<s> from __future__ import print_function , division <EOL> from sympy . core import S , sympify , Expr , Rational , Symbol , Dummy <EOL> from sympy . core import Add , Mul , expand_power_base , expand_log <EOL> from sympy . core . cache import cacheit <EOL> from sympy . core . compatibility import default_sort_key , is_sequence <EOL> from sympy . core . containers import Tuple <EOL> from sympy . utilities . iterables import uniq <EOL> from sympy . sets . sets import Complement <EOL> class Order ( Expr ) : <EOL> r"""<STR_LIT>""" <EOL> is_Order = True <EOL> __slots__ = [ ] <EOL> @ cacheit <EOL> def __new__ ( cls , expr , * args , ** kwargs ) : <EOL> expr = sympify ( expr ) <EOL> if not args : <EOL> if expr . is_Order : <EOL> variables = expr . variables <EOL> point = expr . point <EOL> else : <EOL> variables = list ( expr . free_symbols ) <EOL> point = [ S . Zero ] * len ( variables ) <EOL> else : <EOL> args = list ( args if is_sequence ( args ) else [ args ] ) <EOL> variables , point = [ ] , [ ] <EOL> if is_sequence ( args [ <NUM_LIT:0> ] ) : <EOL> for a in args : <EOL> v , p = list ( map ( sympify , a ) ) <EOL> variables . append ( v ) <EOL> point . append ( p ) <EOL> else : <EOL> variables = list ( map ( sympify , args ) ) <EOL> point = [ S . Zero ] * len ( variables ) <EOL> if not all ( isinstance ( v , Symbol ) for v in variables ) : <EOL> raise TypeError ( '<STR_LIT>' % variables ) <EOL> if len ( list ( uniq ( variables ) ) ) != len ( variables ) : <EOL> raise ValueError ( '<STR_LIT>' % variables ) <EOL> if expr . is_Order : <EOL> expr_vp = dict ( expr . args [ <NUM_LIT:1> : ] ) <EOL> new_vp = dict ( expr_vp ) <EOL> vp = dict ( zip ( variables , point ) ) <EOL> for v , p in vp . items ( ) : <EOL> if v in new_vp . keys ( ) : <EOL> if p != new_vp [ v ] : <EOL> raise NotImplementedError ( <EOL> "<STR_LIT>" ) <EOL> else : <EOL> new_vp [ v ] = p <EOL> if set ( expr_vp . keys ( ) ) == set ( new_vp . keys ( ) ) : <EOL> return expr <EOL> else : <EOL> variables = list ( new_vp . keys ( ) ) <EOL> point = [ new_vp [ v ] for v in variables ] <EOL> if expr is S . NaN : <EOL> return S . NaN <EOL> if any ( x in p . free_symbols for x in variables for p in point ) : <EOL> raise ValueError ( '<STR_LIT>' % point ) <EOL> if variables : <EOL> if any ( p != point [ <NUM_LIT:0> ] for p in point ) : <EOL> raise NotImplementedError <EOL> if point [ <NUM_LIT:0> ] is S . Infinity : <EOL> s = { k : <NUM_LIT:1> / Dummy ( ) for k in variables } <EOL> rs = { <NUM_LIT:1> / v : <NUM_LIT:1> / k for k , v in s . items ( ) } <EOL> elif point [ <NUM_LIT:0> ] is not S . Zero : <EOL> s = dict ( ( k , Dummy ( ) + point [ <NUM_LIT:0> ] ) for k in variables ) <EOL> rs = dict ( ( v - point [ <NUM_LIT:0> ] , k - point [ <NUM_LIT:0> ] ) for k , v in s . items ( ) ) <EOL> else : <EOL> s = ( ) <EOL> rs = ( ) <EOL> expr = expr . subs ( s ) <EOL> if expr . is_Add : <EOL> from sympy import expand_multinomial <EOL> expr = expand_multinomial ( expr ) <EOL> if s : <EOL> args = tuple ( [ r [ <NUM_LIT:0> ] for r in rs . items ( ) ] ) <EOL> else : <EOL> args = tuple ( variables ) <EOL> if len ( variables ) > <NUM_LIT:1> : <EOL> expr = expr . expand ( ) <EOL> if expr . is_Add : <EOL> lst = expr . extract_leading_order ( args ) <EOL> expr = Add ( * [ f . expr for ( e , f ) in lst ] ) <EOL> elif expr : <EOL> expr = expr . as_leading_term ( * args ) <EOL> expr = expr . as_independent ( * args , as_Add = False ) [ <NUM_LIT:1> ] <EOL> expr = expand_power_base ( expr ) <EOL> expr = expand_log ( expr ) <EOL> if len ( args ) == <NUM_LIT:1> : <EOL> x = args [ <NUM_LIT:0> ] <EOL> margs = list ( Mul . make_args ( <EOL> expr . as_independent ( x , as_Add = False ) [ <NUM_LIT:1> ] ) ) <EOL> for i , t in enumerate ( margs ) : <EOL> if t . is_Pow : <EOL> b , q = t . args <EOL> if b in ( x , - x ) and q . is_real and not q . has ( x ) : <EOL> margs [ i ] = x ** q <EOL> elif b . is_Pow and not b . exp . has ( x ) : <EOL> b , r = b . args <EOL> if b in ( x , - x ) and r . is_real : <EOL> margs [ i ] = x ** ( r * q ) <EOL> elif b . is_Mul and b . args [ <NUM_LIT:0> ] is S . NegativeOne : <EOL> b = - b <EOL> if b . is_Pow and not b . exp . has ( x ) : <EOL> b , r = b . args <EOL> if b in ( x , - x ) and r . is_real : <EOL> margs [ i ] = x ** ( r * q ) <EOL> expr = Mul ( * margs ) <EOL> expr = expr . subs ( rs ) <EOL> if expr is S . Zero : <EOL> return expr <EOL> if expr . is_Order : <EOL> expr = expr . expr <EOL> if not expr . has ( * variables ) : <EOL> expr = S . One <EOL> vp = dict ( zip ( variables , point ) ) <EOL> variables . sort ( key = default_sort_key ) <EOL> point = [ vp [ v ] for v in variables ] <EOL> args = ( expr , ) + Tuple ( * zip ( variables , point ) ) <EOL> obj = Expr . __new__ ( cls , * args ) <EOL> return obj <EOL> def _eval_nseries ( self , x , n , logx ) : <EOL> return self <EOL> @ property <EOL> def expr ( self ) : <EOL> return self . args [ <NUM_LIT:0> ] <EOL> @ property <EOL> def variables ( self ) : <EOL> if self . args [ <NUM_LIT:1> : ] : <EOL> return tuple ( x [ <NUM_LIT:0> ] for x in self . args [ <NUM_LIT:1> : ] ) <EOL> else : <EOL> return ( ) <EOL> @ property <EOL> def point ( self ) : <EOL> if self . args [ <NUM_LIT:1> : ] : <EOL> return tuple ( x [ <NUM_LIT:1> ] for x in self . args [ <NUM_LIT:1> : ] ) <EOL> else : <EOL> return ( ) <EOL> @ property <EOL> def free_symbols ( self ) : <EOL> return self . expr . free_symbols | set ( self . variables ) <EOL> def _eval_power ( b , e ) : <EOL> if e . is_Number and e . is_nonnegative : <EOL> return b . func ( b . expr ** e , * b . args [ <NUM_LIT:1> : ] ) <EOL> if e == O ( <NUM_LIT:1> ) : <EOL> return b <EOL> return <EOL> def as_expr_variables ( self , order_symbols ) : <EOL> if order_symbols is None : <EOL> order_symbols = self . args [ <NUM_LIT:1> : ] <EOL> else : <EOL> if not all ( o [ <NUM_LIT:1> ] == order_symbols [ <NUM_LIT:0> ] [ <NUM_LIT:1> ] for o in order_symbols ) and not all ( p == self . point [ <NUM_LIT:0> ] for p in self . point ) : <EOL> raise NotImplementedError ( '<STR_LIT>' <EOL> '<STR_LIT>' % point ) <EOL> if order_symbols and order_symbols [ <NUM_LIT:0> ] [ <NUM_LIT:1> ] != self . point [ <NUM_LIT:0> ] : <EOL> raise NotImplementedError ( <EOL> "<STR_LIT>" ) <EOL> order_symbols = dict ( order_symbols ) <EOL> for s , p in dict ( self . args [ <NUM_LIT:1> : ] ) . items ( ) : <EOL> if s not in order_symbols . keys ( ) : <EOL> order_symbols [ s ] = p <EOL> order_symbols = sorted ( order_symbols . items ( ) , key = lambda x : default_sort_key ( x [ <NUM_LIT:0> ] ) ) <EOL> return self . expr , tuple ( order_symbols ) <EOL> def removeO ( self ) : <EOL> return S . Zero <EOL> def getO ( self ) : <EOL> return self <EOL> @ cacheit <EOL> def contains ( self , expr ) : <EOL> """<STR_LIT>""" <EOL> from sympy import powsimp <EOL> if expr is S . Zero : <EOL> return True <EOL> if expr is S . NaN : <EOL> return False <EOL> if expr . is_Order : <EOL> if not all ( p == expr . point [ <NUM_LIT:0> ] for p in expr . point ) and not all ( p == self . point [ <NUM_LIT:0> ] for p in self . point ) : <EOL> raise NotImplementedError ( '<STR_LIT>' <EOL> '<STR_LIT>' % point ) <EOL> else : <EOL> if any ( not p for p in [ expr . point , self . point ] ) : <EOL> point = self . point + expr . point <EOL> if point : <EOL> point = point [ <NUM_LIT:0> ] <EOL> else : <EOL> point = S . Zero <EOL> else : <EOL> point = self . point [ <NUM_LIT:0> ] <EOL> if expr . expr == self . expr : <EOL> return all ( [ x in self . args [ <NUM_LIT:1> : ] for x in expr . args [ <NUM_LIT:1> : ] ] ) <EOL> if expr . expr . is_Add : <EOL> return all ( [ self . contains ( x ) for x in expr . expr . args ] ) <EOL> if self . expr . is_Add : <EOL> return any ( [ self . func ( x , * self . args [ <NUM_LIT:1> : ] ) . contains ( expr ) <EOL> for x in self . expr . args ] ) <EOL> if self . variables and expr . variables : <EOL> common_symbols = tuple ( <EOL> [ s for s in self . variables if s in expr . variables ] ) <EOL> elif self . variables : <EOL> common_symbols = self . variables <EOL> else : <EOL> common_symbols = expr . variables <EOL> if not common_symbols : <EOL> return None <EOL> if ( self . expr . is_Pow and self . expr . base . is_Symbol <EOL> and self . expr . exp . is_positive ) : <EOL> if expr . expr . is_Pow and self . expr . base == expr . expr . base : <EOL> return not ( self . expr . exp - expr . expr . exp ) . is_positive <EOL> if expr . expr . is_Mul : <EOL> for arg in expr . expr . args : <EOL> if ( arg . is_Pow and self . expr . base == arg . base <EOL> and ( expr . expr / arg ) . is_number ) : <EOL> r = ( self . expr . exp - arg . exp ) . is_positive <EOL> if not ( r is None ) : <EOL> return not r <EOL> r = None <EOL> ratio = self . expr / expr . expr <EOL> ratio = powsimp ( ratio , deep = True , combine = '<STR_LIT>' ) <EOL> for s in common_symbols : <EOL> l = ratio . limit ( s , point ) <EOL> from sympy . series . limits import Limit <EOL> if not isinstance ( l , Limit ) : <EOL> l = l != <NUM_LIT:0> <EOL> else : <EOL> l = None <EOL> if r is None : <EOL> r = l <EOL> else : <EOL> if r != l : <EOL> return <EOL> return r <EOL> if ( self . expr . is_Pow and self . expr . base . is_Symbol <EOL> and self . expr . exp . is_positive ) : <EOL> if expr . is_Pow and self . expr . base == expr . base : <EOL> return not ( self . expr . exp - expr . exp ) . is_positive <EOL> if expr . is_Mul : <EOL> for arg in expr . args : <EOL> if ( arg . is_Pow and self . expr . base == arg . base <EOL> and ( expr / arg ) . is_number ) : <EOL> r = ( self . expr . exp - arg . exp ) . is_positive <EOL> if not ( r is None ) : <EOL> return not r <EOL> obj = self . func ( expr , * self . args [ <NUM_LIT:1> : ] ) <EOL> return self . contains ( obj ) <EOL> def __contains__ ( self , other ) : <EOL> result = self . contains ( other ) <EOL> if result is None : <EOL> raise TypeError ( '<STR_LIT>' ) <EOL> return result <EOL> def _eval_subs ( self , old , new ) : <EOL> if old in self . variables : <EOL> newexpr = self . expr . subs ( old , new ) <EOL> i = self . variables . index ( old ) <EOL> newvars = list ( self . variables ) <EOL> newpt = list ( self . point ) <EOL> if new . is_Symbol : <EOL> newvars [ i ] = new <EOL> else : <EOL> syms = new . free_symbols <EOL> if len ( syms ) == <NUM_LIT:1> or old in syms : <EOL> if old in syms : <EOL> var = self . variables [ i ] <EOL> else : <EOL> var = syms . pop ( ) <EOL> point = new . subs ( var , self . point [ i ] ) <EOL> if point != self . point [ i ] : <EOL> from sympy . solvers . solveset import solveset <EOL> d = Dummy ( ) <EOL> sol = solveset ( old - new . subs ( var , d ) , d ) <EOL> if isinstance ( sol , Complement ) : <EOL> e1 = sol . args [ <NUM_LIT:0> ] <EOL> e2 = sol . args [ <NUM_LIT:1> ] <EOL> sol = set ( e1 ) - set ( e2 ) <EOL> res = [ dict ( zip ( ( d , ) , sol ) ) ] <EOL> point = d . subs ( res [ <NUM_LIT:0> ] ) . limit ( old , self . point [ i ] ) <EOL> newvars [ i ] = var <EOL> newpt [ i ] = point <EOL> elif old not in syms : <EOL> del newvars [ i ] , newpt [ i ] <EOL> if not syms and new == self . point [ i ] : <EOL> newvars . extend ( syms ) <EOL> newpt . extend ( [ S . Zero ] * len ( syms ) ) <EOL> else : <EOL> return <EOL> return Order ( newexpr , * zip ( newvars , newpt ) ) <EOL> def _eval_conjugate ( self ) : <EOL> expr = self . expr . _eval_conjugate ( ) <EOL> if expr is not None : <EOL> return self . func ( expr , * self . args [ <NUM_LIT:1> : ] ) <EOL> def _eval_derivative ( self , x ) : <EOL> return self . func ( self . expr . diff ( x ) , * self . args [ <NUM_LIT:1> : ] ) or self <EOL> def _eval_transpose ( self ) : <EOL> expr = self . expr . _eval_transpose ( ) <EOL> if expr is not None : <EOL> return self . func ( expr , * self . args [ <NUM_LIT:1> : ] ) <EOL> def _sage_ ( self ) : <EOL> return Rational ( <NUM_LIT:0> ) . _sage_ ( ) <EOL> O = Order </s>
