Module ImportFrom alias alias ImportFrom alias ImportFrom alias alias ImportFrom alias alias ImportFrom alias alias ImportFrom alias ImportFrom alias ImportFrom alias ImportFrom alias alias ImportFrom alias alias alias ImportFrom alias alias ImportFrom alias ImportFrom alias alias alias alias alias alias alias alias ImportFrom alias ImportFrom alias ImportFrom alias ClassDef bases NameLoad body Expr Str Assign NameStore NameLoad FunctionDef arguments args NameParam defaults body Assign NameStore Call AttributeLoad NameLoad attr AttributeLoad NameLoad attr If CompareEq AttributeLoad NameLoad attr AttributeLoad NameLoad attr body If BoolOpAnd AttributeLoad SubscriptLoad AttributeLoad NameLoad attr Index Num attr Call NameLoad AttributeLoad SubscriptLoad AttributeLoad NameLoad attr Index Num attr body Return NameLoad orelse Return AttributeLoad NameLoad attr decorator_list FunctionDef arguments args NameParam defaults body Assign NameStore Call AttributeLoad NameLoad attr AttributeLoad NameLoad attr If CompareEq AttributeLoad NameLoad attr AttributeLoad NameLoad attr body If BoolOpAnd Call NameLoad AttributeLoad SubscriptLoad AttributeLoad NameLoad attr Index Num attr AttributeLoad SubscriptLoad AttributeLoad NameLoad attr Index Num attr body Return NameLoad Assign NameStore Call NameLoad SubscriptLoad AttributeLoad NameLoad attr Index Num If BoolOpAnd CompareIsNot NameLoad NameLoad AttributeLoad NameLoad attr body Return NameLoad orelse Return AttributeLoad NameLoad attr decorator_list FunctionDef arguments args NameParam NameParam defaults NameLoad kwarg body Assign TupleStore NameStore NameStore Call AttributeLoad NameLoad attr keyword NameLoad NameLoad Return BinOpAdd NameLoad BinOpMult NameLoad AttributeLoad NameLoad attr decorator_list FunctionDef arguments args NameParam NameParam defaults NameLoad kwarg body If AttributeLoad SubscriptLoad AttributeLoad NameLoad attr Index Num attr body If NameLoad body Assign SubscriptStore NameLoad Index Str NameLoad Return TupleLoad Call AttributeLoad SubscriptLoad AttributeLoad NameLoad attr Index Num attr NameLoad NameLoad AttributeLoad NameLoad attr orelse Return TupleLoad SubscriptLoad AttributeLoad NameLoad attr Index Num AttributeLoad NameLoad attr If NameLoad body Assign TupleStore NameStore NameStore Call AttributeLoad Call AttributeLoad SubscriptLoad AttributeLoad NameLoad attr Index Num attr NameLoad NameLoad attr orelse Assign TupleStore NameStore NameStore Call AttributeLoad SubscriptLoad AttributeLoad NameLoad attr Index Num attr Return TupleLoad NameLoad NameLoad decorator_list decorator_list FunctionDef arguments args NameParam defaults body Expr Str For NameStore Call AttributeLoad NameLoad attr NameLoad body If CompareIs NameLoad AttributeLoad NameLoad attr body Assign NameStore AttributeLoad NameLoad attr Break orelse If AttributeLoad NameLoad attr body Assign TupleStore NameStore NameStore Call AttributeLoad NameLoad attr If BoolOpAnd CompareIs NameLoad AttributeLoad NameLoad attr AttributeLoad NameLoad attr body Break orelse Return TupleLoad NameLoad AttributeLoad NameLoad attr Assign NameStore BinOpMult BinOpMod NameLoad AttributeLoad NameLoad attr AttributeLoad NameLoad attr Assign NameStore BinOpSub BinOpMult NameLoad AttributeLoad NameLoad attr NameLoad Return TupleLoad BinOpSub NameLoad NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults Num body Expr Str Assign NameStore Call NameLoad NameLoad If CompareIs NameLoad AttributeLoad NameLoad attr body Return AttributeLoad NameLoad attr orelse If UnaryOpNot NameLoad body Return AttributeLoad NameLoad attr orelse If AttributeLoad NameLoad attr body Assign NameStore Call AttributeLoad NameLoad attr AttributeLoad NameLoad attr If NameLoad body Assign TupleStore NameStore NameStore Call AttributeLoad NameLoad attr If AttributeLoad NameLoad attr body Assign NameStore BinOpMod Call NameLoad NameLoad Num If CompareNotEq NameLoad Num body Assign NameStore UnaryOpUSub Call NameLoad Call NameLoad Call AttributeLoad Call NameLoad NameLoad Num attr Assign NameStore BinOpPow Num NameLoad Assign NameStore BinOpMult NameLoad NameLoad Assign NameStore Call NameLoad NameLoad If CompareEq NameLoad NameLoad body Assign NameStore Call NameLoad NameLoad NameLoad Assign NameStore BinOpMult NameLoad NameLoad orelse Assign NameStore Call NameLoad Call NameLoad NameLoad Assign NameStore BinOpMult NameLoad NameLoad If AttributeLoad NameLoad attr body Assign NameStore BinOpMod NameLoad Num If CompareEq NameLoad Num body Return NameLoad orelse If UnaryOpNot NameLoad body If CompareIsNot AttributeLoad NameLoad attr NameLoad body Return AttributeLoad NameLoad attr Return Call NameLoad Num orelse Return BinOpMult NameLoad NameLoad Return NameLoad decorator_list ClassDef bases NameLoad body Expr Str FunctionDef arguments args NameParam NameParam defaults Num body If CompareEq NameLoad Num body Return Call NameLoad SubscriptLoad AttributeLoad NameLoad attr Index Num orelse Raise Call NameLoad NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body ImportFrom alias If AttributeLoad NameLoad attr body If CompareIs NameLoad AttributeLoad NameLoad attr body Return AttributeLoad NameLoad attr orelse If CompareIs NameLoad AttributeLoad NameLoad attr body Return AttributeLoad NameLoad attr orelse If BoolOpOr CompareIs NameLoad AttributeLoad NameLoad attr CompareIs NameLoad AttributeLoad NameLoad attr body Return Call NameLoad Num Num If Call NameLoad NameLoad NameLoad body Assign TupleStore NameStore NameStore TupleLoad AttributeLoad NameLoad attr AttributeLoad NameLoad attr Assign NameStore Call NameLoad BinOpDiv NameLoad BinOpMult Num AttributeLoad NameLoad attr If CompareIsNot NameLoad AttributeLoad NameLoad attr body Assign NameStore BinOpSub NameLoad BinOpMult BinOpMult NameLoad Num AttributeLoad NameLoad attr If CompareIsNot NameLoad AttributeLoad NameLoad attr body Assign NameStore BinOpSub NameLoad BinOpMult BinOpMult NameLoad Num AttributeLoad NameLoad attr If BoolOpAnd CompareIsNot Call AttributeLoad Call NameLoad NameLoad NameLoad attr Call NameLoad BinOpDiv AttributeLoad NameLoad attr Num BinOpDiv BinOpMult Num AttributeLoad NameLoad attr Num AttributeLoad NameLoad attr CompareIsNot Call AttributeLoad Call NameLoad NameLoad NameLoad attr Call NameLoad BinOpDiv BinOpMult Num AttributeLoad NameLoad attr Num BinOpDiv BinOpMult Num AttributeLoad NameLoad attr Num AttributeLoad NameLoad attr body Return Call NameLoad Num Num orelse If CompareIsNot Call AttributeLoad Call NameLoad NameLoad NameLoad attr Call NameLoad BinOpDiv AttributeLoad NameLoad attr Num BinOpDiv BinOpMult Num AttributeLoad NameLoad attr Num AttributeLoad NameLoad attr body Return Call NameLoad Call NameLoad Call NameLoad NameLoad Call NameLoad NameLoad Num orelse If CompareIsNot Call AttributeLoad Call NameLoad NameLoad NameLoad attr Call NameLoad BinOpDiv BinOpMult Num AttributeLoad NameLoad attr Num BinOpDiv BinOpMult Num AttributeLoad NameLoad attr Num AttributeLoad NameLoad attr body Return Call NameLoad Num Call NameLoad Call NameLoad NameLoad Call NameLoad NameLoad orelse Return Call NameLoad Call NameLoad Call NameLoad NameLoad Call NameLoad NameLoad Call NameLoad Call NameLoad NameLoad Call NameLoad NameLoad If Call AttributeLoad NameLoad attr body Return UnaryOpUSub Call NameLoad UnaryOpUSub NameLoad Assign NameStore Call AttributeLoad NameLoad attr AttributeLoad NameLoad attr If CompareIsNot NameLoad NameLoad body Return BinOpMult AttributeLoad NameLoad attr Call NameLoad NameLoad Assign NameStore Call NameLoad NameLoad If CompareIsNot NameLoad NameLoad body If AttributeLoad NameLoad attr body Return AttributeLoad NameLoad attr If AttributeLoad BinOpMult Num NameLoad attr body If AttributeLoad NameLoad attr body Return AttributeLoad NameLoad attr orelse If CompareIs AttributeLoad NameLoad attr NameLoad body Return BinOpPow AttributeLoad NameLoad attr BinOpSub NameLoad AttributeLoad NameLoad attr If UnaryOpNot AttributeLoad NameLoad attr body Assign NameStore BinOpMult NameLoad AttributeLoad NameLoad attr If CompareNotEq NameLoad NameLoad body Return Call NameLoad NameLoad Return NameLoad If AttributeLoad NameLoad attr body Assign NameStore BinOpMod NameLoad Num If CompareGt NameLoad Num body Return UnaryOpUSub Call NameLoad BinOpMult BinOpMod NameLoad Num AttributeLoad NameLoad attr If CompareGt BinOpMult Num NameLoad Num body Return Call NameLoad BinOpMult BinOpSub Num NameLoad AttributeLoad NameLoad attr Assign NameStore BinOpMult BinOpMod BinOpAdd NameLoad Call NameLoad Num Num Num AttributeLoad NameLoad attr Assign NameStore Call NameLoad NameLoad If UnaryOpNot Call NameLoad NameLoad NameLoad body Return NameLoad If CompareNotEq BinOpMult NameLoad AttributeLoad NameLoad attr NameLoad body Return Call NameLoad BinOpMult NameLoad AttributeLoad NameLoad attr Return NameLoad If AttributeLoad NameLoad attr body Assign TupleStore NameStore NameStore Call NameLoad NameLoad If NameLoad body Return BinOpAdd BinOpMult Call NameLoad NameLoad Call NameLoad NameLoad BinOpMult Call NameLoad NameLoad Call NameLoad NameLoad If CompareIs AttributeLoad NameLoad attr NameLoad body Return SubscriptLoad AttributeLoad NameLoad attr Index Num If CompareIs AttributeLoad NameLoad attr NameLoad body Assign NameStore SubscriptLoad AttributeLoad NameLoad attr Index Num Return BinOpDiv NameLoad Call NameLoad BinOpAdd Num BinOpPow NameLoad Num If CompareIs AttributeLoad NameLoad attr NameLoad body Assign TupleStore NameStore NameStore AttributeLoad NameLoad attr Return BinOpDiv NameLoad Call NameLoad BinOpAdd BinOpPow NameLoad Num BinOpPow NameLoad Num If CompareIs AttributeLoad NameLoad attr NameLoad body Assign NameStore SubscriptLoad AttributeLoad NameLoad attr Index Num Return Call NameLoad BinOpSub Num BinOpPow NameLoad Num If CompareIs AttributeLoad NameLoad attr NameLoad body Assign NameStore SubscriptLoad AttributeLoad NameLoad attr Index Num Return BinOpDiv Num BinOpMult Call NameLoad BinOpAdd Num BinOpDiv Num BinOpPow NameLoad Num NameLoad decorator_list NameLoad FunctionDef arguments args NameParam NameParam defaults vararg body If BoolOpOr CompareLt NameLoad Num CompareEq BinOpMod NameLoad Num Num body Return AttributeLoad NameLoad attr orelse Assign NameStore Call NameLoad NameLoad If CompareGt Call NameLoad NameLoad Num body Assign NameStore SubscriptLoad NameLoad Index Num Return BinOpDiv BinOpMult UnaryOpUSub NameLoad BinOpPow NameLoad Num BinOpMult NameLoad BinOpSub NameLoad Num orelse Return BinOpDiv BinOpMult BinOpPow Num BinOpFloorDiv NameLoad Num BinOpPow NameLoad NameLoad Call NameLoad NameLoad decorator_list NameLoad NameLoad FunctionDef arguments args NameParam NameParam defaults body Assign NameStore AttributeLoad NameLoad attr If BoolOpOr Call NameLoad NameLoad NameLoad Call NameLoad NameLoad NameLoad body Assign NameStore Call AttributeLoad Call AttributeLoad NameLoad attr SubscriptLoad AttributeLoad NameLoad attr Index Num attr NameLoad Return BinOpDiv BinOpSub Call NameLoad BinOpMult NameLoad NameLoad Call NameLoad BinOpMult UnaryOpUSub NameLoad NameLoad BinOpMult Num NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body If CompareIs AttributeLoad NameLoad attr NameLoad body Assign NameStore AttributeLoad NameLoad attr Assign NameStore SubscriptLoad AttributeLoad NameLoad attr Index Num Return BinOpSub BinOpDiv BinOpMult NameLoad BinOpPow NameLoad UnaryOpUSub NameLoad Num BinOpDiv BinOpMult NameLoad BinOpPow NameLoad NameLoad Num decorator_list FunctionDef arguments args NameParam NameParam defaults body Return UnaryOpUSub Call NameLoad BinOpAdd NameLoad BinOpDiv AttributeLoad NameLoad attr Num decorator_list FunctionDef arguments args NameParam NameParam defaults body Assign NameStore Call NameLoad BinOpMult AttributeLoad NameLoad attr NameLoad Return BinOpDiv BinOpMult Num NameLoad BinOpAdd Num BinOpPow NameLoad Num decorator_list FunctionDef arguments args NameParam NameParam defaults body Return BinOpDiv BinOpMult Call NameLoad NameLoad Call NameLoad NameLoad Call NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body Assign NameStore Call NameLoad BinOpMult AttributeLoad NameLoad attr NameLoad Return BinOpDiv BinOpMult Num NameLoad BinOpAdd Num BinOpPow NameLoad Num decorator_list FunctionDef arguments args NameParam NameParam defaults body Return Call AttributeLoad Call AttributeLoad NameLoad attr NameLoad attr NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body Return Call AttributeLoad Call AttributeLoad NameLoad attr NameLoad attr NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body Return BinOpDiv Num Call NameLoad NameLoad decorator_list FunctionDef arguments args NameParam defaults body Return Call AttributeLoad NameLoad attr Call AttributeLoad SubscriptLoad AttributeLoad NameLoad attr Index Num attr decorator_list FunctionDef arguments args NameParam NameParam defaults NameLoad kwarg body Assign TupleStore NameStore NameStore Call AttributeLoad NameLoad attr keyword NameLoad NameLoad Return TupleLoad BinOpMult Call NameLoad NameLoad Call NameLoad NameLoad BinOpMult Call NameLoad NameLoad Call NameLoad NameLoad decorator_list FunctionDef arguments args NameParam defaults kwarg body ImportFrom alias ImportFrom alias alias Assign NameStore SubscriptLoad AttributeLoad NameLoad attr Index Num Assign NameStore NameLoad If AttributeLoad NameLoad attr body Assign TupleStore NameStore NameStore Call AttributeLoad NameLoad attr Assign NameStore Call AttributeLoad Call NameLoad NameLoad keyword NameLoad attr Assign NameStore Call AttributeLoad Call NameLoad NameLoad keyword NameLoad attr Assign NameStore Call AttributeLoad Call NameLoad NameLoad keyword NameLoad attr Assign NameStore Call AttributeLoad Call NameLoad NameLoad keyword NameLoad attr Return BinOpAdd BinOpMult NameLoad NameLoad BinOpMult NameLoad NameLoad orelse Assign TupleStore NameStore NameStore Call AttributeLoad NameLoad attr keyword NameLoad If AttributeLoad NameLoad attr body If AttributeLoad NameLoad attr body Return BinOpMult BinOpPow Num BinOpDiv BinOpSub NameLoad Num Num Call NameLoad NameLoad Call NameLoad NameLoad orelse Return Call NameLoad BinOpMult BinOpMult BinOpPow Num BinOpSub BinOpDiv NameLoad Num Num Call NameLoad NameLoad Call NameLoad BinOpSub NameLoad Num Call NameLoad NameLoad keyword NameLoad Assign NameStore Call NameLoad NameLoad If CompareIsNot NameLoad NameLoad body If AttributeLoad NameLoad attr body Return Call AttributeLoad NameLoad attr NameLoad Return Call NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body ImportFrom alias Assign NameStore Call AttributeLoad SubscriptLoad AttributeLoad NameLoad attr Index Num attr NameLoad If BoolOpAnd CompareIn NameLoad AttributeLoad NameLoad attr Call AttributeLoad Call NameLoad Num NameLoad attr NameLoad body Return NameLoad orelse Return Call AttributeLoad NameLoad attr NameLoad decorator_list FunctionDef arguments args NameParam defaults body Return AttributeLoad SubscriptLoad AttributeLoad NameLoad attr Index Num attr decorator_list FunctionDef arguments args NameParam defaults body Assign NameStore SubscriptLoad AttributeLoad NameLoad attr Index Num If AttributeLoad NameLoad attr body Return NameLoad decorator_list decorator_list ClassDef bases NameLoad body Expr Str FunctionDef arguments args NameParam NameParam defaults Num body If CompareEq NameLoad Num body Return UnaryOpUSub Call NameLoad SubscriptLoad AttributeLoad NameLoad attr Index Num orelse Raise Call NameLoad NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body ImportFrom alias ImportFrom alias If AttributeLoad NameLoad attr body If CompareIs NameLoad AttributeLoad NameLoad attr body Return AttributeLoad NameLoad attr orelse If CompareIs NameLoad AttributeLoad NameLoad attr body Return AttributeLoad NameLoad attr orelse If BoolOpOr CompareIs NameLoad AttributeLoad NameLoad attr CompareIs NameLoad AttributeLoad NameLoad attr body Return Call NameLoad Num Num If Call NameLoad NameLoad NameLoad body Return Call NameLoad BinOpAdd NameLoad BinOpDiv AttributeLoad NameLoad attr Num If Call AttributeLoad NameLoad attr body Return Call NameLoad UnaryOpUSub NameLoad Assign NameStore Call AttributeLoad NameLoad attr AttributeLoad NameLoad attr If CompareIsNot NameLoad NameLoad body Return Call NameLoad NameLoad Assign NameStore Call NameLoad NameLoad If CompareIsNot NameLoad NameLoad body If AttributeLoad NameLoad attr body Return BinOpPow AttributeLoad NameLoad attr NameLoad If AttributeLoad BinOpMult Num NameLoad attr body If AttributeLoad NameLoad attr body Return BinOpPow AttributeLoad NameLoad attr BinOpDiv NameLoad Num orelse If CompareIs AttributeLoad NameLoad attr NameLoad body Return AttributeLoad NameLoad attr If UnaryOpNot AttributeLoad NameLoad attr body Assign NameStore BinOpMult NameLoad AttributeLoad NameLoad attr If CompareNotEq NameLoad NameLoad body Return Call NameLoad NameLoad Return NameLoad Assign NameStore Dict Num Num AttributeLoad NameLoad attr BinOpDiv BinOpAdd Call NameLoad Num Num Num If AttributeLoad NameLoad attr body Assign NameStore AttributeLoad NameLoad attr Assign NameStore BinOpMod AttributeLoad NameLoad attr BinOpMult Num NameLoad If CompareGt NameLoad NameLoad body Assign NameStore BinOpMult BinOpSub NameLoad Num AttributeLoad NameLoad attr Return UnaryOpUSub Call NameLoad NameLoad If CompareGt BinOpMult Num NameLoad NameLoad body Assign NameStore BinOpMult BinOpSub Num NameLoad AttributeLoad NameLoad attr Return UnaryOpUSub Call NameLoad NameLoad Assign NameStore Dict Num Num Num Num Num Num Num Num TupleLoad Num Num TupleLoad Num Num TupleLoad Num Num TupleLoad Num Num TupleLoad Num Num TupleLoad Num Num TupleLoad Num Num TupleLoad Num Num If CompareIn NameLoad NameLoad body Assign TupleStore NameStore NameStore TupleLoad BinOpDiv BinOpMult NameLoad AttributeLoad NameLoad attr SubscriptLoad SubscriptLoad NameLoad Index NameLoad Index Num BinOpDiv BinOpMult NameLoad AttributeLoad NameLoad attr SubscriptLoad SubscriptLoad NameLoad Index NameLoad Index Num Assign TupleStore NameStore NameStore TupleLoad Call NameLoad NameLoad Call NameLoad NameLoad If BoolOpOr CompareEq NameLoad NameLoad CompareEq NameLoad NameLoad body Return NameLoad Return BinOpAdd BinOpMult NameLoad NameLoad BinOpMult Call NameLoad BinOpSub BinOpDiv AttributeLoad NameLoad attr Num NameLoad Call NameLoad BinOpSub BinOpDiv AttributeLoad NameLoad attr Num NameLoad If CompareGt NameLoad Num body Return NameLoad If CompareIn NameLoad NameLoad body Assign NameStore SubscriptLoad NameLoad Index AttributeLoad NameLoad attr Return Call AttributeLoad Call NameLoad AttributeLoad NameLoad attr NameLoad attr If CompareEq Num BinOpMod NameLoad Num body Assign NameStore BinOpMult BinOpMult NameLoad Num AttributeLoad NameLoad attr Assign NameStore Call NameLoad NameLoad If CompareEq NameLoad NameLoad body Return NameLoad Assign NameStore BinOpDiv BinOpAdd BinOpMult Num NameLoad Num Num Assign NameStore BinOpPow Num BinOpMult IfExp CompareLt NameLoad Num Num Num Call NameLoad Call NameLoad NameLoad Return BinOpMult NameLoad Call NameLoad BinOpDiv BinOpAdd Num NameLoad Num Return NameLoad If AttributeLoad NameLoad attr body Assign TupleStore NameStore NameStore Call NameLoad NameLoad If NameLoad body Return BinOpSub BinOpMult Call NameLoad NameLoad Call NameLoad NameLoad BinOpMult Call NameLoad NameLoad Call NameLoad NameLoad If CompareIs AttributeLoad NameLoad attr NameLoad body Return SubscriptLoad AttributeLoad NameLoad attr Index Num If CompareIs AttributeLoad NameLoad attr NameLoad body Assign NameStore SubscriptLoad AttributeLoad NameLoad attr Index Num Return BinOpDiv Num Call NameLoad BinOpAdd Num BinOpPow NameLoad Num If CompareIs AttributeLoad NameLoad attr NameLoad body Assign TupleStore NameStore NameStore AttributeLoad NameLoad attr Return BinOpDiv NameLoad Call NameLoad BinOpAdd BinOpPow NameLoad Num BinOpPow NameLoad Num If CompareIs AttributeLoad NameLoad attr NameLoad body Assign NameStore SubscriptLoad AttributeLoad NameLoad attr Index Num Return Call NameLoad BinOpSub Num BinOpPow NameLoad Num If CompareIs AttributeLoad NameLoad attr NameLoad body Assign NameStore SubscriptLoad AttributeLoad NameLoad attr Index Num Return BinOpDiv Num Call NameLoad BinOpAdd Num BinOpDiv Num BinOpPow NameLoad Num decorator_list NameLoad FunctionDef arguments args NameParam NameParam defaults vararg body If BoolOpOr CompareLt NameLoad Num CompareEq BinOpMod NameLoad Num Num body Return AttributeLoad NameLoad attr orelse Assign NameStore Call NameLoad NameLoad If CompareGt Call NameLoad NameLoad Num body Assign NameStore SubscriptLoad NameLoad Index Num Return BinOpDiv BinOpMult UnaryOpUSub NameLoad BinOpPow NameLoad Num BinOpMult NameLoad BinOpSub NameLoad Num orelse Return BinOpDiv BinOpMult BinOpPow Num BinOpFloorDiv NameLoad Num BinOpPow NameLoad NameLoad Call NameLoad NameLoad decorator_list NameLoad NameLoad FunctionDef arguments args NameParam NameParam defaults body Assign NameStore AttributeLoad NameLoad attr If BoolOpOr Call NameLoad NameLoad NameLoad Call NameLoad NameLoad NameLoad body Assign NameStore Call AttributeLoad Call AttributeLoad NameLoad attr SubscriptLoad AttributeLoad NameLoad attr Index Num attr NameLoad Return BinOpDiv BinOpAdd Call NameLoad BinOpMult NameLoad NameLoad Call NameLoad BinOpMult UnaryOpUSub NameLoad NameLoad Num decorator_list FunctionDef arguments args NameParam NameParam defaults body If CompareIs AttributeLoad NameLoad attr NameLoad body Assign NameStore AttributeLoad NameLoad attr Assign NameStore SubscriptLoad AttributeLoad NameLoad attr Index Num Return BinOpAdd BinOpDiv BinOpPow NameLoad NameLoad Num BinOpDiv BinOpPow NameLoad UnaryOpUSub NameLoad Num decorator_list FunctionDef arguments args NameParam NameParam defaults body Return Call NameLoad BinOpAdd NameLoad BinOpDiv AttributeLoad NameLoad attr Num decorator_list FunctionDef arguments args NameParam NameParam defaults body Assign NameStore BinOpPow Call NameLoad BinOpMult AttributeLoad NameLoad attr NameLoad Num Return BinOpDiv BinOpSub Num NameLoad BinOpAdd Num NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body Return BinOpDiv BinOpMult Call NameLoad NameLoad Call NameLoad NameLoad Call NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body Assign NameStore BinOpPow Call NameLoad BinOpMult AttributeLoad NameLoad attr NameLoad Num Return BinOpDiv BinOpSub NameLoad Num BinOpAdd NameLoad Num decorator_list FunctionDef arguments args NameParam NameParam defaults body Return Call AttributeLoad NameLoad attr NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body ImportFrom alias FunctionDef arguments args NameParam defaults body If CompareEq Call NameLoad NameLoad Num body Return TupleLoad Num SubscriptLoad NameLoad Index Num If CompareEq Call NameLoad NameLoad Num body Return Call NameLoad SubscriptLoad NameLoad Index Num SubscriptLoad NameLoad Index Num Assign NameStore Call NameLoad SubscriptLoad NameLoad Slice Num Assign TupleStore NameStore NameStore NameStore Call NameLoad SubscriptLoad NameLoad Index Num SubscriptLoad NameLoad Index Num Return Call NameLoad BinOpAdd BinOpAdd ListLoad NameLoad ListComp BinOpMult NameLoad NameLoad comprehension NameStore SubscriptLoad NameLoad Slice Num Num ListLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults NameLoad body ImportFrom alias If Call NameLoad NameLoad NameLoad body Return NameLoad If UnaryOpNot Call NameLoad NameLoad NameLoad body Raise Call NameLoad Str Assign NameStore AttributeLoad NameLoad attr If CompareGt Num BinOpMult AttributeLoad NameLoad attr AttributeLoad NameLoad attr body Return AttributeLoad NameLoad attr If CompareEq NameLoad NameLoad body Assign NameStore ListComp BinOpFloorDiv NameLoad BinOpPow NameLoad NameLoad comprehension TupleStore NameStore NameStore Call AttributeLoad Call NameLoad AttributeLoad NameLoad attr attr orelse Assign NameStore ListComp BinOpFloorDiv NameLoad NameLoad comprehension NameStore NameLoad If CompareEq Call NameLoad NameLoad Num body Return ListLoad NameLoad Assign NameStore Call NameLoad NameLoad Assign NameStore ListComp BinOpMult AttributeLoad NameLoad attr Call NameLoad BinOpMult NameLoad NameLoad AttributeLoad NameLoad attr comprehension TupleStore NameStore NameStore Call NameLoad SubscriptLoad NameLoad Slice Num NameLoad Assert CompareEq NameLoad Call NameLoad NameLoad Return NameLoad decorator_list Assign NameStore Call NameLoad NameLoad If CompareIs NameLoad NameLoad body Return NameLoad If AttributeLoad NameLoad attr body Return Call AttributeLoad NameLoad attr BinOpMult NameLoad AttributeLoad NameLoad attr If UnaryOpNot AttributeLoad NameLoad attr body Return NameLoad FunctionDef arguments args defaults body Expr Str FunctionDef arguments args NameParam NameParam defaults body Return TupleLoad BinOpDiv BinOpAdd NameLoad Call NameLoad BinOpAdd BinOpPow NameLoad Num NameLoad Num BinOpDiv BinOpSub NameLoad Call NameLoad BinOpAdd BinOpPow NameLoad Num NameLoad Num decorator_list FunctionDef arguments args NameParam NameParam defaults body Return BinOpDiv BinOpSub NameLoad Call NameLoad BinOpAdd BinOpPow NameLoad Num NameLoad Num decorator_list Assign TupleStore NameStore NameStore Call NameLoad Num Num Assign TupleStore NameStore NameStore Call NameLoad NameLoad Num Assign TupleStore NameStore NameStore Call NameLoad NameLoad Num Assign TupleStore NameStore NameStore Call NameLoad NameLoad BinOpMult Num BinOpAdd BinOpAdd Num NameLoad BinOpMult Num NameLoad Assign TupleStore NameStore NameStore Call NameLoad NameLoad BinOpMult Num BinOpAdd BinOpAdd Num NameLoad BinOpMult Num NameLoad Assign TupleStore NameStore NameStore Call NameLoad NameLoad BinOpMult Num BinOpAdd BinOpAdd Num NameLoad BinOpMult Num NameLoad Assign TupleStore NameStore NameStore Call NameLoad NameLoad BinOpMult Num BinOpAdd BinOpAdd Num NameLoad BinOpMult Num NameLoad Assign TupleStore NameStore NameStore Call NameLoad NameLoad BinOpMult Num BinOpAdd BinOpAdd BinOpAdd NameLoad NameLoad NameLoad BinOpMult Num NameLoad Assign TupleStore NameStore NameStore Call NameLoad NameLoad BinOpMult Num BinOpAdd BinOpAdd BinOpAdd NameLoad NameLoad NameLoad BinOpMult Num NameLoad Assign TupleStore NameStore NameStore Call NameLoad NameLoad BinOpMult Num BinOpAdd BinOpAdd BinOpAdd NameLoad NameLoad NameLoad BinOpMult Num NameLoad Assign TupleStore NameStore NameStore Call NameLoad NameLoad BinOpMult Num BinOpAdd BinOpAdd BinOpAdd NameLoad NameLoad NameLoad BinOpMult Num NameLoad Assign TupleStore NameStore NameStore Call NameLoad NameLoad BinOpMult Num BinOpAdd BinOpAdd BinOpAdd NameLoad NameLoad NameLoad BinOpMult Num NameLoad Assign TupleStore NameStore NameStore Call NameLoad NameLoad BinOpMult Num BinOpAdd BinOpAdd BinOpAdd NameLoad NameLoad NameLoad BinOpMult Num NameLoad Assign TupleStore NameStore NameStore Call NameLoad NameLoad BinOpMult Num BinOpAdd BinOpAdd BinOpAdd NameLoad NameLoad NameLoad BinOpMult Num NameLoad Assign TupleStore NameStore NameStore Call NameLoad NameLoad BinOpMult Num BinOpAdd BinOpAdd BinOpAdd NameLoad NameLoad NameLoad BinOpMult Num NameLoad Assign NameStore Call NameLoad NameLoad BinOpMult Num BinOpAdd BinOpAdd BinOpAdd NameLoad NameLoad NameLoad NameLoad Assign NameStore Call NameLoad NameLoad BinOpMult Num BinOpAdd BinOpAdd BinOpAdd NameLoad NameLoad NameLoad NameLoad Assign NameStore Call NameLoad NameLoad BinOpMult Num BinOpAdd BinOpAdd BinOpAdd NameLoad NameLoad NameLoad NameLoad Assign NameStore Call NameLoad NameLoad BinOpMult Num BinOpAdd BinOpAdd BinOpAdd NameLoad NameLoad NameLoad NameLoad Assign NameStore Call NameLoad NameLoad BinOpMult Num BinOpAdd BinOpAdd BinOpAdd NameLoad NameLoad NameLoad NameLoad Assign NameStore Call NameLoad NameLoad BinOpMult Num BinOpAdd BinOpAdd BinOpAdd NameLoad NameLoad NameLoad NameLoad Assign NameStore UnaryOpUSub Call NameLoad UnaryOpUSub NameLoad BinOpMult Num BinOpAdd NameLoad NameLoad Assign NameStore UnaryOpUSub Call NameLoad UnaryOpUSub NameLoad BinOpMult Num BinOpAdd NameLoad NameLoad Assign NameStore BinOpMult Num Call NameLoad UnaryOpUSub NameLoad BinOpMult Num NameLoad Return Call NameLoad BinOpAdd BinOpDiv BinOpMult Call NameLoad Num Call NameLoad BinOpAdd NameLoad Num Num AttributeLoad NameLoad attr decorator_list Assign NameStore Dict Num Num Num Num AttributeLoad NameLoad attr BinOpDiv BinOpAdd Call NameLoad Num Num Num Call NameLoad BinOpAdd BinOpDiv BinOpAdd Num Call NameLoad Num Num BinOpDiv BinOpMult Call NameLoad Num BinOpAdd Call NameLoad BinOpSub Num Call NameLoad Num Call NameLoad BinOpAdd BinOpAdd BinOpMult Call NameLoad Num BinOpSub BinOpMult Num Call NameLoad BinOpAdd Num Call NameLoad Num BinOpMult BinOpSub Num Call NameLoad Num Call NameLoad BinOpSub Num Call NameLoad Num BinOpMult Num Call NameLoad Num Num Num Call NameLoad FunctionDef arguments args NameParam defaults body ImportFrom alias Assign NameStore ListLoad For NameStore NameLoad body Assign TupleStore NameStore NameStore Call NameLoad NameLoad NameLoad If UnaryOpNot NameLoad body Expr Call AttributeLoad NameLoad attr NameLoad If CompareEq NameLoad Num body Return Call NameLoad NameLoad Return NameLoad decorator_list If CompareIn AttributeLoad NameLoad attr NameLoad body Assign NameStore Call NameLoad AttributeLoad NameLoad attr SubscriptLoad NameLoad Index AttributeLoad NameLoad attr If CompareLt AttributeLoad NameLoad attr Num body Assign NameStore Call AttributeLoad NameLoad attr Return NameLoad If UnaryOpNot BinOpMod AttributeLoad NameLoad attr Num body Assign NameStore BinOpMult NameLoad Num Assign NameStore Call AttributeLoad Call NameLoad BinOpMult NameLoad AttributeLoad NameLoad attr attr NameLoad Assign NameStore BinOpDiv BinOpAdd NameLoad Num Num Assign NameStore IfExp BinOpMod Call NameLoad NameLoad Num Num Num Return BinOpMult NameLoad Call NameLoad BinOpDiv BinOpAdd Num NameLoad Num Assign NameStore Call NameLoad AttributeLoad NameLoad attr If NameLoad body Assign NameStore Call NameLoad NameLoad NameLoad Assign NameStore ListComp TupleLoad SubscriptLoad NameLoad Index Num BinOpMult SubscriptLoad NameLoad Index Num AttributeLoad NameLoad attr comprehension NameStore Call NameLoad NameLoad Call NameLoad Str Assign NameStore Call AttributeLoad Call AttributeLoad Call NameLoad Call NameLoad ListComp SubscriptLoad NameLoad Index Num comprehension NameStore NameLoad attr attr NameLoad Return Call AttributeLoad NameLoad attr NameLoad orelse Assign NameStore Call NameLoad NameLoad Assign NameStore ListComp TupleLoad SubscriptLoad NameLoad Index Num BinOpMult SubscriptLoad NameLoad Index Num AttributeLoad NameLoad attr comprehension NameStore Call NameLoad NameLoad Call NameLoad Str Assign NameStore Call AttributeLoad Call AttributeLoad Call NameLoad Call NameLoad ListComp SubscriptLoad NameLoad Index Num comprehension NameStore NameLoad attr attr NameLoad Return NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body Return BinOpDiv Num Call NameLoad NameLoad decorator_list FunctionDef arguments args NameParam defaults body Return Call AttributeLoad NameLoad attr Call AttributeLoad SubscriptLoad AttributeLoad NameLoad attr Index Num attr decorator_list FunctionDef arguments args NameParam NameParam defaults NameLoad kwarg body Assign TupleStore NameStore NameStore Call AttributeLoad NameLoad attr keyword NameLoad NameLoad Return TupleLoad BinOpMult Call NameLoad NameLoad Call NameLoad NameLoad BinOpMult UnaryOpUSub Call NameLoad NameLoad Call NameLoad NameLoad decorator_list FunctionDef arguments args NameParam defaults kwarg body ImportFrom alias Assign NameStore SubscriptLoad AttributeLoad NameLoad attr Index Num Assign NameStore NameLoad If AttributeLoad NameLoad attr body Assign TupleStore NameStore NameStore Call AttributeLoad NameLoad attr Assign NameStore Call AttributeLoad Call NameLoad NameLoad keyword NameLoad attr Assign NameStore Call AttributeLoad Call NameLoad NameLoad keyword NameLoad attr Assign NameStore Call AttributeLoad Call NameLoad NameLoad keyword NameLoad attr Assign NameStore Call AttributeLoad Call NameLoad NameLoad keyword NameLoad attr Return BinOpSub BinOpMult NameLoad NameLoad BinOpMult NameLoad NameLoad orelse Assign TupleStore NameStore NameStore Call AttributeLoad NameLoad attr keyword NameLoad If AttributeLoad NameLoad attr body Return Call NameLoad NameLoad Call NameLoad NameLoad Assign NameStore Call NameLoad NameLoad If CompareIsNot NameLoad NameLoad body If AttributeLoad NameLoad attr body Return Call AttributeLoad NameLoad attr NameLoad Return Call NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body ImportFrom alias Assign NameStore Call AttributeLoad SubscriptLoad AttributeLoad NameLoad attr Index Num attr NameLoad If BoolOpAnd CompareIn NameLoad AttributeLoad NameLoad attr Call AttributeLoad Call NameLoad Num NameLoad attr NameLoad body Return AttributeLoad NameLoad attr orelse Return Call AttributeLoad NameLoad attr NameLoad decorator_list FunctionDef arguments args NameParam defaults body Return AttributeLoad SubscriptLoad AttributeLoad NameLoad attr Index Num attr decorator_list FunctionDef arguments args NameParam defaults body Assign NameStore SubscriptLoad AttributeLoad NameLoad attr Index Num If AttributeLoad NameLoad attr body Return NameLoad decorator_list decorator_list ClassDef bases NameLoad body Expr Str FunctionDef arguments args NameParam NameParam defaults Num body If CompareEq NameLoad Num body Return BinOpAdd AttributeLoad NameLoad attr BinOpPow NameLoad Num orelse Raise Call NameLoad NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults Num body Expr Str Return NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body ImportFrom alias If AttributeLoad NameLoad attr body If CompareIs NameLoad AttributeLoad NameLoad attr body Return AttributeLoad NameLoad attr orelse If CompareIs NameLoad AttributeLoad NameLoad attr body Return AttributeLoad NameLoad attr orelse If BoolOpOr CompareIs NameLoad AttributeLoad NameLoad attr CompareIs NameLoad AttributeLoad NameLoad attr body Return Call NameLoad AttributeLoad NameLoad attr AttributeLoad NameLoad attr If Call NameLoad NameLoad NameLoad body Assign TupleStore NameStore NameStore TupleLoad AttributeLoad NameLoad attr AttributeLoad NameLoad attr Assign NameStore Call NameLoad BinOpDiv NameLoad AttributeLoad NameLoad attr If CompareIsNot NameLoad AttributeLoad NameLoad attr body Assign NameStore BinOpSub NameLoad BinOpMult NameLoad AttributeLoad NameLoad attr If CompareIsNot NameLoad AttributeLoad NameLoad attr body Assign NameStore BinOpSub NameLoad BinOpMult NameLoad AttributeLoad NameLoad attr If Call AttributeLoad Call NameLoad NameLoad NameLoad attr Call NameLoad BinOpDiv AttributeLoad NameLoad attr Num BinOpDiv BinOpMult Num AttributeLoad NameLoad attr Num body Return Call NameLoad AttributeLoad NameLoad attr AttributeLoad NameLoad attr orelse Return Call NameLoad Call NameLoad NameLoad Call NameLoad NameLoad If Call AttributeLoad NameLoad attr body Return UnaryOpUSub Call NameLoad UnaryOpUSub NameLoad Assign NameStore Call AttributeLoad NameLoad attr AttributeLoad NameLoad attr If CompareIsNot NameLoad NameLoad body Return BinOpMult AttributeLoad NameLoad attr Call NameLoad NameLoad Assign NameStore Call NameLoad NameLoad Num If CompareIsNot NameLoad NameLoad body If AttributeLoad NameLoad attr body Return AttributeLoad NameLoad attr If UnaryOpNot AttributeLoad NameLoad attr body Assign NameStore BinOpMult NameLoad AttributeLoad NameLoad attr If CompareNotEq NameLoad NameLoad body Return Call NameLoad NameLoad Return NameLoad If AttributeLoad NameLoad attr body If UnaryOpNot BinOpMod AttributeLoad NameLoad attr Num body Assign NameStore BinOpMult BinOpMult NameLoad AttributeLoad NameLoad attr Num Assign TupleStore NameStore NameStore TupleLoad Call NameLoad NameLoad Call NameLoad BinOpSub NameLoad BinOpDiv AttributeLoad NameLoad attr Num If BoolOpAnd UnaryOpNot Call NameLoad NameLoad NameLoad UnaryOpNot Call NameLoad NameLoad NameLoad body If CompareEq NameLoad Num body Return AttributeLoad NameLoad attr Return BinOpDiv BinOpSub Num NameLoad NameLoad Assign NameStore Dict Num Num Num Num Num Num Num Num TupleLoad Num Num TupleLoad Num Num TupleLoad Num Num TupleLoad Num Num TupleLoad Num Num TupleLoad Num Num TupleLoad Num Num TupleLoad Num Num Assign NameStore AttributeLoad NameLoad attr Assign NameStore BinOpMod AttributeLoad NameLoad attr NameLoad If CompareIn NameLoad NameLoad body Assign TupleStore NameStore NameStore TupleLoad Call NameLoad BinOpDiv BinOpMult NameLoad AttributeLoad NameLoad attr SubscriptLoad SubscriptLoad NameLoad Index NameLoad Index Num Call NameLoad BinOpDiv BinOpMult NameLoad AttributeLoad NameLoad attr SubscriptLoad SubscriptLoad NameLoad Index NameLoad Index Num If BoolOpOr CompareEq NameLoad NameLoad CompareEq NameLoad NameLoad body Return NameLoad Return BinOpDiv BinOpSub NameLoad NameLoad BinOpAdd Num BinOpMult NameLoad NameLoad Assign NameStore BinOpMult BinOpSub BinOpMod BinOpAdd NameLoad AttributeLoad NameLoad attr Num AttributeLoad NameLoad attr AttributeLoad NameLoad attr Assign TupleStore NameStore NameStore TupleLoad Call NameLoad NameLoad Call NameLoad BinOpSub NameLoad BinOpDiv AttributeLoad NameLoad attr Num If BoolOpAnd UnaryOpNot Call NameLoad NameLoad NameLoad UnaryOpNot Call NameLoad NameLoad NameLoad body If CompareEq NameLoad Num body Return AttributeLoad NameLoad attr Return BinOpDiv NameLoad NameLoad If CompareNotEq NameLoad NameLoad body Return Call NameLoad NameLoad If AttributeLoad NameLoad attr body Assign TupleStore NameStore NameStore Call NameLoad NameLoad If NameLoad body Assign NameStore Call NameLoad NameLoad Assign NameStore Call NameLoad NameLoad If CompareIs NameLoad AttributeLoad NameLoad attr body Return UnaryOpUSub Call NameLoad NameLoad Return BinOpDiv BinOpAdd NameLoad NameLoad BinOpSub Num BinOpMult NameLoad NameLoad If CompareIs AttributeLoad NameLoad attr NameLoad body Return SubscriptLoad AttributeLoad NameLoad attr Index Num If CompareIs AttributeLoad NameLoad attr NameLoad body Assign TupleStore NameStore NameStore AttributeLoad NameLoad attr Return BinOpDiv NameLoad NameLoad If CompareIs AttributeLoad NameLoad attr NameLoad body Assign NameStore SubscriptLoad AttributeLoad NameLoad attr Index Num Return BinOpDiv NameLoad Call NameLoad BinOpSub Num BinOpPow NameLoad Num If CompareIs AttributeLoad NameLoad attr NameLoad body Assign NameStore SubscriptLoad AttributeLoad NameLoad attr Index Num Return BinOpDiv Call NameLoad BinOpSub Num BinOpPow NameLoad Num NameLoad If CompareIs AttributeLoad NameLoad attr NameLoad body Assign NameStore SubscriptLoad AttributeLoad NameLoad attr Index Num Return BinOpDiv Num NameLoad decorator_list NameLoad FunctionDef arguments args NameParam NameParam defaults vararg body ImportFrom alias If BoolOpOr CompareLt NameLoad Num CompareEq BinOpMod NameLoad Num Num body Return AttributeLoad NameLoad attr orelse Assign NameStore Call NameLoad NameLoad Assign TupleStore NameStore NameStore TupleLoad BinOpFloorDiv BinOpSub NameLoad Num Num BinOpPow Num BinOpAdd NameLoad Num Assign NameStore Call NameLoad BinOpAdd NameLoad Num Assign NameStore Call NameLoad BinOpAdd NameLoad Num Return BinOpMult BinOpDiv BinOpMult BinOpMult BinOpMult BinOpPow Num NameLoad NameLoad BinOpSub NameLoad Num NameLoad NameLoad BinOpPow NameLoad NameLoad decorator_list NameLoad NameLoad FunctionDef arguments args NameParam NameParam NameParam NameParam defaults body Assign NameStore BinOpDiv BinOpMult Call AttributeLoad SubscriptLoad AttributeLoad NameLoad attr Index Num attr NameLoad Num Num AttributeLoad NameLoad attr If BoolOpAnd NameLoad AttributeLoad NameLoad attr body Return Call AttributeLoad Call AttributeLoad NameLoad attr NameLoad attr NameLoad keyword NameLoad keyword NameLoad Return Call AttributeLoad NameLoad attr NameLoad NameLoad keyword NameLoad keyword NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body If CompareIs AttributeLoad NameLoad attr NameLoad body Assign NameStore AttributeLoad NameLoad attr Assign NameStore SubscriptLoad AttributeLoad NameLoad attr Index Num Return BinOpDiv BinOpMult NameLoad BinOpSub BinOpPow NameLoad UnaryOpUSub NameLoad BinOpPow NameLoad NameLoad BinOpAdd BinOpPow NameLoad UnaryOpUSub NameLoad BinOpPow NameLoad NameLoad decorator_list FunctionDef arguments args NameParam defaults body Return Call AttributeLoad NameLoad attr Call AttributeLoad SubscriptLoad AttributeLoad NameLoad attr Index Num attr decorator_list FunctionDef arguments args NameParam NameParam defaults NameLoad kwarg body Assign TupleStore NameStore NameStore Call AttributeLoad NameLoad attr keyword NameLoad NameLoad If NameLoad body Assign NameStore BinOpAdd Call NameLoad BinOpMult Num NameLoad Call NameLoad BinOpMult Num NameLoad Return TupleLoad BinOpDiv Call NameLoad BinOpMult Num NameLoad NameLoad BinOpDiv Call NameLoad BinOpMult Num NameLoad NameLoad orelse Return TupleLoad Call AttributeLoad NameLoad attr NameLoad AttributeLoad NameLoad attr decorator_list FunctionDef arguments args NameParam defaults kwarg body ImportFrom alias alias Assign NameStore SubscriptLoad AttributeLoad NameLoad attr Index Num Assign NameStore NameLoad If AttributeLoad NameLoad attr body ImportFrom alias Assign NameStore Call NameLoad AttributeLoad NameLoad attr Assign NameStore ListLoad For NameStore AttributeLoad NameLoad attr body Assign NameStore Call AttributeLoad Call NameLoad NameLoad keyword NameLoad attr Expr Call AttributeLoad NameLoad attr NameLoad Assign NameStore Call NameLoad Str Assign NameStore ListComp Call NameLoad NameLoad comprehension NameStore Call NameLoad NameLoad Assign NameStore ListLoad Num Num For NameStore Call NameLoad BinOpAdd NameLoad Num body AugAssignAdd SubscriptStore NameLoad Index BinOpSub Num BinOpMod NameLoad Num BinOpMult Call NameLoad NameLoad NameLoad BinOpPow Num BinOpFloorDiv BinOpMod NameLoad Num Num Return Call AttributeLoad BinOpDiv SubscriptLoad NameLoad Index Num SubscriptLoad NameLoad Index Num attr Call NameLoad Call NameLoad NameLoad NameLoad orelse Assign TupleStore NameStore NameStore Call AttributeLoad NameLoad attr keyword NameLoad If BoolOpAnd AttributeLoad NameLoad attr CompareGt NameLoad Num body Assign NameStore AttributeLoad NameLoad attr Assign NameStore Call NameLoad Str keyword NameLoad Assign NameStore Call AttributeLoad BinOpPow BinOpAdd Num BinOpMult NameLoad NameLoad NameLoad attr Return Call AttributeLoad BinOpDiv Call NameLoad NameLoad Call NameLoad NameLoad attr ListLoad TupleLoad NameLoad Call NameLoad NameLoad Return Call NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body Assign NameStore AttributeLoad NameLoad attr If BoolOpOr Call NameLoad NameLoad NameLoad Call NameLoad NameLoad NameLoad body Assign NameStore Call AttributeLoad Call AttributeLoad NameLoad attr SubscriptLoad AttributeLoad NameLoad attr Index Num attr NameLoad Assign TupleStore NameStore NameStore TupleLoad Call NameLoad BinOpMult UnaryOpUSub NameLoad NameLoad Call NameLoad BinOpMult NameLoad NameLoad Return BinOpDiv BinOpMult NameLoad BinOpSub NameLoad NameLoad BinOpAdd NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body Return BinOpDiv BinOpMult Num BinOpPow Call NameLoad NameLoad Num Call NameLoad BinOpMult Num NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body Return BinOpDiv UnaryOpUSub Call NameLoad BinOpAdd NameLoad BinOpDiv AttributeLoad NameLoad attr Num Call NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body Return BinOpDiv Call NameLoad NameLoad Call NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body Return BinOpDiv Num Call NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body Assign NameStore Call AttributeLoad Call AttributeLoad NameLoad attr NameLoad attr NameLoad If Call AttributeLoad NameLoad attr NameLoad body Return NameLoad Return NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body Assign NameStore Call AttributeLoad Call AttributeLoad NameLoad attr NameLoad attr NameLoad If Call AttributeLoad NameLoad attr NameLoad body Return NameLoad Return NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body ImportFrom alias Assign NameStore Call AttributeLoad SubscriptLoad AttributeLoad NameLoad attr Index Num attr NameLoad If BoolOpAnd CompareIn NameLoad AttributeLoad NameLoad attr Call AttributeLoad Call NameLoad Num NameLoad attr NameLoad body Return NameLoad orelse Return Call AttributeLoad NameLoad attr NameLoad decorator_list FunctionDef arguments args NameParam defaults body Return AttributeLoad SubscriptLoad AttributeLoad NameLoad attr Index Num attr decorator_list FunctionDef arguments args NameParam defaults body Assign NameStore SubscriptLoad AttributeLoad NameLoad attr Index Num If AttributeLoad NameLoad attr body Return NameLoad decorator_list decorator_list ClassDef bases NameLoad body Expr Str FunctionDef arguments args NameParam NameParam defaults Num body If CompareEq NameLoad Num body Return BinOpSub AttributeLoad NameLoad attr BinOpPow NameLoad Num orelse Raise Call NameLoad NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults Num body Expr Str Return NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body ImportFrom alias If AttributeLoad NameLoad attr body If CompareIs NameLoad AttributeLoad NameLoad attr body Return AttributeLoad NameLoad attr If CompareIs NameLoad AttributeLoad NameLoad attr body Return AttributeLoad NameLoad attr If Call NameLoad NameLoad NameLoad body Return UnaryOpUSub Call NameLoad BinOpAdd NameLoad BinOpDiv AttributeLoad NameLoad attr Num If Call AttributeLoad NameLoad attr body Return UnaryOpUSub Call NameLoad UnaryOpUSub NameLoad Assign NameStore Call AttributeLoad NameLoad attr AttributeLoad NameLoad attr If CompareIsNot NameLoad NameLoad body Return BinOpMult UnaryOpUSub AttributeLoad NameLoad attr Call NameLoad NameLoad Assign NameStore Call NameLoad NameLoad Num If CompareIsNot NameLoad NameLoad body If AttributeLoad NameLoad attr body Return AttributeLoad NameLoad attr If UnaryOpNot AttributeLoad NameLoad attr body Assign NameStore BinOpMult NameLoad AttributeLoad NameLoad attr If CompareNotEq NameLoad NameLoad body Return Call NameLoad NameLoad Return NameLoad If AttributeLoad NameLoad attr body If BoolOpAnd CompareGt AttributeLoad NameLoad attr Num UnaryOpNot BinOpMod AttributeLoad NameLoad attr Num body Assign NameStore BinOpMult BinOpMult NameLoad AttributeLoad NameLoad attr Num Assign TupleStore NameStore NameStore TupleLoad Call NameLoad NameLoad Call NameLoad BinOpSub NameLoad BinOpDiv AttributeLoad NameLoad attr Num If BoolOpAnd UnaryOpNot Call NameLoad NameLoad NameLoad UnaryOpNot Call NameLoad NameLoad NameLoad body Return BinOpDiv BinOpAdd Num NameLoad NameLoad Assign NameStore Dict Num Num Num Num Num Num Num Num TupleLoad Num Num TupleLoad Num Num TupleLoad Num Num TupleLoad Num Num TupleLoad Num Num TupleLoad Num Num TupleLoad Num Num TupleLoad Num Num Assign NameStore AttributeLoad NameLoad attr Assign NameStore BinOpMod AttributeLoad NameLoad attr NameLoad If CompareIn NameLoad NameLoad body Assign TupleStore NameStore NameStore TupleLoad Call NameLoad BinOpDiv BinOpMult NameLoad AttributeLoad NameLoad attr SubscriptLoad SubscriptLoad NameLoad Index NameLoad Index Num Call NameLoad BinOpDiv BinOpMult NameLoad AttributeLoad NameLoad attr SubscriptLoad SubscriptLoad NameLoad Index NameLoad Index Num If BoolOpOr CompareEq NameLoad NameLoad CompareEq NameLoad NameLoad body Return NameLoad Return BinOpDiv BinOpAdd Num BinOpMult NameLoad NameLoad BinOpSub NameLoad NameLoad Assign NameStore BinOpMult BinOpSub BinOpMod BinOpAdd NameLoad AttributeLoad NameLoad attr Num AttributeLoad NameLoad attr AttributeLoad NameLoad attr Assign TupleStore NameStore NameStore TupleLoad Call NameLoad NameLoad Call NameLoad BinOpSub NameLoad BinOpDiv AttributeLoad NameLoad attr Num If BoolOpAnd UnaryOpNot Call NameLoad NameLoad NameLoad UnaryOpNot Call NameLoad NameLoad NameLoad body If CompareEq NameLoad Num body Return AttributeLoad NameLoad attr Return BinOpDiv NameLoad NameLoad If CompareNotEq NameLoad NameLoad body Return Call NameLoad NameLoad If AttributeLoad NameLoad attr body Assign TupleStore NameStore NameStore Call NameLoad NameLoad If NameLoad body Assign NameStore Call NameLoad NameLoad If CompareEq NameLoad Num body Return UnaryOpUSub Call NameLoad NameLoad Assign NameStore Call NameLoad NameLoad If CompareIs NameLoad AttributeLoad NameLoad attr body Return NameLoad If AttributeLoad NameLoad attr body Return BinOpDiv BinOpSub BinOpMult NameLoad NameLoad Num BinOpAdd NameLoad NameLoad Return NameLoad If CompareIs AttributeLoad NameLoad attr NameLoad body Return SubscriptLoad AttributeLoad NameLoad attr Index Num If CompareIs AttributeLoad NameLoad attr NameLoad body Assign NameStore SubscriptLoad AttributeLoad NameLoad attr Index Num Return BinOpDiv Num NameLoad If CompareIs AttributeLoad NameLoad attr NameLoad body Assign TupleStore NameStore NameStore AttributeLoad NameLoad attr Return BinOpDiv NameLoad NameLoad If CompareIs AttributeLoad NameLoad attr NameLoad body Assign NameStore SubscriptLoad AttributeLoad NameLoad attr Index Num Return BinOpDiv Call NameLoad BinOpSub Num BinOpPow NameLoad Num NameLoad If CompareIs AttributeLoad NameLoad attr NameLoad body Assign NameStore SubscriptLoad AttributeLoad NameLoad attr Index Num Return BinOpDiv NameLoad Call NameLoad BinOpSub Num BinOpPow NameLoad Num decorator_list NameLoad FunctionDef arguments args NameParam NameParam defaults vararg body ImportFrom alias If CompareEq NameLoad Num body Return BinOpDiv Num Call NameLoad NameLoad orelse If BoolOpOr CompareLt NameLoad Num CompareEq BinOpMod NameLoad Num Num body Return AttributeLoad NameLoad attr orelse Assign NameStore Call NameLoad NameLoad Assign NameStore Call NameLoad BinOpAdd NameLoad Num Assign NameStore Call NameLoad BinOpAdd NameLoad Num Return BinOpMult BinOpDiv BinOpMult BinOpMult BinOpPow Num BinOpFloorDiv BinOpAdd NameLoad Num Num BinOpPow Num BinOpAdd NameLoad Num NameLoad NameLoad BinOpPow NameLoad NameLoad decorator_list NameLoad NameLoad FunctionDef arguments args NameParam NameParam NameParam NameParam defaults body Assign NameStore BinOpDiv Call AttributeLoad SubscriptLoad AttributeLoad NameLoad attr Index Num attr NameLoad Num AttributeLoad NameLoad attr If BoolOpAnd NameLoad AttributeLoad NameLoad attr body Return Call AttributeLoad Call AttributeLoad NameLoad attr NameLoad attr NameLoad keyword NameLoad keyword NameLoad Return Call AttributeLoad Call AttributeLoad NameLoad attr NameLoad attr NameLoad keyword NameLoad keyword NameLoad decorator_list FunctionDef arguments args NameParam defaults body Return Call AttributeLoad NameLoad attr Call AttributeLoad SubscriptLoad AttributeLoad NameLoad attr Index Num attr decorator_list FunctionDef arguments args NameParam NameParam defaults NameLoad kwarg body Assign TupleStore NameStore NameStore Call AttributeLoad NameLoad attr keyword NameLoad NameLoad If NameLoad body Assign NameStore BinOpSub Call NameLoad BinOpMult Num NameLoad Call NameLoad BinOpMult Num NameLoad Return TupleLoad BinOpDiv UnaryOpUSub Call NameLoad BinOpMult Num NameLoad NameLoad BinOpDiv UnaryOpUSub Call NameLoad BinOpMult Num NameLoad NameLoad orelse Return TupleLoad Call AttributeLoad NameLoad attr NameLoad AttributeLoad NameLoad attr decorator_list FunctionDef arguments args NameParam NameParam defaults body Assign NameStore AttributeLoad NameLoad attr If BoolOpOr Call NameLoad NameLoad NameLoad Call NameLoad NameLoad NameLoad body Assign NameStore Call AttributeLoad Call AttributeLoad NameLoad attr SubscriptLoad AttributeLoad NameLoad attr Index Num attr NameLoad Assign TupleStore NameStore NameStore TupleLoad Call NameLoad BinOpMult UnaryOpUSub NameLoad NameLoad Call NameLoad BinOpMult NameLoad NameLoad Return BinOpDiv BinOpMult NameLoad BinOpAdd NameLoad NameLoad BinOpSub NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body If CompareIs AttributeLoad NameLoad attr NameLoad body Assign NameStore AttributeLoad NameLoad attr Assign NameStore SubscriptLoad AttributeLoad NameLoad attr Index Num Return BinOpDiv BinOpMult UnaryOpUSub NameLoad BinOpAdd BinOpPow NameLoad UnaryOpUSub NameLoad BinOpPow NameLoad NameLoad BinOpSub BinOpPow NameLoad UnaryOpUSub NameLoad BinOpPow NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body Return BinOpDiv BinOpMult Num Call NameLoad BinOpMult Num NameLoad BinOpPow Call NameLoad NameLoad Num decorator_list FunctionDef arguments args NameParam NameParam defaults body Return BinOpDiv UnaryOpUSub Call NameLoad NameLoad Call NameLoad BinOpAdd NameLoad BinOpDiv AttributeLoad NameLoad attr Num decorator_list FunctionDef arguments args NameParam NameParam defaults body Return BinOpDiv Call NameLoad NameLoad Call NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body Return BinOpDiv Num Call NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body Assign NameStore Call AttributeLoad Call AttributeLoad NameLoad attr NameLoad attr NameLoad If Call AttributeLoad NameLoad attr NameLoad body Return NameLoad Return NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body Assign NameStore Call AttributeLoad Call AttributeLoad NameLoad attr NameLoad attr NameLoad If Call AttributeLoad NameLoad attr NameLoad body Return NameLoad Return NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body ImportFrom alias Assign NameStore Call AttributeLoad SubscriptLoad AttributeLoad NameLoad attr Index Num attr NameLoad If BoolOpAnd CompareIn NameLoad AttributeLoad NameLoad attr Call AttributeLoad Call NameLoad Num NameLoad attr NameLoad body Return BinOpDiv Num NameLoad orelse Return Call AttributeLoad NameLoad attr NameLoad decorator_list FunctionDef arguments args NameParam defaults body Return AttributeLoad SubscriptLoad AttributeLoad NameLoad attr Index Num attr decorator_list FunctionDef arguments args NameParam defaults kwarg body ImportFrom alias alias Assign NameStore SubscriptLoad AttributeLoad NameLoad attr Index Num Assign NameStore NameLoad If AttributeLoad NameLoad attr body ImportFrom alias Assign NameStore Call NameLoad AttributeLoad NameLoad attr Assign NameStore ListLoad For NameStore AttributeLoad NameLoad attr body Assign NameStore Call AttributeLoad Call NameLoad NameLoad keyword NameLoad attr Expr Call AttributeLoad NameLoad attr NameLoad Assign NameStore Call NameLoad Str Assign NameStore ListComp Call NameLoad NameLoad comprehension NameStore Call NameLoad NameLoad Assign NameStore ListLoad Num Num For NameStore Call NameLoad NameLoad Num Num body AugAssignAdd SubscriptStore NameLoad Index BinOpMod BinOpSub NameLoad NameLoad Num BinOpMult Call NameLoad NameLoad NameLoad BinOpPow Num BinOpFloorDiv BinOpMod BinOpSub NameLoad NameLoad Num Num Return Call AttributeLoad BinOpDiv SubscriptLoad NameLoad Index Num SubscriptLoad NameLoad Index Num attr Call NameLoad Call NameLoad NameLoad NameLoad orelse Assign TupleStore NameStore NameStore Call AttributeLoad NameLoad attr keyword NameLoad If BoolOpAnd AttributeLoad NameLoad attr CompareGt NameLoad Num body Assign NameStore AttributeLoad NameLoad attr Assign NameStore Call NameLoad Str keyword NameLoad Assign NameStore Call AttributeLoad BinOpPow BinOpAdd NameLoad NameLoad NameLoad attr Return Call AttributeLoad BinOpDiv Call NameLoad NameLoad Call NameLoad NameLoad attr ListLoad TupleLoad NameLoad Call NameLoad NameLoad Return Call NameLoad NameLoad decorator_list FunctionDef arguments args NameParam defaults body Assign NameStore SubscriptLoad AttributeLoad NameLoad attr Index Num If AttributeLoad NameLoad attr body Return NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam defaults body If CompareEq NameLoad NameLoad body Return NameLoad Assign NameStore SubscriptLoad AttributeLoad NameLoad attr Index Num Assign NameStore Call AttributeLoad NameLoad attr NameLoad NameLoad If BoolOpAnd CompareNotEq NameLoad NameLoad AttributeLoad BinOpDiv NameLoad AttributeLoad NameLoad attr attr body Return AttributeLoad NameLoad attr Return Call NameLoad NameLoad decorator_list decorator_list ClassDef bases NameLoad body Expr Str Assign NameStore NameLoad Assign NameStore NameLoad Assign NameStore NameLoad FunctionDef arguments args NameParam NameParam defaults body If Call AttributeLoad NameLoad attr body If AttributeLoad NameLoad attr body Return Call NameLoad UnaryOpUSub NameLoad If AttributeLoad NameLoad attr body Return UnaryOpUSub Call NameLoad UnaryOpUSub NameLoad Assign NameStore Call NameLoad NameLoad If BoolOpAnd CompareIsNot NameLoad NameLoad UnaryOpNot AttributeLoad BinOpMult Num NameLoad attr AttributeLoad NameLoad attr body Assign NameStore AttributeLoad NameLoad attr Assign NameStore BinOpMod AttributeLoad NameLoad attr BinOpMult Num NameLoad If CompareGt NameLoad NameLoad body Assign NameStore BinOpMult BinOpSub NameLoad Num AttributeLoad NameLoad attr Return UnaryOpUSub Call NameLoad NameLoad If CompareGt BinOpMult Num NameLoad NameLoad body Assign NameStore BinOpMult BinOpSub Num NameLoad AttributeLoad NameLoad attr If AttributeLoad NameLoad attr body Return Call NameLoad NameLoad orelse If AttributeLoad NameLoad attr body Return UnaryOpUSub Call NameLoad NameLoad Assign NameStore Call AttributeLoad AttributeLoad NameLoad attr attr NameLoad If BoolOpAnd Call NameLoad NameLoad Str CompareEq Call AttributeLoad NameLoad attr NameLoad body Return SubscriptLoad AttributeLoad NameLoad attr Index Num Return IfExp CompareNotEq NameLoad NameLoad BinOpDiv Num NameLoad NameLoad decorator_list NameLoad FunctionDef arguments args NameParam NameParam defaults vararg kwarg body Assign NameStore Call AttributeLoad NameLoad attr SubscriptLoad AttributeLoad NameLoad attr Index Num Return Call Call NameLoad NameLoad NameLoad NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults vararg kwarg body Assign NameStore Call AttributeLoad NameLoad attr NameLoad NameLoad NameLoad Return IfExp CompareNotEq NameLoad NameLoad BinOpDiv Num NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam defaults body Assign NameStore Call AttributeLoad NameLoad attr NameLoad NameLoad If BoolOpAnd CompareNotEq NameLoad NameLoad CompareNotEq NameLoad Call AttributeLoad NameLoad attr NameLoad body Return BinOpDiv Num NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults Num body Return BinOpDiv UnaryOpUSub Call AttributeLoad NameLoad attr Str NameLoad BinOpPow NameLoad Num decorator_list FunctionDef arguments args NameParam NameParam defaults body Return Call AttributeLoad NameLoad attr Str NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body Return Call AttributeLoad NameLoad attr Str NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body Return Call AttributeLoad NameLoad attr Str NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body Return Call AttributeLoad NameLoad attr Str NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body Return Call AttributeLoad NameLoad attr Str NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body Return Call AttributeLoad NameLoad attr Str NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body Return Call AttributeLoad NameLoad attr Str NameLoad decorator_list FunctionDef arguments args NameParam defaults body Return Call AttributeLoad NameLoad attr Call AttributeLoad SubscriptLoad AttributeLoad NameLoad attr Index Num attr decorator_list FunctionDef arguments args NameParam NameParam defaults NameLoad kwarg body Return Call AttributeLoad BinOpDiv Num Call AttributeLoad NameLoad attr SubscriptLoad AttributeLoad NameLoad attr Index Num attr NameLoad NameLoad decorator_list FunctionDef arguments args NameParam defaults kwarg body Return Call AttributeLoad NameLoad attr Str NameLoad decorator_list FunctionDef arguments args NameParam defaults body Return Call AttributeLoad Call AttributeLoad NameLoad attr SubscriptLoad AttributeLoad NameLoad attr Index Num attr decorator_list FunctionDef arguments args NameParam NameParam defaults body Return Call AttributeLoad BinOpDiv Num Call AttributeLoad NameLoad attr SubscriptLoad AttributeLoad NameLoad attr Index Num attr NameLoad decorator_list FunctionDef arguments args NameParam defaults body Return AttributeLoad BinOpDiv Num Call AttributeLoad NameLoad attr SubscriptLoad AttributeLoad NameLoad attr Index Num attr decorator_list FunctionDef arguments args NameParam NameParam NameParam NameParam defaults body Return Call AttributeLoad BinOpDiv Num Call AttributeLoad NameLoad attr SubscriptLoad AttributeLoad NameLoad attr Index Num attr NameLoad NameLoad NameLoad decorator_list decorator_list ClassDef bases NameLoad body Expr Str Assign NameStore NameLoad Assign NameStore NameLoad FunctionDef arguments args NameParam NameParam defaults body Assign NameStore BinOpPow Call NameLoad BinOpDiv NameLoad Num Num Return BinOpDiv BinOpAdd NameLoad Num BinOpSub NameLoad Num decorator_list FunctionDef arguments args NameParam NameParam defaults body Return BinOpDiv Num Call NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body Return BinOpDiv Call NameLoad NameLoad BinOpMult Call NameLoad NameLoad Call NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults Num body If CompareEq NameLoad Num body Return BinOpMult Call NameLoad SubscriptLoad AttributeLoad NameLoad attr Index Num Call NameLoad SubscriptLoad AttributeLoad NameLoad attr Index Num orelse Raise Call NameLoad NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults vararg body ImportFrom alias If BoolOpOr CompareLt NameLoad Num CompareEq BinOpMod NameLoad Num Num body Return AttributeLoad NameLoad attr orelse Assign NameStore Call NameLoad NameLoad Assign NameStore BinOpFloorDiv NameLoad Num Return BinOpMult BinOpDiv BinOpMult BinOpPow Num NameLoad Call NameLoad BinOpMult Num NameLoad Call NameLoad BinOpMult Num NameLoad BinOpPow NameLoad BinOpMult Num NameLoad decorator_list NameLoad NameLoad decorator_list ClassDef bases NameLoad body Expr Str Assign NameStore NameLoad Assign NameStore NameLoad FunctionDef arguments args NameParam NameParam defaults body Return BinOpDiv Num Call NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body Return BinOpDiv Call NameLoad NameLoad BinOpMult Call NameLoad NameLoad Call NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body Assign NameStore Call NameLoad BinOpDiv NameLoad Num Return BinOpDiv BinOpAdd Num BinOpPow NameLoad Num BinOpMult Num NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults Num body If CompareEq NameLoad Num body Return BinOpMult UnaryOpUSub Call NameLoad SubscriptLoad AttributeLoad NameLoad attr Index Num Call NameLoad SubscriptLoad AttributeLoad NameLoad attr Index Num orelse Raise Call NameLoad NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults vararg body ImportFrom alias If CompareEq NameLoad Num body Return BinOpDiv Num Call NameLoad NameLoad orelse If BoolOpOr CompareLt NameLoad Num CompareEq BinOpMod NameLoad Num Num body Return AttributeLoad NameLoad attr orelse Assign NameStore Call NameLoad NameLoad Assign NameStore BinOpAdd BinOpFloorDiv NameLoad Num Num Return BinOpDiv BinOpMult BinOpMult BinOpMult BinOpMult BinOpPow Num BinOpSub NameLoad Num Num BinOpSub BinOpPow Num BinOpSub BinOpMult Num NameLoad Num Num Call NameLoad BinOpMult Num NameLoad BinOpPow NameLoad BinOpSub BinOpMult Num NameLoad Num Call NameLoad BinOpMult Num NameLoad decorator_list NameLoad NameLoad decorator_list ClassDef bases NameLoad body Expr Str FunctionDef arguments args NameParam NameParam defaults Num body Assign NameStore SubscriptLoad AttributeLoad NameLoad attr Index Num If CompareEq NameLoad Num body Return BinOpDiv BinOpSub BinOpMult NameLoad Call NameLoad NameLoad Call NameLoad NameLoad BinOpPow NameLoad Num orelse Raise Call NameLoad NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body If AttributeLoad NameLoad attr body Return AttributeLoad NameLoad attr If AttributeLoad NameLoad attr body If CompareIn NameLoad ListLoad AttributeLoad NameLoad attr UnaryOpUSub AttributeLoad NameLoad attr body Return AttributeLoad NameLoad attr orelse If CompareIs NameLoad AttributeLoad NameLoad attr body Return AttributeLoad NameLoad attr If CompareIs NameLoad AttributeLoad NameLoad attr body Return AttributeLoad NameLoad attr If Call AttributeLoad NameLoad attr body Return Call NameLoad UnaryOpUSub NameLoad Assign NameStore Call NameLoad NameLoad If CompareIsNot NameLoad NameLoad body If AttributeLoad NameLoad attr body If Call NameLoad AttributeLoad NameLoad attr body Return AttributeLoad NameLoad attr orelse If AttributeLoad BinOpMult Num NameLoad attr body Return BinOpDiv BinOpPow AttributeLoad NameLoad attr BinOpSub NameLoad AttributeLoad NameLoad attr NameLoad decorator_list NameLoad FunctionDef arguments args NameParam NameParam NameParam NameParam defaults body Assign NameStore SubscriptLoad AttributeLoad NameLoad attr Index Num Return Call AttributeLoad BinOpDiv Call NameLoad NameLoad NameLoad attr NameLoad NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body ImportFrom alias Return Call NameLoad Num NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body Return BinOpDiv Call NameLoad NameLoad NameLoad decorator_list decorator_list ClassDef bases NameLoad body Expr Str Pass decorator_list ClassDef bases NameLoad body Expr Str FunctionDef arguments args NameParam NameParam defaults Num body If CompareEq NameLoad Num body Return BinOpDiv Num Call NameLoad BinOpSub Num BinOpPow SubscriptLoad AttributeLoad NameLoad attr Index Num Num orelse Raise Call NameLoad NameLoad NameLoad decorator_list FunctionDef arguments args NameParam defaults body Assign NameStore Call AttributeLoad NameLoad attr AttributeLoad NameLoad attr If CompareEq AttributeLoad NameLoad attr AttributeLoad NameLoad attr body If AttributeLoad SubscriptLoad AttributeLoad NameLoad attr Index Num attr body Return NameLoad orelse Return AttributeLoad NameLoad attr decorator_list FunctionDef arguments args NameParam defaults body If AttributeLoad SubscriptLoad AttributeLoad NameLoad attr Index Num attr body Return AttributeLoad BinOpSub SubscriptLoad AttributeLoad NameLoad attr Index Num Num attr If AttributeLoad SubscriptLoad AttributeLoad NameLoad attr Index Num attr body Return UnaryOpNot AttributeLoad BinOpAdd SubscriptLoad AttributeLoad NameLoad attr Index Num Num attr decorator_list FunctionDef arguments args NameParam NameParam defaults body If AttributeLoad NameLoad attr body If CompareIs NameLoad AttributeLoad NameLoad attr body Return AttributeLoad NameLoad attr orelse If CompareIs NameLoad AttributeLoad NameLoad attr body Return BinOpMult AttributeLoad NameLoad attr AttributeLoad NameLoad attr orelse If CompareIs NameLoad AttributeLoad NameLoad attr body Return BinOpMult AttributeLoad NameLoad attr AttributeLoad NameLoad attr orelse If CompareIs NameLoad AttributeLoad NameLoad attr body Return AttributeLoad NameLoad attr orelse If CompareIs NameLoad AttributeLoad NameLoad attr body Return BinOpDiv AttributeLoad NameLoad attr Num orelse If CompareIs NameLoad AttributeLoad NameLoad attr body Return BinOpDiv UnaryOpUSub AttributeLoad NameLoad attr Num If Call AttributeLoad NameLoad attr body Return UnaryOpUSub Call NameLoad UnaryOpUSub NameLoad If AttributeLoad NameLoad attr body Assign NameStore Dict BinOpDiv Call NameLoad Num Num BinOpDiv UnaryOpUSub Call NameLoad Num Num BinOpDiv Call NameLoad Num Num BinOpDiv UnaryOpUSub Call NameLoad Num Num BinOpDiv Num Call NameLoad Num BinOpDiv Num Call NameLoad Num Call NameLoad BinOpDiv BinOpSub Num Call NameLoad Num Num UnaryOpUSub Call NameLoad BinOpDiv BinOpSub Num Call NameLoad Num Num AttributeLoad NameLoad attr UnaryOpUSub AttributeLoad NameLoad attr BinOpDiv Call NameLoad BinOpSub Num Call NameLoad Num Num BinOpDiv UnaryOpUSub Call NameLoad BinOpSub Num Call NameLoad Num Num BinOpDiv BinOpSub Call NameLoad Num Num Num BinOpDiv BinOpSub Num Call NameLoad Num Num BinOpDiv BinOpSub Call NameLoad Num Num Call NameLoad BinOpPow Num Num BinOpDiv BinOpSub Num Call NameLoad Num Call NameLoad BinOpPow Num Num BinOpDiv BinOpAdd Call NameLoad Num Num Num BinOpDiv UnaryOpUSub BinOpAdd Call NameLoad Num Num Num Num Num Num Num Num Num Num Num Num Num Num Num Num Num Num Num BinOpDiv Call NameLoad Num Num BinOpDiv UnaryOpUSub Call NameLoad Num Num If CompareIn NameLoad NameLoad body Return BinOpDiv AttributeLoad NameLoad attr SubscriptLoad NameLoad Index NameLoad Assign NameStore Call AttributeLoad NameLoad attr AttributeLoad NameLoad attr If CompareIsNot NameLoad NameLoad body Return BinOpMult AttributeLoad NameLoad attr Call NameLoad NameLoad decorator_list NameLoad FunctionDef arguments args NameParam NameParam defaults vararg body If BoolOpOr CompareLt NameLoad Num CompareEq BinOpMod NameLoad Num Num body Return AttributeLoad NameLoad attr orelse Assign NameStore Call NameLoad NameLoad If BoolOpAnd CompareGtE Call NameLoad NameLoad Num CompareGt NameLoad Num body Assign NameStore SubscriptLoad NameLoad Index Num Return BinOpMult BinOpDiv BinOpMult NameLoad BinOpPow BinOpSub NameLoad Num Num BinOpMult NameLoad BinOpSub NameLoad Num BinOpPow NameLoad Num orelse Assign NameStore BinOpFloorDiv BinOpSub NameLoad Num Num Assign NameStore Call NameLoad AttributeLoad NameLoad attr NameLoad Assign NameStore Call NameLoad NameLoad Return BinOpDiv BinOpMult BinOpDiv NameLoad NameLoad BinOpPow NameLoad NameLoad NameLoad decorator_list NameLoad NameLoad FunctionDef arguments args NameParam NameParam defaults body ImportFrom alias Assign NameStore Call AttributeLoad SubscriptLoad AttributeLoad NameLoad attr Index Num attr NameLoad If BoolOpAnd CompareIn 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decorator_list FunctionDef arguments args NameParam NameParam defaults body Return BinOpSub BinOpDiv AttributeLoad NameLoad attr Num Call NameLoad BinOpDiv Num NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body Return Call NameLoad BinOpDiv Num NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body Return BinOpMult BinOpDiv Call NameLoad BinOpPow NameLoad Num NameLoad BinOpAdd BinOpDiv UnaryOpUSub AttributeLoad NameLoad attr Num BinOpMult Num Call NameLoad BinOpAdd NameLoad Call NameLoad BinOpSub BinOpPow NameLoad Num Num decorator_list FunctionDef arguments args NameParam NameParam defaults body Return BinOpMult BinOpDiv Call NameLoad BinOpPow NameLoad Num NameLoad BinOpAdd BinOpDiv UnaryOpUSub AttributeLoad NameLoad attr Num BinOpMult Num Call NameLoad BinOpSub NameLoad Call NameLoad BinOpSub BinOpPow NameLoad Num Num decorator_list FunctionDef arguments args NameParam NameParam defaults body Return BinOpSub BinOpDiv 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attr Index Num Num orelse Raise Call NameLoad NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults Num body Expr Str Return NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body ImportFrom alias Assign NameStore Call AttributeLoad SubscriptLoad AttributeLoad NameLoad attr Index Num attr NameLoad If Call AttributeLoad Call NameLoad Num NameLoad attr NameLoad body Return Call NameLoad NameLoad orelse Return Call AttributeLoad NameLoad attr NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body Return BinOpMult UnaryOpUSub AttributeLoad NameLoad attr Call NameLoad BinOpAdd BinOpDiv AttributeLoad NameLoad attr NameLoad Call NameLoad BinOpSub Num BinOpDiv Num BinOpPow NameLoad Num decorator_list FunctionDef arguments args NameParam NameParam defaults body Return Call NameLoad BinOpDiv Num NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body Return BinOpSub 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attr body If AttributeLoad NameLoad attr body Return BinOpDiv AttributeLoad NameLoad attr Num orelse If AttributeLoad NameLoad attr body Return BinOpDiv UnaryOpUSub AttributeLoad NameLoad attr Num orelse If AttributeLoad NameLoad attr body Return AttributeLoad NameLoad attr If BoolOpAnd AttributeLoad NameLoad attr AttributeLoad NameLoad attr Call NameLoad AttributeLoad NameLoad attr body Return BinOpMult AttributeLoad NameLoad attr BinOpSub AttributeLoad NameLoad attr Call NameLoad NameLoad If BoolOpAnd AttributeLoad NameLoad attr AttributeLoad NameLoad attr body Return BinOpMult UnaryOpUSub AttributeLoad NameLoad attr Call NameLoad BinOpDiv BinOpAdd NameLoad BinOpMult AttributeLoad NameLoad attr NameLoad Call NameLoad BinOpAdd BinOpPow NameLoad Num BinOpPow NameLoad Num decorator_list NameLoad FunctionDef arguments args NameParam NameParam NameParam defaults body Return BinOpMult UnaryOpUSub AttributeLoad NameLoad attr Call NameLoad BinOpDiv BinOpAdd NameLoad BinOpMult AttributeLoad NameLoad attr NameLoad Call NameLoad BinOpAdd BinOpPow NameLoad Num BinOpPow NameLoad Num decorator_list FunctionDef arguments args NameParam NameParam NameParam defaults body Return BinOpMult Num Call NameLoad BinOpDiv NameLoad BinOpAdd Call NameLoad BinOpAdd BinOpPow NameLoad Num BinOpPow NameLoad Num NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam defaults body ImportFrom alias If BoolOpAnd AttributeLoad NameLoad attr AttributeLoad NameLoad attr body Return Call NameLoad BinOpAdd NameLoad BinOpMult NameLoad AttributeLoad NameLoad attr Assign NameStore AttributeLoad NameLoad attr Assign NameStore BinOpAdd NameLoad BinOpMult NameLoad NameLoad Assign NameStore BinOpAdd BinOpPow NameLoad Num BinOpPow NameLoad Num Return BinOpSub Call NameLoad BinOpDiv NameLoad Call NameLoad NameLoad BinOpMult NameLoad Call NameLoad BinOpDiv Call NameLoad NameLoad Call NameLoad Call NameLoad NameLoad decorator_list FunctionDef arguments args NameParam defaults body Return BoolOpAnd AttributeLoad SubscriptLoad AttributeLoad NameLoad attr Index Num attr AttributeLoad SubscriptLoad AttributeLoad NameLoad attr Index Num attr decorator_list FunctionDef arguments args NameParam defaults body Return Call AttributeLoad NameLoad attr Call AttributeLoad SubscriptLoad AttributeLoad NameLoad attr Index Num attr Call AttributeLoad SubscriptLoad AttributeLoad NameLoad attr Index Num attr decorator_list FunctionDef arguments args NameParam NameParam defaults body Assign TupleStore NameStore NameStore AttributeLoad NameLoad attr If CompareEq NameLoad Num body Return BinOpDiv NameLoad BinOpAdd BinOpPow NameLoad Num BinOpPow NameLoad Num orelse If CompareEq NameLoad Num body Return BinOpDiv UnaryOpUSub NameLoad BinOpAdd BinOpPow NameLoad Num BinOpPow NameLoad Num orelse Raise Call NameLoad NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body Assign TupleStore NameStore NameStore AttributeLoad NameLoad attr If BoolOpAnd AttributeLoad NameLoad attr AttributeLoad NameLoad attr body Expr Call AttributeLoad Call NameLoad NameLoad NameLoad attr NameLoad decorator_list decorator_list
N/A __future__ print_function division sympy.core.add Add sympy.core.basic sympify cacheit sympy.core.function Function ArgumentIndexError sympy.core.numbers igcdex Rational sympy.core.singleton S sympy.core.symbol Symbol sympy.core.logic fuzzy_not sympy.functions.combinatorial.factorials factorial RisingFactorial sympy.functions.elementary.miscellaneous sqrt Min Max sympy.functions.elementary.exponential log exp sympy.functions.elementary.integers floor sympy.functions.elementary.hyperbolic acoth asinh atanh cosh coth HyperbolicFunction sinh tanh sympy.sets.sets FiniteSet sympy.utilities.iterables numbered_symbols sympy.core.compatibility range TrigonometricFunction N/A Function N/A N/A Base class for trigonometric functions.  N/A unbranched True _eval_is_rational N/A N/A self N/A N/A N/A s N/A N/A self func N/A self args N/A N/A N/A s func N/A self func N/A N/A N/A N/A N/A N/A s args N/A 0 is_rational N/A fuzzy_not N/A N/A N/A s args N/A 0 is_zero N/A N/A False N/A N/A N/A s is_rational N/A _eval_is_algebraic N/A N/A self N/A N/A N/A s N/A N/A self func N/A self args N/A N/A N/A s func N/A self func N/A N/A N/A N/A fuzzy_not N/A N/A N/A self args N/A 0 is_zero N/A N/A N/A self args N/A 0 is_algebraic N/A N/A False N/A pi_coeff N/A _pi_coeff N/A N/A self args N/A 0 N/A N/A N/A pi_coeff None N/A pi_coeff is_rational N/A N/A True N/A N/A N/A s is_algebraic N/A _eval_expand_complex N/A N/A self deep N/A True hints N/A N/A N/A re_part im_part N/A N/A self as_real_imag deep deep hints N/A N/A re_part N/A im_part N/A S ImaginaryUnit N/A _as_real_imag N/A N/A self deep N/A True hints N/A N/A N/A N/A N/A self args N/A 0 is_real N/A N/A deep N/A N/A N/A hints N/A complex False N/A N/A N/A N/A N/A N/A self args N/A 0 expand deep hints N/A S Zero N/A N/A N/A N/A N/A self args N/A 0 N/A S Zero N/A deep N/A N/A N/A re im N/A N/A N/A N/A N/A N/A self args N/A 0 expand deep hints as_real_imag N/A N/A N/A re im N/A N/A N/A N/A self args N/A 0 as_real_imag N/A N/A re im N/A N/A _peeloff_pi N/A N/A arg N/A N/A N/A 
    Split ARG into two parts, a "rest" and a multiple of pi/2.
    This assumes ARG to be an Add.
    The multiple of pi returned in the second position is always a Rational.

    Examples
    ========

    >>> from sympy.functions.elementary.trigonometric import _peeloff_pi as peel
    >>> from sympy import pi
    >>> from sympy.abc import x, y
    >>> peel(x + pi/2)
    (x, pi/2)
    >>> peel(x + 2*pi/3 + pi*y)
    (x + pi*y + pi/6, pi/2)
     N/A a N/A N/A Add make_args arg N/A N/A N/A a N/A S Pi N/A N/A K N/A S One N/A N/A N/A N/A a is_Mul N/A N/A N/A K p N/A N/A a as_two_terms N/A N/A N/A p N/A S Pi N/A K is_Rational N/A N/A N/A N/A N/A arg N/A S Zero N/A m1 N/A N/A K N/A S Half N/A S Pi N/A m2 N/A N/A K N/A S Pi m1 N/A N/A N/A arg m2 m2 N/A _pi_coeff N/A N/A arg cycles N/A 1 N/A N/A 
    When arg is a Number times pi (e.g. 3*pi/2) then return the Number
    normalized to be in the range [0, 2], else None.

    When an even multiple of pi is encountered, if it is multiplying
    something with known parity then the multiple is returned as 0 otherwise
    as 2.

    Examples
    ========

    >>> from sympy.functions.elementary.trigonometric import _pi_coeff as coeff
    >>> from sympy import pi, Dummy
    >>> from sympy.abc import x, y
    >>> coeff(3*x*pi)
    3*x
    >>> coeff(11*pi/7)
    11/7
    >>> coeff(-11*pi/7)
    3/7
    >>> coeff(4*pi)
    0
    >>> coeff(5*pi)
    1
    >>> coeff(5.0*pi)
    1
    >>> coeff(5.5*pi)
    3/2
    >>> coeff(2 + pi)

    >>> coeff(2*Dummy(integer=True)*pi)
    2
    >>> coeff(2*Dummy(even=True)*pi)
    0
     N/A arg N/A sympify arg N/A N/A arg N/A S Pi N/A N/A N/A S One N/A N/A N/A arg N/A N/A N/A S Zero N/A N/A N/A arg is_Mul N/A N/A cx N/A N/A arg coeff N/A S Pi N/A cx N/A N/A N/A c x N/A N/A cx as_coeff_Mul N/A N/A c is_Float N/A N/A f N/A N/A abs c 1 N/A N/A f 0 N/A N/A p N/A N/A int N/A round N/A N/A N/A log f 2 evalf N/A m N/A 2 p N/A cm N/A c m N/A i N/A int cm N/A N/A i cm N/A N/A c N/A Rational i m N/A cx N/A c x N/A N/A c N/A Rational N/A int c N/A cx N/A c x N/A N/A x is_integer N/A N/A c2 N/A c 2 N/A N/A c2 1 N/A N/A x N/A N/A N/A c2 N/A N/A N/A N/A x is_even None N/A N/A N/A S Zero N/A N/A S 2 N/A N/A N/A c2 x N/A cx N/A sin N/A TrigonometricFunction N/A N/A 
    The sine function.

    Returns the sine of x (measured in radians).

    Notes
    =====

    This function will evaluate automatically in the
    case x/pi is some rational number [4]_.  For example,
    if x is a multiple of pi, pi/2, pi/3, pi/4 and pi/6.

    Examples
    ========

    >>> from sympy import sin, pi
    >>> from sympy.abc import x
    >>> sin(x**2).diff(x)
    2*x*cos(x**2)
    >>> sin(1).diff(x)
    0
    >>> sin(pi)
    0
    >>> sin(pi/2)
    1
    >>> sin(pi/6)
    1/2
    >>> sin(pi/12)
    -sqrt(2)/4 + sqrt(6)/4


    See Also
    ========

    csc, cos, sec, tan, cot
    asin, acsc, acos, asec, atan, acot, atan2

    References
    ==========

    .. [1] http://en.wikipedia.org/wiki/Trigonometric_functions
    .. [2] http://dlmf.nist.gov/4.14
    .. [3] http://functions.wolfram.com/ElementaryFunctions/Sin
    .. [4] http://mathworld.wolfram.com/TrigonometryAngles.html
     fdiff N/A N/A self argindex N/A 1 N/A N/A N/A argindex 1 N/A N/A N/A cos N/A N/A self args N/A 0 N/A N/A N/A ArgumentIndexError self argindex N/A eval N/A N/A cls arg N/A N/A sympy.calculus AccumBounds N/A N/A arg is_Number N/A N/A N/A arg N/A S NaN N/A N/A N/A S NaN N/A N/A N/A arg N/A S Zero N/A N/A N/A S Zero N/A N/A N/A N/A arg N/A S Infinity N/A arg N/A S NegativeInfinity N/A N/A N/A AccumBounds -1 1 N/A N/A isinstance arg AccumBounds N/A N/A N/A min max N/A N/A arg min N/A arg max N/A d N/A floor N/A min N/A 2 N/A S Pi N/A N/A min N/A S NegativeInfinity N/A N/A min N/A min N/A N/A d 2 N/A S Pi N/A N/A max N/A S Infinity N/A N/A max N/A max N/A N/A d 2 N/A S Pi N/A N/A N/A N/A N/A N/A AccumBounds min max intersection N/A FiniteSet N/A N/A S Pi 2 N/A N/A 5 N/A S Pi 2 N/A S EmptySet N/A N/A N/A N/A AccumBounds min max intersection N/A FiniteSet N/A N/A 3 N/A S Pi 2 N/A N/A 7 N/A S Pi 2 N/A S EmptySet N/A N/A N/A AccumBounds -1 1 N/A N/A N/A N/A N/A N/A AccumBounds min max intersection N/A FiniteSet N/A N/A S Pi 2 N/A N/A 5 N/A S Pi 2 N/A S EmptySet N/A N/A N/A AccumBounds N/A Min N/A sin min N/A sin max 1 N/A N/A N/A N/A N/A N/A AccumBounds min max intersection N/A FiniteSet N/A N/A 3 N/A S Pi 2 N/A N/A 8 N/A S Pi 2 N/A S EmptySet N/A N/A N/A AccumBounds -1 N/A Max N/A sin min N/A sin max N/A N/A N/A AccumBounds N/A Min N/A sin min N/A sin max N/A Max N/A sin min N/A sin max N/A N/A N/A arg could_extract_minus_sign N/A N/A N/A N/A cls N/A arg N/A i_coeff N/A N/A arg as_coefficient N/A S ImaginaryUnit N/A N/A i_coeff None N/A N/A N/A N/A S ImaginaryUnit N/A sinh i_coeff N/A pi_coeff N/A _pi_coeff arg N/A N/A pi_coeff None N/A N/A N/A pi_coeff is_integer N/A N/A N/A S Zero N/A N/A N/A 2 pi_coeff is_integer N/A N/A N/A pi_coeff is_even N/A N/A N/A S Zero N/A N/A N/A N/A pi_coeff is_even False N/A N/A N/A N/A S NegativeOne N/A pi_coeff N/A S Half N/A N/A N/A pi_coeff is_Rational N/A N/A narg N/A pi_coeff N/A S Pi N/A N/A narg arg N/A N/A N/A cls narg N/A None N/A N/A pi_coeff is_Rational N/A N/A x N/A pi_coeff 2 N/A N/A x 1 N/A N/A N/A N/A cls N/A N/A x 1 N/A S Pi N/A N/A N/A 2 x 1 N/A N/A N/A cls N/A N/A 1 x N/A S Pi N/A narg N/A N/A N/A pi_coeff N/A Rational 3 2 2 N/A S Pi N/A result N/A cos narg N/A N/A N/A isinstance result cos N/A N/A result N/A N/A N/A pi_coeff N/A S Pi arg N/A N/A N/A cls N/A pi_coeff N/A S Pi N/A None N/A N/A arg is_Add N/A N/A N/A x m N/A _peeloff_pi arg N/A m N/A N/A N/A N/A N/A sin m N/A cos x N/A N/A cos m N/A sin x N/A N/A N/A arg func asin N/A N/A N/A N/A arg args N/A 0 N/A N/A N/A arg func atan N/A N/A x N/A N/A arg args N/A 0 N/A N/A x N/A sqrt N/A 1 N/A x 2 N/A N/A N/A arg func atan2 N/A N/A N/A y x N/A arg args N/A N/A y N/A sqrt N/A N/A x 2 N/A y 2 N/A N/A N/A arg func acos N/A N/A x N/A N/A arg args N/A 0 N/A N/A sqrt N/A 1 N/A x 2 N/A N/A N/A arg func acot N/A N/A x N/A N/A arg args N/A 0 N/A N/A 1 N/A N/A sqrt N/A 1 N/A 1 N/A x 2 x N/A classmethod taylor_term N/A N/A n x N/A previous_terms N/A N/A N/A N/A n 0 N/A N/A n 2 0 N/A N/A N/A S Zero N/A N/A x N/A sympify x N/A N/A N/A len previous_terms 2 N/A N/A p N/A previous_terms N/A -2 N/A N/A N/A N/A p N/A x 2 N/A n N/A n 1 N/A N/A N/A N/A N/A -1 N/A n 2 N/A x n N/A factorial n N/A staticmethod cacheit _eval_rewrite_as_exp N/A N/A self arg N/A N/A N/A I N/A S ImaginaryUnit N/A N/A N/A isinstance arg TrigonometricFunction N/A isinstance arg HyperbolicFunction N/A N/A arg N/A N/A N/A N/A arg func N/A N/A arg args N/A 0 rewrite exp N/A N/A N/A N/A exp N/A arg I N/A exp N/A N/A arg I N/A 2 I N/A _eval_rewrite_as_Pow N/A N/A self arg N/A N/A N/A N/A N/A arg func log N/A N/A I N/A S ImaginaryUnit N/A x N/A N/A arg args N/A 0 N/A N/A N/A N/A I N/A x N/A I 2 N/A N/A I N/A x I 2 N/A _eval_rewrite_as_cos N/A N/A self arg N/A N/A N/A N/A N/A cos N/A arg N/A N/A S Pi 2 N/A _eval_rewrite_as_tan N/A N/A self arg N/A N/A N/A tan_half N/A tan N/A N/A S Half arg N/A N/A N/A 2 tan_half N/A 1 N/A tan_half 2 N/A _eval_rewrite_as_sincos N/A N/A self arg N/A N/A N/A N/A N/A N/A sin arg N/A cos arg N/A cos arg N/A _eval_rewrite_as_cot N/A N/A self arg N/A N/A N/A cot_half N/A cot N/A N/A S Half arg N/A N/A N/A 2 cot_half N/A 1 N/A cot_half 2 N/A _eval_rewrite_as_pow N/A N/A self arg N/A N/A N/A N/A N/A N/A N/A self rewrite cos rewrite pow N/A _eval_rewrite_as_sqrt N/A N/A self arg N/A N/A N/A N/A N/A N/A N/A self rewrite cos rewrite sqrt N/A _eval_rewrite_as_csc N/A N/A self arg N/A N/A N/A N/A 1 N/A csc arg N/A _eval_conjugate N/A N/A self N/A N/A N/A N/A N/A self func N/A N/A N/A N/A self args N/A 0 conjugate N/A as_real_imag N/A N/A self deep N/A True hints N/A N/A N/A re im N/A N/A self _as_real_imag deep deep hints N/A N/A N/A N/A sin re N/A cosh im N/A N/A cos re N/A sinh im N/A _eval_expand_trig N/A N/A self N/A hints N/A sympy expand_mul sympy.functions.special.polynomials chebyshevt chebyshevu N/A arg N/A N/A self args N/A 0 N/A x None N/A N/A arg is_Add N/A N/A N/A x y N/A N/A arg as_two_terms N/A sx N/A N/A N/A sin x evaluate False _eval_expand_trig N/A sy N/A N/A N/A sin y evaluate False _eval_expand_trig N/A cx N/A N/A N/A cos x evaluate False _eval_expand_trig N/A cy N/A N/A N/A cos y evaluate False _eval_expand_trig N/A N/A N/A sx cy N/A sy cx N/A N/A N/A n x N/A N/A arg as_coeff_Mul rational True N/A N/A n is_Integer N/A N/A N/A n is_odd N/A N/A N/A N/A -1 N/A N/A n 1 2 N/A chebyshevt n N/A sin x N/A N/A N/A expand_mul N/A N/A N/A -1 N/A N/A n 2 1 N/A cos x N/A chebyshevu N/A n 1 N/A sin x deep False N/A pi_coeff N/A _pi_coeff arg N/A N/A pi_coeff None N/A N/A N/A pi_coeff is_Rational N/A N/A N/A N/A self rewrite sqrt N/A N/A sin arg N/A _eval_as_leading_term N/A N/A self x N/A N/A sympy Order N/A arg N/A N/A N/A N/A self args N/A 0 as_leading_term x N/A N/A N/A x N/A arg free_symbols N/A N/A N/A Order 1 x contains arg N/A N/A arg N/A N/A N/A N/A self func arg N/A _eval_is_real N/A N/A self N/A N/A N/A N/A N/A N/A self args N/A 0 is_real N/A _eval_is_finite N/A N/A self N/A N/A N/A arg N/A N/A self args N/A 0 N/A N/A arg is_real N/A N/A True N/A N/A cos N/A TrigonometricFunction N/A N/A 
    The cosine function.

    Returns the cosine of x (measured in radians).

    Notes
    =====

    See :func:`sin` for notes about automatic evaluation.

    Examples
    ========

    >>> from sympy import cos, pi
    >>> from sympy.abc import x
    >>> cos(x**2).diff(x)
    -2*x*sin(x**2)
    >>> cos(1).diff(x)
    0
    >>> cos(pi)
    -1
    >>> cos(pi/2)
    0
    >>> cos(2*pi/3)
    -1/2
    >>> cos(pi/12)
    sqrt(2)/4 + sqrt(6)/4

    See Also
    ========

    sin, csc, sec, tan, cot
    asin, acsc, acos, asec, atan, acot, atan2

    References
    ==========

    .. [1] http://en.wikipedia.org/wiki/Trigonometric_functions
    .. [2] http://dlmf.nist.gov/4.14
    .. [3] http://functions.wolfram.com/ElementaryFunctions/Cos
     fdiff N/A N/A self argindex N/A 1 N/A N/A N/A argindex 1 N/A N/A N/A N/A sin N/A N/A self args N/A 0 N/A N/A N/A ArgumentIndexError self argindex N/A eval N/A N/A cls arg N/A N/A sympy.functions.special.polynomials chebyshevt sympy.calculus.util AccumBounds N/A N/A arg is_Number N/A N/A N/A arg N/A S NaN N/A N/A N/A S NaN N/A N/A N/A arg N/A S Zero N/A N/A N/A S One N/A N/A N/A N/A arg N/A S Infinity N/A arg N/A S NegativeInfinity N/A N/A N/A AccumBounds -1 1 N/A N/A isinstance arg AccumBounds N/A N/A N/A sin N/A arg N/A N/A S Pi 2 N/A N/A N/A arg could_extract_minus_sign N/A N/A N/A cls N/A arg N/A i_coeff N/A N/A arg as_coefficient N/A S ImaginaryUnit N/A N/A i_coeff None N/A N/A N/A cosh i_coeff N/A pi_coeff N/A _pi_coeff arg N/A N/A pi_coeff None N/A N/A N/A pi_coeff is_integer N/A N/A N/A N/A S NegativeOne pi_coeff N/A N/A N/A 2 pi_coeff is_integer N/A N/A N/A pi_coeff is_even N/A N/A N/A N/A S NegativeOne N/A pi_coeff 2 N/A N/A N/A N/A pi_coeff is_even False N/A N/A N/A S Zero N/A N/A N/A pi_coeff is_Rational N/A N/A narg N/A pi_coeff N/A S Pi N/A N/A narg arg N/A N/A N/A cls narg N/A None N/A cst_table_some N/A 3 5 N/A S Half N/A N/A N/A sqrt 5 1 4 N/A N/A pi_coeff is_Rational N/A N/A q N/A pi_coeff q N/A p N/A N/A pi_coeff p N/A 2 q N/A N/A p q N/A N/A narg N/A N/A pi_coeff 1 N/A S Pi N/A N/A N/A cls narg N/A N/A N/A 2 p q N/A N/A narg N/A N/A 1 pi_coeff N/A S Pi N/A N/A N/A cls narg N/A table2 N/A 12 20 30 15 24 40 60 120 N/A 3 4 N/A 4 5 N/A 5 6 N/A 6 10 N/A 6 8 N/A 8 10 N/A 20 30 N/A 40 60 N/A N/A q table2 N/A N/A N/A a b N/A N/A N/A p N/A S Pi N/A N/A table2 N/A q N/A 0 N/A N/A p N/A S Pi N/A N/A table2 N/A q N/A 1 N/A N/A nvala nvalb N/A N/A cls a N/A cls b N/A N/A N/A None nvala N/A None nvalb N/A N/A None N/A N/A N/A nvala nvalb N/A N/A cls N/A N/A N/A S Pi 2 a N/A cls N/A N/A N/A S Pi 2 b N/A N/A q 12 N/A N/A None N/A N/A q cst_table_some N/A N/A cts N/A cst_table_some N/A N/A pi_coeff q N/A N/A N/A N/A chebyshevt N/A pi_coeff p cts expand N/A N/A 0 N/A q 2 N/A N/A narg N/A N/A pi_coeff 2 N/A S Pi N/A nval N/A cls narg N/A N/A None nval N/A N/A None N/A x N/A N/A N/A 2 pi_coeff 1 2 N/A sign_cos N/A -1 N/A N/A N/A x 0 -1 1 N/A int N/A abs x N/A N/A sign_cos N/A sqrt N/A N/A 1 nval 2 N/A None N/A N/A arg is_Add N/A N/A N/A x m N/A _peeloff_pi arg N/A m N/A N/A N/A N/A N/A cos m N/A cos x N/A N/A sin m N/A sin x N/A N/A N/A arg func acos N/A N/A N/A N/A arg args N/A 0 N/A N/A N/A arg func atan N/A N/A x N/A N/A arg args N/A 0 N/A N/A 1 N/A sqrt N/A 1 N/A x 2 N/A N/A N/A arg func atan2 N/A N/A N/A y x N/A arg args N/A N/A x N/A sqrt N/A N/A x 2 N/A y 2 N/A N/A N/A arg func asin N/A N/A x N/A N/A arg args N/A 0 N/A N/A sqrt N/A 1 N/A x 2 N/A N/A N/A arg func acot N/A N/A x N/A N/A arg args N/A 0 N/A N/A 1 N/A sqrt N/A 1 N/A 1 N/A x 2 N/A classmethod taylor_term N/A N/A n x N/A previous_terms N/A N/A N/A N/A n 0 N/A N/A n 2 1 N/A N/A N/A S Zero N/A N/A x N/A sympify x N/A N/A N/A len previous_terms 2 N/A N/A p N/A previous_terms N/A -2 N/A N/A N/A N/A p N/A x 2 N/A n N/A n 1 N/A N/A N/A N/A N/A -1 N/A n 2 N/A x n N/A factorial n N/A staticmethod cacheit _eval_rewrite_as_exp N/A N/A self arg N/A N/A N/A I N/A S ImaginaryUnit N/A N/A N/A isinstance arg TrigonometricFunction N/A isinstance arg HyperbolicFunction N/A N/A arg N/A N/A N/A N/A arg func N/A N/A arg args N/A 0 rewrite exp N/A N/A N/A N/A exp N/A arg I N/A exp N/A N/A arg I 2 N/A _eval_rewrite_as_Pow N/A N/A self arg N/A N/A N/A N/A N/A arg func log N/A N/A I N/A S ImaginaryUnit N/A x N/A N/A arg args N/A 0 N/A N/A N/A N/A x I 2 N/A N/A x N/A I 2 N/A _eval_rewrite_as_sin N/A N/A self arg N/A N/A N/A N/A sin N/A arg N/A N/A S Pi 2 N/A _eval_rewrite_as_tan N/A N/A self arg N/A N/A N/A tan_half N/A N/A tan N/A N/A S Half arg 2 N/A N/A N/A 1 tan_half N/A 1 tan_half N/A _eval_rewrite_as_sincos N/A N/A self arg N/A N/A N/A N/A N/A N/A sin arg N/A cos arg N/A sin arg N/A _eval_rewrite_as_cot N/A N/A self arg N/A N/A N/A cot_half N/A N/A cot N/A N/A S Half arg 2 N/A N/A N/A cot_half 1 N/A cot_half 1 N/A _eval_rewrite_as_pow N/A N/A self arg N/A N/A N/A N/A N/A self _eval_rewrite_as_sqrt arg N/A _eval_rewrite_as_sqrt N/A N/A self arg N/A N/A sympy.functions.special.polynomials chebyshevt migcdex N/A N/A x N/A N/A N/A N/A N/A len x 1 N/A N/A N/A 1 N/A x N/A 0 N/A N/A N/A len x 2 N/A N/A N/A igcdex N/A x N/A 0 N/A x N/A -1 N/A g N/A migcdex N/A x N/A 1 N/A N/A u v h N/A igcdex N/A x N/A 0 N/A g N/A -1 N/A N/A tuple N/A N/A N/A u N/A N/A v i N/A i N/A g N/A 0 -1 N/A h N/A ipartfrac N/A N/A r factors N/A None N/A sympy.ntheory factorint N/A N/A isinstance r int N/A N/A r N/A N/A N/A isinstance r Rational N/A N/A N/A TypeError r is not rational N/A n N/A r q N/A N/A 2 N/A N/A r q N/A r q N/A N/A N/A r q N/A N/A None factors N/A N/A a N/A N/A n N/A x y N/A N/A x y N/A N/A N/A factorint N/A r q items N/A N/A a N/A N/A n x N/A x factors N/A N/A N/A len a 1 N/A N/A N/A r N/A h N/A migcdex a N/A ans N/A N/A N/A r p N/A Rational N/A i j N/A r q N/A N/A i j N/A zip N/A h N/A -1 a N/A N/A r N/A sum ans N/A ans N/A N/A pi_coeff N/A _pi_coeff arg N/A N/A pi_coeff None N/A N/A None N/A N/A pi_coeff is_integer N/A N/A N/A N/A self func N/A pi_coeff N/A S Pi N/A N/A N/A pi_coeff is_Rational N/A N/A None _cospi257 N/A N/A N/A N/A N/A  Express cos(pi/257) explicitly as a function of radicals
                Based upon the equations in
                http://math.stackexchange.com/questions/516142/how-does-cos2-pi-257-look-like-in-real-radicals
                See also http://www.susqu.edu/brakke/constructions/257-gon.m.txt
             f1 N/A N/A a b N/A N/A N/A N/A N/A N/A a N/A sqrt N/A N/A a 2 b 2 N/A N/A a N/A sqrt N/A N/A a 2 b 2 N/A f2 N/A N/A a b N/A N/A N/A N/A N/A a N/A sqrt N/A N/A a 2 b 2 N/A N/A N/A t1 t2 N/A f1 -1 256 N/A N/A z1 z3 N/A f1 t1 64 N/A N/A z2 z4 N/A f1 t2 64 N/A N/A y1 y5 N/A f1 z1 N/A 4 N/A N/A 5 t1 N/A 2 z1 N/A N/A y6 y2 N/A f1 z2 N/A 4 N/A N/A 5 t2 N/A 2 z2 N/A N/A y3 y7 N/A f1 z3 N/A 4 N/A N/A 5 t1 N/A 2 z3 N/A N/A y8 y4 N/A f1 z4 N/A 4 N/A N/A 5 t2 N/A 2 z4 N/A N/A x1 x9 N/A f1 y1 N/A -4 N/A N/A N/A t1 y1 y3 N/A 2 y6 N/A N/A x2 x10 N/A f1 y2 N/A -4 N/A N/A N/A t2 y2 y4 N/A 2 y7 N/A N/A x3 x11 N/A f1 y3 N/A -4 N/A N/A N/A t1 y3 y5 N/A 2 y8 N/A N/A x4 x12 N/A f1 y4 N/A -4 N/A N/A N/A t2 y4 y6 N/A 2 y1 N/A N/A x5 x13 N/A f1 y5 N/A -4 N/A N/A N/A t1 y5 y7 N/A 2 y2 N/A N/A x6 x14 N/A f1 y6 N/A -4 N/A N/A N/A t2 y6 y8 N/A 2 y3 N/A N/A x15 x7 N/A f1 y7 N/A -4 N/A N/A N/A t1 y7 y1 N/A 2 y4 N/A N/A x8 x16 N/A f1 y8 N/A -4 N/A N/A N/A t2 y8 y2 N/A 2 y5 N/A v1 N/A f2 x1 N/A -4 N/A N/A N/A x1 x2 x3 x6 N/A v2 N/A f2 x2 N/A -4 N/A N/A N/A x2 x3 x4 x7 N/A v3 N/A f2 x8 N/A -4 N/A N/A N/A x8 x9 x10 x13 N/A v4 N/A f2 x9 N/A -4 N/A N/A N/A x9 x10 x11 x14 N/A v5 N/A f2 x10 N/A -4 N/A N/A N/A x10 x11 x12 x15 N/A v6 N/A f2 x16 N/A -4 N/A N/A N/A x16 x1 x2 x5 N/A u1 N/A N/A f2 N/A v1 N/A -4 N/A v2 v3 N/A u2 N/A N/A f2 N/A v4 N/A -4 N/A v5 v6 N/A w1 N/A -2 N/A f2 N/A u1 N/A -4 u2 N/A N/A sqrt N/A N/A N/A N/A sqrt 2 N/A sqrt N/A w1 4 8 N/A S Half N/A N/A cst_table_some N/A 3 5 17 257 N/A S Half N/A N/A N/A sqrt 5 1 4 N/A sqrt N/A N/A N/A 15 N/A sqrt 17 32 N/A N/A N/A sqrt 2 N/A N/A sqrt N/A 17 N/A sqrt 17 N/A sqrt N/A N/A N/A N/A sqrt 2 N/A N/A -8 N/A sqrt N/A 17 N/A sqrt 17 N/A N/A 1 N/A sqrt 17 N/A sqrt N/A 17 N/A sqrt 17 N/A 6 N/A sqrt 17 34 32 N/A _cospi257 _fermatCoords N/A N/A n N/A N/A sympy chebyshevt N/A primes N/A N/A p_i cst_table_some N/A N/A N/A n r N/A divmod n p_i N/A N/A r N/A N/A N/A N/A primes append p_i N/A N/A n 1 N/A N/A N/A tuple primes N/A False N/A N/A N/A N/A pi_coeff q cst_table_some N/A N/A rv N/A chebyshevt N/A pi_coeff p N/A cst_table_some N/A N/A pi_coeff q N/A N/A N/A pi_coeff q 257 N/A N/A rv N/A N/A rv expand N/A rv N/A N/A N/A N/A pi_coeff q 2 N/A N/A pico2 N/A pi_coeff 2 N/A nval N/A N/A N/A cos N/A pico2 N/A S Pi rewrite sqrt N/A x N/A N/A pico2 1 2 N/A sign_cos N/A N/A N/A int x 2 -1 1 N/A N/A sign_cos N/A sqrt N/A N/A 1 nval 2 N/A FC N/A _fermatCoords N/A pi_coeff q N/A FC N/A N/A decomp N/A ipartfrac pi_coeff FC N/A X N/A N/A N/A x N/A 1 N/A N/A x N/A 0 N/A S Pi N/A x N/A zip decomp N/A numbered_symbols z N/A pcls N/A N/A N/A N/A N/A cos N/A sum N/A N/A x N/A 0 N/A x X _eval_expand_trig subs X N/A N/A N/A pcls rewrite sqrt N/A N/A decomp N/A ipartfrac pi_coeff N/A X N/A N/A N/A x N/A 1 N/A N/A x N/A 0 N/A S Pi N/A x N/A zip decomp N/A numbered_symbols z N/A pcls N/A N/A N/A N/A N/A cos N/A sum N/A N/A x N/A 0 N/A x X _eval_expand_trig subs X N/A pcls N/A _eval_rewrite_as_sec N/A N/A self arg N/A N/A N/A N/A 1 N/A sec arg N/A _eval_conjugate N/A N/A self N/A N/A N/A N/A N/A self func N/A N/A N/A N/A self args N/A 0 conjugate N/A as_real_imag N/A N/A self deep N/A True hints N/A N/A N/A re im N/A N/A self _as_real_imag deep deep hints N/A N/A N/A N/A cos re N/A cosh im N/A N/A N/A sin re N/A sinh im N/A _eval_expand_trig N/A N/A self N/A hints N/A sympy.functions.special.polynomials chebyshevt N/A arg N/A N/A self args N/A 0 N/A x None N/A N/A arg is_Add N/A N/A N/A x y N/A N/A arg as_two_terms N/A sx N/A N/A N/A sin x evaluate False _eval_expand_trig N/A sy N/A N/A N/A sin y evaluate False _eval_expand_trig N/A cx N/A N/A N/A cos x evaluate False _eval_expand_trig N/A cy N/A N/A N/A cos y evaluate False _eval_expand_trig N/A N/A N/A cx cy N/A sx sy N/A N/A N/A coeff terms N/A N/A arg as_coeff_Mul rational True N/A N/A coeff is_Integer N/A N/A N/A chebyshevt coeff N/A cos terms N/A pi_coeff N/A _pi_coeff arg N/A N/A pi_coeff None N/A N/A N/A pi_coeff is_Rational N/A N/A N/A N/A self rewrite sqrt N/A N/A cos arg N/A _eval_as_leading_term N/A N/A self x N/A N/A sympy Order N/A arg N/A N/A N/A N/A self args N/A 0 as_leading_term x N/A N/A N/A x N/A arg free_symbols N/A N/A N/A Order 1 x contains arg N/A N/A N/A S One N/A N/A N/A N/A self func arg N/A _eval_is_real N/A N/A self N/A N/A N/A N/A N/A N/A self args N/A 0 is_real N/A _eval_is_finite N/A N/A self N/A N/A N/A arg N/A N/A self args N/A 0 N/A N/A arg is_real N/A N/A True N/A N/A tan N/A TrigonometricFunction N/A N/A 
    The tangent function.

    Returns the tangent of x (measured in radians).

    Notes
    =====

    See :func:`sin` for notes about automatic evaluation.

    Examples
    ========

    >>> from sympy import tan, pi
    >>> from sympy.abc import x
    >>> tan(x**2).diff(x)
    2*x*(tan(x**2)**2 + 1)
    >>> tan(1).diff(x)
    0
    >>> tan(pi/8).expand()
    -1 + sqrt(2)

    See Also
    ========

    sin, csc, cos, sec, cot
    asin, acsc, acos, asec, atan, acot, atan2

    References
    ==========

    .. [1] http://en.wikipedia.org/wiki/Trigonometric_functions
    .. [2] http://dlmf.nist.gov/4.14
    .. [3] http://functions.wolfram.com/ElementaryFunctions/Tan
     fdiff N/A N/A self argindex N/A 1 N/A N/A N/A argindex 1 N/A N/A N/A N/A S One N/A self 2 N/A N/A N/A ArgumentIndexError self argindex N/A inverse N/A N/A self argindex N/A 1 N/A N/A 
        Returns the inverse of this function.
         N/A atan N/A eval N/A N/A cls arg N/A N/A sympy.calculus.util AccumBounds N/A N/A arg is_Number N/A N/A N/A arg N/A S NaN N/A N/A N/A S NaN N/A N/A N/A arg N/A S Zero N/A N/A N/A S Zero N/A N/A N/A N/A arg N/A S Infinity N/A arg N/A S NegativeInfinity N/A N/A N/A AccumBounds N/A S NegativeInfinity N/A S Infinity N/A N/A isinstance arg AccumBounds N/A N/A N/A min max N/A N/A arg min N/A arg max N/A d N/A floor N/A min N/A S Pi N/A N/A min N/A S NegativeInfinity N/A N/A min N/A min N/A d N/A S Pi N/A N/A max N/A S Infinity N/A N/A max N/A max N/A d N/A S Pi N/A N/A N/A N/A AccumBounds min max intersection N/A FiniteSet N/A N/A S Pi 2 N/A N/A 3 N/A S Pi 2 N/A N/A N/A AccumBounds N/A S NegativeInfinity N/A S Infinity N/A N/A N/A AccumBounds N/A tan min N/A tan max N/A N/A N/A arg could_extract_minus_sign N/A N/A N/A N/A cls N/A arg N/A i_coeff N/A N/A arg as_coefficient N/A S ImaginaryUnit N/A N/A i_coeff None N/A N/A N/A N/A S ImaginaryUnit N/A tanh i_coeff N/A pi_coeff N/A _pi_coeff arg 2 N/A N/A pi_coeff None N/A N/A N/A pi_coeff is_integer N/A N/A N/A S Zero N/A N/A N/A pi_coeff is_Rational N/A N/A narg N/A pi_coeff N/A S Pi N/A N/A narg arg N/A N/A N/A cls narg N/A None N/A N/A pi_coeff is_Rational N/A N/A N/A N/A N/A pi_coeff q 2 N/A N/A narg N/A N/A pi_coeff N/A S Pi 2 N/A N/A cresult sresult N/A N/A cos narg N/A cos N/A narg N/A N/A S Pi 2 N/A N/A N/A N/A isinstance cresult cos N/A N/A isinstance sresult cos N/A N/A N/A sresult 0 N/A N/A N/A S ComplexInfinity N/A N/A N/A 1 cresult sresult N/A table2 N/A 12 20 30 15 24 40 60 120 N/A 3 4 N/A 4 5 N/A 5 6 N/A 6 10 N/A 6 8 N/A 8 10 N/A 20 30 N/A 40 60 N/A q N/A pi_coeff q N/A p N/A N/A pi_coeff p q N/A N/A q table2 N/A N/A N/A nvala nvalb N/A N/A cls N/A N/A p N/A S Pi N/A N/A table2 N/A q N/A 0 N/A cls N/A N/A p N/A S Pi N/A N/A table2 N/A q N/A 1 N/A N/A N/A None nvala N/A None nvalb N/A N/A None N/A N/A N/A nvala nvalb N/A 1 N/A nvala nvalb N/A narg N/A N/A N/A N/A pi_coeff N/A S Half 1 N/A S Half N/A S Pi N/A N/A cresult sresult N/A N/A cos narg N/A cos N/A narg N/A N/A S Pi 2 N/A N/A N/A N/A isinstance cresult cos N/A N/A isinstance sresult cos N/A N/A N/A cresult 0 N/A N/A N/A S ComplexInfinity N/A N/A sresult cresult N/A N/A narg arg N/A N/A N/A cls narg N/A N/A arg is_Add N/A N/A N/A x m N/A _peeloff_pi arg N/A m N/A N/A tanm N/A tan m N/A tanx N/A tan x N/A N/A tanm N/A S ComplexInfinity N/A N/A N/A N/A cot x N/A N/A N/A tanm tanx N/A 1 N/A tanm tanx N/A N/A N/A arg func atan N/A N/A N/A N/A arg args N/A 0 N/A N/A N/A arg func atan2 N/A N/A N/A y x N/A arg args N/A N/A y x N/A N/A N/A arg func asin N/A N/A x N/A N/A arg args N/A 0 N/A N/A x N/A sqrt N/A 1 N/A x 2 N/A N/A N/A arg func acos N/A N/A x N/A N/A arg args N/A 0 N/A N/A N/A sqrt N/A 1 N/A x 2 x N/A N/A N/A arg func acot N/A N/A x N/A N/A arg args N/A 0 N/A N/A 1 x N/A classmethod taylor_term N/A N/A n x N/A previous_terms N/A sympy bernoulli N/A N/A N/A n 0 N/A N/A n 2 0 N/A N/A N/A S Zero N/A N/A x N/A sympify x N/A N/A a b N/A N/A N/A n 1 2 N/A 2 N/A n 1 N/A B N/A bernoulli N/A n 1 N/A F N/A factorial N/A n 1 N/A N/A N/A N/A N/A N/A N/A -1 a b N/A b 1 B F N/A x n N/A staticmethod cacheit _eval_nseries N/A N/A self x n logx N/A N/A N/A i N/A N/A N/A N/A N/A N/A self args N/A 0 limit x 0 2 N/A S Pi N/A N/A i N/A i is_Integer N/A N/A N/A N/A N/A N/A self rewrite cos _eval_nseries x n n logx logx N/A N/A N/A Function _eval_nseries self x n n logx logx N/A _eval_rewrite_as_Pow N/A N/A self arg N/A N/A N/A N/A N/A arg func log N/A N/A I N/A S ImaginaryUnit N/A x N/A N/A arg args N/A 0 N/A N/A N/A I N/A N/A x N/A I N/A x I N/A N/A x N/A I N/A x I N/A _eval_conjugate N/A N/A self N/A N/A N/A N/A N/A self func N/A N/A N/A N/A self args N/A 0 conjugate N/A as_real_imag N/A N/A self deep N/A True hints N/A N/A N/A re im N/A N/A self _as_real_imag deep deep hints N/A im N/A N/A denom N/A N/A cos N/A 2 re N/A cosh N/A 2 im N/A N/A N/A N/A sin N/A 2 re denom N/A N/A sinh N/A 2 im denom N/A N/A N/A N/A N/A self func re N/A S Zero N/A _eval_expand_trig N/A N/A self N/A hints N/A sympy im re N/A arg N/A N/A self args N/A 0 N/A x None N/A N/A arg is_Add N/A sympy symmetric_poly N/A n N/A len N/A arg args N/A TX N/A N/A x N/A arg args N/A N/A tx N/A N/A N/A tan x evaluate False _eval_expand_trig N/A N/A N/A TX append tx N/A Yg N/A numbered_symbols Y N/A Y N/A N/A next Yg N/A i N/A range n N/A p N/A 0 0 N/A i N/A range N/A n 1 N/A N/A N/A p N/A N/A 1 N/A i 2 N/A N/A symmetric_poly i Y N/A -1 N/A N/A i 4 2 N/A N/A N/A N/A N/A p N/A 0 N/A p N/A 1 subs N/A list N/A zip Y TX N/A N/A N/A coeff terms N/A N/A arg as_coeff_Mul rational True N/A N/A N/A coeff is_Integer N/A coeff 1 N/A N/A I N/A S ImaginaryUnit N/A z N/A Symbol dummy real True N/A P N/A N/A N/A N/A 1 N/A I z coeff expand N/A N/A N/A N/A N/A im P N/A re P subs N/A N/A z N/A tan terms N/A N/A tan arg N/A _eval_rewrite_as_exp N/A N/A self arg N/A N/A N/A I N/A S ImaginaryUnit N/A N/A N/A isinstance arg TrigonometricFunction N/A isinstance arg HyperbolicFunction N/A N/A arg N/A N/A N/A N/A arg func N/A N/A arg args N/A 0 rewrite exp N/A N/A neg_exp pos_exp N/A N/A exp N/A N/A arg I N/A exp N/A arg I N/A N/A N/A I N/A neg_exp pos_exp N/A neg_exp pos_exp N/A _eval_rewrite_as_sin N/A N/A self x N/A N/A N/A N/A N/A 2 N/A N/A sin x 2 N/A sin N/A 2 x N/A _eval_rewrite_as_cos N/A N/A self x N/A N/A N/A N/A N/A N/A cos N/A x N/A N/A S Pi 2 N/A cos x N/A _eval_rewrite_as_sincos N/A N/A self arg N/A N/A N/A N/A N/A sin arg N/A cos arg N/A _eval_rewrite_as_cot N/A N/A self arg N/A N/A N/A N/A 1 N/A cot arg N/A _eval_rewrite_as_pow N/A N/A self arg N/A N/A N/A y N/A N/A N/A N/A self rewrite cos rewrite pow N/A N/A N/A y has cos N/A N/A None N/A y N/A _eval_rewrite_as_sqrt N/A N/A self arg N/A N/A N/A y N/A N/A N/A N/A self rewrite cos rewrite sqrt N/A N/A N/A y has cos N/A N/A None N/A y N/A _eval_as_leading_term N/A N/A self x N/A N/A sympy Order N/A arg N/A N/A N/A N/A self args N/A 0 as_leading_term x N/A N/A N/A x N/A arg free_symbols N/A N/A N/A Order 1 x contains arg N/A N/A arg N/A N/A N/A N/A self func arg N/A _eval_is_real N/A N/A self N/A N/A N/A N/A N/A N/A self args N/A 0 is_real N/A _eval_is_finite N/A N/A self N/A N/A N/A arg N/A N/A self args N/A 0 N/A N/A arg is_imaginary N/A N/A True N/A N/A cot N/A TrigonometricFunction N/A N/A 
    The cotangent function.

    Returns the cotangent of x (measured in radians).

    Notes
    =====

    See :func:`sin` for notes about automatic evaluation.

    Examples
    ========

    >>> from sympy import cot, pi
    >>> from sympy.abc import x
    >>> cot(x**2).diff(x)
    2*x*(-cot(x**2)**2 - 1)
    >>> cot(1).diff(x)
    0
    >>> cot(pi/12)
    sqrt(3) + 2

    See Also
    ========

    sin, csc, cos, sec, tan
    asin, acsc, acos, asec, atan, acot, atan2

    References
    ==========

    .. [1] http://en.wikipedia.org/wiki/Trigonometric_functions
    .. [2] http://dlmf.nist.gov/4.14
    .. [3] http://functions.wolfram.com/ElementaryFunctions/Cot
     fdiff N/A N/A self argindex N/A 1 N/A N/A N/A argindex 1 N/A N/A N/A N/A S NegativeOne N/A self 2 N/A N/A N/A ArgumentIndexError self argindex N/A inverse N/A N/A self argindex N/A 1 N/A N/A 
        Returns the inverse of this function.
         N/A acot N/A eval N/A N/A cls arg N/A N/A sympy.calculus.util AccumBounds N/A N/A arg is_Number N/A N/A N/A arg N/A S NaN N/A N/A N/A S NaN N/A N/A arg N/A S Zero N/A N/A N/A S ComplexInfinity N/A N/A isinstance arg AccumBounds N/A N/A N/A N/A tan N/A arg N/A N/A S Pi 2 N/A N/A N/A arg could_extract_minus_sign N/A N/A N/A N/A cls N/A arg N/A i_coeff N/A N/A arg as_coefficient N/A S ImaginaryUnit N/A N/A i_coeff None N/A N/A N/A N/A N/A S ImaginaryUnit N/A coth i_coeff N/A pi_coeff N/A _pi_coeff arg 2 N/A N/A pi_coeff None N/A N/A N/A pi_coeff is_integer N/A N/A N/A S ComplexInfinity N/A N/A N/A pi_coeff is_Rational N/A N/A narg N/A pi_coeff N/A S Pi N/A N/A narg arg N/A N/A N/A cls narg N/A None N/A N/A pi_coeff is_Rational N/A N/A N/A N/A N/A pi_coeff q 2 N/A N/A N/A pi_coeff q 2 N/A N/A narg N/A N/A pi_coeff N/A S Pi 2 N/A N/A cresult sresult N/A N/A cos narg N/A cos N/A narg N/A N/A S Pi 2 N/A N/A N/A N/A isinstance cresult cos N/A N/A isinstance sresult cos N/A N/A N/A N/A 1 cresult sresult N/A table2 N/A 12 20 30 15 24 40 60 120 N/A 3 4 N/A 4 5 N/A 5 6 N/A 6 10 N/A 6 8 N/A 8 10 N/A 20 30 N/A 40 60 N/A q N/A pi_coeff q N/A p N/A N/A pi_coeff p q N/A N/A q table2 N/A N/A N/A nvala nvalb N/A N/A cls N/A N/A p N/A S Pi N/A N/A table2 N/A q N/A 0 N/A cls N/A N/A p N/A S Pi N/A N/A table2 N/A q N/A 1 N/A N/A N/A None nvala N/A None nvalb N/A N/A None N/A N/A N/A 1 N/A nvala nvalb N/A nvalb nvala N/A narg N/A N/A N/A N/A pi_coeff N/A S Half 1 N/A S Half N/A S Pi N/A N/A cresult sresult N/A N/A cos narg N/A cos N/A narg N/A N/A S Pi 2 N/A N/A N/A N/A isinstance cresult cos N/A N/A isinstance sresult cos N/A N/A N/A sresult 0 N/A N/A N/A S ComplexInfinity N/A N/A cresult sresult N/A N/A narg arg N/A N/A N/A cls narg N/A N/A arg is_Add N/A N/A N/A x m N/A _peeloff_pi arg N/A m N/A N/A cotm N/A cot m N/A N/A cotm 0 N/A N/A N/A N/A tan x N/A cotx N/A cot x N/A N/A cotm N/A S ComplexInfinity N/A N/A cotx N/A N/A cotm is_Rational N/A N/A N/A N/A N/A cotm cotx 1 N/A cotm cotx N/A None N/A N/A N/A arg func acot N/A N/A N/A N/A arg args N/A 0 N/A N/A N/A arg func atan N/A N/A x N/A N/A arg args N/A 0 N/A N/A 1 x N/A N/A N/A arg func atan2 N/A N/A N/A y x N/A arg args N/A N/A x y N/A N/A N/A arg func asin N/A N/A x N/A N/A arg args N/A 0 N/A N/A N/A sqrt N/A 1 N/A x 2 x N/A N/A N/A arg func acos N/A N/A x N/A N/A arg args N/A 0 N/A N/A x N/A sqrt N/A 1 N/A x 2 N/A classmethod taylor_term N/A N/A n x N/A previous_terms N/A sympy bernoulli N/A N/A n 0 N/A N/A N/A 1 N/A sympify x N/A N/A N/A N/A n 0 N/A N/A n 2 0 N/A N/A N/A S Zero N/A N/A x N/A sympify x N/A B N/A bernoulli N/A n 1 N/A F N/A factorial N/A n 1 N/A N/A N/A N/A N/A N/A -1 N/A N/A n 1 2 N/A 2 N/A n 1 B F N/A x n N/A staticmethod cacheit _eval_nseries N/A N/A self x n logx N/A N/A N/A i N/A N/A N/A N/A N/A self args N/A 0 limit x 0 N/A S Pi N/A N/A i N/A i is_Integer N/A N/A N/A N/A N/A N/A self rewrite cos _eval_nseries x n n logx logx N/A N/A N/A N/A N/A self rewrite tan _eval_nseries x n n logx logx N/A _eval_conjugate N/A N/A self N/A N/A N/A N/A N/A self func N/A N/A N/A N/A self args N/A 0 conjugate N/A as_real_imag N/A N/A self deep N/A True hints N/A N/A N/A re im N/A N/A self _as_real_imag deep deep hints N/A im N/A N/A denom N/A N/A cos N/A 2 re N/A cosh N/A 2 im N/A N/A N/A N/A N/A sin N/A 2 re denom N/A N/A N/A sinh N/A 2 im denom N/A N/A N/A N/A N/A self func re N/A S Zero N/A _eval_rewrite_as_exp N/A N/A self arg N/A N/A N/A I N/A S ImaginaryUnit N/A N/A N/A isinstance arg TrigonometricFunction N/A isinstance arg HyperbolicFunction N/A N/A arg N/A N/A N/A N/A arg func N/A N/A arg args N/A 0 rewrite exp N/A N/A neg_exp pos_exp N/A N/A exp N/A N/A arg I N/A exp N/A arg I N/A N/A N/A I N/A pos_exp neg_exp N/A pos_exp neg_exp N/A _eval_rewrite_as_Pow N/A N/A self arg N/A N/A N/A N/A N/A arg func log N/A N/A I N/A S ImaginaryUnit N/A x N/A N/A arg args N/A 0 N/A N/A N/A N/A I N/A N/A x N/A I N/A x I N/A N/A x N/A I N/A x I N/A _eval_rewrite_as_sin N/A N/A self x N/A N/A N/A N/A N/A 2 N/A sin N/A 2 x N/A N/A sin x 2 N/A _eval_rewrite_as_cos N/A N/A self x N/A N/A N/A N/A N/A N/A cos x N/A cos N/A x N/A N/A S Pi 2 N/A _eval_rewrite_as_sincos N/A N/A self arg N/A N/A N/A N/A N/A cos arg N/A sin arg N/A _eval_rewrite_as_tan N/A N/A self arg N/A N/A N/A N/A 1 N/A tan arg N/A _eval_rewrite_as_pow N/A N/A self arg N/A N/A N/A y N/A N/A N/A N/A self rewrite cos rewrite pow N/A N/A N/A y has cos N/A N/A None N/A y N/A _eval_rewrite_as_sqrt N/A N/A self arg N/A N/A N/A y N/A N/A N/A N/A self rewrite cos rewrite sqrt N/A N/A N/A y has cos N/A N/A None N/A y N/A _eval_as_leading_term N/A N/A self x N/A N/A sympy Order N/A arg N/A N/A N/A N/A self args N/A 0 as_leading_term x N/A N/A N/A x N/A arg free_symbols N/A N/A N/A Order 1 x contains arg N/A N/A N/A 1 arg N/A N/A N/A N/A self func arg N/A _eval_is_real N/A N/A self N/A N/A N/A N/A N/A N/A self args N/A 0 is_real N/A _eval_expand_trig N/A N/A self N/A hints N/A sympy im re N/A arg N/A N/A self args N/A 0 N/A x None N/A N/A arg is_Add N/A sympy symmetric_poly N/A n N/A len N/A arg args N/A CX N/A N/A x N/A arg args N/A N/A cx N/A N/A N/A cot x evaluate False _eval_expand_trig N/A N/A N/A CX append cx N/A Yg N/A numbered_symbols Y N/A Y N/A N/A next Yg N/A i N/A range n N/A p N/A 0 0 N/A i N/A range n -1 -1 N/A N/A N/A p N/A N/A N/A n i 2 N/A N/A symmetric_poly i Y N/A -1 N/A N/A N/A n i 4 2 N/A N/A N/A N/A N/A p N/A 0 N/A p N/A 1 subs N/A list N/A zip Y CX N/A N/A N/A coeff terms N/A N/A arg as_coeff_Mul rational True N/A N/A N/A coeff is_Integer N/A coeff 1 N/A N/A I N/A S ImaginaryUnit N/A z N/A Symbol dummy real True N/A P N/A N/A N/A N/A z I coeff expand N/A N/A N/A N/A N/A re P N/A im P subs N/A N/A z N/A cot terms N/A N/A cot arg N/A _eval_is_finite N/A N/A self N/A N/A N/A arg N/A N/A self args N/A 0 N/A N/A arg is_imaginary N/A N/A True N/A _eval_subs N/A N/A self old new N/A N/A N/A N/A self old N/A N/A new N/A arg N/A N/A self args N/A 0 N/A argnew N/A N/A arg subs old new N/A N/A N/A arg argnew N/A N/A argnew N/A S Pi is_integer N/A N/A N/A S ComplexInfinity N/A N/A cot argnew N/A N/A ReciprocalTrigonometricFunction N/A TrigonometricFunction N/A N/A Base class for reciprocal functions of trigonometric functions.  N/A _reciprocal_of None N/A _is_even None N/A _is_odd None eval N/A N/A cls arg N/A N/A N/A N/A N/A arg could_extract_minus_sign N/A N/A N/A cls _is_even N/A N/A N/A cls N/A arg N/A N/A cls _is_odd N/A N/A N/A N/A cls N/A arg N/A pi_coeff N/A _pi_coeff arg N/A N/A N/A pi_coeff None N/A N/A N/A 2 pi_coeff is_integer N/A pi_coeff is_Rational N/A N/A q N/A pi_coeff q N/A p N/A N/A pi_coeff p N/A 2 q N/A N/A p q N/A N/A narg N/A N/A pi_coeff 1 N/A S Pi N/A N/A N/A cls narg N/A N/A N/A 2 p q N/A N/A narg N/A N/A 1 pi_coeff N/A S Pi N/A N/A cls _is_odd N/A N/A N/A cls narg N/A N/A N/A cls _is_even N/A N/A N/A N/A cls narg N/A t N/A N/A N/A cls _reciprocal_of eval arg N/A N/A N/A hasattr arg inverse N/A N/A N/A arg inverse cls N/A N/A N/A N/A arg args N/A 0 N/A N/A N/A t None N/A 1 t t N/A classmethod _call_reciprocal N/A N/A self method_name N/A args kwargs N/A N/A o N/A N/A self _reciprocal_of N/A N/A self args N/A 0 N/A N/A N/A getattr o method_name args kwargs N/A _calculate_reciprocal N/A N/A self method_name N/A args kwargs N/A N/A t N/A N/A self _call_reciprocal method_name args kwargs N/A N/A N/A t None N/A 1 t t N/A _rewrite_reciprocal N/A N/A self method_name arg N/A N/A N/A t N/A N/A self _call_reciprocal method_name arg N/A N/A N/A t None N/A t N/A N/A self _reciprocal_of arg N/A N/A N/A 1 t N/A fdiff N/A N/A self argindex N/A 1 N/A N/A N/A N/A N/A N/A self _calculate_reciprocal fdiff argindex N/A self 2 N/A _eval_rewrite_as_exp N/A N/A self arg N/A N/A N/A N/A N/A self _rewrite_reciprocal _eval_rewrite_as_exp arg N/A _eval_rewrite_as_Pow N/A N/A self arg N/A N/A N/A N/A N/A self _rewrite_reciprocal _eval_rewrite_as_Pow arg N/A _eval_rewrite_as_sin N/A N/A self arg N/A N/A N/A N/A N/A self _rewrite_reciprocal _eval_rewrite_as_sin arg N/A _eval_rewrite_as_cos N/A N/A self arg N/A N/A N/A N/A N/A self _rewrite_reciprocal _eval_rewrite_as_cos arg N/A _eval_rewrite_as_tan N/A N/A self arg N/A N/A N/A N/A N/A self _rewrite_reciprocal _eval_rewrite_as_tan arg N/A _eval_rewrite_as_pow N/A N/A self arg N/A N/A N/A N/A N/A self _rewrite_reciprocal _eval_rewrite_as_pow arg N/A _eval_rewrite_as_sqrt N/A N/A self arg N/A N/A N/A N/A N/A self _rewrite_reciprocal _eval_rewrite_as_sqrt arg N/A _eval_conjugate N/A N/A self N/A N/A N/A N/A N/A self func N/A N/A N/A N/A self args N/A 0 conjugate N/A as_real_imag N/A N/A self deep N/A True hints N/A N/A N/A N/A N/A 1 N/A N/A self _reciprocal_of N/A N/A self args N/A 0 as_real_imag deep hints N/A _eval_expand_trig N/A N/A self N/A hints N/A N/A N/A N/A self _calculate_reciprocal _eval_expand_trig hints N/A _eval_is_real N/A N/A self N/A N/A N/A N/A N/A N/A N/A self _reciprocal_of N/A N/A self args N/A 0 _eval_is_real N/A _eval_as_leading_term N/A N/A self x N/A N/A N/A N/A N/A N/A 1 N/A N/A self _reciprocal_of N/A N/A self args N/A 0 _eval_as_leading_term x N/A _eval_is_finite N/A N/A self N/A N/A N/A N/A N/A 1 N/A N/A self _reciprocal_of N/A N/A self args N/A 0 is_finite N/A _eval_nseries N/A N/A self x n logx N/A N/A N/A N/A N/A N/A 1 N/A N/A self _reciprocal_of N/A N/A self args N/A 0 _eval_nseries x n logx N/A N/A sec N/A ReciprocalTrigonometricFunction N/A N/A 
    The secant function.

    Returns the secant of x (measured in radians).

    Notes
    =====

    See :func:`sin` for notes about automatic evaluation.

    Examples
    ========

    >>> from sympy import sec
    >>> from sympy.abc import x
    >>> sec(x**2).diff(x)
    2*x*tan(x**2)*sec(x**2)
    >>> sec(1).diff(x)
    0

    See Also
    ========

    sin, csc, cos, tan, cot
    asin, acsc, acos, asec, atan, acot, atan2

    References
    ==========

    .. [1] http://en.wikipedia.org/wiki/Trigonometric_functions
    .. [2] http://dlmf.nist.gov/4.14
    .. [3] http://functions.wolfram.com/ElementaryFunctions/Sec
     N/A _reciprocal_of cos N/A _is_even True _eval_rewrite_as_cot N/A N/A self arg N/A N/A N/A cot_half_sq N/A N/A cot N/A arg 2 2 N/A N/A N/A cot_half_sq 1 N/A cot_half_sq 1 N/A _eval_rewrite_as_cos N/A N/A self arg N/A N/A N/A N/A 1 N/A cos arg N/A _eval_rewrite_as_sincos N/A N/A self arg N/A N/A N/A N/A N/A sin arg N/A N/A cos arg N/A sin arg N/A fdiff N/A N/A self argindex N/A 1 N/A N/A N/A argindex 1 N/A N/A N/A N/A tan N/A N/A self args N/A 0 N/A sec N/A N/A self args N/A 0 N/A N/A N/A ArgumentIndexError self argindex N/A taylor_term N/A N/A n x N/A previous_terms N/A sympy.functions.combinatorial.numbers euler N/A N/A N/A n 0 N/A N/A n 2 1 N/A N/A N/A S Zero N/A N/A x N/A sympify x N/A k N/A n 2 N/A N/A N/A N/A N/A -1 k N/A euler N/A 2 k N/A factorial N/A 2 k N/A x N/A 2 k N/A staticmethod cacheit N/A csc N/A ReciprocalTrigonometricFunction N/A N/A 
    The cosecant function.

    Returns the cosecant of x (measured in radians).

    Notes
    =====

    See :func:`sin` for notes about automatic evaluation.

    Examples
    ========

    >>> from sympy import csc
    >>> from sympy.abc import x
    >>> csc(x**2).diff(x)
    -2*x*cot(x**2)*csc(x**2)
    >>> csc(1).diff(x)
    0

    See Also
    ========

    sin, cos, sec, tan, cot
    asin, acsc, acos, asec, atan, acot, atan2

    References
    ==========

    .. [1] http://en.wikipedia.org/wiki/Trigonometric_functions
    .. [2] http://dlmf.nist.gov/4.14
    .. [3] http://functions.wolfram.com/ElementaryFunctions/Csc
     N/A _reciprocal_of sin N/A _is_odd True _eval_rewrite_as_sin N/A N/A self arg N/A N/A N/A N/A 1 N/A sin arg N/A _eval_rewrite_as_sincos N/A N/A self arg N/A N/A N/A N/A N/A cos arg N/A N/A sin arg N/A cos arg N/A _eval_rewrite_as_cot N/A N/A self arg N/A N/A N/A cot_half N/A cot N/A arg 2 N/A N/A N/A 1 N/A cot_half 2 N/A 2 cot_half N/A fdiff N/A N/A self argindex N/A 1 N/A N/A N/A argindex 1 N/A N/A N/A N/A N/A cot N/A N/A self args N/A 0 N/A csc N/A N/A self args N/A 0 N/A N/A N/A ArgumentIndexError self argindex N/A taylor_term N/A N/A n x N/A previous_terms N/A sympy bernoulli N/A N/A n 0 N/A N/A N/A 1 N/A sympify x N/A N/A N/A N/A n 0 N/A N/A n 2 0 N/A N/A N/A S Zero N/A N/A x N/A sympify x N/A k N/A N/A n 2 1 N/A N/A N/A N/A N/A N/A N/A -1 N/A k 1 2 N/A N/A 2 N/A N/A 2 k 1 1 N/A bernoulli N/A 2 k N/A x N/A N/A 2 k 1 N/A factorial N/A 2 k N/A staticmethod cacheit N/A sinc N/A TrigonometricFunction N/A N/A Represents unnormalized sinc function

    Examples
    ========

    >>> from sympy import sinc, oo, jn, Product, Symbol
    >>> from sympy.abc import x
    >>> sinc(x)
    sinc(x)

    * Automated Evaluation

    >>> sinc(0)
    1
    >>> sinc(oo)
    0

    * Differentiation

    >>> sinc(x).diff()
    (x*cos(x) - sin(x))/x**2

    * Series Expansion

    >>> sinc(x).series()
    1 - x**2/6 + x**4/120 + O(x**6)

    * As zero'th order spherical Bessel Function

    >>> sinc(x).rewrite(jn)
    jn(0, x)

    References
    ==========

    .. [1] http://en.wikipedia.org/wiki/Sinc_function

     fdiff N/A N/A self argindex N/A 1 N/A N/A x N/A N/A self args N/A 0 N/A N/A argindex 1 N/A N/A N/A N/A N/A x N/A cos x N/A sin x N/A x 2 N/A N/A N/A ArgumentIndexError self argindex N/A eval N/A N/A cls arg N/A N/A N/A N/A arg is_zero N/A N/A N/A S One N/A N/A arg is_Number N/A N/A N/A arg N/A N/A S Infinity N/A N/A S Infinity N/A N/A N/A S Zero N/A N/A N/A arg N/A S NaN N/A N/A N/A S NaN N/A N/A arg N/A S ComplexInfinity N/A N/A N/A S NaN N/A N/A N/A arg could_extract_minus_sign N/A N/A N/A cls N/A arg N/A pi_coeff N/A _pi_coeff arg N/A N/A pi_coeff None N/A N/A N/A pi_coeff is_integer N/A N/A N/A fuzzy_not N/A arg is_zero N/A N/A N/A S Zero N/A N/A N/A N/A 2 pi_coeff is_integer N/A N/A N/A N/A N/A S NegativeOne N/A pi_coeff N/A S Half arg N/A classmethod _eval_nseries N/A N/A self x n logx N/A N/A N/A x N/A N/A self args N/A 0 N/A N/A N/A N/A N/A sin x x _eval_nseries x n logx N/A _eval_rewrite_as_jn N/A N/A self arg N/A N/A sympy.functions.special.bessel jn N/A N/A jn 0 arg N/A _eval_rewrite_as_sin N/A N/A self arg N/A N/A N/A N/A N/A sin arg arg N/A N/A InverseTrigonometricFunction N/A Function N/A N/A Base class for inverse trigonometric functions. N/A N/A asin N/A InverseTrigonometricFunction N/A N/A 
    The inverse sine function.

    Returns the arcsine of x in radians.

    Notes
    =====

    asin(x) will evaluate automatically in the cases oo, -oo, 0, 1,
    -1 and for some instances when the result is a rational multiple
    of pi (see the eval class method).

    Examples
    ========

    >>> from sympy import asin, oo, pi
    >>> asin(1)
    pi/2
    >>> asin(-1)
    -pi/2

    See Also
    ========

    sin, csc, cos, sec, tan, cot
    acsc, acos, asec, atan, acot, atan2

    References
    ==========

    .. [1] http://en.wikipedia.org/wiki/Inverse_trigonometric_functions
    .. [2] http://dlmf.nist.gov/4.23
    .. [3] http://functions.wolfram.com/ElementaryFunctions/ArcSin
     fdiff N/A N/A self argindex N/A 1 N/A N/A N/A argindex 1 N/A N/A N/A 1 N/A sqrt N/A 1 N/A N/A N/A self args N/A 0 2 N/A N/A N/A ArgumentIndexError self argindex N/A _eval_is_rational N/A N/A self N/A N/A N/A s N/A N/A self func N/A self args N/A N/A N/A s func N/A self func N/A N/A N/A N/A N/A s args N/A 0 is_rational N/A N/A False N/A N/A N/A s is_rational N/A _eval_is_positive N/A N/A self N/A N/A N/A N/A N/A N/A self args N/A 0 is_positive N/A N/A N/A N/A N/A N/A self args N/A 0 1 is_negative N/A N/A N/A N/A self args N/A 0 is_negative N/A N/A N/A N/A N/A N/A N/A self args N/A 0 1 is_positive N/A eval N/A N/A cls arg N/A N/A N/A N/A arg is_Number N/A N/A N/A arg N/A S NaN N/A N/A N/A S NaN N/A N/A N/A arg N/A S Infinity N/A N/A N/A N/A S NegativeInfinity N/A S ImaginaryUnit N/A N/A N/A arg N/A S NegativeInfinity N/A N/A N/A N/A S Infinity N/A S ImaginaryUnit N/A N/A N/A arg N/A S Zero N/A N/A N/A S Zero N/A N/A N/A arg N/A S One N/A N/A N/A N/A S Pi 2 N/A N/A N/A arg N/A S NegativeOne N/A N/A N/A N/A N/A S Pi 2 N/A N/A N/A arg could_extract_minus_sign N/A N/A N/A N/A cls N/A arg N/A N/A arg is_number N/A N/A cst_table N/A N/A N/A sqrt 3 2 N/A N/A N/A sqrt 3 2 N/A N/A sqrt 2 2 N/A N/A N/A sqrt 2 2 N/A 1 N/A sqrt 2 N/A -1 N/A sqrt 2 N/A sqrt N/A N/A 5 N/A sqrt 5 8 N/A N/A sqrt N/A N/A 5 N/A sqrt 5 8 N/A S Half N/A N/A S Half N/A N/A sqrt N/A 2 N/A sqrt 2 2 N/A N/A N/A sqrt N/A 2 N/A sqrt 2 2 N/A N/A N/A sqrt 5 1 4 N/A N/A 1 N/A sqrt 5 4 N/A N/A N/A sqrt 3 1 N/A sqrt N/A 2 3 N/A N/A 1 N/A sqrt 3 N/A sqrt N/A 2 3 N/A N/A N/A sqrt 5 1 4 N/A N/A N/A N/A sqrt 5 1 4 3 -3 4 -4 4 -4 5 -5 6 -6 8 -8 10 -10 12 -12 N/A N/A S 10 3 N/A N/A N/A S 10 3 N/A N/A arg cst_table N/A N/A N/A N/A S Pi N/A cst_table N/A arg N/A i_coeff N/A N/A arg as_coefficient N/A S ImaginaryUnit N/A N/A i_coeff None N/A N/A N/A N/A S ImaginaryUnit N/A asinh i_coeff N/A classmethod taylor_term N/A N/A n x N/A previous_terms N/A N/A N/A N/A n 0 N/A N/A n 2 0 N/A N/A N/A S Zero N/A N/A x N/A sympify x N/A N/A N/A N/A len previous_terms 2 N/A n 2 N/A N/A p N/A previous_terms N/A -2 N/A N/A N/A N/A p N/A N/A n 2 2 N/A n N/A n 1 N/A x 2 N/A N/A k N/A N/A n 1 2 N/A R N/A RisingFactorial N/A S Half k N/A F N/A factorial k N/A N/A N/A N/A R F N/A x n n N/A staticmethod cacheit _eval_as_leading_term N/A N/A self x N/A N/A sympy Order N/A arg N/A N/A N/A N/A self args N/A 0 as_leading_term x N/A N/A N/A x N/A arg free_symbols N/A N/A N/A Order 1 x contains arg N/A N/A arg N/A N/A N/A N/A self func arg N/A _eval_rewrite_as_acos N/A N/A self x N/A N/A N/A N/A N/A N/A S Pi 2 N/A acos x N/A _eval_rewrite_as_atan N/A N/A self x N/A N/A N/A N/A 2 N/A atan N/A x N/A 1 N/A sqrt N/A 1 N/A x 2 N/A _eval_rewrite_as_log N/A N/A self x N/A N/A N/A N/A N/A N/A S ImaginaryUnit N/A log N/A N/A N/A S ImaginaryUnit x N/A sqrt N/A 1 N/A x 2 N/A _eval_rewrite_as_acot N/A N/A self arg N/A N/A N/A N/A 2 N/A acot N/A N/A 1 N/A sqrt N/A 1 N/A arg 2 arg N/A _eval_rewrite_as_asec N/A N/A self arg N/A N/A N/A N/A N/A N/A S Pi 2 N/A asec N/A 1 arg N/A _eval_rewrite_as_acsc N/A N/A self arg N/A N/A N/A N/A acsc N/A 1 arg N/A _eval_is_real N/A N/A self N/A N/A N/A x N/A N/A self args N/A 0 N/A N/A N/A x is_real N/A N/A 1 N/A abs x is_nonnegative N/A inverse N/A N/A self argindex N/A 1 N/A N/A 
        Returns the inverse of this function.
         N/A sin N/A N/A acos N/A InverseTrigonometricFunction N/A N/A 
    The inverse cosine function.

    Returns the arc cosine of x (measured in radians).

    Notes
    =====

    ``acos(x)`` will evaluate automatically in the cases
    ``oo``, ``-oo``, ``0``, ``1``, ``-1``.

    ``acos(zoo)`` evaluates to ``zoo``
    (see note in :py:class`sympy.functions.elementary.trigonometric.asec`)

    Examples
    ========

    >>> from sympy import acos, oo, pi
    >>> acos(1)
    0
    >>> acos(0)
    pi/2
    >>> acos(oo)
    oo*I

    See Also
    ========

    sin, csc, cos, sec, tan, cot
    asin, acsc, asec, atan, acot, atan2

    References
    ==========

    .. [1] http://en.wikipedia.org/wiki/Inverse_trigonometric_functions
    .. [2] http://dlmf.nist.gov/4.23
    .. [3] http://functions.wolfram.com/ElementaryFunctions/ArcCos
     fdiff N/A N/A self argindex N/A 1 N/A N/A N/A argindex 1 N/A N/A N/A -1 N/A sqrt N/A 1 N/A N/A N/A self args N/A 0 2 N/A N/A N/A ArgumentIndexError self argindex N/A _eval_is_rational N/A N/A self N/A N/A N/A s N/A N/A self func N/A self args N/A N/A N/A s func N/A self func N/A N/A N/A N/A N/A s args N/A 0 is_rational N/A N/A False N/A N/A N/A s is_rational N/A _eval_is_positive N/A N/A self N/A N/A N/A x N/A N/A self args N/A 0 N/A N/A N/A 1 N/A abs x is_nonnegative N/A eval N/A N/A cls arg N/A N/A N/A N/A arg is_Number N/A N/A N/A arg N/A S NaN N/A N/A N/A S NaN N/A N/A N/A arg N/A S Infinity N/A N/A N/A N/A S Infinity N/A S ImaginaryUnit N/A N/A N/A arg N/A S NegativeInfinity N/A N/A N/A N/A S NegativeInfinity N/A S ImaginaryUnit N/A N/A N/A arg N/A S Zero N/A N/A N/A N/A S Pi 2 N/A N/A N/A arg N/A S One N/A N/A N/A S Zero N/A N/A N/A arg N/A S NegativeOne N/A N/A N/A S Pi N/A N/A arg N/A S ComplexInfinity N/A N/A N/A S ComplexInfinity N/A N/A arg is_number N/A N/A cst_table N/A N/A S Half N/A N/A S Half N/A N/A sqrt 2 2 N/A N/A N/A sqrt 2 2 N/A 1 N/A sqrt 2 N/A -1 N/A sqrt 2 N/A N/A sqrt 3 2 N/A N/A N/A sqrt 3 2 N/A N/A S Pi 3 N/A N/A 2 N/A S Pi 3 N/A N/A S Pi 4 N/A N/A 3 N/A S Pi 4 N/A N/A S Pi 4 N/A N/A 3 N/A S Pi 4 N/A N/A S Pi 6 N/A N/A 5 N/A S Pi 6 N/A N/A arg cst_table N/A N/A N/A cst_table N/A arg N/A classmethod taylor_term N/A N/A n x N/A previous_terms N/A N/A N/A n 0 N/A N/A N/A N/A S Pi 2 N/A N/A N/A N/A n 0 N/A N/A n 2 0 N/A N/A N/A S Zero N/A N/A x N/A sympify x N/A N/A N/A N/A len previous_terms 2 N/A n 2 N/A N/A p N/A previous_terms N/A -2 N/A N/A N/A N/A p N/A N/A n 2 2 N/A n N/A n 1 N/A x 2 N/A N/A k N/A N/A n 1 2 N/A R N/A RisingFactorial N/A S Half k N/A F N/A factorial k N/A N/A N/A N/A N/A R F N/A x n n N/A staticmethod cacheit _eval_as_leading_term N/A N/A self x N/A N/A sympy Order N/A arg N/A N/A N/A N/A self args N/A 0 as_leading_term x N/A N/A N/A x N/A arg free_symbols N/A N/A N/A Order 1 x contains arg N/A N/A arg N/A N/A N/A N/A self func arg N/A _eval_is_real N/A N/A self N/A N/A N/A x N/A N/A self args N/A 0 N/A N/A N/A x is_real N/A N/A 1 N/A abs x is_nonnegative N/A _eval_rewrite_as_log N/A N/A self x N/A N/A N/A N/A N/A N/A S Pi 2 N/A N/A S ImaginaryUnit N/A log N/A N/A N/A S ImaginaryUnit x N/A sqrt N/A 1 N/A x 2 N/A _eval_rewrite_as_asin N/A N/A self x N/A N/A N/A N/A N/A N/A S Pi 2 N/A asin x N/A _eval_rewrite_as_atan N/A N/A self x N/A N/A N/A N/A N/A atan N/A N/A sqrt N/A 1 N/A x 2 x N/A N/A N/A S Pi 2 N/A 1 N/A x N/A sqrt N/A 1 N/A x 2 N/A inverse N/A N/A self argindex N/A 1 N/A N/A 
        Returns the inverse of this function.
         N/A cos N/A _eval_rewrite_as_acot N/A N/A self arg N/A N/A N/A N/A N/A N/A S Pi 2 N/A 2 N/A acot N/A N/A 1 N/A sqrt N/A 1 N/A arg 2 arg N/A _eval_rewrite_as_asec N/A N/A self arg N/A N/A N/A N/A asec N/A 1 arg N/A _eval_rewrite_as_acsc N/A N/A self arg N/A N/A N/A N/A N/A N/A S Pi 2 N/A acsc N/A 1 arg N/A _eval_conjugate N/A N/A self N/A N/A N/A z N/A N/A self args N/A 0 N/A r N/A N/A self func N/A N/A N/A N/A self args N/A 0 conjugate N/A N/A N/A z is_real False N/A N/A r N/A N/A N/A N/A z is_real N/A N/A z 1 is_nonnegative N/A N/A z 1 is_nonpositive N/A N/A r N/A N/A atan N/A InverseTrigonometricFunction N/A N/A 
    The inverse tangent function.

    Returns the arc tangent of x (measured in radians).

    Notes
    =====

    atan(x) will evaluate automatically in the cases
    oo, -oo, 0, 1, -1.

    Examples
    ========

    >>> from sympy import atan, oo, pi
    >>> atan(0)
    0
    >>> atan(1)
    pi/4
    >>> atan(oo)
    pi/2

    See Also
    ========

    sin, csc, cos, sec, tan, cot
    asin, acsc, acos, asec, acot, atan2

    References
    ==========

    .. [1] http://en.wikipedia.org/wiki/Inverse_trigonometric_functions
    .. [2] http://dlmf.nist.gov/4.23
    .. [3] http://functions.wolfram.com/ElementaryFunctions/ArcTan
     fdiff N/A N/A self argindex N/A 1 N/A N/A N/A argindex 1 N/A N/A N/A 1 N/A 1 N/A N/A N/A self args N/A 0 2 N/A N/A N/A ArgumentIndexError self argindex N/A _eval_is_rational N/A N/A self N/A N/A N/A s N/A N/A self func N/A self args N/A N/A N/A s func N/A self func N/A N/A N/A N/A N/A s args N/A 0 is_rational N/A N/A False N/A N/A N/A s is_rational N/A _eval_is_positive N/A N/A self N/A N/A N/A N/A N/A N/A self args N/A 0 is_positive N/A _eval_is_nonnegative N/A N/A self N/A N/A N/A N/A N/A N/A self args N/A 0 is_nonnegative N/A eval N/A N/A cls arg N/A N/A N/A N/A arg is_Number N/A N/A N/A arg N/A S NaN N/A N/A N/A S NaN N/A N/A N/A arg N/A S Infinity N/A N/A N/A N/A S Pi 2 N/A N/A N/A arg N/A S NegativeInfinity N/A N/A N/A N/A N/A S Pi 2 N/A N/A N/A arg N/A S Zero N/A N/A N/A S Zero N/A N/A N/A arg N/A S One N/A N/A N/A N/A S Pi 4 N/A N/A N/A arg N/A S NegativeOne N/A N/A N/A N/A N/A S Pi 4 N/A N/A N/A arg could_extract_minus_sign N/A N/A N/A N/A cls N/A arg N/A N/A arg is_number N/A N/A cst_table N/A N/A N/A sqrt 3 3 N/A N/A N/A sqrt 3 3 N/A 1 N/A sqrt 3 N/A -1 N/A sqrt 3 N/A sqrt 3 N/A N/A sqrt 3 N/A 1 N/A sqrt 2 N/A N/A 1 N/A sqrt 2 N/A N/A sqrt 2 1 N/A 1 N/A sqrt 2 N/A sqrt N/A 5 N/A 2 N/A sqrt 5 N/A N/A sqrt N/A 5 N/A 2 N/A sqrt 5 N/A 2 N/A sqrt 3 N/A N/A 2 N/A sqrt 3 6 -6 6 -6 3 -3 N/A N/A S 8 3 N/A N/A S 8 3 8 -8 N/A N/A S 5 2 N/A N/A N/A S 5 2 12 -12 N/A N/A arg cst_table N/A N/A N/A N/A S Pi N/A cst_table N/A arg N/A i_coeff N/A N/A arg as_coefficient N/A S ImaginaryUnit N/A N/A i_coeff None N/A N/A N/A N/A S ImaginaryUnit N/A atanh i_coeff N/A classmethod taylor_term N/A N/A n x N/A previous_terms N/A N/A N/A N/A n 0 N/A N/A n 2 0 N/A N/A N/A S Zero N/A N/A x N/A sympify x N/A N/A N/A N/A -1 N/A N/A n 1 2 N/A x n n N/A staticmethod cacheit _eval_as_leading_term N/A N/A self x N/A N/A sympy Order N/A arg N/A N/A N/A N/A self args N/A 0 as_leading_term x N/A N/A N/A x N/A arg free_symbols N/A N/A N/A Order 1 x contains arg N/A N/A arg N/A N/A N/A N/A self func arg N/A _eval_is_real N/A N/A self N/A N/A N/A N/A N/A N/A self args N/A 0 is_real N/A _eval_rewrite_as_log N/A N/A self x N/A N/A N/A N/A N/A N/A S ImaginaryUnit 2 N/A log N/A N/A N/A S 1 N/A N/A S ImaginaryUnit x N/A N/A S 1 N/A N/A S ImaginaryUnit x N/A _eval_aseries N/A N/A self n args0 x logx N/A N/A N/A N/A N/A args0 N/A 0 N/A S Infinity N/A N/A N/A N/A N/A N/A N/A S Pi 2 N/A atan N/A 1 N/A N/A self args N/A 0 _eval_nseries x n logx N/A N/A N/A N/A args0 N/A 0 N/A S NegativeInfinity N/A N/A N/A N/A N/A N/A N/A N/A S Pi 2 N/A atan N/A 1 N/A N/A self args N/A 0 _eval_nseries x n logx N/A N/A N/A N/A N/A super atan self _eval_aseries n args0 x logx N/A inverse N/A N/A self argindex N/A 1 N/A N/A 
        Returns the inverse of this function.
         N/A tan N/A _eval_rewrite_as_asin N/A N/A self arg N/A N/A N/A N/A N/A N/A sqrt N/A arg 2 arg N/A N/A N/A S Pi 2 N/A asin N/A 1 N/A sqrt N/A 1 N/A arg 2 N/A _eval_rewrite_as_acos N/A N/A self arg N/A N/A N/A N/A N/A N/A sqrt N/A arg 2 arg N/A acos N/A 1 N/A sqrt N/A 1 N/A arg 2 N/A _eval_rewrite_as_acot N/A N/A self arg N/A N/A N/A N/A acot N/A 1 arg N/A _eval_rewrite_as_asec N/A N/A self arg N/A N/A N/A N/A N/A N/A sqrt N/A arg 2 arg N/A asec N/A sqrt N/A 1 N/A arg 2 N/A _eval_rewrite_as_acsc N/A N/A self arg N/A N/A N/A N/A N/A N/A sqrt N/A arg 2 arg N/A N/A N/A S Pi 2 N/A acsc N/A sqrt N/A 1 N/A arg 2 N/A N/A acot N/A InverseTrigonometricFunction N/A N/A 
    The inverse cotangent function.

    Returns the arc cotangent of x (measured in radians).

    See Also
    ========

    sin, csc, cos, sec, tan, cot
    asin, acsc, acos, asec, atan, atan2

    References
    ==========

    .. [1] http://en.wikipedia.org/wiki/Inverse_trigonometric_functions
    .. [2] http://dlmf.nist.gov/4.23
    .. [3] http://functions.wolfram.com/ElementaryFunctions/ArcCot
     fdiff N/A N/A self argindex N/A 1 N/A N/A N/A argindex 1 N/A N/A N/A -1 N/A 1 N/A N/A N/A self args N/A 0 2 N/A N/A N/A ArgumentIndexError self argindex N/A _eval_is_rational N/A N/A self N/A N/A N/A s N/A N/A self func N/A self args N/A N/A N/A s func N/A self func N/A N/A N/A N/A N/A s args N/A 0 is_rational N/A N/A False N/A N/A N/A s is_rational N/A _eval_is_positive N/A N/A self N/A N/A N/A N/A N/A N/A self args N/A 0 is_real N/A eval N/A N/A cls arg N/A N/A N/A N/A arg is_Number N/A N/A N/A arg N/A S NaN N/A N/A N/A S NaN N/A N/A N/A arg N/A S Infinity N/A N/A N/A S Zero N/A N/A N/A arg N/A S NegativeInfinity N/A N/A N/A S Zero N/A N/A N/A arg N/A S Zero N/A N/A N/A N/A S Pi 2 N/A N/A N/A arg N/A S One N/A N/A N/A N/A S Pi 4 N/A N/A N/A arg N/A S NegativeOne N/A N/A N/A N/A N/A S Pi 4 N/A N/A N/A arg could_extract_minus_sign N/A N/A N/A N/A cls N/A arg N/A N/A arg is_number N/A N/A cst_table N/A N/A N/A sqrt 3 3 N/A N/A N/A sqrt 3 3 N/A 1 N/A sqrt 3 N/A -1 N/A sqrt 3 N/A sqrt 3 N/A N/A sqrt 3 N/A 1 N/A sqrt 2 N/A N/A 1 N/A sqrt 2 N/A 1 N/A sqrt 2 N/A N/A sqrt 2 1 N/A sqrt N/A 5 N/A 2 N/A sqrt 5 N/A N/A sqrt N/A 5 N/A 2 N/A sqrt 5 N/A 2 N/A sqrt 3 N/A N/A 2 N/A sqrt 3 N/A 2 N/A sqrt 3 N/A N/A 2 N/A sqrt 3 3 -3 3 -3 6 -6 8 -8 N/A N/A N/A S 8 3 N/A N/A S 8 3 10 -10 12 -12 N/A N/A S 12 5 N/A N/A N/A S 12 5 N/A N/A arg cst_table N/A N/A N/A N/A S Pi N/A cst_table N/A arg N/A i_coeff N/A N/A arg as_coefficient N/A S ImaginaryUnit N/A N/A i_coeff None N/A N/A N/A N/A N/A S ImaginaryUnit N/A acoth i_coeff N/A classmethod taylor_term N/A N/A n x N/A previous_terms N/A N/A N/A n 0 N/A N/A N/A N/A S Pi 2 N/A N/A N/A N/A n 0 N/A N/A n 2 0 N/A N/A N/A S Zero N/A N/A x N/A sympify x N/A N/A N/A N/A -1 N/A N/A n 1 2 N/A x n n N/A staticmethod cacheit _eval_as_leading_term N/A N/A self x N/A N/A sympy Order N/A arg N/A N/A N/A N/A self args N/A 0 as_leading_term x N/A N/A N/A x N/A arg free_symbols N/A N/A N/A Order 1 x contains arg N/A N/A arg N/A N/A N/A N/A self func arg N/A _eval_is_real N/A N/A self N/A N/A N/A N/A N/A N/A self args N/A 0 is_real N/A _eval_aseries N/A N/A self n args0 x logx N/A N/A N/A N/A N/A args0 N/A 0 N/A S Infinity N/A N/A N/A N/A N/A N/A N/A S Pi 2 N/A acot N/A 1 N/A N/A self args N/A 0 _eval_nseries x n logx N/A N/A N/A N/A args0 N/A 0 N/A S NegativeInfinity N/A N/A N/A N/A N/A N/A N/A 3 N/A S Pi 2 N/A acot N/A 1 N/A N/A self args N/A 0 _eval_nseries x n logx N/A N/A N/A N/A N/A super atan self _eval_aseries n args0 x logx N/A _eval_rewrite_as_log N/A N/A self x N/A N/A N/A N/A N/A N/A S ImaginaryUnit 2 N/A log N/A N/A x N/A S ImaginaryUnit N/A x N/A S ImaginaryUnit N/A inverse N/A N/A self argindex N/A 1 N/A N/A 
        Returns the inverse of this function.
         N/A cot N/A _eval_rewrite_as_asin N/A N/A self arg N/A N/A N/A N/A N/A arg N/A sqrt N/A 1 N/A arg 2 N/A N/A N/A S Pi 2 N/A asin N/A N/A sqrt N/A N/A arg 2 N/A sqrt N/A N/A N/A arg 2 1 N/A _eval_rewrite_as_acos N/A N/A self arg N/A N/A N/A N/A N/A arg N/A sqrt N/A 1 N/A arg 2 N/A acos N/A N/A sqrt N/A N/A arg 2 N/A sqrt N/A N/A N/A arg 2 1 N/A _eval_rewrite_as_atan N/A N/A self arg N/A N/A N/A N/A atan N/A 1 arg N/A _eval_rewrite_as_asec N/A N/A self arg N/A N/A N/A N/A N/A arg N/A sqrt N/A 1 N/A arg 2 N/A asec N/A sqrt N/A N/A 1 N/A arg 2 N/A arg 2 N/A _eval_rewrite_as_acsc N/A N/A self arg N/A N/A N/A N/A N/A arg N/A sqrt N/A 1 N/A arg 2 N/A N/A N/A S Pi 2 N/A acsc N/A sqrt N/A N/A 1 N/A arg 2 N/A arg 2 N/A N/A asec N/A InverseTrigonometricFunction N/A N/A 
    The inverse secant function.

    Returns the arc secant of x (measured in radians).

    Notes
    =====

    ``asec(x)`` will evaluate automatically in the cases
    ``oo``, ``-oo``, ``0``, ``1``, ``-1``.

    ``asec(x)`` has branch cut in the interval [-1, 1]. For complex arguments,
    it can be defined [4]_ as

    .. math::
        sec^{-1}(z) = -i*(log(\sqrt{1 - z^2} + 1) / z)

    At ``x = 0``, for positive branch cut, the limit evaluates to ``zoo``. For
    negative branch cut, the limit

    .. math::
        \lim_{z 	o 0}-i*(log(-\sqrt{1 - z^2} + 1) / z)

    simplifies to :math:`-i*log(z/2 + O(z^3))` which ultimately evaluates to
    ``zoo``.

    As ``asex(x)`` = ``asec(1/x)``, a similar argument can be given for
    ``acos(x)``.

    Examples
    ========

    >>> from sympy import asec, oo, pi
    >>> asec(1)
    0
    >>> asec(-1)
    pi

    See Also
    ========

    sin, csc, cos, sec, tan, cot
    asin, acsc, acos, atan, acot, atan2

    References
    ==========

    .. [1] http://en.wikipedia.org/wiki/Inverse_trigonometric_functions
    .. [2] http://dlmf.nist.gov/4.23
    .. [3] http://functions.wolfram.com/ElementaryFunctions/ArcSec
    .. [4] http://refrence.wolfram.com/language/ref/ArcSec.html
     eval N/A N/A cls arg N/A N/A N/A N/A arg is_zero N/A N/A N/A S ComplexInfinity N/A N/A arg is_Number N/A N/A N/A arg N/A S NaN N/A N/A N/A S NaN N/A N/A N/A arg N/A S One N/A N/A N/A S Zero N/A N/A N/A arg N/A S NegativeOne N/A N/A N/A S Pi N/A N/A arg N/A N/A S Infinity N/A S NegativeInfinity N/A S ComplexInfinity N/A N/A N/A N/A S Pi 2 N/A classmethod fdiff N/A N/A self argindex N/A 1 N/A N/A N/A argindex 1 N/A N/A N/A 1 N/A N/A N/A N/A self args N/A 0 2 N/A sqrt N/A 1 N/A 1 N/A N/A N/A self args N/A 0 2 N/A N/A N/A ArgumentIndexError self argindex N/A inverse N/A N/A self argindex N/A 1 N/A N/A 
        Returns the inverse of this function.
         N/A sec N/A _eval_as_leading_term N/A N/A self x N/A N/A sympy Order N/A arg N/A N/A N/A N/A self args N/A 0 as_leading_term x N/A N/A N/A N/A Order 1 x contains arg N/A N/A N/A log arg N/A N/A N/A N/A self func arg N/A _eval_is_real N/A N/A self N/A N/A N/A x N/A N/A self args N/A 0 N/A N/A N/A x is_real False N/A N/A False N/A N/A N/A N/A x 1 is_nonnegative N/A N/A N/A x 1 is_nonnegative N/A _eval_rewrite_as_log N/A N/A self arg N/A N/A N/A N/A N/A N/A S Pi 2 N/A N/A S ImaginaryUnit N/A log N/A N/A N/A S ImaginaryUnit arg N/A sqrt N/A 1 N/A 1 N/A arg 2 N/A _eval_rewrite_as_asin N/A N/A self arg N/A N/A N/A N/A N/A N/A S Pi 2 N/A asin N/A 1 arg N/A _eval_rewrite_as_acos N/A N/A self arg N/A N/A N/A N/A acos N/A 1 arg N/A _eval_rewrite_as_atan N/A N/A self arg N/A N/A N/A N/A N/A N/A sqrt N/A arg 2 arg N/A N/A N/A N/A S Pi 2 N/A 2 N/A atan N/A arg N/A sqrt N/A N/A arg 2 1 N/A _eval_rewrite_as_acot N/A N/A self arg N/A N/A N/A N/A N/A N/A sqrt N/A arg 2 arg N/A N/A N/A N/A S Pi 2 N/A 2 N/A acot N/A arg N/A sqrt N/A N/A arg 2 1 N/A _eval_rewrite_as_acsc N/A N/A self arg N/A N/A N/A N/A N/A N/A S Pi 2 N/A acsc arg N/A N/A acsc N/A InverseTrigonometricFunction N/A N/A 
    The inverse cosecant function.

    Returns the arc cosecant of x (measured in radians).

    Notes
    =====

    acsc(x) will evaluate automatically in the cases
    oo, -oo, 0, 1, -1.

    Examples
    ========

    >>> from sympy import acsc, oo, pi
    >>> acsc(1)
    pi/2
    >>> acsc(-1)
    -pi/2

    See Also
    ========

    sin, csc, cos, sec, tan, cot
    asin, acos, asec, atan, acot, atan2

    References
    ==========

    .. [1] http://en.wikipedia.org/wiki/Inverse_trigonometric_functions
    .. [2] http://dlmf.nist.gov/4.23
    .. [3] http://functions.wolfram.com/ElementaryFunctions/ArcCsc
     eval N/A N/A cls arg N/A N/A N/A N/A arg is_Number N/A N/A N/A arg N/A S NaN N/A N/A N/A S NaN N/A N/A N/A arg N/A S One N/A N/A N/A N/A S Pi 2 N/A N/A N/A arg N/A S NegativeOne N/A N/A N/A N/A N/A S Pi 2 N/A N/A arg N/A N/A S Infinity N/A S NegativeInfinity N/A S ComplexInfinity N/A N/A N/A S Zero N/A classmethod fdiff N/A N/A self argindex N/A 1 N/A N/A N/A argindex 1 N/A N/A N/A -1 N/A N/A N/A N/A self args N/A 0 2 N/A sqrt N/A 1 N/A 1 N/A N/A N/A self args N/A 0 2 N/A N/A N/A ArgumentIndexError self argindex N/A inverse N/A N/A self argindex N/A 1 N/A N/A 
        Returns the inverse of this function.
         N/A csc N/A _eval_as_leading_term N/A N/A self x N/A N/A sympy Order N/A arg N/A N/A N/A N/A self args N/A 0 as_leading_term x N/A N/A N/A N/A Order 1 x contains arg N/A N/A N/A log arg N/A N/A N/A N/A self func arg N/A _eval_rewrite_as_log N/A N/A self arg N/A N/A N/A N/A N/A N/A S ImaginaryUnit N/A log N/A N/A N/A S ImaginaryUnit arg N/A sqrt N/A 1 N/A 1 N/A arg 2 N/A _eval_rewrite_as_asin N/A N/A self arg N/A N/A N/A N/A asin N/A 1 arg N/A _eval_rewrite_as_acos N/A N/A self arg N/A N/A N/A N/A N/A N/A S Pi 2 N/A acos N/A 1 arg N/A _eval_rewrite_as_atan N/A N/A self arg N/A N/A N/A N/A N/A N/A sqrt N/A arg 2 arg N/A N/A N/A S Pi 2 N/A atan N/A sqrt N/A N/A arg 2 1 N/A _eval_rewrite_as_acot N/A N/A self arg N/A N/A N/A N/A N/A N/A sqrt N/A arg 2 arg N/A N/A N/A S Pi 2 N/A acot N/A 1 N/A sqrt N/A N/A arg 2 1 N/A _eval_rewrite_as_asec N/A N/A self arg N/A N/A N/A N/A N/A N/A S Pi 2 N/A asec arg N/A N/A atan2 N/A InverseTrigonometricFunction N/A N/A 
    The function ``atan2(y, x)`` computes `\operatorname{atan}(y/x)` taking
    two arguments `y` and `x`.  Signs of both `y` and `x` are considered to
    determine the appropriate quadrant of `\operatorname{atan}(y/x)`.
    The range is `(-\pi, \pi]`. The complete definition reads as follows:

    .. math::

        \operatorname{atan2}(y, x) =
        \begin{cases}
          \arctan\left(\frac y x\right) & \qquad x > 0 \\
          \arctan\left(\frac y x\right) + \pi& \qquad y \ge 0 , x < 0 \\
          \arctan\left(\frac y x\right) - \pi& \qquad y < 0 , x < 0 \\
          +\frac{\pi}{2} & \qquad y > 0 , x = 0 \\
          -\frac{\pi}{2} & \qquad y < 0 , x = 0 \\
          \text{undefined} & \qquad y = 0, x = 0
        \end{cases}

    Attention: Note the role reversal of both arguments. The `y`-coordinate
    is the first argument and the `x`-coordinate the second.

    Examples
    ========

    Going counter-clock wise around the origin we find the
    following angles:

    >>> from sympy import atan2
    >>> atan2(0, 1)
    0
    >>> atan2(1, 1)
    pi/4
    >>> atan2(1, 0)
    pi/2
    >>> atan2(1, -1)
    3*pi/4
    >>> atan2(0, -1)
    pi
    >>> atan2(-1, -1)
    -3*pi/4
    >>> atan2(-1, 0)
    -pi/2
    >>> atan2(-1, 1)
    -pi/4

    which are all correct. Compare this to the results of the ordinary
    `\operatorname{atan}` function for the point `(x, y) = (-1, 1)`

    >>> from sympy import atan, S
    >>> atan(S(1) / -1)
    -pi/4
    >>> atan2(1, -1)
    3*pi/4

    where only the `\operatorname{atan2}` function reurns what we expect.
    We can differentiate the function with respect to both arguments:

    >>> from sympy import diff
    >>> from sympy.abc import x, y
    >>> diff(atan2(y, x), x)
    -y/(x**2 + y**2)

    >>> diff(atan2(y, x), y)
    x/(x**2 + y**2)

    We can express the `\operatorname{atan2}` function in terms of
    complex logarithms:

    >>> from sympy import log
    >>> atan2(y, x).rewrite(log)
    -I*log((x + I*y)/sqrt(x**2 + y**2))

    and in terms of `\operatorname(atan)`:

    >>> from sympy import atan
    >>> atan2(y, x).rewrite(atan)
    2*atan(y/(x + sqrt(x**2 + y**2)))

    but note that this form is undefined on the negative real axis.

    See Also
    ========

    sin, csc, cos, sec, tan, cot
    asin, acsc, acos, asec, atan, acot

    References
    ==========

    .. [1] http://en.wikipedia.org/wiki/Inverse_trigonometric_functions
    .. [2] http://en.wikipedia.org/wiki/Atan2
    .. [3] http://functions.wolfram.com/ElementaryFunctions/ArcTan2
     eval N/A N/A cls y x N/A N/A sympy Heaviside im re N/A N/A x N/A S NegativeInfinity N/A N/A N/A y is_zero N/A N/A N/A S Pi N/A N/A N/A N/A 2 N/A S Pi N/A Heaviside N/A re y N/A S Pi N/A N/A N/A x N/A S Infinity N/A N/A N/A S Zero N/A N/A N/A N/A x is_imaginary N/A y is_imaginary N/A x is_number N/A y is_number N/A N/A x N/A im x N/A y N/A im y N/A N/A N/A x is_real N/A y is_real N/A N/A N/A x is_positive N/A N/A N/A atan N/A y x N/A N/A N/A x is_negative N/A N/A N/A y is_negative N/A N/A N/A N/A atan N/A y x N/A S Pi N/A N/A N/A y is_nonnegative N/A N/A N/A N/A atan N/A y x N/A S Pi N/A N/A N/A x is_zero N/A N/A N/A y is_positive N/A N/A N/A N/A S Pi 2 N/A N/A N/A y is_negative N/A N/A N/A N/A N/A S Pi 2 N/A N/A N/A y is_zero N/A N/A N/A S NaN N/A N/A N/A y is_zero N/A x is_real N/A fuzzy_not N/A x is_zero N/A N/A N/A N/A S Pi N/A N/A S One N/A Heaviside x N/A N/A N/A x is_number N/A y is_number N/A N/A N/A N/A N/A S ImaginaryUnit N/A log N/A N/A x N/A N/A S ImaginaryUnit y N/A sqrt N/A N/A x 2 N/A y 2 N/A classmethod _eval_rewrite_as_log N/A N/A self y x N/A N/A N/A N/A N/A N/A S ImaginaryUnit N/A log N/A N/A x N/A N/A S ImaginaryUnit y N/A sqrt N/A N/A x 2 N/A y 2 N/A _eval_rewrite_as_atan N/A N/A self y x N/A N/A N/A N/A 2 N/A atan N/A y N/A N/A sqrt N/A N/A x 2 N/A y 2 x N/A _eval_rewrite_as_arg N/A N/A self y x N/A N/A sympy arg N/A N/A N/A x is_real N/A y is_real N/A N/A N/A arg N/A x N/A y N/A S ImaginaryUnit N/A I N/A S ImaginaryUnit N/A n N/A x N/A I y N/A d N/A N/A x 2 N/A y 2 N/A N/A N/A arg N/A n N/A sqrt d N/A I N/A log N/A N/A abs n N/A sqrt N/A abs d N/A _eval_is_real N/A N/A self N/A N/A N/A N/A N/A N/A N/A self args N/A 0 is_real N/A N/A N/A self args N/A 1 is_real N/A _eval_conjugate N/A N/A self N/A N/A N/A N/A N/A self func N/A N/A N/A N/A self args N/A 0 conjugate N/A N/A N/A N/A self args N/A 1 conjugate N/A fdiff N/A N/A self argindex N/A N/A N/A N/A y x N/A self args N/A N/A argindex 1 N/A N/A N/A x N/A N/A x 2 N/A y 2 N/A N/A N/A argindex 2 N/A N/A N/A N/A y N/A N/A x 2 N/A y 2 N/A N/A N/A ArgumentIndexError self argindex N/A _eval_evalf N/A N/A self prec N/A N/A N/A N/A y x N/A self args N/A N/A N/A x is_real N/A y is_real N/A N/A N/A N/A N/A super atan2 self _eval_evalf prec N/A N/A