def __new__(cls, lhs, rhs=0, **options):
from sympy.core.add import Add
from sympy.core.logic import fuzzy_bool
from sympy.core.expr import _n2
from sympy.simplify.simplify import clear_coefficients
lhs = _sympify(lhs)
rhs = _sympify(rhs)
evaluate = options.pop('evaluate', global_evaluate[0])
if evaluate:
# If one expression has an _eval_Eq, return its results.
if hasattr(lhs, '_eval_Eq'):
r = lhs._eval_Eq(rhs)
if r is not None:
return r
if hasattr(rhs, '_eval_Eq'):
r = rhs._eval_Eq(lhs)
if r is not None:
return r
# If expressions have the same structure, they must be equal.
if lhs == rhs:
return S.true
elif all(isinstance(i, BooleanAtom) for i in (rhs, lhs)):
return S.false
# check finiteness
fin = L, R = [i.is_finite for i in (lhs, rhs)]
if None not in fin:
if L != R:
return S.false
if L is False:
if lhs == -rhs: # Eq(oo, -oo)
return S.false
return S.true
elif None in fin and False in fin:
return Relational.__new__(cls, lhs, rhs, **options)
if all(isinstance(i, Expr) for i in (lhs, rhs)):
# see if the difference evaluates
dif = lhs - rhs
z = dif.is_zero
if z is not None:
if z is False and dif.is_commutative: # issue 10728
return S.false
if z:
return S.true
# evaluate numerically if possible
n2 = _n2(lhs, rhs)
if n2 is not None:
return _sympify(n2 == 0)
# see if the ratio evaluates
n, d = dif.as_numer_denom()
rv = None
if n.is_zero:
rv = d.is_nonzero
elif n.is_finite:
if d.is_infinite:
rv = S.true
elif n.is_zero is False:
rv = d.is_infinite
if rv is None:
# if the condition that makes the denominator infinite does not
# make the original expression True then False can be returned
l, r = clear_coefficients(d, S.Infinity)
args = [_.subs(l, r) for _ in (lhs, rhs)]
if args != [lhs, rhs]:
rv = fuzzy_bool(Eq(*args))
if rv is True:
rv = None
elif any(a.is_infinite for a in Add.make_args(n)): # (inf or nan)/x != 0
rv = S.false
if rv is not None:
return _sympify(rv)
return Relational.__new__(cls, lhs, rhs, **options)
def __new__(cls, lhs, rhs=0, **options):
from sympy.core.add import Add
from sympy.core.logic import fuzzy_bool
from sympy.core.expr import _n2
from sympy.simplify.simplify import clear_coefficients
lhs = _sympify(lhs)
rhs = _sympify(rhs)
evaluate = options.pop('evaluate', global_evaluate[0])
if evaluate:
# If one expression has an _eval_Eq, return its results.
if hasattr(lhs, '_eval_Eq'):
r = lhs._eval_Eq(rhs)
if r is not None:
return r
if hasattr(rhs, '_eval_Eq'):
r = rhs._eval_Eq(lhs)
if r is not None:
return r
# If expressions have the same structure, they must be equal.
if lhs == rhs:
return S.true # e.g. True == True
elif all(isinstance(i, BooleanAtom) for i in (rhs, lhs)):
return S.false # True != False
elif not (lhs.is_Symbol or rhs.is_Symbol) and (isinstance(
lhs, Boolean) != isinstance(rhs, Boolean)):
return S.false # only Booleans can equal Booleans
# check finiteness
fin = L, R = [i.is_finite for i in (lhs, rhs)]
if None not in fin:
if L != R:
return S.false
if L is False:
if lhs == -rhs: # Eq(oo, -oo)
return S.false
return S.true
elif None in fin and False in fin:
return Relational.__new__(cls, lhs, rhs, **options)
if all(isinstance(i, Expr) for i in (lhs, rhs)):
# see if the difference evaluates
dif = lhs - rhs
z = dif.is_zero
if z is not None:
if z is False and dif.is_commutative: # issue 10728
return S.false
if z:
return S.true
# evaluate numerically if possible
n2 = _n2(lhs, rhs)
if n2 is not None:
return _sympify(n2 == 0)
# see if the ratio evaluates
n, d = dif.as_numer_denom()
rv = None
if n.is_zero:
rv = d.is_nonzero
elif n.is_finite:
if d.is_infinite:
rv = S.true
elif n.is_zero is False:
rv = d.is_infinite
if rv is None:
# if the condition that makes the denominator infinite does not
# make the original expression True then False can be returned
l, r = clear_coefficients(d, S.Infinity)
args = [_.subs(l, r) for _ in (lhs, rhs)]
if args != [lhs, rhs]:
rv = fuzzy_bool(Eq(*args))
if rv is True:
rv = None
elif any(a.is_infinite
for a in Add.make_args(n)): # (inf or nan)/x != 0
rv = S.false
if rv is not None:
return _sympify(rv)
return Relational.__new__(cls, lhs, rhs, **options)
def __new__(cls, lhs, rhs=None, **options):
from sympy.core.add import Add
from sympy.core.containers import Tuple
from sympy.core.logic import fuzzy_bool, fuzzy_xor, fuzzy_and, fuzzy_not
from sympy.core.expr import _n2
from sympy.functions.elementary.complexes import arg
from sympy.simplify.simplify import clear_coefficients
from sympy.utilities.iterables import sift
if rhs is None:
SymPyDeprecationWarning(feature="Eq(expr) with rhs default to 0",
useinstead="Eq(expr, 0)",
issue=16587,
deprecated_since_version="1.5").warn()
rhs = 0
lhs = _sympify(lhs)
rhs = _sympify(rhs)
evaluate = options.pop('evaluate', global_parameters.evaluate)
if evaluate:
# If one expression has an _eval_Eq, return its results.
if hasattr(lhs, '_eval_Eq'):
r = lhs._eval_Eq(rhs)
if r is not None:
return r
if hasattr(rhs, '_eval_Eq'):
r = rhs._eval_Eq(lhs)
if r is not None:
return r
# If expressions have the same structure, they must be equal.
if lhs == rhs:
return S.true # e.g. True == True
elif all(isinstance(i, BooleanAtom) for i in (rhs, lhs)):
return S.false # True != False
elif not (lhs.is_Symbol or rhs.is_Symbol) and (isinstance(
lhs, Boolean) != isinstance(rhs, Boolean)):
return S.false # only Booleans can equal Booleans
if lhs.is_infinite or rhs.is_infinite:
if fuzzy_xor([lhs.is_infinite, rhs.is_infinite]):
return S.false
if fuzzy_xor([lhs.is_extended_real, rhs.is_extended_real]):
return S.false
if fuzzy_and([lhs.is_extended_real, rhs.is_extended_real]):
r = fuzzy_xor([
lhs.is_extended_positive,
fuzzy_not(rhs.is_extended_positive)
])
return S(r)
# Try to split real/imaginary parts and equate them
I = S.ImaginaryUnit
def split_real_imag(expr):
real_imag = lambda t: ('real'
if t.is_extended_real else 'imag' if
(I * t).is_extended_real else None)
return sift(Add.make_args(expr), real_imag)
lhs_ri = split_real_imag(lhs)
if not lhs_ri[None]:
rhs_ri = split_real_imag(rhs)
if not rhs_ri[None]:
eq_real = Eq(Add(*lhs_ri['real']),
Add(*rhs_ri['real']))
eq_imag = Eq(I * Add(*lhs_ri['imag']),
I * Add(*rhs_ri['imag']))
res = fuzzy_and(map(fuzzy_bool, [eq_real, eq_imag]))
if res is not None:
return S(res)
# Compare e.g. zoo with 1+I*oo by comparing args
arglhs = arg(lhs)
argrhs = arg(rhs)
# Guard against Eq(nan, nan) -> False
if not (arglhs == S.NaN and argrhs == S.NaN):
res = fuzzy_bool(Eq(arglhs, argrhs))
if res is not None:
return S(res)
return Relational.__new__(cls, lhs, rhs, **options)
if all(isinstance(i, Expr) for i in (lhs, rhs)):
# see if the difference evaluates
dif = lhs - rhs
z = dif.is_zero
if z is not None:
if z is False and dif.is_commutative: # issue 10728
return S.false
if z:
return S.true
# evaluate numerically if possible
n2 = _n2(lhs, rhs)
if n2 is not None:
return _sympify(n2 == 0)
# see if the ratio evaluates
n, d = dif.as_numer_denom()
rv = None
if n.is_zero:
rv = d.is_nonzero
elif n.is_finite:
if d.is_infinite:
rv = S.true
elif n.is_zero is False:
rv = d.is_infinite
if rv is None:
# if the condition that makes the denominator
# infinite does not make the original expression
# True then False can be returned
l, r = clear_coefficients(d, S.Infinity)
args = [_.subs(l, r) for _ in (lhs, rhs)]
if args != [lhs, rhs]:
rv = fuzzy_bool(Eq(*args))
if rv is True:
rv = None
elif any(a.is_infinite for a in Add.make_args(n)):
# (inf or nan)/x != 0
rv = S.false
if rv is not None:
return _sympify(rv)
return Relational.__new__(cls, lhs, rhs, **options)
