def __new__(cls):
from sympy.core.sets import FiniteSet
x = C.Dummy('x')
#construct "by hand" to avoid infinite loop
obj = Expr.__new__(cls, Tuple(x), x)
obj.nargs = FiniteSet(1)
return obj
def __new__(cls, *args, **assumptions):
if not args:
raise ValueError("The Max/Min functions must have arguments.")
args = (sympify(arg) for arg in args)
# first standard filter, for cls.zero and cls.identity
# also reshape Max(a, Max(b, c)) to Max(a, b, c)
try:
_args = frozenset(cls._new_args_filter(args))
except ShortCircuit:
return cls.zero
# second filter
# variant I: remove ones which can be removed
# args = cls._collapse_arguments(set(_args), **assumptions)
# variant II: find local zeros
args = cls._find_localzeros(set(_args), **assumptions)
_args = frozenset(args)
if not _args:
return cls.identity
elif len(_args) == 1:
return set(_args).pop()
else:
# base creation
obj = Expr.__new__(cls, _args, **assumptions)
obj._argset = _args
return obj
def __new__(cls, function, *symbols, **assumptions):
from sympy.integrals.integrals import _process_limits
# Any embedded piecewise functions need to be brought out to the
# top level so that integration can go into piecewise mode at the
# earliest possible moment.
function = piecewise_fold(sympify(function))
if function is S.NaN:
return S.NaN
if not symbols:
raise ValueError("Summation variables must be given")
limits, sign = _process_limits(*symbols)
# Only limits with lower and upper bounds are supported; the indefinite Sum
# is not supported
if any(len(l) != 3 or None in l for l in limits):
raise ValueError('Sum requires values for lower and upper bounds.')
obj = Expr.__new__(cls, **assumptions)
arglist = [sign*function]
arglist.extend(limits)
obj._args = tuple(arglist)
obj.is_commutative = function.is_commutative # limits already checked
return obj
def __new__(cls, function, *symbols, **assumptions):
# Any embedded piecewise functions need to be brought out to the
# top level so that integration can go into piecewise mode at the
# earliest possible moment.
#
# This constructor only differs from ExprWithLimits
# in the application of the orientation variable. Perhaps merge?
function = piecewise_fold(sympify(function))
if function is S.NaN:
return S.NaN
if symbols:
limits, orientation = _process_limits(*symbols)
else:
# symbol not provided -- we can still try to compute a general form
free = function.free_symbols
if len(free) != 1:
raise ValueError(
"specify dummy variables for %s" % function)
limits, orientation = [Tuple(s) for s in free], 1
# denest any nested calls
while cls == type(function):
limits = list(function.limits) + limits
function = function.function
obj = Expr.__new__(cls, **assumptions)
arglist = [orientation*function]
arglist.extend(limits)
obj._args = tuple(arglist)
obj.is_commutative = function.is_commutative # limits already checked
return obj
def __new__(cls, *args, **assumptions):
evaluate = assumptions.pop('evaluate', True)
args = (sympify(arg) for arg in args)
# first standard filter, for cls.zero and cls.identity
# also reshape Max(a, Max(b, c)) to Max(a, b, c)
if evaluate:
try:
args = frozenset(cls._new_args_filter(args))
except ShortCircuit:
return cls.zero
else:
args = frozenset(args)
if evaluate:
# remove redundant args that are easily identified
args = cls._collapse_arguments(args, **assumptions)
# find local zeros
args = cls._find_localzeros(args, **assumptions)
if not args:
return cls.identity
if len(args) == 1:
return list(args).pop()
# base creation
_args = frozenset(args)
obj = Expr.__new__(cls, _args, **assumptions)
obj._argset = _args
return obj
def __new__(cls, f, limits, exprs):
if not (type(exprs) == tuple and len(exprs) == 3): # exprs is not of form (a0, an, bn)
# Converts the expression to fourier form
c, e = exprs.as_coeff_add()
rexpr = c + Add(*[TR10(i) for i in e])
a0, exp_ls = rexpr.expand(trig=False, power_base=False, power_exp=False, log=False).as_coeff_add()
x = limits[0]
L = abs(limits[2] - limits[1]) / 2
a = Wild('a', properties=[lambda k: k.is_Integer, lambda k: k is not S.Zero, ])
b = Wild('b', properties=[lambda k: x not in k.free_symbols, ])
an = dict()
bn = dict()
# separates the coefficients of sin and cos terms in dictionaries an, and bn
for p in exp_ls:
t = p.match(b * cos(a * (pi / L) * x))
q = p.match(b * sin(a * (pi / L) * x))
if t:
an[t[a]] = t[b] + an.get(t[a], S.Zero)
elif q:
bn[q[a]] = q[b] + bn.get(q[a], S.Zero)
else:
a0 += p
exprs = (a0, an, bn)
args = map(sympify, (f, limits, exprs))
return Expr.__new__(cls, *args)
def __new__(cls, expr1, expr2):
expr1 = sympify(expr1)
expr2 = sympify(expr2)
expr1, expr2 = sorted([expr1, expr2], key=default_sort_key)
obj = Expr.__new__(cls, expr1, expr2)
obj._expr1 = expr1
obj._expr2 = expr2
return obj
def __new__(cls, expr1, expr2):
if not (isinstance(expr1, Vector) and isinstance(expr2, Vector)):
raise ValueError('Arguments must be the vectors.')
expr1 = sympify(expr1)
expr2 = sympify(expr2)
obj = Expr.__new__(cls, expr1, expr2)
obj._expr1 = expr1
obj._expr2 = expr2
return obj
def __new__(cls, expr1, expr2):
expr1 = sympify(expr1)
expr2 = sympify(expr2)
if default_sort_key(expr1) > default_sort_key(expr2):
return -Cross(expr2, expr1)
obj = Expr.__new__(cls, expr1, expr2)
obj._expr1 = expr1
obj._expr2 = expr2
return obj
def _from_args(cls, args, is_commutative=None):
"""Create new instance with already-processed args"""
if len(args) == 0:
return cls.identity
elif len(args) == 1:
return args[0]
obj = Expr.__new__(cls, *args)
if is_commutative is None:
is_commutative = fuzzy_and(a.is_commutative for a in args)
obj.is_commutative = is_commutative
return obj
def __new__(cls, function, *symbols, **assumptions):
# Any embedded piecewise functions need to be brought out to the
# top level so that integration can go into piecewise mode at the
# earliest possible moment.
#
# This constructor only differs from ExprWithLimits
# in the application of the orientation variable. Perhaps merge?
function = piecewise_fold(sympify(function))
if function is S.NaN:
return S.NaN
# delete dx, dy, dx, etc.
free = function.free_symbols
for f in free:
if len(f.name) > 1 and f.name[0] == "d":
function = function.subs(f, 1)
if symbols:
limits, orientation = _process_limits(*symbols)
else:
# symbol not provided -- we can still try to compute a general form
new_free = set()
limits = []
# if f is dx, then the variable is x
for f in free:
if len(f.name) > 1 and f.name[0] == "d":
limits.append((Symbol(f.name[1:]),))
else:
new_free.add(f)
free = new_free
del new_free
if len(limits) == 0:
if len(free) != 1:
raise ValueError(
"specify dummy variables for %s" % function)
limits = [Tuple(s) for s in free]
orientation = 1
# denest any nested calls
while cls == type(function):
limits = list(function.limits) + limits
function = function.function
obj = Expr.__new__(cls, **assumptions)
arglist = [orientation*function]
arglist.extend(limits)
obj._args = tuple(arglist)
obj.is_commutative = function.is_commutative # limits already checked
return obj
def __new__(cls, *args, **options):
args = (sympify(arg) for arg in args)
try:
_args = frozenset(cls._new_args_filter(args))
except ShortCircuit:
return cls.zero
if not _args:
return cls.identity
elif len(_args) == 1:
return set(_args).pop()
else:
obj = Expr.__new__(cls, _args)
obj._argset = _args
return obj
def __new__(cls, function, *symbols, **assumptions):
pre = _common_new(cls, function, *symbols, **assumptions)
if type(pre) is tuple:
function, limits, orientation = pre
else:
return pre
obj = Expr.__new__(cls, **assumptions)
arglist = [orientation*function] # orientation not used in ExprWithLimits
arglist.extend(limits)
obj._args = tuple(arglist)
obj.is_commutative = function.is_commutative # limits already checked
return obj
def __new__(cls, name, symbol=None):
if isinstance(name, string_types):
name = Symbol(name)
else:
name = sympify(name)
if not isinstance(name, Expr):
raise TypeError("Dimension name needs to be a valid math expression")
if isinstance(symbol, string_types):
symbol = Symbol(symbol)
elif symbol is not None:
assert isinstance(symbol, Symbol)
if symbol is not None:
obj = Expr.__new__(cls, name, symbol)
else:
obj = Expr.__new__(cls, name)
obj._name = name
obj._symbol = symbol
return obj
def __new__(cls, a=0, b=0, c=0, d=0, real_field = True):
a = sympify(a)
b = sympify(b)
c = sympify(c)
d = sympify(d)
if any(i.is_commutative is False for i in [a, b, c, d]):
raise ValueError("arguments have to be commutative")
else:
obj = Expr.__new__(cls, a, b, c, d)
obj._a = a
obj._b = b
obj._c = c
obj._d = d
obj._real_field = real_field
return obj
def __new__(cls, function, *symbols, **assumptions):
# Any embedded piecewise functions need to be brought out to the
# top level so that integration can go into piecewise mode at the
# earliest possible moment.
#
# This constructor only differs from ExprWithLimits
# in the application of the orientation variable. Perhaps merge?
function = sympify(function)
if hasattr(function, 'func') and function.func is Equality:
lhs = function.lhs
rhs = function.rhs
return Equality(cls(lhs, *symbols, **assumptions), \
cls(rhs, *symbols, **assumptions))
function = piecewise_fold(function)
if function is S.NaN:
return S.NaN
if symbols:
limits, orientation = _process_limits(*symbols)
else:
# symbol not provided -- we can still try to compute a general form
free = function.free_symbols
if len(free) != 1:
raise ValueError(
" specify dummy variables for %s. If the integrand contains"
" more than one free symbol, an integration variable should"
" be supplied explicitly e.g., integrate(f(x, y), x)"
% function)
limits, orientation = [Tuple(s) for s in free], 1
# denest any nested calls
while cls == type(function):
limits = list(function.limits) + limits
function = function.function
obj = Expr.__new__(cls, **assumptions)
arglist = [orientation*function]
arglist.extend(limits)
obj._args = tuple(arglist)
obj.is_commutative = function.is_commutative # limits already checked
return obj
def __new__(cls, function, *symbols, **assumptions):
pre = _common_new(cls, function, *symbols, **assumptions)
if type(pre) is tuple:
function, limits, _ = pre
else:
return pre
# limits must have upper and lower bounds; the indefinite form
# is not supported. This restriction does not apply to AddWithLimits
if any(len(l) != 3 or None in l for l in limits):
raise ValueError('ExprWithLimits requires values for lower and upper bounds.')
obj = Expr.__new__(cls, **assumptions)
arglist = [function]
arglist.extend(limits)
obj._args = tuple(arglist)
obj.is_commutative = function.is_commutative # limits already checked
return obj
def __new__(cls, function, *symbols, **assumptions):
# Any embedded piecewise functions need to be brought out to the
# top level so that integration can go into piecewise mode at the
# earliest possible moment.
function = sympify(function)
if hasattr(function, 'func') and function.func is C.Equality:
lhs = function.lhs
rhs = function.rhs
return C.Equality(cls(lhs, *symbols, **assumptions), \
cls(rhs, *symbols, **assumptions))
function = piecewise_fold(function)
if function is S.NaN:
return S.NaN
if symbols:
limits, orientation = _process_limits(*symbols)
else:
# symbol not provided -- we can still try to compute a general form
free = function.free_symbols
if len(free) != 1:
raise ValueError(
"specify dummy variables for %s" % function)
limits, orientation = [Tuple(s) for s in free], 1
# denest any nested calls
while cls == type(function):
limits = list(function.limits) + limits
function = function.function
# Only limits with lower and upper bounds are supported; the indefinite form
# is not supported
if any(len(l) != 3 or None in l for l in limits):
raise ValueError('ExprWithLimits requires values for lower and upper bounds.')
obj = Expr.__new__(cls, **assumptions)
arglist = [function]
arglist.extend(limits)
obj._args = tuple(arglist)
obj.is_commutative = function.is_commutative # limits already checked
return obj
def __new__(cls):
obj = Expr.__new__(cls)
obj.p = -1
return obj
def __hash__(self):
return Expr.__hash__(self)
def __new__(cls, *args):
args = map(sympify, args)
return Expr.__new__(cls, *args)
def __new__(cls):
x = C.Dummy('x')
#construct "by hand" to avoid infinite loop
return Expr.__new__(cls, Tuple(x), x)
def __new__(cls, expr):
expr = sympify(expr)
obj = Expr.__new__(cls, expr)
obj._expr = expr
return obj