(cls, seq)
Takes the sequence "seq" of nested Adds and returns a flatten list.

        Returns: (commutative_part, noncommutative_part, order_symbols)

        Applies associativity, all terms are commutable with respect to
        addition.

        NB: the removal of 0 is already handled by AssocOp.__new__

        See also
        ========

        sympy.core.mul.Mul.flatten
Takes the sequence "seq" of nested Adds and returns a flatten list.
Takes the sequence seq of nested Adds and returns a flatten list .
def flatten(cls, seq):
        """
        Takes the sequence "seq" of nested Adds and returns a flatten list.

        Returns: (commutative_part, noncommutative_part, order_symbols)

        Applies associativity, all terms are commutable with respect to
        addition.

        NB: the removal of 0 is already handled by AssocOp.__new__

        See also
        ========

        sympy.core.mul.Mul.flatten

        """
        rv = None
        if len(seq) == 2:
            a, b = seq
            if b.is_Rational:
                a, b = b, a
            if a.is_Rational:
                if b.is_Mul:
                    rv = [a, b], [], None
            if rv:
                if all(s.is_commutative for s in rv[0]):
                    return rv
                return [], rv[0], None

        terms = {}      # term -> coeff
                        # e.g. x**2 -> 5   for ... + 5*x**2 + ...

        coeff = S.Zero  # coefficient (Number or zoo) to always be in slot 0
                        # e.g. 3 + ...
        order_factors = []

        for o in seq:

            # O(x)
            if o.is_Order:
                for o1 in order_factors:
                    if o1.contains(o):
                        o = None
                        break
                if o is None:
                    continue
                order_factors = [o] + [
                    o1 for o1 in order_factors if not o.contains(o1)]
                continue

            # 3 or NaN
            elif o.is_Number:
                if (o is S.NaN or coeff is S.ComplexInfinity and
                        o.is_bounded is False):
                    # we know for sure the result will be nan
                    return [S.NaN], [], None
                if coeff.is_Number:
                    coeff += o
                    if coeff is S.NaN:
                        # we know for sure the result will be nan
                        return [S.NaN], [], None
                continue

            elif o is S.ComplexInfinity:
                if coeff.is_bounded is False:
                    # we know for sure the result will be nan
                    return [S.NaN], [], None
                coeff = S.ComplexInfinity
                continue

            # Add([...])
            elif o.is_Add:
                # NB: here we assume Add is always commutative
                seq.extend(o.args)  # TODO zerocopy?
                continue

            # Mul([...])
            elif o.is_Mul:
                c, s = o.as_coeff_Mul()

            # check for unevaluated Pow, e.g. 2**3 or 2**(-1/2)
            elif o.is_Pow:
                b, e = o.as_base_exp()
                if b.is_Number and (e.is_Integer or
                                   (e.is_Rational and e.is_negative)):
                    seq.append(b**e)
                    continue
                c, s = S.One, o

            else:
                # everything else
                c = S.One
                s = o

            # now we have:
            # o = c*s, where
            #
            # c is a Number
            # s is an expression with number factor extracted
            # let's collect terms with the same s, so e.g.
            # 2*x**2 + 3*x**2  ->  5*x**2
            if s in terms:
                terms[s] += c
                if terms[s] is S.NaN:
                    # we know for sure the result will be nan
                    return [S.NaN], [], None
            else:
                terms[s] = c

        # now let's construct new args:
        # [2*x**2, x**3, 7*x**4, pi, ...]
        newseq = []
        noncommutative = False
        for s, c in terms.items():
            # 0*s
            if c is S.Zero:
                continue
            # 1*s
            elif c is S.One:
                newseq.append(s)
            # c*s
            else:
                if s.is_Mul:
                    # Mul, already keeps its arguments in perfect order.
                    # so we can simply put c in slot0 and go the fast way.
                    cs = s._new_rawargs(*((c,) + s.args))
                    newseq.append(cs)
                elif s.is_Add:
                    # we just re-create the unevaluated Mul
                    newseq.append(Mul(c, s, evaluate=False))
                else:
                    # alternatively we have to call all Mul's machinery (slow)
                    newseq.append(Mul(c, s))

            noncommutative = noncommutative or not s.is_commutative

        # oo, -oo
        if coeff is S.Infinity:
            newseq = [f for f in newseq if not
                      (f.is_nonnegative or f.is_real and
                       (f.is_bounded or f.is_infinitesimal))]

        elif coeff is S.NegativeInfinity:
            newseq = [f for f in newseq if not
                      (f.is_nonpositive or f.is_real and
                       (f.is_bounded or f.is_infinitesimal))]

        if coeff is S.ComplexInfinity:
            # zoo might be
            #   unbounded_real + bounded_im
            #   bounded_real + unbounded_im
            #   unbounded_real + unbounded_im
            # addition of a bounded real or imaginary number won't be able to
            # change the zoo nature; if unbounded a NaN condition could result
            # if the unbounded symbol had sign opposite of the unbounded
            # portion of zoo, e.g., unbounded_real - unbounded_real.
            newseq = [c for c in newseq if not (c.is_bounded and
                                                c.is_real is not None)]

        # process O(x)
        if order_factors:
            newseq2 = []
            for t in newseq:
                for o in order_factors:
                    # x + O(x) -> O(x)
                    if o.contains(t):
                        t = None
                        break
                # x + O(x**2) -> x + O(x**2)
                if t is not None:
                    newseq2.append(t)
            newseq = newseq2 + order_factors
            # 1 + O(1) -> O(1)
            for o in order_factors:
                if o.contains(coeff):
                    coeff = S.Zero
                    break

        # order args canonically
        _addsort(newseq)

        # current code expects coeff to be first
        if coeff is not S.Zero:
            newseq.insert(0, coeff)

        # we are done
        if noncommutative:
            return [], newseq, None
        else:
            return newseq, [], None
def flatten ( cls , seq ) : rv = None if len ( seq ) == 2 : a , b = seq if b . is_Rational : a , b = b , a if a . is_Rational : if b . is_Mul : rv = [ a , b ] , [ ] , None if rv : if all ( s . is_commutative for s in rv [ 0 ] ) : return rv return [ ] , rv [ 0 ] , None terms = { } # term -> coeff # e.g. x**2 -> 5   for ... + 5*x**2 + ... coeff = S . Zero # coefficient (Number or zoo) to always be in slot 0 # e.g. 3 + ... order_factors = [ ] for o in seq : # O(x) if o . is_Order : for o1 in order_factors : if o1 . contains ( o ) : o = None break if o is None : continue order_factors = [ o ] + [ o1 for o1 in order_factors if not o . contains ( o1 ) ] continue # 3 or NaN elif o . is_Number : if ( o is S . NaN or coeff is S . ComplexInfinity and o . is_bounded is False ) : # we know for sure the result will be nan return [ S . NaN ] , [ ] , None if coeff . is_Number : coeff += o if coeff is S . NaN : # we know for sure the result will be nan return [ S . NaN ] , [ ] , None continue elif o is S . ComplexInfinity : if coeff . is_bounded is False : # we know for sure the result will be nan return [ S . NaN ] , [ ] , None coeff = S . ComplexInfinity continue # Add([...]) elif o . is_Add : # NB: here we assume Add is always commutative seq . extend ( o . args ) # TODO zerocopy? continue # Mul([...]) elif o . is_Mul : c , s = o . as_coeff_Mul ( ) # check for unevaluated Pow, e.g. 2**3 or 2**(-1/2) elif o . is_Pow : b , e = o . as_base_exp ( ) if b . is_Number and ( e . is_Integer or ( e . is_Rational and e . is_negative ) ) : seq . append ( b ** e ) continue c , s = S . One , o else : # everything else c = S . One s = o # now we have: # o = c*s, where # # c is a Number # s is an expression with number factor extracted # let's collect terms with the same s, so e.g. # 2*x**2 + 3*x**2  ->  5*x**2 if s in terms : terms [ s ] += c if terms [ s ] is S . NaN : # we know for sure the result will be nan return [ S . NaN ] , [ ] , None else : terms [ s ] = c # now let's construct new args: # [2*x**2, x**3, 7*x**4, pi, ...] newseq = [ ] noncommutative = False for s , c in terms . items ( ) : # 0*s if c is S . Zero : continue # 1*s elif c is S . One : newseq . append ( s ) # c*s else : if s . is_Mul : # Mul, already keeps its arguments in perfect order. # so we can simply put c in slot0 and go the fast way. cs = s . _new_rawargs ( * ( ( c , ) + s . args ) ) newseq . append ( cs ) elif s . is_Add : # we just re-create the unevaluated Mul newseq . append ( Mul ( c , s , evaluate = False ) ) else : # alternatively we have to call all Mul's machinery (slow) newseq . append ( Mul ( c , s ) ) noncommutative = noncommutative or not s . is_commutative # oo, -oo if coeff is S . Infinity : newseq = [ f for f in newseq if not ( f . is_nonnegative or f . is_real and ( f . is_bounded or f . is_infinitesimal ) ) ] elif coeff is S . NegativeInfinity : newseq = [ f for f in newseq if not ( f . is_nonpositive or f . is_real and ( f . is_bounded or f . is_infinitesimal ) ) ] if coeff is S . ComplexInfinity : # zoo might be #   unbounded_real + bounded_im #   bounded_real + unbounded_im #   unbounded_real + unbounded_im # addition of a bounded real or imaginary number won't be able to # change the zoo nature; if unbounded a NaN condition could result # if the unbounded symbol had sign opposite of the unbounded # portion of zoo, e.g., unbounded_real - unbounded_real. newseq = [ c for c in newseq if not ( c . is_bounded and c . is_real is not None ) ] # process O(x) if order_factors : newseq2 = [ ] for t in newseq : for o in order_factors : # x + O(x) -> O(x) if o . contains ( t ) : t = None break # x + O(x**2) -> x + O(x**2) if t is not None : newseq2 . append ( t ) newseq = newseq2 + order_factors # 1 + O(1) -> O(1) for o in order_factors : if o . contains ( coeff ) : coeff = S . Zero break # order args canonically _addsort ( newseq ) # current code expects coeff to be first if coeff is not S . Zero : newseq . insert ( 0 , coeff ) # we are done if noncommutative : return [ ] , newseq , None else : return newseq , [ ] , None