1, y])) == C1
    assert constant_renumber(constantsimp(x**y**C1, [C1, y])) == x**C1
    assert constant_renumber(
        constantsimp((x**y)**C1, [C1])) == (x**y)**C1
    assert constant_renumber(
        constantsimp(x**(y**C1), [C1, y])) == x**C1
    assert constant_renumber(constantsimp(x**C1**y, [C1, y])) == x**C1
    assert constant_renumber(
        constantsimp(x**(C1**y), [C1, y])) == x**C1
    assert constant_renumber(
        constantsimp((x**C1)**y, [C1])) == (x**C1)**y
    assert constant_renumber(constantsimp(2**C1, [C1])) == C1
    assert constant_renumber(constantsimp(S(2)**C1, [C1])) == C1
    assert constant_renumber(constantsimp(exp(C1), [C1])) == C1
    assert constant_renumber(
        constantsimp(exp(C1 + x), [C1])) == C1*exp(x)
    assert constant_renumber(constantsimp(Pow(2, C1), [C1])) == C1


def test_constant_function():
    assert constant_renumber(constantsimp(sin(C1), [C1])) == C1
    assert constant_renumber(constantsimp(f(C1), [C1])) == C1
    assert constant_renumber(constantsimp(f(C1, C1), [C1])) == C1
    assert constant_renumber(constantsimp(f(C1, C2), [C1, C2])) == C1
    assert constant_renumber(constantsimp(f(C2, C1), [C1, C2])) == C1
    assert constant_renumber(constantsimp(f(C2, C2), [C1, C2])) == C1
    assert constant_renumber(
        constantsimp(f(C1, x), [C1])) == f(C1, x)
    assert constant_renumber(constantsimp(f(C1, y), [C1, y])) == C1
    assert constant_renumber(constantsimp(f(y, C1), [C1, y])) == C1
    assert constant_renumber(constantsimp(f(C1, y, C2), [C1, C2, y])) == C1


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])) == f(C1, C1, x)


def test_constant_multiple():
    assert constant_renumber(constantsimp(C1*2 + 2, [C1])) == C1
    assert constant_renumber(constantsimp(x*2/C1, [C1])) == C1*x
    assert constant_renumber(constantsimp(C1**2*2 + 2, [C1])) == C1
    assert constant_renumber(
        constantsimp(sin(2*C1) + x + sqrt(2), [C1])) == C1 + x
    assert constant_renumber(constantsimp(2*C1 + C2, [C1, C2])) == C1

def test_constant_repeated():
    assert C1 + C1*x == constant_renumber( C1 + C1*x)

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])) == \
        constant_renumber(C1*exp(x) + C2*exp(2*x))
    assert constant_renumber(
        constantsimp(Eq(f(x), I*C1*sinh(x/3) + C2*cosh(x/3)), [C1, C2])
        ) == constant_renumber(Eq(f(x), C1*sinh(x/3) + C2*cosh(x/3)))
    assert constant_renumber(constantsimp(Eq(f(x), acos((-C1)/cos(x))), [C1])) == \
        Eq(f(x), acos(C1/cos(x)))
    assert constant_renumber(
        constantsimp(Eq(log(f(x)/C1) + 2*exp(x/f(x)), 0), [C1])
        ) == 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])) == \
        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])) == \
        Eq(-exp(-f(x)/x)*sin(f(x)/x)/2 + log(C1*x) - cos(f(x)/x)*
           exp(-f(x)/x)/2, 0)
    assert constant_renumber(constantsimp(Eq(-Integral(-1/(sqrt(1 - u2**2)*u2),
        (u2, _a, x/f(x))) + log(f(x)/C1), 0), [C1])) == \
        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)))]


@XFAIL
def test_nonlocal_simplification():
    assert constantsimp(C1 + C2+x*C2, [C1, C2]) == C1 + C2*x


def test_constant_Eq():
    # C1 on the rhs is well-tested, but the lhs is only tested here
    assert constantsimp(Eq(C1, 3 + f(x)*x), [C1]) == Eq(x*f(x), C1)
    assert constantsimp(Eq(C1, 3 * f(x)*x), [C1]) == Eq(f(x)*x, C1)