from __future__ import annotations from operator import attrgetter from collections import defaultdict from sympy.utilities.exceptions import sympy_deprecation_warning from .sympify import _sympify as _sympify_, sympify from .basic import Basic from .cache import cacheit from .sorting import ordered from .logic import fuzzy_and from .parameters import global_parameters from sympy.utilities.iterables import sift from sympy.multipledispatch.dispatcher import (Dispatcher, ambiguity_register_error_ignore_dup, str_signature, RaiseNotImplementedError) class AssocOp(Basic): """ Associative operations, can separate noncommutative and commutative parts. (a op b) op c == a op (b op c) == a op b op c. Base class for Add and Mul. This is an abstract base class, concrete derived classes must define the attribute `identity`. .. deprecated:: 1.7 Using arguments that aren't subclasses of :class:`~.Expr` in core operators (:class:`~.Mul`, :class:`~.Add`, and :class:`~.Pow`) is deprecated. See :ref:`non-expr-args-deprecated` for details. Parameters ========== *args : Arguments which are operated evaluate : bool, optional Evaluate the operation. If not passed, refer to ``global_parameters.evaluate``. """ # for performance reason, we don't let is_commutative go to assumptions, # and keep it right here __slots__: tuple[str, ...] = ('is_commutative',) _args_type: type[Basic] | None = None @cacheit def __new__(cls, *args, evaluate=None, _sympify=True): # Allow faster processing by passing ``_sympify=False``, if all arguments # are already sympified. if _sympify: args = list(map(_sympify_, args)) # Disallow non-Expr args in Add/Mul typ = cls._args_type if typ is not None: from .relational import Relational if any(isinstance(arg, Relational) for arg in args): raise TypeError("Relational cannot be used in %s" % cls.__name__) # This should raise TypeError once deprecation period is over: for arg in args: if not isinstance(arg, typ): sympy_deprecation_warning( f""" Using non-Expr arguments in {cls.__name__} is deprecated (in this case, one of the arguments has type {type(arg).__name__!r}). If you really did intend to use a multiplication or addition operation with this object, use the * or + operator instead. """, deprecated_since_version="1.7", active_deprecations_target="non-expr-args-deprecated", stacklevel=4, ) if evaluate is None: evaluate = global_parameters.evaluate if not evaluate: obj = cls._from_args(args) obj = cls._exec_constructor_postprocessors(obj) return obj args = [a for a in args if a is not cls.identity] if len(args) == 0: return cls.identity if len(args) == 1: return args[0] c_part, nc_part, order_symbols = cls.flatten(args) is_commutative = not nc_part obj = cls._from_args(c_part + nc_part, is_commutative) obj = cls._exec_constructor_postprocessors(obj) if order_symbols is not None: from sympy.series.order import Order return Order(obj, *order_symbols) return obj @classmethod def _from_args(cls, args, is_commutative=None): """Create new instance with already-processed args. If the args are not in canonical order, then a non-canonical result will be returned, so use with caution. The order of args may change if the sign of the args is changed.""" if len(args) == 0: return cls.identity elif len(args) == 1: return args[0] obj = super().__new__(cls, *args) if is_commutative is None: is_commutative = fuzzy_and(a.is_commutative for a in args) obj.is_commutative = is_commutative return obj def _new_rawargs(self, *args, reeval=True, **kwargs): """Create new instance of own class with args exactly as provided by caller but returning the self class identity if args is empty. Examples ======== This is handy when we want to optimize things, e.g. >>> from sympy import Mul, S >>> from sympy.abc import x, y >>> e = Mul(3, x, y) >>> e.args (3, x, y) >>> Mul(*e.args[1:]) x*y >>> e._new_rawargs(*e.args[1:]) # the same as above, but faster x*y Note: use this with caution. There is no checking of arguments at all. This is best used when you are rebuilding an Add or Mul after simply removing one or more args. If, for example, modifications, result in extra 1s being inserted they will show up in the result: >>> m = (x*y)._new_rawargs(S.One, x); m 1*x >>> m == x False >>> m.is_Mul True Another issue to be aware of is that the commutativity of the result is based on the commutativity of self. If you are rebuilding the terms that came from a commutative object then there will be no problem, but if self was non-commutative then what you are rebuilding may now be commutative. Although this routine tries to do as little as possible with the input, getting the commutativity right is important, so this level of safety is enforced: commutativity will always be recomputed if self is non-commutative and kwarg `reeval=False` has not been passed. """ if reeval and self.is_commutative is False: is_commutative = None else: is_commutative = self.is_commutative return self._from_args(args, is_commutative) @classmethod def flatten(cls, seq): """Return seq so that none of the elements are of type `cls`. This is the vanilla routine that will be used if a class derived from AssocOp does not define its own flatten routine.""" # apply associativity, no commutativity property is used new_seq = [] while seq: o = seq.pop() if o.__class__ is cls: # classes must match exactly seq.extend(o.args) else: new_seq.append(o) new_seq.reverse() # c_part, nc_part, order_symbols return [], new_seq, None def _matches_commutative(self, expr, repl_dict=None, old=False): """ Matches Add/Mul "pattern" to an expression "expr". repl_dict ... a dictionary of (wild: expression) pairs, that get returned with the results This function is the main workhorse for Add/Mul. Examples ======== >>> from sympy import symbols, Wild, sin >>> a = Wild("a") >>> b = Wild("b") >>> c = Wild("c") >>> x, y, z = symbols("x y z") >>> (a+sin(b)*c)._matches_commutative(x+sin(y)*z) {a_: x, b_: y, c_: z} In the example above, "a+sin(b)*c" is the pattern, and "x+sin(y)*z" is the expression. The repl_dict contains parts that were already matched. For example here: >>> (x+sin(b)*c)._matches_commutative(x+sin(y)*z, repl_dict={a: x}) {a_: x, b_: y, c_: z} the only function of the repl_dict is to return it in the result, e.g. if you omit it: >>> (x+sin(b)*c)._matches_commutative(x+sin(y)*z) {b_: y, c_: z} the "a: x" is not returned in the result, but otherwise it is equivalent. """ from .function import _coeff_isneg # make sure expr is Expr if pattern is Expr from .expr import Expr if isinstance(self, Expr) and not isinstance(expr, Expr): return None if repl_dict is None: repl_dict = {} # handle simple patterns if self == expr: return repl_dict d = self._matches_simple(expr, repl_dict) if d is not None: return d # eliminate exact part from pattern: (2+a+w1+w2).matches(expr) -> (w1+w2).matches(expr-a-2) from .function import WildFunction from .symbol import Wild wild_part, exact_part = sift(self.args, lambda p: p.has(Wild, WildFunction) and not expr.has(p), binary=True) if not exact_part: wild_part = list(ordered(wild_part)) if self.is_Add: # in addition to normal ordered keys, impose # sorting on Muls with leading Number to put # them in order wild_part = sorted(wild_part, key=lambda x: x.args[0] if x.is_Mul and x.args[0].is_Number else 0) else: exact = self._new_rawargs(*exact_part) free = expr.free_symbols if free and (exact.free_symbols - free): # there are symbols in the exact part that are not # in the expr; but if there are no free symbols, let # the matching continue return None newexpr = self._combine_inverse(expr, exact) if not old and (expr.is_Add or expr.is_Mul): check = newexpr if _coeff_isneg(check): check = -check if check.count_ops() > expr.count_ops(): return None newpattern = self._new_rawargs(*wild_part) return newpattern.matches(newexpr, repl_dict) # now to real work ;) i = 0 saw = set() while expr not in saw: saw.add(expr) args = tuple(ordered(self.make_args(expr))) if self.is_Add and expr.is_Add: # in addition to normal ordered keys, impose # sorting on Muls with leading Number to put # them in order args = tuple(sorted(args, key=lambda x: x.args[0] if x.is_Mul and x.args[0].is_Number else 0)) expr_list = (self.identity,) + args for last_op in reversed(expr_list): for w in reversed(wild_part): d1 = w.matches(last_op, repl_dict) if d1 is not None: d2 = self.xreplace(d1).matches(expr, d1) if d2 is not None: return d2 if i == 0: if self.is_Mul: # make e**i look like Mul if expr.is_Pow and expr.exp.is_Integer: from .mul import Mul if expr.exp > 0: expr = Mul(*[expr.base, expr.base**(expr.exp - 1)], evaluate=False) else: expr = Mul(*[1/expr.base, expr.base**(expr.exp + 1)], evaluate=False) i += 1 continue elif self.is_Add: # make i*e look like Add c, e = expr.as_coeff_Mul() if abs(c) > 1: from .add import Add if c > 0: expr = Add(*[e, (c - 1)*e], evaluate=False) else: expr = Add(*[-e, (c + 1)*e], evaluate=False) i += 1 continue # try collection on non-Wild symbols from sympy.simplify.radsimp import collect was = expr did = set() for w in reversed(wild_part): c, w = w.as_coeff_mul(Wild) free = c.free_symbols - did if free: did.update(free) expr = collect(expr, free) if expr != was: i += 0 continue break # if we didn't continue, there is nothing more to do return def _has_matcher(self): """Helper for .has() that checks for containment of subexpressions within an expr by using sets of args of similar nodes, e.g. x + 1 in x + y + 1 checks to see that {x, 1} & {x, y, 1} == {x, 1} """ def _ncsplit(expr): # this is not the same as args_cnc because here # we don't assume expr is a Mul -- hence deal with args -- # and always return a set. cpart, ncpart = sift(expr.args, lambda arg: arg.is_commutative is True, binary=True) return set(cpart), ncpart c, nc = _ncsplit(self) cls = self.__class__ def is_in(expr): if isinstance(expr, cls): if expr == self: return True _c, _nc = _ncsplit(expr) if (c & _c) == c: if not nc: return True elif len(nc) <= len(_nc): for i in range(len(_nc) - len(nc) + 1): if _nc[i:i + len(nc)] == nc: return True return False return is_in def _eval_evalf(self, prec): """ Evaluate the parts of self that are numbers; if the whole thing was a number with no functions it would have been evaluated, but it wasn't so we must judiciously extract the numbers and reconstruct the object. This is *not* simply replacing numbers with evaluated numbers. Numbers should be handled in the largest pure-number expression as possible. So the code below separates ``self`` into number and non-number parts and evaluates the number parts and walks the args of the non-number part recursively (doing the same thing). """ from .add import Add from .mul import Mul from .symbol import Symbol from .function import AppliedUndef if isinstance(self, (Mul, Add)): x, tail = self.as_independent(Symbol, AppliedUndef) # if x is an AssocOp Function then the _evalf below will # call _eval_evalf (here) so we must break the recursion if not (tail is self.identity or isinstance(x, AssocOp) and x.is_Function or x is self.identity and isinstance(tail, AssocOp)): # here, we have a number so we just call to _evalf with prec; # prec is not the same as n, it is the binary precision so # that's why we don't call to evalf. x = x._evalf(prec) if x is not self.identity else self.identity args = [] tail_args = tuple(self.func.make_args(tail)) for a in tail_args: # here we call to _eval_evalf since we don't know what we # are dealing with and all other _eval_evalf routines should # be doing the same thing (i.e. taking binary prec and # finding the evalf-able args) newa = a._eval_evalf(prec) if newa is None: args.append(a) else: args.append(newa) return self.func(x, *args) # this is the same as above, but there were no pure-number args to # deal with args = [] for a in self.args: newa = a._eval_evalf(prec) if newa is None: args.append(a) else: args.append(newa) return self.func(*args) @classmethod def make_args(cls, expr): """ Return a sequence of elements `args` such that cls(*args) == expr Examples ======== >>> from sympy import Symbol, Mul, Add >>> x, y = map(Symbol, 'xy') >>> Mul.make_args(x*y) (x, y) >>> Add.make_args(x*y) (x*y,) >>> set(Add.make_args(x*y + y)) == set([y, x*y]) True """ if isinstance(expr, cls): return expr.args else: return (sympify(expr),) def doit(self, **hints): if hints.get('deep', True): terms = [term.doit(**hints) for term in self.args] else: terms = self.args return self.func(*terms, evaluate=True) class ShortCircuit(Exception): pass class LatticeOp(AssocOp): """ Join/meet operations of an algebraic lattice[1]. Explanation =========== These binary operations are associative (op(op(a, b), c) = op(a, op(b, c))), commutative (op(a, b) = op(b, a)) and idempotent (op(a, a) = op(a) = a). Common examples are AND, OR, Union, Intersection, max or min. They have an identity element (op(identity, a) = a) and an absorbing element conventionally called zero (op(zero, a) = zero). This is an abstract base class, concrete derived classes must declare attributes zero and identity. All defining properties are then respected. Examples ======== >>> from sympy import Integer >>> from sympy.core.operations import LatticeOp >>> class my_join(LatticeOp): ... zero = Integer(0) ... identity = Integer(1) >>> my_join(2, 3) == my_join(3, 2) True >>> my_join(2, my_join(3, 4)) == my_join(2, 3, 4) True >>> my_join(0, 1, 4, 2, 3, 4) 0 >>> my_join(1, 2) 2 References ========== .. [1] https://en.wikipedia.org/wiki/Lattice_%28order%29 """ is_commutative = True def __new__(cls, *args, **options): args = (_sympify_(arg) for arg in args) try: # /!\ args is a generator and _new_args_filter # must be careful to handle as such; this # is done so short-circuiting can be done # without having to sympify all values _args = frozenset(cls._new_args_filter(args)) except ShortCircuit: return sympify(cls.zero) if not _args: return sympify(cls.identity) elif len(_args) == 1: return set(_args).pop() else: # XXX in almost every other case for __new__, *_args is # passed along, but the expectation here is for _args obj = super(AssocOp, cls).__new__(cls, *ordered(_args)) obj._argset = _args return obj @classmethod def _new_args_filter(cls, arg_sequence, call_cls=None): """Generator filtering args""" ncls = call_cls or cls for arg in arg_sequence: if arg == ncls.zero: raise ShortCircuit(arg) elif arg == ncls.identity: continue elif arg.func == ncls: yield from arg.args else: yield arg @classmethod def make_args(cls, expr): """ Return a set of args such that cls(*arg_set) == expr. """ if isinstance(expr, cls): return expr._argset else: return frozenset([sympify(expr)]) @staticmethod def _compare_pretty(a, b): return (str(a) > str(b)) - (str(a) < str(b)) class AssocOpDispatcher: """ Handler dispatcher for associative operators .. notes:: This approach is experimental, and can be replaced or deleted in the future. See https://github.com/sympy/sympy/pull/19463. Explanation =========== If arguments of different types are passed, the classes which handle the operation for each type are collected. Then, a class which performs the operation is selected by recursive binary dispatching. Dispatching relation can be registered by ``register_handlerclass`` method. Priority registration is unordered. You cannot make ``A*B`` and ``B*A`` refer to different handler classes. All logic dealing with the order of arguments must be implemented in the handler class. Examples ======== >>> from sympy import Add, Expr, Symbol >>> from sympy.core.add import add >>> class NewExpr(Expr): ... @property ... def _add_handler(self): ... return NewAdd >>> class NewAdd(NewExpr, Add): ... pass >>> add.register_handlerclass((Add, NewAdd), NewAdd) >>> a, b = Symbol('a'), NewExpr() >>> add(a, b) == NewAdd(a, b) True """ def __init__(self, name, doc=None): self.name = name self.doc = doc self.handlerattr = "_%s_handler" % name self._handlergetter = attrgetter(self.handlerattr) self._dispatcher = Dispatcher(name) def __repr__(self): return "" % self.name def register_handlerclass(self, classes, typ, on_ambiguity=ambiguity_register_error_ignore_dup): """ Register the handler class for two classes, in both straight and reversed order. Paramteters =========== classes : tuple of two types Classes who are compared with each other. typ: Class which is registered to represent *cls1* and *cls2*. Handler method of *self* must be implemented in this class. """ if not len(classes) == 2: raise RuntimeError( "Only binary dispatch is supported, but got %s types: <%s>." % ( len(classes), str_signature(classes) )) if len(set(classes)) == 1: raise RuntimeError( "Duplicate types <%s> cannot be dispatched." % str_signature(classes) ) self._dispatcher.add(tuple(classes), typ, on_ambiguity=on_ambiguity) self._dispatcher.add(tuple(reversed(classes)), typ, on_ambiguity=on_ambiguity) @cacheit def __call__(self, *args, _sympify=True, **kwargs): """ Parameters ========== *args : Arguments which are operated """ if _sympify: args = tuple(map(_sympify_, args)) handlers = frozenset(map(self._handlergetter, args)) # no need to sympify again return self.dispatch(handlers)(*args, _sympify=False, **kwargs) @cacheit def dispatch(self, handlers): """ Select the handler class, and return its handler method. """ # Quick exit for the case where all handlers are same if len(handlers) == 1: h, = handlers if not isinstance(h, type): raise RuntimeError("Handler {!r} is not a type.".format(h)) return h # Recursively select with registered binary priority for i, typ in enumerate(handlers): if not isinstance(typ, type): raise RuntimeError("Handler {!r} is not a type.".format(typ)) if i == 0: handler = typ else: prev_handler = handler handler = self._dispatcher.dispatch(prev_handler, typ) if not isinstance(handler, type): raise RuntimeError( "Dispatcher for {!r} and {!r} must return a type, but got {!r}".format( prev_handler, typ, handler )) # return handler class return handler @property def __doc__(self): docs = [ "Multiply dispatched associative operator: %s" % self.name, "Note that support for this is experimental, see the docs for :class:`AssocOpDispatcher` for details" ] if self.doc: docs.append(self.doc) s = "Registered handler classes\n" s += '=' * len(s) docs.append(s) amb_sigs = [] typ_sigs = defaultdict(list) for sigs in self._dispatcher.ordering[::-1]: key = self._dispatcher.funcs[sigs] typ_sigs[key].append(sigs) for typ, sigs in typ_sigs.items(): sigs_str = ', '.join('<%s>' % str_signature(sig) for sig in sigs) if isinstance(typ, RaiseNotImplementedError): amb_sigs.append(sigs_str) continue s = 'Inputs: %s\n' % sigs_str s += '-' * len(s) + '\n' s += typ.__name__ docs.append(s) if amb_sigs: s = "Ambiguous handler classes\n" s += '=' * len(s) docs.append(s) s = '\n'.join(amb_sigs) docs.append(s) return '\n\n'.join(docs)