def test_is_constant():
from sympy.solvers.solvers import checksol
Sum(x, (x, 1, 10)).is_constant() == True
Sum(x, (x, 1, n)).is_constant() == False
Sum(x, (x, 1, n)).is_constant(y) == True
Sum(x, (x, 1, n)).is_constant(n) == False
Sum(x, (x, 1, n)).is_constant(x) == True
eq = a * cos(x)**2 + a * sin(x)**2 - a
eq.is_constant() == True
assert eq.subs({x: pi, a: 2}) == eq.subs({x: pi, a: 3}) == 0
assert x.is_constant() is False
assert x.is_constant(y) is True
assert checksol(x, x, Sum(x, (x, 1, n))) == False
assert checksol(x, x, Sum(x, (x, 1, n))) == False
f = Function('f')
assert checksol(x, x, f(x)) == False
p = symbols('p', positive=True)
assert Pow(x, S(0), evaluate=False).is_constant() == True # == 1
assert Pow(S(0), x, evaluate=False).is_constant() == False # == 0 or 1
assert Pow(S(0), p, evaluate=False).is_constant() == True # == 1
assert (2**x).is_constant() == False
assert Pow(S(2), S(3), evaluate=False).is_constant() == True
z1, z2 = symbols('z1 z2', zero=True)
assert (z1 + 2 * z2).is_constant
def test_is_constant():
from sympy.solvers.solvers import checksol
Sum(x, (x, 1, 10)).is_constant() == True
Sum(x, (x, 1, n)).is_constant() == False
Sum(x, (x, 1, n)).is_constant(y) == True
Sum(x, (x, 1, n)).is_constant(n) == False
Sum(x, (x, 1, n)).is_constant(x) == True
eq = a * cos(x) ** 2 + a * sin(x) ** 2 - a
eq.is_constant() == True
assert eq.subs({x: pi, a: 2}) == eq.subs({x: pi, a: 3}) == 0
assert x.is_constant() is False
assert x.is_constant(y) is True
assert checksol(x, x, Sum(x, (x, 1, n))) == False
assert checksol(x, x, Sum(x, (x, 1, n))) == False
f = Function("f")
assert checksol(x, x, f(x)) == False
p = symbols("p", positive=True)
assert Pow(x, S(0), evaluate=False).is_constant() == True # == 1
assert Pow(S(0), x, evaluate=False).is_constant() == False # == 0 or 1
assert Pow(S(0), p, evaluate=False).is_constant() == True # == 1
assert (2 ** x).is_constant() == False
assert Pow(S(2), S(3), evaluate=False).is_constant() == True
z1, z2 = symbols("z1 z2", zero=True)
assert (z1 + 2 * z2).is_constant() is True
assert meter.is_constant() is True
assert (3 * meter).is_constant() is True
assert (x * meter).is_constant() is False
def __eval_cond(cls, cond):
"""Return the truth value of the condition."""
from sympy.solvers.solvers import checksol
if cond is True:
return True
if isinstance(cond, Equality):
if checksol(cond, {}, minimal=True):
# the equality is trivially solved
return True
return None
def __eval_cond(cls, cond):
"""Return the truth value of the condition."""
from sympy.solvers.solvers import checksol
if cond is True:
return True
if isinstance(cond, Equality):
if checksol(cond, {}, minimal=True):
# the equality is trivially solved
return True
return None
def __eval_cond(cls, cond):
"""Return the truth value of the condition."""
from sympy.solvers.solvers import checksol
if cond == True:
return True
if isinstance(cond, Equality):
if checksol(cond, {}, minimal=True):
# the equality is trivially solved
return True
diff = cond.lhs - cond.rhs
if diff.is_commutative:
return diff.is_zero
return None
def __eval_cond(cls, cond):
"""Return the truth value of the condition."""
from sympy.solvers.solvers import checksol
if cond == True:
return True
if isinstance(cond, Equality):
if checksol(cond, {}, minimal=True):
# the equality is trivially solved
return True
diff = cond.lhs - cond.rhs
if diff.is_commutative:
return diff.is_zero
return None
def _solve_radical(f, symbol, solveset_solver):
""" Helper function to solve equations with radicals """
eq, cov = unrad(f)
if not cov:
result = solveset_solver(eq, symbol) - Union(*[solveset_solver(g, symbol) for g in denoms(f, [symbol])])
else:
y, yeq = cov
if not solveset_solver(y - I, y):
yreal = Dummy("yreal", real=True)
yeq = yeq.xreplace({y: yreal})
eq = eq.xreplace({y: yreal})
y = yreal
g_y_s = solveset_solver(yeq, symbol)
f_y_sols = solveset_solver(eq, y)
result = Union(*[imageset(Lambda(y, g_y), f_y_sols) for g_y in g_y_s])
return FiniteSet(*[s for s in result if checksol(f, symbol, s) is True])
def _solve_radical(f, symbol, solveset_solver):
""" Helper function to solve equations with radicals """
eq, cov = unrad(f)
if not cov:
result = solveset_solver(eq, symbol) - \
Union(*[solveset_solver(g, symbol) for g in denoms(f, [symbol])])
else:
y, yeq = cov
if not solveset_solver(y - I, y):
yreal = Dummy('yreal', real=True)
yeq = yeq.xreplace({y: yreal})
eq = eq.xreplace({y: yreal})
y = yreal
g_y_s = solveset_solver(yeq, symbol)
f_y_sols = solveset_solver(eq, y)
result = Union(*[imageset(Lambda(y, g_y), f_y_sols) for g_y in g_y_s])
return FiniteSet(*[s for s in result if checksol(f, symbol, s) is True])
def _solve_radical(f, symbol, solveset_solver):
""" Helper function to solve equations with radicals """
from sympy.solvers.solvers import unrad
try:
eq, cov, dens = unrad(f)
if cov == []:
result = solveset_solver(eq, symbol) - \
Union(*[solveset_solver(g, symbol) for g in dens])
else:
if len(cov) > 1:
raise NotImplementedError("Multivariate solver is "
"not implemented.")
else:
y = cov[0][0]
g_y_s = solveset_solver(cov[0][1], symbol)
f_y_sols = solveset_solver(eq, y)
result = Union(*[imageset(Lambda(y, g_y), f_y_sols)
for g_y in g_y_s])
return FiniteSet(*[s for s in result if checksol(f, symbol, s) is True])
except ValueError:
raise NotImplementedError
def _solve_radical(f, symbol, solveset_solver):
""" Helper function to solve equations with radicals """
from sympy.solvers.solvers import unrad
try:
eq, cov, dens = unrad(f)
if cov == []:
result = solveset_solver(eq, symbol) - \
Union(*[solveset_solver(g, symbol) for g in dens])
else:
if len(cov) > 1:
raise NotImplementedError("Multivariate solver is "
"not implemented.")
else:
y = cov[0][0]
g_y_s = solveset_solver(cov[0][1], symbol)
f_y_sols = solveset_solver(eq, y)
result = Union(
*[imageset(Lambda(y, g_y), f_y_sols) for g_y in g_y_s])
return FiniteSet(
*[s for s in result if checksol(f, symbol, s) is True])
except ValueError:
raise NotImplementedError
def test_issue_2574():
eq = -x + exp(exp(LambertW(log(x)))*LambertW(log(x)))
assert checksol(eq, x, 2) is True
assert checksol(eq, x, 2, numerical=False) is None
def test_issue_2574():
eq = -x + exp(exp(LambertW(log(x))) * LambertW(log(x)))
assert checksol(eq, x, 2) is True
assert checksol(eq, x, 2, numerical=False) is None
