def _eval_simplify(self, **kwargs):
from .add import Add
from .expr import Expr
r = self
r = r.func(*[i.simplify(**kwargs) for i in r.args])
if r.is_Relational:
if not isinstance(r.lhs, Expr) or not isinstance(r.rhs, Expr):
return r
dif = r.lhs - r.rhs
# replace dif with a valid Number that will
# allow a definitive comparison with 0
v = None
if dif.is_comparable:
v = dif.n(2)
elif dif.equals(0): # XXX this is expensive
v = S.Zero
if v is not None:
r = r.func._eval_relation(v, S.Zero)
r = r.canonical
# If there is only one symbol in the expression,
# try to write it on a simplified form
free = list(
filter(lambda x: x.is_real is not False, r.free_symbols))
if len(free) == 1:
try:
from sympy.solvers.solveset import linear_coeffs
x = free.pop()
dif = r.lhs - r.rhs
m, b = linear_coeffs(dif, x)
if m.is_zero is False:
if m.is_negative:
# Dividing with a negative number, so change order of arguments
# canonical will put the symbol back on the lhs later
r = r.func(-b / m, x)
else:
r = r.func(x, -b / m)
else:
r = r.func(b, S.Zero)
except ValueError:
# maybe not a linear function, try polynomial
from sympy.polys.polyerrors import PolynomialError
from sympy.polys.polytools import gcd, Poly, poly
try:
p = poly(dif, x)
c = p.all_coeffs()
constant = c[-1]
c[-1] = 0
scale = gcd(c)
c = [ctmp / scale for ctmp in c]
r = r.func(
Poly.from_list(c, x).as_expr(), -constant / scale)
except PolynomialError:
pass
elif len(free) >= 2:
try:
from sympy.solvers.solveset import linear_coeffs
from sympy.polys.polytools import gcd
free = list(ordered(free))
dif = r.lhs - r.rhs
m = linear_coeffs(dif, *free)
constant = m[-1]
del m[-1]
scale = gcd(m)
m = [mtmp / scale for mtmp in m]
nzm = list(filter(lambda f: f[0] != 0, list(zip(m, free))))
if scale.is_zero is False:
if constant != 0:
# lhs: expression, rhs: constant
newexpr = Add(*[i * j for i, j in nzm])
r = r.func(newexpr, -constant / scale)
else:
# keep first term on lhs
lhsterm = nzm[0][0] * nzm[0][1]
del nzm[0]
newexpr = Add(*[i * j for i, j in nzm])
r = r.func(lhsterm, -newexpr)
else:
r = r.func(constant, S.Zero)
except ValueError:
pass
# Did we get a simplified result?
r = r.canonical
measure = kwargs['measure']
if measure(r) < kwargs['ratio'] * measure(self):
return r
else:
return self
