def _eval_subs(self, old, new):
if old in self.variables:
newexpr = self.expr.subs(old, new)
i = self.variables.index(old)
newvars = list(self.variables)
newpt = list(self.point)
if new.is_Symbol:
newvars[i] = new
else:
syms = new.free_symbols
if len(syms) == 1 or old in syms:
if old in syms:
var = self.variables[i]
else:
var = syms.pop()
# First, try to substitute self.point in the "new"
# expr to see if this is a fixed point.
# E.g. O(y).subs(y, sin(x))
point = new.subs(var, self.point[i])
if point != self.point[i]:
from sympy.solvers import solve
d = Dummy()
res = solve(old - new.subs(var, d), d, dict=True)
point = d.subs(res[0]).limit(old, self.point[i])
newvars[i] = var
newpt[i] = point
elif old not in syms:
del newvars[i], newpt[i]
if not syms and new == self.point[i]:
newvars.extend(syms)
newpt.extend([S.Zero] * len(syms))
else:
return
return Order(newexpr, *zip(newvars, newpt))
def _eval_subs(self, old, new):
if old in self.variables:
newexpr = self.expr.subs(old, new)
i = self.variables.index(old)
newvars = list(self.variables)
newpt = list(self.point)
if new.is_Symbol:
newvars[i] = new
else:
syms = new.free_symbols
if len(syms) == 1 or old in syms:
if old in syms:
var = self.variables[i]
else:
var = syms.pop()
# First, try to substitute self.point in the "new"
# expr to see if this is a fixed point.
# E.g. O(y).subs(y, sin(x))
point = new.subs(var, self.point[i])
if point != self.point[i]:
from sympy.solvers import solve
d = Dummy()
res = solve(old - new.subs(var, d), d, dict=True)
point = d.subs(res[0]).limit(old, self.point[i])
newvars[i] = var
newpt[i] = point
elif old not in syms:
del newvars[i], newpt[i]
if not syms and new == self.point[i]:
newvars.extend(syms)
newpt.extend([S.Zero]*len(syms))
else:
return
return Order(newexpr, *zip(newvars, newpt))
def _eval_subs(self, old, new):
if old in self.variables:
newexpr = self.expr.subs(old, new)
i = self.variables.index(old)
newvars = list(self.variables)
newpt = list(self.point)
if new.is_symbol:
newvars[i] = new
else:
syms = new.free_symbols
if len(syms) == 1 or old in syms:
if old in syms:
var = self.variables[i]
else:
var = syms.pop()
# First, try to substitute self.point in the "new"
# expr to see if this is a fixed point.
# E.g. O(y).subs(y, sin(x))
point = new.subs(var, self.point[i])
if point != self.point[i]:
from sympy.solvers.solveset import solveset
d = Dummy()
sol = solveset(old - new.subs(var, d), d)
if isinstance(sol, Complement):
e1 = sol.args[0]
e2 = sol.args[1]
sol = set(e1) - set(e2)
res = [dict(zip((d, ), sol))]
point = d.subs(res[0]).limit(old, self.point[i])
newvars[i] = var
newpt[i] = point
elif old not in syms:
del newvars[i], newpt[i]
if not syms and new == self.point[i]:
newvars.extend(syms)
newpt.extend([S.Zero] * len(syms))
else:
return
return Order(newexpr, *zip(newvars, newpt))
def _eval_subs(self, old, new):
if old in self.variables:
newexpr = self.expr.subs(old, new)
i = self.variables.index(old)
newvars = list(self.variables)
newpt = list(self.point)
if new.is_symbol:
newvars[i] = new
else:
syms = new.free_symbols
if len(syms) == 1 or old in syms:
if old in syms:
var = self.variables[i]
else:
var = syms.pop()
# First, try to substitute self.point in the "new"
# expr to see if this is a fixed point.
# E.g. O(y).subs(y, sin(x))
point = new.subs(var, self.point[i])
if point != self.point[i]:
from sympy.solvers.solveset import solveset
d = Dummy()
sol = solveset(old - new.subs(var, d), d)
if isinstance(sol, Complement):
e1 = sol.args[0]
e2 = sol.args[1]
sol = set(e1) - set(e2)
res = [dict(zip((d, ), sol))]
point = d.subs(res[0]).limit(old, self.point[i])
newvars[i] = var
newpt[i] = point
elif old not in syms:
del newvars[i], newpt[i]
if not syms and new == self.point[i]:
newvars.extend(syms)
newpt.extend([S.Zero]*len(syms))
else:
return
return Order(newexpr, *zip(newvars, newpt))