(self, x, n=1, right=False)
Returns the coefficient from the term(s) containing ``x**n`` or None. If ``n``
        is zero then all terms independent of ``x`` will be returned.

        When x is noncommutative, the coeff to the left (default) or right of x
        can be returned. The keyword 'right' is ignored when x is commutative.

        See Also
        ========

        as_coefficient: separate the expression into a coefficient and factor
        as_coeff_Add: separate the additive constant from an expression
        as_coeff_Mul: separate the multiplicative constant from an expression
        as_independent: separate x-dependent terms/factors from others
        sympy.polys.polytools.coeff_monomial: efficiently find the single coefficient of a monomial in Poly
        sympy.polys.polytools.nth: like coeff_monomial but powers of monomial terms are used

        Examples
        ========

        >>> from sympy import symbols
        >>> from sympy.abc import x, y, z

        You can select terms that have an explicit negative in front of them:

        >>> (-x + 2*y).coeff(-1)
        x
        >>> (x - 2*y).coeff(-1)
        2*y

        You can select terms with no Rational coefficient:

        >>> (x + 2*y).coeff(1)
        x
        >>> (3 + 2*x + 4*x**2).coeff(1)
        0

        You can select terms independent of x by making n=0; in this case
        expr.as_independent(x)[0] is returned (and 0 will be returned instead
        of None):

        >>> (3 + 2*x + 4*x**2).coeff(x, 0)
        3
        >>> eq = ((x + 1)**3).expand() + 1
        >>> eq
        x**3 + 3*x**2 + 3*x + 2
        >>> [eq.coeff(x, i) for i in reversed(range(4))]
        [1, 3, 3, 2]
        >>> eq -= 2
        >>> [eq.coeff(x, i) for i in reversed(range(4))]
        [1, 3, 3, 0]

        You can select terms that have a numerical term in front of them:

        >>> (-x - 2*y).coeff(2)
        -y
        >>> from sympy import sqrt
        >>> (x + sqrt(2)*x).coeff(sqrt(2))
        x

        The matching is exact:

        >>> (3 + 2*x + 4*x**2).coeff(x)
        2
        >>> (3 + 2*x + 4*x**2).coeff(x**2)
        4
        >>> (3 + 2*x + 4*x**2).coeff(x**3)
        0
        >>> (z*(x + y)**2).coeff((x + y)**2)
        z
        >>> (z*(x + y)**2).coeff(x + y)
        0

        In addition, no factoring is done, so 1 + z*(1 + y) is not obtained
        from the following:

        >>> (x + z*(x + x*y)).coeff(x)
        1

        If such factoring is desired, factor_terms can be used first:

        >>> from sympy import factor_terms
        >>> factor_terms(x + z*(x + x*y)).coeff(x)
        z*(y + 1) + 1

        >>> n, m, o = symbols('n m o', commutative=False)
        >>> n.coeff(n)
        1
        >>> (3*n).coeff(n)
        3
        >>> (n*m + m*n*m).coeff(n) # = (1 + m)*n*m
        1 + m
        >>> (n*m + m*n*m).coeff(n, right=True) # = (1 + m)*n*m
        m

        If there is more than one possible coefficient 0 is returned:

        >>> (n*m + m*n).coeff(n)
        0

        If there is only one possible coefficient, it is returned:

        >>> (n*m + x*m*n).coeff(m*n)
        x
        >>> (n*m + x*m*n).coeff(m*n, right=1)
        1
Returns the coefficient from the term(s) containing ``x**n`` or None. If ``n``
        is zero then all terms independent of ``x`` will be returned.
Returns the coefficient from the term ( s ) containing x ** n or None . If n is zero then all terms independent of x will be returned .
def coeff(self, x, n=1, right=False):
        """
        Returns the coefficient from the term(s) containing ``x**n`` or None. If ``n``
        is zero then all terms independent of ``x`` will be returned.

        When x is noncommutative, the coeff to the left (default) or right of x
        can be returned. The keyword 'right' is ignored when x is commutative.

        See Also
        ========

        as_coefficient: separate the expression into a coefficient and factor
        as_coeff_Add: separate the additive constant from an expression
        as_coeff_Mul: separate the multiplicative constant from an expression
        as_independent: separate x-dependent terms/factors from others
        sympy.polys.polytools.coeff_monomial: efficiently find the single coefficient of a monomial in Poly
        sympy.polys.polytools.nth: like coeff_monomial but powers of monomial terms are used

        Examples
        ========

        >>> from sympy import symbols
        >>> from sympy.abc import x, y, z

        You can select terms that have an explicit negative in front of them:

        >>> (-x + 2*y).coeff(-1)
        x
        >>> (x - 2*y).coeff(-1)
        2*y

        You can select terms with no Rational coefficient:

        >>> (x + 2*y).coeff(1)
        x
        >>> (3 + 2*x + 4*x**2).coeff(1)
        0

        You can select terms independent of x by making n=0; in this case
        expr.as_independent(x)[0] is returned (and 0 will be returned instead
        of None):

        >>> (3 + 2*x + 4*x**2).coeff(x, 0)
        3
        >>> eq = ((x + 1)**3).expand() + 1
        >>> eq
        x**3 + 3*x**2 + 3*x + 2
        >>> [eq.coeff(x, i) for i in reversed(range(4))]
        [1, 3, 3, 2]
        >>> eq -= 2
        >>> [eq.coeff(x, i) for i in reversed(range(4))]
        [1, 3, 3, 0]

        You can select terms that have a numerical term in front of them:

        >>> (-x - 2*y).coeff(2)
        -y
        >>> from sympy import sqrt
        >>> (x + sqrt(2)*x).coeff(sqrt(2))
        x

        The matching is exact:

        >>> (3 + 2*x + 4*x**2).coeff(x)
        2
        >>> (3 + 2*x + 4*x**2).coeff(x**2)
        4
        >>> (3 + 2*x + 4*x**2).coeff(x**3)
        0
        >>> (z*(x + y)**2).coeff((x + y)**2)
        z
        >>> (z*(x + y)**2).coeff(x + y)
        0

        In addition, no factoring is done, so 1 + z*(1 + y) is not obtained
        from the following:

        >>> (x + z*(x + x*y)).coeff(x)
        1

        If such factoring is desired, factor_terms can be used first:

        >>> from sympy import factor_terms
        >>> factor_terms(x + z*(x + x*y)).coeff(x)
        z*(y + 1) + 1

        >>> n, m, o = symbols('n m o', commutative=False)
        >>> n.coeff(n)
        1
        >>> (3*n).coeff(n)
        3
        >>> (n*m + m*n*m).coeff(n) # = (1 + m)*n*m
        1 + m
        >>> (n*m + m*n*m).coeff(n, right=True) # = (1 + m)*n*m
        m

        If there is more than one possible coefficient 0 is returned:

        >>> (n*m + m*n).coeff(n)
        0

        If there is only one possible coefficient, it is returned:

        >>> (n*m + x*m*n).coeff(m*n)
        x
        >>> (n*m + x*m*n).coeff(m*n, right=1)
        1

        """
        x = sympify(x)
        if not isinstance(x, Basic):
            return S.Zero

        n = as_int(n)

        if not x:
            return S.Zero

        if x == self:
            if n == 1:
                return S.One
            return S.Zero

        if x is S.One:
            co = [a for a in Add.make_args(self)
                  if a.as_coeff_Mul()[0] is S.One]
            if not co:
                return S.Zero
            return Add(*co)

        if n == 0:
            if x.is_Add and self.is_Add:
                c = self.coeff(x, right=right)
                if not c:
                    return S.Zero
                if not right:
                    return self - Add(*[a*x for a in Add.make_args(c)])
                return self - Add(*[x*a for a in Add.make_args(c)])
            return self.as_independent(x, as_Add=True)[0]

        # continue with the full method, looking for this power of x:
        x = x**n

        def incommon(l1, l2):
            if not l1 or not l2:
                return []
            n = min(len(l1), len(l2))
            for i in xrange(n):
                if l1[i] != l2[i]:
                    return l1[:i]
            return l1[:]

        def find(l, sub, first=True):
            """ Find where list sub appears in list l. When ``first`` is True
            the first occurance from the left is returned, else the last
            occurance is returned. Return None if sub is not in l.

            >> l = range(5)*2
            >> find(l, [2, 3])
            2
            >> find(l, [2, 3], first=0)
            7
            >> find(l, [2, 4])
            None

            """
            if not sub or not l or len(sub) > len(l):
                return None
            n = len(sub)
            if not first:
                l.reverse()
                sub.reverse()
            for i in xrange(0, len(l) - n + 1):
                if all(l[i + j] == sub[j] for j in range(n)):
                    break
            else:
                i = None
            if not first:
                l.reverse()
                sub.reverse()
            if i is not None and not first:
                i = len(l) - (i + n)
            return i

        co = []
        args = Add.make_args(self)
        self_c = self.is_commutative
        x_c = x.is_commutative
        if self_c and not x_c:
            return S.Zero

        if self_c:
            xargs = x.args_cnc(cset=True, warn=False)[0]
            for a in args:
                margs = a.args_cnc(cset=True, warn=False)[0]
                if len(xargs) > len(margs):
                    continue
                resid = margs.difference(xargs)
                if len(resid) + len(xargs) == len(margs):
                    co.append(Mul(*resid))
            if co == []:
                return S.Zero
            elif co:
                return Add(*co)
        elif x_c:
            xargs = x.args_cnc(cset=True, warn=False)[0]
            for a in args:
                margs, nc = a.args_cnc(cset=True)
                if len(xargs) > len(margs):
                    continue
                resid = margs.difference(xargs)
                if len(resid) + len(xargs) == len(margs):
                    co.append(Mul(*(list(resid) + nc)))
            if co == []:
                return S.Zero
            elif co:
                return Add(*co)
        else:  # both nc
            xargs, nx = x.args_cnc(cset=True)
            # find the parts that pass the commutative terms
            for a in args:
                margs, nc = a.args_cnc(cset=True)
                if len(xargs) > len(margs):
                    continue
                resid = margs.difference(xargs)
                if len(resid) + len(xargs) == len(margs):
                    co.append((resid, nc))
            # now check the non-comm parts
            if not co:
                return S.Zero
            if all(n == co[0][1] for r, n in co):
                ii = find(co[0][1], nx, right)
                if ii is not None:
                    if not right:
                        return Mul(Add(*[Mul(*r) for r, c in co]), Mul(*co[0][1][:ii]))
                    else:
                        return Mul(*co[0][1][ii + len(nx):])
            beg = reduce(incommon, (n[1] for n in co))
            if beg:
                ii = find(beg, nx, right)
                if ii is not None:
                    if not right:
                        gcdc = co[0][0]
                        for i in xrange(1, len(co)):
                            gcdc = gcdc.intersection(co[i][0])
                            if not gcdc:
                                break
                        return Mul(*(list(gcdc) + beg[:ii]))
                    else:
                        m = ii + len(nx)
                        return Add(*[Mul(*(list(r) + n[m:])) for r, n in co])
            end = list(reversed(
                reduce(incommon, (list(reversed(n[1])) for n in co))))
            if end:
                ii = find(end, nx, right)
                if ii is not None:
                    if not right:
                        return Add(*[Mul(*(list(r) + n[:-len(end) + ii])) for r, n in co])
                    else:
                        return Mul(*end[ii + len(nx):])
            # look for single match
            hit = None
            for i, (r, n) in enumerate(co):
                ii = find(n, nx, right)
                if ii is not None:
                    if not hit:
                        hit = ii, r, n
                    else:
                        break
            else:
                if hit:
                    ii, r, n = hit
                    if not right:
                        return Mul(*(list(r) + n[:ii]))
                    else:
                        return Mul(*n[ii + len(nx):])

            return S.Zero
def coeff ( self , x , n = 1 , right = False ) : x = sympify ( x ) if not isinstance ( x , Basic ) : return S . Zero n = as_int ( n ) if not x : return S . Zero if x == self : if n == 1 : return S . One return S . Zero if x is S . One : co = [ a for a in Add . make_args ( self ) if a . as_coeff_Mul ( ) [ 0 ] is S . One ] if not co : return S . Zero return Add ( * co ) if n == 0 : if x . is_Add and self . is_Add : c = self . coeff ( x , right = right ) if not c : return S . Zero if not right : return self - Add ( * [ a * x for a in Add . make_args ( c ) ] ) return self - Add ( * [ x * a for a in Add . make_args ( c ) ] ) return self . as_independent ( x , as_Add = True ) [ 0 ] # continue with the full method, looking for this power of x: x = x ** n def incommon ( l1 , l2 ) : if not l1 or not l2 : return [ ] n = min ( len ( l1 ) , len ( l2 ) ) for i in xrange ( n ) : if l1 [ i ] != l2 [ i ] : return l1 [ : i ] return l1 [ : ] def find ( l , sub , first = True ) : """ Find where list sub appears in list l. When ``first`` is True
            the first occurance from the left is returned, else the last
            occurance is returned. Return None if sub is not in l.

            >> l = range(5)*2
            >> find(l, [2, 3])
            2
            >> find(l, [2, 3], first=0)
            7
            >> find(l, [2, 4])
            None

            """ if not sub or not l or len ( sub ) > len ( l ) : return None n = len ( sub ) if not first : l . reverse ( ) sub . reverse ( ) for i in xrange ( 0 , len ( l ) - n + 1 ) : if all ( l [ i + j ] == sub [ j ] for j in range ( n ) ) : break else : i = None if not first : l . reverse ( ) sub . reverse ( ) if i is not None and not first : i = len ( l ) - ( i + n ) return i co = [ ] args = Add . make_args ( self ) self_c = self . is_commutative x_c = x . is_commutative if self_c and not x_c : return S . Zero if self_c : xargs = x . args_cnc ( cset = True , warn = False ) [ 0 ] for a in args : margs = a . args_cnc ( cset = True , warn = False ) [ 0 ] if len ( xargs ) > len ( margs ) : continue resid = margs . difference ( xargs ) if len ( resid ) + len ( xargs ) == len ( margs ) : co . append ( Mul ( * resid ) ) if co == [ ] : return S . Zero elif co : return Add ( * co ) elif x_c : xargs = x . args_cnc ( cset = True , warn = False ) [ 0 ] for a in args : margs , nc = a . args_cnc ( cset = True ) if len ( xargs ) > len ( margs ) : continue resid = margs . difference ( xargs ) if len ( resid ) + len ( xargs ) == len ( margs ) : co . append ( Mul ( * ( list ( resid ) + nc ) ) ) if co == [ ] : return S . Zero elif co : return Add ( * co ) else : # both nc xargs , nx = x . args_cnc ( cset = True ) # find the parts that pass the commutative terms for a in args : margs , nc = a . args_cnc ( cset = True ) if len ( xargs ) > len ( margs ) : continue resid = margs . difference ( xargs ) if len ( resid ) + len ( xargs ) == len ( margs ) : co . append ( ( resid , nc ) ) # now check the non-comm parts if not co : return S . Zero if all ( n == co [ 0 ] [ 1 ] for r , n in co ) : ii = find ( co [ 0 ] [ 1 ] , nx , right ) if ii is not None : if not right : return Mul ( Add ( * [ Mul ( * r ) for r , c in co ] ) , Mul ( * co [ 0 ] [ 1 ] [ : ii ] ) ) else : return Mul ( * co [ 0 ] [ 1 ] [ ii + len ( nx ) : ] ) beg = reduce ( incommon , ( n [ 1 ] for n in co ) ) if beg : ii = find ( beg , nx , right ) if ii is not None : if not right : gcdc = co [ 0 ] [ 0 ] for i in xrange ( 1 , len ( co ) ) : gcdc = gcdc . intersection ( co [ i ] [ 0 ] ) if not gcdc : break return Mul ( * ( list ( gcdc ) + beg [ : ii ] ) ) else : m = ii + len ( nx ) return Add ( * [ Mul ( * ( list ( r ) + n [ m : ] ) ) for r , n in co ] ) end = list ( reversed ( reduce ( incommon , ( list ( reversed ( n [ 1 ] ) ) for n in co ) ) ) ) if end : ii = find ( end , nx , right ) if ii is not None : if not right : return Add ( * [ Mul ( * ( list ( r ) + n [ : - len ( end ) + ii ] ) ) for r , n in co ] ) else : return Mul ( * end [ ii + len ( nx ) : ] ) # look for single match hit = None for i , ( r , n ) in enumerate ( co ) : ii = find ( n , nx , right ) if ii is not None : if not hit : hit = ii , r , n else : break else : if hit : ii , r , n = hit if not right : return Mul ( * ( list ( r ) + n [ : ii ] ) ) else : return Mul ( * n [ ii + len ( nx ) : ] ) return S . Zero