def _eval_is_negative(self):
from sympy.core.exprtools import _monotonic_sign
if self.is_number:
return super(Add, self)._eval_is_negative()
c, a = self.as_coeff_Add()
if not c.is_zero:
v = _monotonic_sign(a)
if v is not None:
s = v + c
if s.is_negative and a.is_nonpositive:
return True
if len(self.free_symbols) == 1:
v = _monotonic_sign(self)
if v is not None and v.is_negative:
return True
neg = nonpos = nonneg = unknown_sign = False
saw_INF = set()
args = [a for a in self.args if not a.is_zero]
if not args:
return False
for a in args:
isneg = a.is_negative
infinite = a.is_infinite
if infinite:
saw_INF.add(fuzzy_or((isneg, a.is_nonpositive)))
if True in saw_INF and False in saw_INF:
return
if isneg:
neg = True
continue
elif a.is_nonpositive:
nonpos = True
continue
elif a.is_nonnegative:
nonneg = True
continue
if infinite is None:
return
unknown_sign = True
if saw_INF:
if len(saw_INF) > 1:
return
return saw_INF.pop()
elif unknown_sign:
return
elif not nonneg and not nonpos and neg:
return True
elif not nonneg and neg:
return True
elif not neg and not nonpos:
return False
def _eval_is_extended_negative(self):
from sympy.core.exprtools import _monotonic_sign
if self.is_number:
return super(Add, self)._eval_is_extended_negative()
c, a = self.as_coeff_Add()
if not c.is_zero:
v = _monotonic_sign(a)
if v is not None:
s = v + c
if s != self and s.is_extended_negative and a.is_extended_nonpositive:
return True
if len(self.free_symbols) == 1:
v = _monotonic_sign(self)
if v is not None and v != self and v.is_extended_negative:
return True
neg = nonpos = nonneg = unknown_sign = False
saw_INF = set()
args = [a for a in self.args if not a.is_zero]
if not args:
return False
for a in args:
isneg = a.is_extended_negative
infinite = a.is_infinite
if infinite:
saw_INF.add(fuzzy_or((isneg, a.is_extended_nonpositive)))
if True in saw_INF and False in saw_INF:
return
if isneg:
neg = True
continue
elif a.is_extended_nonpositive:
nonpos = True
continue
elif a.is_extended_nonnegative:
nonneg = True
continue
if infinite is None:
return
unknown_sign = True
if saw_INF:
if len(saw_INF) > 1:
return
return saw_INF.pop()
elif unknown_sign:
return
elif not nonneg and not nonpos and neg:
return True
elif not nonneg and neg:
return True
elif not neg and not nonpos:
return False
def _eval_is_nonpositive(self):
from sympy.core.exprtools import _monotonic_sign
if not self.is_number:
c, a = self.as_coeff_Add()
if not c.is_zero and a.is_nonpositive:
v = _monotonic_sign(a)
if v is not None:
s = v + c
if s != self and s.is_nonpositive:
return True
if len(self.free_symbols) == 1:
v = _monotonic_sign(self)
if v is not None and v != self and v.is_nonpositive:
return True
def _eval_is_nonpositive(self):
from sympy.core.exprtools import _monotonic_sign
if not self.is_number:
c, a = self.as_coeff_Add()
if not c.is_zero and a.is_nonpositive:
v = _monotonic_sign(a)
if v is not None:
s = v + c
if s.is_nonpositive:
return True
if len(self.free_symbols) == 1:
v = _monotonic_sign(self)
if v is not None and v.is_nonpositive:
return True
