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357 lines
9.9 KiB
357 lines
9.9 KiB
5 months ago
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"""Tools for manipulation of expressions using paths. """
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from sympy.core import Basic
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class EPath:
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r"""
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Manipulate expressions using paths.
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EPath grammar in EBNF notation::
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literal ::= /[A-Za-z_][A-Za-z_0-9]*/
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number ::= /-?\d+/
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type ::= literal
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attribute ::= literal "?"
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all ::= "*"
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slice ::= "[" number? (":" number? (":" number?)?)? "]"
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range ::= all | slice
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query ::= (type | attribute) ("|" (type | attribute))*
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selector ::= range | query range?
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path ::= "/" selector ("/" selector)*
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See the docstring of the epath() function.
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"""
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__slots__ = ("_path", "_epath")
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def __new__(cls, path):
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"""Construct new EPath. """
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if isinstance(path, EPath):
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return path
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if not path:
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raise ValueError("empty EPath")
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_path = path
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if path[0] == '/':
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path = path[1:]
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else:
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raise NotImplementedError("non-root EPath")
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epath = []
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for selector in path.split('/'):
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selector = selector.strip()
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if not selector:
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raise ValueError("empty selector")
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index = 0
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for c in selector:
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if c.isalnum() or c in ('_', '|', '?'):
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index += 1
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else:
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break
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attrs = []
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types = []
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if index:
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elements = selector[:index]
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selector = selector[index:]
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for element in elements.split('|'):
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element = element.strip()
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if not element:
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raise ValueError("empty element")
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if element.endswith('?'):
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attrs.append(element[:-1])
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else:
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types.append(element)
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span = None
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if selector == '*':
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pass
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else:
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if selector.startswith('['):
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try:
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i = selector.index(']')
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except ValueError:
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raise ValueError("expected ']', got EOL")
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_span, span = selector[1:i], []
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if ':' not in _span:
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span = int(_span)
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else:
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for elt in _span.split(':', 3):
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if not elt:
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span.append(None)
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else:
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span.append(int(elt))
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span = slice(*span)
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selector = selector[i + 1:]
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if selector:
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raise ValueError("trailing characters in selector")
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epath.append((attrs, types, span))
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obj = object.__new__(cls)
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obj._path = _path
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obj._epath = epath
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return obj
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def __repr__(self):
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return "%s(%r)" % (self.__class__.__name__, self._path)
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def _get_ordered_args(self, expr):
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"""Sort ``expr.args`` using printing order. """
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if expr.is_Add:
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return expr.as_ordered_terms()
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elif expr.is_Mul:
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return expr.as_ordered_factors()
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else:
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return expr.args
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def _hasattrs(self, expr, attrs):
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"""Check if ``expr`` has any of ``attrs``. """
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for attr in attrs:
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if not hasattr(expr, attr):
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return False
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return True
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def _hastypes(self, expr, types):
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"""Check if ``expr`` is any of ``types``. """
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_types = [ cls.__name__ for cls in expr.__class__.mro() ]
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return bool(set(_types).intersection(types))
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def _has(self, expr, attrs, types):
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"""Apply ``_hasattrs`` and ``_hastypes`` to ``expr``. """
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if not (attrs or types):
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return True
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if attrs and self._hasattrs(expr, attrs):
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return True
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if types and self._hastypes(expr, types):
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return True
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return False
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def apply(self, expr, func, args=None, kwargs=None):
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"""
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Modify parts of an expression selected by a path.
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Examples
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========
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>>> from sympy.simplify.epathtools import EPath
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>>> from sympy import sin, cos, E
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>>> from sympy.abc import x, y, z, t
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>>> path = EPath("/*/[0]/Symbol")
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>>> expr = [((x, 1), 2), ((3, y), z)]
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>>> path.apply(expr, lambda expr: expr**2)
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[((x**2, 1), 2), ((3, y**2), z)]
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>>> path = EPath("/*/*/Symbol")
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>>> expr = t + sin(x + 1) + cos(x + y + E)
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>>> path.apply(expr, lambda expr: 2*expr)
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t + sin(2*x + 1) + cos(2*x + 2*y + E)
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"""
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def _apply(path, expr, func):
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if not path:
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return func(expr)
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else:
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selector, path = path[0], path[1:]
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attrs, types, span = selector
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if isinstance(expr, Basic):
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if not expr.is_Atom:
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args, basic = self._get_ordered_args(expr), True
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else:
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return expr
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elif hasattr(expr, '__iter__'):
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args, basic = expr, False
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else:
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return expr
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args = list(args)
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if span is not None:
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if isinstance(span, slice):
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indices = range(*span.indices(len(args)))
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else:
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indices = [span]
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else:
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indices = range(len(args))
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for i in indices:
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try:
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arg = args[i]
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except IndexError:
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continue
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if self._has(arg, attrs, types):
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args[i] = _apply(path, arg, func)
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if basic:
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return expr.func(*args)
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else:
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return expr.__class__(args)
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_args, _kwargs = args or (), kwargs or {}
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_func = lambda expr: func(expr, *_args, **_kwargs)
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return _apply(self._epath, expr, _func)
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def select(self, expr):
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"""
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Retrieve parts of an expression selected by a path.
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Examples
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========
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>>> from sympy.simplify.epathtools import EPath
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>>> from sympy import sin, cos, E
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>>> from sympy.abc import x, y, z, t
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>>> path = EPath("/*/[0]/Symbol")
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>>> expr = [((x, 1), 2), ((3, y), z)]
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>>> path.select(expr)
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[x, y]
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>>> path = EPath("/*/*/Symbol")
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>>> expr = t + sin(x + 1) + cos(x + y + E)
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>>> path.select(expr)
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[x, x, y]
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"""
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result = []
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def _select(path, expr):
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if not path:
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result.append(expr)
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else:
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selector, path = path[0], path[1:]
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attrs, types, span = selector
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if isinstance(expr, Basic):
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args = self._get_ordered_args(expr)
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elif hasattr(expr, '__iter__'):
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args = expr
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else:
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return
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if span is not None:
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if isinstance(span, slice):
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args = args[span]
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else:
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try:
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args = [args[span]]
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except IndexError:
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return
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for arg in args:
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if self._has(arg, attrs, types):
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_select(path, arg)
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_select(self._epath, expr)
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return result
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def epath(path, expr=None, func=None, args=None, kwargs=None):
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r"""
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Manipulate parts of an expression selected by a path.
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Explanation
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===========
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This function allows to manipulate large nested expressions in single
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line of code, utilizing techniques to those applied in XML processing
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standards (e.g. XPath).
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If ``func`` is ``None``, :func:`epath` retrieves elements selected by
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the ``path``. Otherwise it applies ``func`` to each matching element.
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Note that it is more efficient to create an EPath object and use the select
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and apply methods of that object, since this will compile the path string
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only once. This function should only be used as a convenient shortcut for
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interactive use.
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This is the supported syntax:
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* select all: ``/*``
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Equivalent of ``for arg in args:``.
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* select slice: ``/[0]`` or ``/[1:5]`` or ``/[1:5:2]``
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Supports standard Python's slice syntax.
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* select by type: ``/list`` or ``/list|tuple``
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Emulates ``isinstance()``.
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* select by attribute: ``/__iter__?``
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Emulates ``hasattr()``.
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Parameters
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==========
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path : str | EPath
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A path as a string or a compiled EPath.
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expr : Basic | iterable
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An expression or a container of expressions.
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func : callable (optional)
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A callable that will be applied to matching parts.
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args : tuple (optional)
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Additional positional arguments to ``func``.
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kwargs : dict (optional)
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Additional keyword arguments to ``func``.
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Examples
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========
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>>> from sympy.simplify.epathtools import epath
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>>> from sympy import sin, cos, E
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>>> from sympy.abc import x, y, z, t
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>>> path = "/*/[0]/Symbol"
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>>> expr = [((x, 1), 2), ((3, y), z)]
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>>> epath(path, expr)
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[x, y]
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>>> epath(path, expr, lambda expr: expr**2)
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[((x**2, 1), 2), ((3, y**2), z)]
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>>> path = "/*/*/Symbol"
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>>> expr = t + sin(x + 1) + cos(x + y + E)
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>>> epath(path, expr)
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[x, x, y]
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>>> epath(path, expr, lambda expr: 2*expr)
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t + sin(2*x + 1) + cos(2*x + 2*y + E)
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"""
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_epath = EPath(path)
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if expr is None:
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return _epath
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if func is None:
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return _epath.select(expr)
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else:
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return _epath.apply(expr, func, args, kwargs)
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