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Ticket #7377: 7377-abstract-maxima.patch

File 7377-abstract-maxima.patch, 131.0 KB (added by robertwb, 9 years ago)

sage/interfaces/maxima.py

# HG changeset patch
# User Robert Bradshaw <robertwb@math.washington.edu>
# Date 1263685289 28800
# Node ID a44619a880c4de5e18cf646a23d3e65d09cfe474
# Parent  604c0fdf356f0bbfef70253ea04b5ca7a28440af
Split maxima interface up into abstract and concrete methods.

diff -r 604c0fdf356f -r a44619a880c4 sage/interfaces/maxima.py

-                      a
     sage: F
     -(y-x)*(y^4+x*y^3+x^2*y^2+x^3*y+x^4)
     sage: type(F)
     <class 'sage.interfaces.maxima.MaximaElement'>
+    <class 'sage.interfaces.maxima_abstract.MaximaElement'>
 Note that Maxima objects can also be displayed using "ASCII art";
 to see a normal linear representation of any Maxima object x. Just
 …
 import sage.server.support
+import maxima_abstract
+from maxima_abstract import MaximaFunctionElement, MaximaExpectFunction, MaximaElement, MaximaFunction, maxima_console
 # The Maxima "apropos" command, e.g., apropos(det) gives a list
 # of all identifiers that begin in a certain way.  This could
 # maybe be useful somehow... (?)  Also maxima has a lot for getting
 # documentation from the system -- this could also be useful.
 class Maxima(Expect):
+class Maxima(maxima_abstract.Maxima):
     """
     Interface to the Maxima interpreter.
     """
 …
         EXAMPLES::
             sage: maxima._function_class()
             <class 'sage.interfaces.maxima.MaximaExpectFunction'>
+            <class 'sage.interfaces.maxima_abstract.MaximaExpectFunction'>
         """
         return MaximaExpectFunction
 …
         """
         return reduce_load_Maxima, tuple([])
-    def _quit_string(self):
-        """
-        EXAMPLES::
-            sage: maxima._quit_string()
-            'quit();'
-        """
-        return 'quit();'
     def _sendline(self, str):
         self._sendstr(str)
         os.write(self._expect.child_fd, os.linesep)
-    def _crash_msg(self):
-        """
-        EXAMPLES::
-            sage: maxima._crash_msg()
-            Maxima crashed -- automatically restarting.
-        """
-        print "Maxima crashed -- automatically restarting."
     def _expect_expr(self, expr=None, timeout=None):
         """
         EXAMPLES:
 …
                     break
             raise KeyboardInterrupt, msg
-    def _batch(self, s, batchload=True):
-        filename = '%s-%s'%(self._local_tmpfile(),randrange(2147483647))
-        F = open(filename, 'w')
-        F.write(s)
-        F.close()
-        if self.is_remote():
-            self._send_tmpfile_to_server(local_file=filename)
-            tmp_to_use = self._remote_tmpfile()
-        tmp_to_use = filename
-        if batchload:
-            cmd = 'batchload("%s");'%tmp_to_use
-        else:
-            cmd = 'batch("%s");'%tmp_to_use
-        r = randrange(2147483647)
-        s = str(r+1)
-        cmd = "%s1+%s;\n"%(cmd,r)
-        self._sendline(cmd)
-        self._expect_expr(s)
-        out = self._before()
-        self._error_check(str, out)
-        os.unlink(filename)
-        return out
-    def _error_check(self, str, out):
-        r = self._error_re
-        m = r.search(out)
-        if not m is None:
-            self._error_msg(str, out)
-    def _error_msg(self, str, out):
-        raise TypeError, "Error executing code in Maxima\nCODE:\n\t%s\nMaxima ERROR:\n\t%s"%(str, out.replace('-- an error.  To debug this try debugmode(true);',''))
     def _eval_line(self, line, allow_use_file=False,
                    wait_for_prompt=True, reformat=True, error_check=True):
         if len(line) == 0:
 …
             self._crash_msg()
             self.quit()
-    ###########################################
-    # System -- change directory, etc
-    ###########################################
-    def chdir(self, dir):
-        """
-        Change Maxima's current working directory.
-        EXAMPLES::
-            sage: maxima.chdir('/')
-        """
-        self.lisp('(ext::cd "%s")'%dir)
     ###########################################
     # Direct access to underlying lisp interpreter.
     ###########################################
 …
             return AsciiArtString(res)
         else:
             subprocess.Popen(cmd, shell=True)
+    def help(self, s):
+        """
+        EXAMPLES::
+            sage: maxima.help('gcd')
+            -- Function: gcd (<p_1>, <p_2>, <x_1>, ...)
+            ...
+        """
+        return self._command_runner("describe", s)
+    def example(self, s):
+        """
+        EXAMPLES::
+            sage: maxima.example('arrays')
+            a[n]:=n*a[n-1]
+                                            a  := n a
+                                             n       n - 1
+            a[0]:1
+            a[5]
+            a[n]:=n
+            a[6]
+            a[4]
+                                                 done
+        """
+        return self._command_runner("example", s)
+    describe = help
+    def demo(self, s):
+        """
+        EXAMPLES::
+            sage: maxima.demo('array') # not tested
+            batching /opt/sage/local/share/maxima/5.16.3/demo/array.dem
+        At the _ prompt, type ';' followed by enter to get next demo
+        subscrmap : true _
+        """
+        return self._command_runner("demo", s, redirect=False)
+    def completions(self, s, verbose=True):
+        """
+        Return all commands that complete the command starting with the
+        string s. This is like typing s[tab] in the Maxima interpreter.
+        EXAMPLES::
+            sage: sorted(maxima.completions('gc', verbose=False))
+            ['gcd', 'gcdex', 'gcfactor', 'gcprint', 'gctime']
+        """
+        if verbose:
+            print s,
+            sys.stdout.flush()
+        # in Maxima 5.19.1, apropos returns all commands that contain
+        # the given string, instead of all commands that start with
+        # the given string
+        cmd_list = self._eval_line('apropos("%s")'%s, error_check=False).replace('\\ - ','-')
+        cmd_list = [x for x in cmd_list[1:-1].split(',') if x[0] != '?']
+        return [x for x in cmd_list if x.find(s) == 0]
+    def _commands(self, verbose=True):
+        """
+        Return list of all commands defined in Maxima.
+        EXAMPLES::
+            sage: sorted(maxima._commands(verbose=False))
+            ['Alpha',
+             'Beta',
+             ...
+             'zunderflow']
+        """
+        try:
+            return self.__commands
+        except AttributeError:
+            self.__commands = sum(
+                [self.completions(chr(65+n), verbose=verbose)+
+                 self.completions(chr(97+n), verbose=verbose)
+                 for n in range(26)], [])
+        return self.__commands
+    def trait_names(self, verbose=True, use_disk_cache=True):
+        """
+        Return all Maxima commands, which is useful for tab completion.
+        EXAMPLES::
+            sage: t = maxima.trait_names(verbose=False)
+            sage: 'gcd' in t
+            True
+            sage: len(t)    # random output
+        """
+        try:
+            return self.__trait_names
+        except AttributeError:
+            import sage.misc.persist
+            if use_disk_cache:
+                try:
+                    self.__trait_names = sage.misc.persist.load(COMMANDS_CACHE)
+                    return self.__trait_names
+                except IOError:
+                    pass
+            if verbose:
+                print "\nBuilding Maxima command completion list (this takes"
+                print "a few seconds only the first time you do it)."
+                print "To force rebuild later, delete %s."%COMMANDS_CACHE
+            v = self._commands(verbose=verbose)
+            if verbose:
+                print "\nDone!"
+            self.__trait_names = v
+            sage.misc.persist.save(v, COMMANDS_CACHE)
+            return v
     def _object_class(self):
         """
         Return the Python class of Maxima elements.
 …
         EXAMPLES::
             sage: maxima._object_class()
             <class 'sage.interfaces.maxima.MaximaElement'>
+            <class 'sage.interfaces.maxima_abstract.MaximaElement'>
         """
         return MaximaElement
 …
         EXAMPLES::
             sage: maxima._function_element_class()
             <class 'sage.interfaces.maxima.MaximaFunctionElement'>
+            <class 'sage.interfaces.maxima_abstract.MaximaFunctionElement'>
         """
         return MaximaFunctionElement
-    def _true_symbol(self):
-        """
-        Return the true symbol in Maxima.
-        EXAMPLES::
-            sage: maxima._true_symbol()
-            'true'
-            sage: maxima.eval('is(2 = 2)')
-            'true'
-        """
-        return 'true'
-    def _false_symbol(self):
-        """
-        Return the false symbol in Maxima.
-        EXAMPLES::
-            sage: maxima._false_symbol()
-            'false'
-            sage: maxima.eval('is(2 = 4)')
-            'false'
-        """
-        return 'false'
-    def _equality_symbol(self):
-        """
-        Returns the equality symbol in Maxima.
-        EXAMPLES::
-             sage: maxima._equality_symbol()
-             '='
-        """
-        return '='
-    def _inequality_symbol(self):
-        """
-        Returns the equality symbol in Maxima.
-        EXAMPLES::
-             sage: maxima._inequality_symbol()
-             '#'
-             sage: maxima((x != 1))
-             x#1
-        """
-        return '#'
     def function(self, args, defn, rep=None, latex=None):
         """
         Return the Maxima function with given arguments and definition.
 …
         """
         s = self._eval_line('%s;'%var)
         return s
-    def console(self):
-        r"""
-        Start the interactive Maxima console. This is a completely separate
-        maxima session from this interface. To interact with this session,
-        you should instead use ``maxima.interact()``.
-        EXAMPLES::
-            sage: maxima.console()             # not tested (since we can't)
-            Maxima 5.13.0 http://maxima.sourceforge.net
-            Using Lisp CLISP 2.41 (2006-10-13)
-            Distributed under the GNU Public License. See the file COPYING.
-            Dedicated to the memory of William Schelter.
-            This is a development version of Maxima. The function bug_report()
-            provides bug reporting information.
-            (%i1)
-        ::
-            sage: maxima.interact()     # this is not tested either
-              --> Switching to Maxima <--
-            maxima: 2+2
-            maxima:
-              --> Exiting back to Sage <--
-        """
-        maxima_console()
     def version(self):
         """
 …
         """
         return maxima_version()
-    def cputime(self, t=None):
-        r"""
-        Returns the amount of CPU time that this Maxima session has used.
-        If \var{t} is not None, then it returns the difference between
-        the current CPU time and \var{t}.
-        EXAMPLES:
-            sage: t = maxima.cputime()
-            sage: _ = maxima.de_solve('diff(y,x,2) + 3*x = y', ['x','y'], [1,1,1])
-            sage: maxima.cputime(t) # output random
-.568913
-        """
-        if t:
-            return float(self.eval('elapsed_run_time()')) - t
-        else:
-            return float(self.eval('elapsed_run_time()'))
 ##     def display2d(self, flag=True):
 ##         """
 …
 ##         """
 ##         self._display2d = bool(flag)
-    def plot2d(self, *args):
-        r"""
-        Plot a 2d graph using Maxima / gnuplot.
-        maxima.plot2d(f, '[var, min, max]', options)
-        INPUT:
-        -  ``f`` - a string representing a function (such as
-           f="sin(x)") [var, xmin, xmax]
-        -  ``options`` - an optional string representing plot2d
-           options in gnuplot format
-        EXAMPLES::
-            sage: maxima.plot2d('sin(x)','[x,-5,5]')   # not tested
-            sage: opts = '[gnuplot_term, ps], [gnuplot_out_file, "sin-plot.eps"]'
-            sage: maxima.plot2d('sin(x)','[x,-5,5]',opts)    # not tested
-        The eps file is saved in the current directory.
-        """
-        self('plot2d(%s)'%(','.join([str(x) for x in args])))
-    def plot2d_parametric(self, r, var, trange, nticks=50, options=None):
-        r"""
-        Plots r = [x(t), y(t)] for t = tmin...tmax using gnuplot with
-        options
-        INPUT:
-        -  ``r`` - a string representing a function (such as
-           r="[x(t),y(t)]")
-        -  ``var`` - a string representing the variable (such
-           as var = "t")
-        -  ``trange`` - [tmin, tmax] are numbers with tmintmax
-        -  ``nticks`` - int (default: 50)
-        -  ``options`` - an optional string representing plot2d
-           options in gnuplot format
-        EXAMPLES::
-            sage: maxima.plot2d_parametric(["sin(t)","cos(t)"], "t",[-3.1,3.1])   # not tested
-        ::
-            sage: opts = '[gnuplot_preamble, "set nokey"], [gnuplot_term, ps], [gnuplot_out_file, "circle-plot.eps"]'
-            sage: maxima.plot2d_parametric(["sin(t)","cos(t)"], "t", [-3.1,3.1], options=opts)   # not tested
-        The eps file is saved to the current working directory.
-        Here is another fun plot::
-            sage: maxima.plot2d_parametric(["sin(5*t)","cos(11*t)"], "t", [0,2*pi()], nticks=400)    # not tested
-        """
-        tmin = trange[0]
-        tmax = trange[1]
-        cmd = "plot2d([parametric, %s, %s, [%s, %s, %s], [nticks, %s]]"%( \
-                   r[0], r[1], var, tmin, tmax, nticks)
-        if options is None:
-            cmd += ")"
-        else:
-            cmd += ", %s)"%options
-        self(cmd)
-    def plot3d(self, *args):
-        r"""
-        Plot a 3d graph using Maxima / gnuplot.
-        maxima.plot3d(f, '[x, xmin, xmax]', '[y, ymin, ymax]', '[grid, nx,
-        ny]', options)
-        INPUT:
-        -  ``f`` - a string representing a function (such as
-           f="sin(x)") [var, min, max]
-        EXAMPLES::
-            sage: maxima.plot3d('1 + x^3 - y^2', '[x,-2,2]', '[y,-2,2]', '[grid,12,12]')    # not tested
-            sage: maxima.plot3d('sin(x)*cos(y)', '[x,-2,2]', '[y,-2,2]', '[grid,30,30]')   # not tested
-            sage: opts = '[gnuplot_term, ps], [gnuplot_out_file, "sin-plot.eps"]'
-            sage: maxima.plot3d('sin(x+y)', '[x,-5,5]', '[y,-1,1]', opts)    # not tested
-        The eps file is saved in the current working directory.
-        """
-        self('plot3d(%s)'%(','.join([str(x) for x in args])))
-    def plot3d_parametric(self, r, vars, urange, vrange, options=None):
-        r"""
-        Plot a 3d parametric graph with r=(x,y,z), x = x(u,v), y = y(u,v),
-        z = z(u,v), for u = umin...umax, v = vmin...vmax using gnuplot with
-        options.
-        INPUT:
-        -  ``x, y, z`` - a string representing a function (such
-           as ``x="u2+v2"``, ...) vars is a list or two strings
-           representing variables (such as vars = ["u","v"])
-        -  ``urange`` - [umin, umax]
-        -  ``vrange`` - [vmin, vmax] are lists of numbers with
-           umin umax, vmin vmax
-        -  ``options`` - optional string representing plot2d
-           options in gnuplot format
-        OUTPUT: displays a plot on screen or saves to a file
-        EXAMPLES::
-            sage: maxima.plot3d_parametric(["v*sin(u)","v*cos(u)","v"], ["u","v"],[-3.2,3.2],[0,3])     # not tested
-            sage: opts = '[gnuplot_term, ps], [gnuplot_out_file, "sin-cos-plot.eps"]'
-            sage: maxima.plot3d_parametric(["v*sin(u)","v*cos(u)","v"], ["u","v"],[-3.2,3.2],[0,3],opts)      # not tested
-        The eps file is saved in the current working directory.
-        Here is a torus::
-            sage: _ = maxima.eval("expr_1: cos(y)*(10.0+6*cos(x)); expr_2: sin(y)*(10.0+6*cos(x)); expr_3: -6*sin(x);")  # optional
-            sage: maxima.plot3d_parametric(["expr_1","expr_2","expr_3"], ["x","y"],[0,6],[0,6])   # not tested
-        Here is a Mobius strip::
-            sage: x = "cos(u)*(3 + v*cos(u/2))"
-            sage: y = "sin(u)*(3 + v*cos(u/2))"
-            sage: z = "v*sin(u/2)"
-            sage: maxima.plot3d_parametric([x,y,z],["u","v"],[-3.1,3.2],[-1/10,1/10])   # not tested
-        """
-        umin = urange[0]
-        umax = urange[1]
-        vmin = vrange[0]
-        vmax = vrange[1]
-        cmd = 'plot3d([%s, %s, %s], [%s, %s, %s], [%s, %s, %s]'%(
-            r[0], r[1], r[2], vars[0], umin, umax, vars[1], vmin, vmax)
-        if options is None:
-            cmd += ')'
-        else:
-            cmd += ', %s)'%options
-        maxima(cmd)
-    def de_solve(maxima, de, vars, ics=None):
-        """
-        Solves a 1st or 2nd order ordinary differential equation (ODE) in
-        two variables, possibly with initial conditions.
-        INPUT:
-        -  ``de`` - a string representing the ODE
-        -  ``vars`` - a list of strings representing the two
-           variables.
-        -  ``ics`` - a triple of numbers [a,b1,b2] representing
-           y(a)=b1, y'(a)=b2
-        EXAMPLES::
-            sage: maxima.de_solve('diff(y,x,2) + 3*x = y', ['x','y'], [1,1,1])
-            y=3*x-2*%e^(x-1)
-            sage: maxima.de_solve('diff(y,x,2) + 3*x = y', ['x','y'])
-            y=%k1*%e^x+%k2*%e^-x+3*x
-            sage: maxima.de_solve('diff(y,x) + 3*x = y', ['x','y'])
-            y=(%c-3*(-x-1)*%e^-x)*%e^x
-            sage: maxima.de_solve('diff(y,x) + 3*x = y', ['x','y'],[1,1])
-            y=-%e^-1*(5*%e^x-3*%e*x-3*%e)
-        """
-        if not isinstance(vars, str):
-            str_vars = '%s, %s'%(vars[1], vars[0])
-        else:
-            str_vars = vars
-        maxima.eval('depends(%s)'%str_vars)
-        m = maxima(de)
-        a = 'ode2(%s, %s)'%(m.name(), str_vars)
-        if ics != None:
-            if len(ics) == 3:
-                cmd = "ic2("+a+",%s=%s,%s=%s,diff(%s,%s)=%s);"%(vars[0],ics[0], vars[1],ics[1], vars[1], vars[0], ics[2])
-                return maxima(cmd)
-            if len(ics) == 2:
-                return maxima("ic1("+a+",%s=%s,%s=%s);"%(vars[0],ics[0], vars[1],ics[1]))
-        return maxima(a+";")
-    def de_solve_laplace(self, de, vars, ics=None):
-        """
-        Solves an ordinary differential equation (ODE) using Laplace
-        transforms.
-        INPUT:
-        -  ``de`` - a string representing the ODE (e.g., de =
-           "diff(f(x),x,2)=diff(f(x),x)+sin(x)")
-        -  ``vars`` - a list of strings representing the
-           variables (e.g., vars = ["x","f"])
-        -  ``ics`` - a list of numbers representing initial
-           conditions, with symbols allowed which are represented by strings
-           (eg, f(0)=1, f'(0)=2 is ics = [0,1,2])
-        EXAMPLES::
-            sage: maxima.clear('x'); maxima.clear('f')
-            sage: maxima.de_solve_laplace("diff(f(x),x,2) = 2*diff(f(x),x)-f(x)", ["x","f"], [0,1,2])
-            f(x)=x*%e^x+%e^x
-        ::
-            sage: maxima.clear('x'); maxima.clear('f')
-            sage: f = maxima.de_solve_laplace("diff(f(x),x,2) = 2*diff(f(x),x)-f(x)", ["x","f"])
-            sage: f
-            f(x)=x*%e^x*('at('diff(f(x),x,1),x=0))-f(0)*x*%e^x+f(0)*%e^x
-            sage: print f
+                                               !
-                                   x  d        !                  x          x
-                        f(x) = x %e  (-- (f(x))!     ) - f(0) x %e  + f(0) %e
-                                      dx       !
-                                               !x = 0
-        .. note::
-           The second equation sets the values of `f(0)` and
-           `f'(0)` in Maxima, so subsequent ODEs involving these
-           variables will have these initial conditions automatically
-           imposed.
-        """
-        if not (ics is None):
-            d = len(ics)
-            for i in range(0,d-1):
-                ic = 'atvalue(diff(%s(%s), %s, %s), %s = %s, %s)'%(
-                    vars[1], vars[0], vars[0], i, vars[0], ics[0], ics[1+i])
-                maxima.eval(ic)
-        return maxima('desolve(%s, %s(%s))'%(de, vars[1], vars[0]))
-    def solve_linear(self, eqns,vars):
-        """
-        Wraps maxima's linsolve.
-        INPUT: eqns is a list of m strings, each representing a linear
-        question in m = n variables vars is a list of n strings, each
-        representing a variable
-        EXAMPLES::
-            sage: eqns = ["x + z = y","2*a*x - y = 2*a^2","y - 2*z = 2"]
-            sage: vars = ["x","y","z"]
-            sage: maxima.solve_linear(eqns, vars)
-            [x=a+1,y=2*a,z=a-1]
-        """
-        eqs = "["
-        for i in range(len(eqns)):
-            if i<len(eqns)-1:
-                eqs = eqs + eqns[i]+","
-            if  i==len(eqns)-1:
-                eqs = eqs + eqns[i]+"]"
-        vrs = "["
-        for i in range(len(vars)):
-            if i<len(vars)-1:
-                vrs = vrs + vars[i]+","
-            if  i==len(vars)-1:
-                vrs = vrs + vars[i]+"]"
-        return self('linsolve(%s, %s)'%(eqs, vrs))
-    def unit_quadratic_integer(self, n):
-        r"""
-        Finds a unit of the ring of integers of the quadratic number field
-        `\QQ(\sqrt{n})`, `n>1`, using the qunit maxima
-        command.
-        EXAMPLES::
-            sage: u = maxima.unit_quadratic_integer(101); u
-            a + 10
-            sage: u.parent()
-            Number Field in a with defining polynomial x^2 - 101
-            sage: u = maxima.unit_quadratic_integer(13)
-            sage: u
-*a + 18
-            sage: u.parent()
-            Number Field in a with defining polynomial x^2 - 13
-        """
-        from sage.rings.all import QuadraticField, Integer
-        # Take square-free part so sqrt(n) doesn't get simplified further by maxima
-        # (The original version of this function would yield wrong answers if
-        # n is not squarefree.)
-        n = Integer(n).squarefree_part()
-        if n < 1:
-            raise ValueError, "n (=%s) must be >= 1"%n
-        s = repr(self('qunit(%s)'%n)).lower()
-        r = re.compile('sqrt\(.*\)')
-        s = r.sub('a', s)
-        a = QuadraticField(n, 'a').gen()
-        return eval(s)
-    def plot_list(self, ptsx, ptsy, options=None):
-        r"""
-        Plots a curve determined by a sequence of points.
-        INPUT:
-        -  ``ptsx`` - [x1,...,xn], where the xi and yi are
-           real,
-        -  ``ptsy`` - [y1,...,yn]
-        -  ``options`` - a string representing maxima plot2d
-           options.
-        The points are (x1,y1), (x2,y2), etc.
-        This function requires maxima 5.9.2 or newer.
-        .. note::
-           More that 150 points can sometimes lead to the program
-           hanging. Why?
-        EXAMPLES::
-            sage: zeta_ptsx = [ (pari(1/2 + i*I/10).zeta().real()).precision(1) for i in range (70,150)]
-            sage: zeta_ptsy = [ (pari(1/2 + i*I/10).zeta().imag()).precision(1) for i in range (70,150)]
-            sage: maxima.plot_list(zeta_ptsx, zeta_ptsy)         # not tested
-            sage: opts='[gnuplot_preamble, "set nokey"], [gnuplot_term, ps], [gnuplot_out_file, "zeta.eps"]'
-            sage: maxima.plot_list(zeta_ptsx, zeta_ptsy, opts)      # not tested
-        """
-        cmd = 'plot2d([discrete,%s, %s]'%(ptsx, ptsy)
-        if options is None:
-            cmd += ')'
-        else:
-            cmd += ', %s)'%options
-        self(cmd)
-    def plot_multilist(self, pts_list, options=None):
-        r"""
-        Plots a list of list of points pts_list=[pts1,pts2,...,ptsn],
-        where each ptsi is of the form [[x1,y1],...,[xn,yn]] x's must be
-        integers and y's reals options is a string representing maxima
-        plot2d options.
-        Requires maxima 5.9.2 at least.
-        .. note::
-           More that 150 points can sometimes lead to the program
-           hanging.
-        EXAMPLES::
-            sage: xx = [ i/10.0 for i in range (-10,10)]
-            sage: yy = [ i/10.0 for i in range (-10,10)]
-            sage: x0 = [ 0 for i in range (-10,10)]
-            sage: y0 = [ 0 for i in range (-10,10)]
-            sage: zeta_ptsx1 = [ (pari(1/2+i*I/10).zeta().real()).precision(1) for i in range (10)]
-            sage: zeta_ptsy1 = [ (pari(1/2+i*I/10).zeta().imag()).precision(1) for i in range (10)]
-            sage: maxima.plot_multilist([[zeta_ptsx1,zeta_ptsy1],[xx,y0],[x0,yy]])       # not tested
-            sage: zeta_ptsx1 = [ (pari(1/2+i*I/10).zeta().real()).precision(1) for i in range (10,150)]
-            sage: zeta_ptsy1 = [ (pari(1/2+i*I/10).zeta().imag()).precision(1) for i in range (10,150)]
-            sage: maxima.plot_multilist([[zeta_ptsx1,zeta_ptsy1],[xx,y0],[x0,yy]])      # not tested
-            sage: opts='[gnuplot_preamble, "set nokey"]'
-            sage: maxima.plot_multilist([[zeta_ptsx1,zeta_ptsy1],[xx,y0],[x0,yy]],opts)    # not tested
-        """
-        n = len(pts_list)
-        cmd = '['
-        for i in range(n):
-            if i < n-1:
-                cmd = cmd+'[discrete,'+str(pts_list[i][0])+','+str(pts_list[i][1])+'],'
-            if i==n-1:
-                cmd = cmd+'[discrete,'+str(pts_list[i][0])+','+str(pts_list[i][1])+']]'
-        #print cmd
-        if options is None:
-            self('plot2d('+cmd+')')
-        else:
-            self('plot2d('+cmd+','+options+')')
-class MaximaElement(ExpectElement):
-    def __str__(self):
-        """
-        Printing an object explicitly gives ASCII art:
-        EXAMPLES::
-            sage: f = maxima('1/(x-1)^3'); f
-/(x-1)^3
-            sage: print f
-                                               --------
-                                               (x - 1)
-        """
-        return self.display2d(onscreen=False)
-    def bool(self):
-        """
-        EXAMPLES::
-            sage: maxima(0).bool()
-            False
-            sage: maxima(1).bool()
-            True
-        """
-        P = self._check_valid()
-        return P.eval('is(%s = 0);'%self.name()) == P._false_symbol() # but be careful, since for relations things like is(equal(a,b)) are what Maxima needs
-    def __cmp__(self, other):
-        """
-        EXAMPLES::
-            sage: a = maxima(1); b = maxima(2)
-            sage: a == b
-            False
-            sage: a < b
-            True
-            sage: a > b
-            False
-            sage: b < a
-            False
-            sage: b > a
-            True
-        We can also compare more complicated object such as functions::
-            sage: f = maxima('sin(x)'); g = maxima('cos(x)')
-            sage: -f == g.diff('x')
-            True
-        """
-        # thanks to David Joyner for telling me about using "is".
-        # but be careful, since for relations things like is(equal(a,b)) are what Maxima needs
-        P = self.parent()
-        try:
-            if P.eval("is (%s < %s)"%(self.name(), other.name())) == P._true_symbol():
-                return -1
-            elif P.eval("is (%s > %s)"%(self.name(), other.name())) == P._true_symbol():
-                return 1
-            elif P.eval("is (%s = %s)"%(self.name(), other.name())) == P._true_symbol():
-                return 0
-        except TypeError:
-            pass
-        return cmp(repr(self),repr(other))
-                   # everything is supposed to be comparable in Python, so we define
-                   # the comparison thus when no comparable in interfaced system.
-    def _sage_(self):
-        """
-        Attempt to make a native Sage object out of this maxima object.
-        This is useful for automatic coercions in addition to other
-        things.
-        EXAMPLES::
-            sage: a = maxima('sqrt(2) + 2.5'); a
-            sqrt(2)+2.5
-            sage: b = a._sage_(); b
-            sqrt(2) + 2.5
-            sage: type(b)
-            <type 'sage.symbolic.expression.Expression'>
-        We illustrate an automatic coercion::
-            sage: c = b + sqrt(3); c
-            sqrt(2) + sqrt(3) + 2.5
-            sage: type(c)
-            <type 'sage.symbolic.expression.Expression'>
-            sage: d = sqrt(3) + b; d
-            sqrt(2) + sqrt(3) + 2.5
-            sage: type(d)
-            <type 'sage.symbolic.expression.Expression'>
-        """
-        from sage.calculus.calculus import symbolic_expression_from_maxima_string
-        #return symbolic_expression_from_maxima_string(self.name(), maxima=self.parent())
-        return symbolic_expression_from_maxima_string(repr(self))
-    def _symbolic_(self, R):
-        """
-        Return a symbolic expression equivalent to this maxima object.
-        EXAMPLES::
-            sage: t = sqrt(2)._maxima_()
-            sage: u = t._symbolic_(SR); u
-            sqrt(2)
-            sage: u.parent()
-            Symbolic Ring
-        This is used when converting maxima objects to the Symbolic Ring::
-            sage: SR(t)
-            sqrt(2)
-        """
-        return R(self._sage_())
-    def __complex__(self):
-        """
-        EXAMPLES::
-            sage: complex(maxima('sqrt(-2)+1'))
-            (1+1.4142135623730951j)
-        """
-        return complex(self._sage_())
-    def _complex_mpfr_field_(self, C):
-        """
-        EXAMPLES::
-            sage: CC(maxima('1+%i'))
-.00000000000000 + 1.00000000000000*I
-            sage: CC(maxima('2342.23482943872+234*%i'))
-.23482943872 + 234.000000000000*I
-            sage: ComplexField(10)(maxima('2342.23482943872+234*%i'))
-. + 230.*I
-            sage: ComplexField(200)(maxima('1+%i'))
-.0000000000000000000000000000000000000000000000000000000000 + 1.0000000000000000000000000000000000000000000000000000000000*I
-            sage: ComplexField(200)(maxima('sqrt(-2)'))
-.4142135623730950488016887242096980785696718753769480731767*I
-            sage: N(sqrt(-2), 200)
-.0751148893563733350506651837615871941533119425962889089783e-62 + 1.4142135623730950488016887242096980785696718753769480731767*I
-        """
-        return C(self._sage_())
-    def _mpfr_(self, R):
-        """
-        EXAMPLES::
-            sage: RealField(100)(maxima('sqrt(2)+1'))
-.4142135623730950488016887242
-        """
-        return R(self._sage_())
-    def _complex_double_(self, C):
-        """
-        EXAMPLES::
-            sage: CDF(maxima('sqrt(2)+1'))
-.41421356237
-        """
-        return C(self._sage_())
-    def _real_double_(self, R):
-        """
-        EXAMPLES::
-            sage: RDF(maxima('sqrt(2)+1'))
-.41421356237
-        """
-        return R(self._sage_())
-    def real(self):
-        """
-        Return the real part of this maxima element.
-        EXAMPLES::
-            sage: maxima('2 + (2/3)*%i').real()
-        """
-        return self.realpart()
-    def imag(self):
-        """
-        Return the imaginary part of this maxima element.
-        EXAMPLES::
-            sage: maxima('2 + (2/3)*%i').imag()
-/3
-        """
-        return self.imagpart()
-    def numer(self):
-        """
-        Return numerical approximation to self as a Maxima object.
-        EXAMPLES::
-            sage: a = maxima('sqrt(2)').numer(); a
-.414213562373095
-            sage: type(a)
-            <class 'sage.interfaces.maxima.MaximaElement'>
-        """
-        return self.comma('numer')
-    def str(self):
-        """
-        Return string representation of this maxima object.
-        EXAMPLES::
-            sage: maxima('sqrt(2) + 1/3').str()
-            'sqrt(2)+1/3'
-        """
-        P = self._check_valid()
-        return P.get(self._name)
-    def __repr__(self):
-        """
-        Return print representation of this object.
-        EXAMPLES::
-            sage: maxima('sqrt(2) + 1/3').__repr__()
-            'sqrt(2)+1/3'
-        """
-        P = self._check_valid()
-        try:
-            return self.__repr
-        except AttributeError:
-            pass
-        r = P.get(self._name)
-        self.__repr = r
-        return r
-    def display2d(self, onscreen=True):
-        """
-        EXAMPLES::
-            sage: F = maxima('x^5 - y^5').factor()
-            sage: F.display2d ()
-      3    2  2    3      4
-                       - (y - x) (y  + x y  + x  y  + x  y + x )
-        """
-        self._check_valid()
-        P = self.parent()
-        with gc_disabled():
-            P._eval_line('display2d : true$')
-            s = P._eval_line('disp(%s)$'%self.name(), reformat=False)
-            P._eval_line('display2d: false$')
-        s = s.strip('\r\n')
-        # if ever want to dedent, see
-        # http://mail.python.org/pipermail/python-list/2006-December/420033.html
-        if onscreen:
-            print s
-        else:
-            return s
-    def diff(self, var='x', n=1):
-        """
-        Return the n-th derivative of self.
-        INPUT:
-        -  ``var`` - variable (default: 'x')
-        -  ``n`` - integer (default: 1)
-        OUTPUT: n-th derivative of self with respect to the variable var
-        EXAMPLES::
-            sage: f = maxima('x^2')
-            sage: f.diff()
-*x
-            sage: f.diff('x')
-*x
-            sage: f.diff('x', 2)
-            sage: maxima('sin(x^2)').diff('x',4)
-*x^4*sin(x^2)-12*sin(x^2)-48*x^2*cos(x^2)
-        ::
-            sage: f = maxima('x^2 + 17*y^2')
-            sage: f.diff('x')
-*y*'diff(y,x,1)+2*x
-            sage: f.diff('y')
-*y
-        """
-        return ExpectElement.__getattr__(self, 'diff')(var, n)
-    derivative = diff
-    def nintegral(self, var='x', a=0, b=1,
-                  desired_relative_error='1e-8',
-                  maximum_num_subintervals=200):
-        r"""
-        Return a numerical approximation to the integral of self from a to
-        b.
-        INPUT:
-        -  ``var`` - variable to integrate with respect to
-        -  ``a`` - lower endpoint of integration
-        -  ``b`` - upper endpoint of integration
-        -  ``desired_relative_error`` - (default: '1e-8') the
-           desired relative error
-        -  ``maximum_num_subintervals`` - (default: 200)
-           maxima number of subintervals
-        OUTPUT:
-        -  approximation to the integral
-        -  estimated absolute error of the
-           approximation
-        -  the number of integrand evaluations
-        -  an error code:
-            -  ``0`` - no problems were encountered
-            -  ``1`` - too many subintervals were done
-            -  ``2`` - excessive roundoff error
-            -  ``3`` - extremely bad integrand behavior
-            -  ``4`` - failed to converge
-            -  ``5`` - integral is probably divergent or slowly convergent
-            -  ``6`` - the input is invalid
-        EXAMPLES::
-            sage: maxima('exp(-sqrt(x))').nintegral('x',0,1)
-            (.5284822353142306, 4.163314137883845e-11, 231, 0)
-        Note that GP also does numerical integration, and can do so to very
-        high precision very quickly::
-            sage: gp('intnum(x=0,1,exp(-sqrt(x)))')
-.5284822353142307136179049194             # 32-bit
-.52848223531423071361790491935415653021   # 64-bit
-            sage: _ = gp.set_precision(80)
-            sage: gp('intnum(x=0,1,exp(-sqrt(x)))')
-.52848223531423071361790491935415653021675547587292866196865279321015401702040079
-        """
-        from sage.rings.all import Integer
-        v = self.quad_qags(var, a, b, epsrel=desired_relative_error,
-                           limit=maximum_num_subintervals)
-        return v[0], v[1], Integer(v[2]), Integer(v[3])
-    def integral(self, var='x', min=None, max=None):
-        r"""
-        Return the integral of self with respect to the variable x.
-        INPUT:
-        -  ``var`` - variable
-        -  ``min`` - default: None
-        -  ``max`` - default: None
-        Returns the definite integral if xmin is not None, otherwise
-        returns an indefinite integral.
-        EXAMPLES::
-            sage: maxima('x^2+1').integral()
-            x^3/3+x
-            sage: maxima('x^2+ 1 + y^2').integral('y')
-            y^3/3+x^2*y+y
-            sage: maxima('x / (x^2+1)').integral()
-            log(x^2+1)/2
-            sage: maxima('1/(x^2+1)').integral()
-            atan(x)
-            sage: maxima('1/(x^2+1)').integral('x', 0, infinity)
-            %pi/2
-            sage: maxima('x/(x^2+1)').integral('x', -1, 1)
-        ::
-            sage: f = maxima('exp(x^2)').integral('x',0,1); f
-            -sqrt(%pi)*%i*erf(%i)/2
-            sage: f.numer()
-.462651745907182
-        """
-        I = ExpectElement.__getattr__(self, 'integrate')
-        if min is None:
-            return I(var)
-        else:
-            if max is None:
-                raise ValueError, "neither or both of min/max must be specified."
-            return I(var, min, max)
-    integrate = integral
-    def __float__(self):
-        """
-        Return floating point version of this maxima element.
-        EXAMPLES::
-            sage: float(maxima("3.14"))
-.1400000000000001
-            sage: float(maxima("1.7e+17"))
-.7e+17
-            sage: float(maxima("1.7e-17"))
-.6999999999999999e-17
-        """
-        try:
-            return float(repr(self.numer()))
-        except ValueError:
-            raise TypeError, "unable to coerce '%s' to float"%repr(self)
-    def __len__(self):
-        """
-        Return the length of a list.
-        EXAMPLES::
-            sage: v = maxima('create_list(x^i,i,0,5)')
-            sage: len(v)
-        """
-        P = self._check_valid()
-        return int(P.eval('length(%s)'%self.name()))
-    def dot(self, other):
-        """
-        Implements the notation self . other.
-        EXAMPLES::
-            sage: A = maxima('matrix ([a1],[a2])')
-            sage: B = maxima('matrix ([b1, b2])')
-            sage: A.dot(B)
-            matrix([a1*b1,a1*b2],[a2*b1,a2*b2])
-        """
-        P = self._check_valid()
-        Q = P(other)
-        return P('%s . %s'%(self.name(), Q.name()))
-    def __getitem__(self, n):
-        r"""
-        Return the n-th element of this list.
-        .. note::
-           Lists are 0-based when accessed via the Sage interface, not
--based as they are in the Maxima interpreter.
-        EXAMPLES::
-            sage: v = maxima('create_list(i*x^i,i,0,5)'); v
-            [0,x,2*x^2,3*x^3,4*x^4,5*x^5]
-            sage: v[3]
-*x^3
-            sage: v[0]
-            sage: v[10]
-            Traceback (most recent call last):
-            ...
-            IndexError: n = (10) must be between 0 and 5
-        """
-        n = int(n)
-        if n < 0 or n >= len(self):
-            raise IndexError, "n = (%s) must be between %s and %s"%(n, 0, len(self)-1)
-        # If you change the n+1 to n below, better change __iter__ as well.
-        return ExpectElement.__getitem__(self, n+1)
-    def __iter__(self):
-        """
-        EXAMPLE::
-            sage: v = maxima('create_list(i*x^i,i,0,5)')
-            sage: L = list(v)
-            sage: [e._sage_() for e in L]
-            [0, x, 2*x^2, 3*x^3, 4*x^4, 5*x^5]
-        """
-        for i in range(len(self)):
-            yield self[i]
-    def subst(self, val):
-        """
-        Substitute a value or several values into this Maxima object.
-        EXAMPLES::
-            sage: maxima('a^2 + 3*a + b').subst('b=2')
-            a^2+3*a+2
-            sage: maxima('a^2 + 3*a + b').subst('a=17')
-            b+340
-            sage: maxima('a^2 + 3*a + b').subst('a=17, b=2')
-        """
-        return self.comma(val)
-    def comma(self, args):
-        """
-        Form the expression that would be written 'self, args' in Maxima.
-        EXAMPLES::
-            sage: maxima('sqrt(2) + I').comma('numer')
-            I+1.414213562373095
-            sage: maxima('sqrt(2) + I*a').comma('a=5')
-*I+sqrt(2)
-        """
-        self._check_valid()
-        P = self.parent()
-        return P('%s, %s'%(self.name(), args))
-    def _latex_(self):
-        """
-        Return Latex representation of this Maxima object.
-        This calls the tex command in Maxima, then does a little
-        post-processing to fix bugs in the resulting Maxima output.
-        EXAMPLES::
-            sage: maxima('sqrt(2) + 1/3 + asin(5)')._latex_()
-            '\\sin^{-1}\\cdot5+\\sqrt{2}+{{1}\\over{3}}'
-            sage: y,d = var('y,d')
-            sage: latex(maxima(derivative(ceil(x*y*d), d,x,x,y)))
-            d^3\,\left({{{\it \partial}^4}\over{{\it \partial}\,d^4}}\,  {\it ceil}\left(d , x , y\right)\right)\,x^2\,y^3+5\,d^2\,\left({{  {\it \partial}^3}\over{{\it \partial}\,d^3}}\,{\it ceil}\left(d , x   , y\right)\right)\,x\,y^2+4\,d\,\left({{{\it \partial}^2}\over{  {\it \partial}\,d^2}}\,{\it ceil}\left(d , x , y\right)\right)\,y
-            sage: latex(maxima(d/(d-2)))
-            {{d}\over{d-2}}
-        """
-        self._check_valid()
-        P = self.parent()
-        s = P._eval_line('tex(%s);'%self.name(), reformat=False)
-        if not '$$' in s:
-            raise RuntimeError, "Error texing maxima object."
-        i = s.find('$$')
-        j = s.rfind('$$')
-        s = s[i+2:j]
-        s = multiple_replace({'\r\n':' ',
-                              '\\%':'',
-                              '\\arcsin ':'\\sin^{-1} ',
-                              '\\arccos ':'\\cos^{-1} ',
-                              '\\arctan ':'\\tan^{-1} '}, s)
-        # Fix a maxima bug, which gives a latex representation of multiplying
-        # two numbers as a single space. This was really bad when 2*17^(1/3)
-        # gets TeXed as '2 17^{\frac{1}{3}}'
+        #
-        # This regex matches a string of spaces preceded by either a '}', a
-        # decimal digit, or a ')', and followed by a decimal digit. The spaces
-        # get replaced by a '\cdot'.
-        s = re.sub(r'(?<=[})\d]) +(?=\d)', '\cdot', s)
-        return s
-    def trait_names(self, verbose=False):
-        """
-        Return all Maxima commands, which is useful for tab completion.
-        EXAMPLES::
-            sage: m = maxima(2)
-            sage: 'gcd' in m.trait_names()
-            True
-        """
-        return self.parent().trait_names(verbose=False)
-    def _matrix_(self, R):
-        r"""
-        If self is a Maxima matrix, return the corresponding Sage matrix
-        over the Sage ring `R`.
-        This may or may not work depending in how complicated the entries
-        of self are! It only works if the entries of self can be coerced as
-        strings to produce meaningful elements of `R`.
-        EXAMPLES::
-            sage: _ = maxima.eval("f[i,j] := i/j")
-            sage: A = maxima('genmatrix(f,4,4)'); A
-            matrix([1,1/2,1/3,1/4],[2,1,2/3,1/2],[3,3/2,1,3/4],[4,2,4/3,1])
-            sage: A._matrix_(QQ)
-            [  1 1/2 1/3 1/4]
-            [  2   1 2/3 1/2]
-            [  3 3/2   1 3/4]
-            [  4   2 4/3   1]
-        You can also use the ``matrix`` command (which is
-        defined in ``sage.misc.functional``)::
-            sage: matrix(QQ, A)
-            [  1 1/2 1/3 1/4]
-            [  2   1 2/3 1/2]
-            [  3 3/2   1 3/4]
-            [  4   2 4/3   1]
-        """
-        from sage.matrix.all import MatrixSpace
-        self._check_valid()
-        P = self.parent()
-        nrows = int(P.eval('length(%s)'%self.name()))
-        if nrows == 0:
-            return MatrixSpace(R, 0, 0)(0)
-        ncols = int(P.eval('length(%s[1])'%self.name()))
-        M = MatrixSpace(R, nrows, ncols)
-        s = self.str().replace('matrix','').replace(',',"','").\
-            replace("]','[","','").replace('([',"['").replace('])',"']")
-        s = eval(s)
-        return M([R(x) for x in s])
-    def partial_fraction_decomposition(self, var='x'):
-        """
-        Return the partial fraction decomposition of self with respect to
-        the variable var.
-        EXAMPLES::
-            sage: f = maxima('1/((1+x)*(x-1))')
-            sage: f.partial_fraction_decomposition('x')
-/(2*(x-1))-1/(2*(x+1))
-            sage: print f.partial_fraction_decomposition('x')
-           1
-                             --------- - ---------
-(x - 1)   2 (x + 1)
-        """
-        return self.partfrac(var)
-    def _operation(self, operation, right):
-        r"""
-        Note that right's parent should already be Maxima since this should
-        be called after coercion has been performed.
-        If right is a ``MaximaFunction``, then we convert
-        ``self`` to a ``MaximaFunction`` that takes
-        no arguments, and let the
-        ``MaximaFunction._operation`` code handle everything
-        from there.
-        EXAMPLES::
-            sage: f = maxima.cos(x)
-            sage: f._operation("+", f)
-*cos(x)
-        """
-        P = self._check_valid()
-        if isinstance(right, MaximaFunction):
-            fself = P.function('', repr(self))
-            return fself._operation(operation, right)
-        try:
-            return P.new('%s %s %s'%(self._name, operation, right._name))
-        except Exception, msg:
-            raise TypeError, msg
-class MaximaFunctionElement(FunctionElement):
-    def _sage_doc_(self):
-        """
-        EXAMPLES::
-            sage: m = maxima(4)
-            sage: m.gcd._sage_doc_()
-            -- Function: gcd (<p_1>, <p_2>, <x_1>, ...)
-            ...
-        """
-        return self._obj.parent().help(self._name)
-class MaximaExpectFunction(ExpectFunction):
-    def _sage_doc_(self):
-        """
-        EXAMPLES::
-            sage: maxima.gcd._sage_doc_()
-            -- Function: gcd (<p_1>, <p_2>, <x_1>, ...)
-            ...
-        """
-        M = self._parent
-        return M.help(self._name)
-class MaximaFunction(MaximaElement):
-    def __init__(self, parent, name, defn, args, latex):
-        """
-        EXAMPLES::
-            sage: f = maxima.function('x,y','sin(x+y)')
-            sage: f == loads(dumps(f))
-            True
-        """
-        MaximaElement.__init__(self, parent, name, is_name=True)
-        self.__defn = defn
-        self.__args = args
-        self.__latex = latex
-    def __reduce__(self):
-        """
-        EXAMPLES::
-            sage: f = maxima.function('x,y','sin(x+y)')
-            sage: f.__reduce__()
-            (<function reduce_load_Maxima_function at 0x...>,
-             (Maxima, 'sin(x+y)', 'x,y', None))
-        """
-        return reduce_load_Maxima_function, (self.parent(), self.__defn, self.__args, self.__latex)
-    def __call__(self, *x):
-        """
-        EXAMPLES::
-            sage: f = maxima.function('x,y','sin(x+y)')
-            sage: f(1,2)
-            sin(3)
-            sage: f(x,x)
-            sin(2*x)
-        """
-        P = self._check_valid()
-        if len(x) == 1:
-            x = '(%s)'%x
-        return P('%s%s'%(self.name(), x))
-    def __repr__(self):
-        """
-        EXAMPLES::
-            sage: f = maxima.function('x,y','sin(x+y)')
-            sage: repr(f)
-            'sin(x+y)'
-        """
-        return self.definition()
-    def _latex_(self):
-        """
-        EXAMPLES::
-            sage: f = maxima.function('x,y','sin(x+y)')
-            sage: latex(f)
-            \mathrm{sin(x+y)}
-        """
-        if self.__latex is None:
-            return r'\mathrm{%s}'%self.__defn
-        else:
-            return self.__latex
-    def arguments(self, split=True):
-        r"""
-        Returns the arguments of this Maxima function.
-        EXAMPLES::
-            sage: f = maxima.function('x,y','sin(x+y)')
-            sage: f.arguments()
-            ['x', 'y']
-            sage: f.arguments(split=False)
-            'x,y'
-            sage: f = maxima.function('', 'sin(x)')
-            sage: f.arguments()
-            []
-        """
-        if split:
-            return self.__args.split(',') if self.__args != '' else []
-        else:
-            return self.__args
-    def definition(self):
-        """
-        Returns the definition of this Maxima function as a string.
-        EXAMPLES::
-            sage: f = maxima.function('x,y','sin(x+y)')
-            sage: f.definition()
-            'sin(x+y)'
-        """
-        return self.__defn
-    def integral(self, var):
-        """
-        Returns the integral of self with respect to the variable var.
-        Note that integrate is an alias of integral.
-        EXAMPLES::
-            sage: x,y = var('x,y')
-            sage: f = maxima.function('x','sin(x)')
-            sage: f.integral(x)
-            -cos(x)
-            sage: f.integral(y)
-            sin(x)*y
-        """
-        var = str(var)
-        P = self._check_valid()
-        f = P('integrate(%s(%s), %s)'%(self.name(), self.arguments(split=False), var))
-        args = self.arguments()
-        if var not in args:
-            args.append(var)
-        return P.function(",".join(args), repr(f))
-    integrate = integral
-    def _operation(self, operation, f=None):
-        r"""
-        This is a utility function which factors out much of the
-        commonality used in the arithmetic operations for
-        ``MaximaFunctions``.
-        INPUT:
-        -  ``operation`` - A string representing the operation
-           being performed. For example, '\*', or '1/'.
-        -  ``f`` - The other operand. If f is
-           ``None``, than the operation is assumed to be unary
-           rather than binary.
-        EXAMPLES::
-            sage: f = maxima.function('x,y','sin(x+y)')
-            sage: f._operation("+", f)
-*sin(y+x)
-            sage: f._operation("+", 2)
-            sin(y+x)+2
-            sage: f._operation('-')
-            -sin(y+x)
-            sage: f._operation('1/')
-/sin(y+x)
-        """
-        P = self._check_valid()
-        if isinstance(f, MaximaFunction):
-            tmp = list(sorted(set(self.arguments() + f.arguments())))
-            args = ','.join(tmp)
-            defn = "(%s)%s(%s)"%(self.definition(), operation, f.definition())
-        elif f is None:
-            args = self.arguments(split=False)
-            defn = "%s(%s)"%(operation, self.definition())
-        else:
-            args = self.arguments(split=False)
-            defn = "(%s)%s(%s)"%(self.definition(), operation, repr(f))
-        return P.function(args,P.eval(defn))
-    def _add_(self, f):
-        """
-        MaximaFunction as left summand.
-        EXAMPLES::
-            sage: x,y = var('x,y')
-            sage: f = maxima.function('x','sin(x)')
-            sage: g = maxima.function('x','-cos(x)')
-            sage: f+g
-            sin(x)-cos(x)
-            sage: f+3
-            sin(x)+3
-        ::
-            sage: (f+maxima.cos(x))(2)
-            sin(2)+cos(2)
-            sage: (f+maxima.cos(y)) # This is a function with only ONE argument!
-            cos(y)+sin(x)
-            sage: (f+maxima.cos(y))(2)
-            cos(y)+sin(2)
-        ::
-            sage: f = maxima.function('x','sin(x)')
-            sage: g = -maxima.cos(x)
-            sage: g+f
-            sin(x)-cos(x)
-            sage: (g+f)(2) # The sum IS a function
-            sin(2)-cos(2)
-            sage: 2+f
-            sin(x)+2
-        """
-        return self._operation("+", f)
-    def _sub_(self, f):
-        r"""
-        ``MaximaFunction`` as minuend.
-        EXAMPLES::
-            sage: x,y = var('x,y')
-            sage: f = maxima.function('x','sin(x)')
-            sage: g = -maxima.cos(x) # not a function
-            sage: f-g
-            sin(x)+cos(x)
-            sage: (f-g)(2)
-            sin(2)+cos(2)
-            sage: (f-maxima.cos(y)) # This function only has the argument x!
-            sin(x)-cos(y)
-            sage: _(2)
-            sin(2)-cos(y)
-        ::
-            sage: g-f
-            -sin(x)-cos(x)
-        """
-        return self._operation("-", f)
-    def _mul_(self, f):
-        r"""
-        ``MaximaFunction`` as left factor.
-        EXAMPLES::
-            sage: f = maxima.function('x','sin(x)')
-            sage: g = maxima('-cos(x)') # not a function!
-            sage: f*g
-            -cos(x)*sin(x)
-            sage: _(2)
-            -cos(2)*sin(2)
-        ::
-            sage: f = maxima.function('x','sin(x)')
-            sage: g = maxima('-cos(x)')
-            sage: g*f
-            -cos(x)*sin(x)
-            sage: _(2)
-            -cos(2)*sin(2)
-            sage: 2*f
-*sin(x)
-        """
-        return self._operation("*", f)
-    def _div_(self, f):
-        r"""
-        ``MaximaFunction`` as dividend.
-        EXAMPLES::
-            sage: f=maxima.function('x','sin(x)')
-            sage: g=maxima('-cos(x)')
-            sage: f/g
-            -sin(x)/cos(x)
-            sage: _(2)
-            -sin(2)/cos(2)
-        ::
-            sage: f=maxima.function('x','sin(x)')
-            sage: g=maxima('-cos(x)')
-            sage: g/f
-            -cos(x)/sin(x)
-            sage: _(2)
-            -cos(2)/sin(2)
-            sage: 2/f
-/sin(x)
-        """
-        return self._operation("/", f)
-    def __neg__(self):
-        r"""
-        Additive inverse of a ``MaximaFunction``.
-        EXAMPLES::
-            sage: f=maxima.function('x','sin(x)')
-            sage: -f
-            -sin(x)
-        """
-        return self._operation('-')
-    def __inv__(self):
-        r"""
-        Multiplicative inverse of a ``MaximaFunction``.
-        EXAMPLES::
-            sage: f = maxima.function('x','sin(x)')
-            sage: ~f
-/sin(x)
-        """
-        return self._operation('1/')
-    def __pow__(self,f):
-        r"""
-        ``MaximaFunction`` raised to some power.
-        EXAMPLES::
-            sage: f=maxima.function('x','sin(x)')
-            sage: g=maxima('-cos(x)')
-            sage: f^g
-/sin(x)^cos(x)
-        ::
-            sage: f=maxima.function('x','sin(x)')
-            sage: g=maxima('-cos(x)') # not a function
-            sage: g^f
-            (-cos(x))^sin(x)
-        """
-        return self._operation("^", f)
 def is_MaximaElement(x):
     """
     Returns True if x is of type MaximaElement.
 …
     """
     return maxima
-def reduce_load_Maxima_function(parent, defn, args, latex):
-    return parent.function(args, defn, defn, latex)
-import os
-def maxima_console():
-    """
-    Spawn a new Maxima command-line session.
-    EXAMPLES::
-        sage: from sage.interfaces.maxima import maxima_console
-        sage: maxima_console()                    # not tested
-        Maxima 5.16.3 http://maxima.sourceforge.net
-        ...
-    """
-    os.system('maxima')
 def maxima_version():
     """
     EXAMPLES::

new file sage/interfaces/maxima_abstract.py

diff -r 604c0fdf356f -r a44619a880c4 sage/interfaces/maxima_abstract.py

-                      -
+r"""
+Interface to Maxima
+Maxima is a free GPL'd general purpose computer algebra system
+whose development started in 1968 at MIT. It contains symbolic
+manipulation algorithms, as well as implementations of special
+functions, including elliptic functions and generalized
+hypergeometric functions. Moreover, Maxima has implementations of
+many functions relating to the invariant theory of the symmetric
+group `S_n`. (However, the commands for group invariants,
+and the corresponding Maxima documentation, are in French.) For many
+links to Maxima documentation see
+http://maxima.sourceforge.net/docs.shtml/.
+AUTHORS:
+- William Stein (2005-12): Initial version
+- David Joyner: Improved documentation
+- William Stein (2006-01-08): Fixed bug in parsing
+- William Stein (2006-02-22): comparisons (following suggestion of
+  David Joyner)
+- William Stein (2006-02-24): *greatly* improved robustness by adding
+  sequence numbers to IO bracketing in _eval_line
+If the string "error" (case insensitive) occurs in the output of
+anything from Maxima, a RuntimeError exception is raised.
+EXAMPLES: We evaluate a very simple expression in Maxima.
+::
+    sage: maxima('3 * 5')
+We factor `x^5 - y^5` in Maxima in several different ways.
+The first way yields a Maxima object.
+::
+    sage: F = maxima.factor('x^5 - y^5')
+    sage: F
+    -(y-x)*(y^4+x*y^3+x^2*y^2+x^3*y+x^4)
+    sage: type(F)
+    <class 'sage.interfaces.maxima_abstract.MaximaElement'>
+Note that Maxima objects can also be displayed using "ASCII art";
+to see a normal linear representation of any Maxima object x. Just
+use the print command: use ``str(x)``.
+::
+    sage: print F
+      3    2  2    3      4
+                   - (y - x) (y  + x y  + x  y  + x  y + x )
+You can always use ``repr(x)`` to obtain the linear
+representation of an object. This can be useful for moving maxima
+data to other systems.
+::
+    sage: repr(F)
+    '-(y-x)*(y^4+x*y^3+x^2*y^2+x^3*y+x^4)'
+    sage: F.str()
+    '-(y-x)*(y^4+x*y^3+x^2*y^2+x^3*y+x^4)'
+The ``maxima.eval`` command evaluates an expression in
+maxima and returns the result as a *string* not a maxima object.
+::
+    sage: print maxima.eval('factor(x^5 - y^5)')
+    -(y-x)*(y^4+x*y^3+x^2*y^2+x^3*y+x^4)
+We can create the polynomial `f` as a Maxima polynomial,
+then call the factor method on it. Notice that the notation
+``f.factor()`` is consistent with how the rest of Sage
+works.
+::
+    sage: f = maxima('x^5 - y^5')
+    sage: f^2
+    (x^5-y^5)^2
+    sage: f.factor()
+    -(y-x)*(y^4+x*y^3+x^2*y^2+x^3*y+x^4)
+Control-C interruption works well with the maxima interface,
+because of the excellent implementation of maxima. For example, try
+the following sum but with a much bigger range, and hit control-C.
+::
+    sage: maxima('sum(1/x^2, x, 1, 10)')
+    1968329/1270080
+Tutorial
+--------
+We follow the tutorial at
+http://maxima.sourceforge.net/docs/intromax/.
+::
+    sage: maxima('1/100 + 1/101')
+/10100
+::
+    sage: a = maxima('(1 + sqrt(2))^5'); a
+    (sqrt(2)+1)^5
+    sage: a.expand()
+*2^(7/2)+5*sqrt(2)+41
+::
+    sage: a = maxima('(1 + sqrt(2))^5')
+    sage: float(a)
+.012193308819747
+    sage: a.numer()
+.01219330881975
+::
+    sage: maxima.eval('fpprec : 100')
+    '100'
+    sage: a.bfloat()
+.20121933088197564152489730020812442785204843859314941221237124017312418754011041266612384955016056b1
+::
+    sage: maxima('100!')
+    93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000
+::
+    sage: f = maxima('(x + 3*y + x^2*y)^3')
+    sage: f.expand()
+    x^6*y^3+9*x^4*y^3+27*x^2*y^3+27*y^3+3*x^5*y^2+18*x^3*y^2+27*x*y^2+3*x^4*y+9*x^2*y+x^3
+    sage: f.subst('x=5/z')
+    (5/z+25*y/z^2+3*y)^3
+    sage: g = f.subst('x=5/z')
+    sage: h = g.ratsimp(); h
+    (27*y^3*z^6+135*y^2*z^5+(675*y^3+225*y)*z^4+(2250*y^2+125)*z^3+(5625*y^3+1875*y)*z^2+9375*y^2*z+15625*y^3)/z^6
+    sage: h.factor()
+    (3*y*z^2+5*z+25*y)^3/z^6
+::
+    sage: eqn = maxima(['a+b*c=1', 'b-a*c=0', 'a+b=5'])
+    sage: s = eqn.solve('[a,b,c]'); s
+    [[a=(25*sqrt(79)*%i+25)/(6*sqrt(79)*%i-34),b=(5*sqrt(79)*%i+5)/(sqrt(79)*%i+11),c=(sqrt(79)*%i+1)/10],[a=(25*sqrt(79)*%i-25)/(6*sqrt(79)*%i+34),b=(5*sqrt(79)*%i-5)/(sqrt(79)*%i-11),c=-(sqrt(79)*%i-1)/10]]
+Here is an example of solving an algebraic equation::
+    sage: maxima('x^2+y^2=1').solve('y')
+    [y=-sqrt(1-x^2),y=sqrt(1-x^2)]
+    sage: maxima('x^2 + y^2 = (x^2 - y^2)/sqrt(x^2 + y^2)').solve('y')
+    [y=-sqrt((-y^2-x^2)*sqrt(y^2+x^2)+x^2),y=sqrt((-y^2-x^2)*sqrt(y^2+x^2)+x^2)]
+You can even nicely typeset the solution in latex::
+    sage: latex(s)
+    \left[ \left[ a={{25\,\sqrt{79}\,i+25}\over{6\,\sqrt{79}\,i-34}} ,   b={{5\,\sqrt{79}\,i+5}\over{\sqrt{79}\,i+11}} , c={{\sqrt{79}\,i+1  }\over{10}} \right]  , \left[ a={{25\,\sqrt{79}\,i-25}\over{6\,  \sqrt{79}\,i+34}} , b={{5\,\sqrt{79}\,i-5}\over{\sqrt{79}\,i-11}} ,   c=-{{\sqrt{79}\,i-1}\over{10}} \right]  \right]
+To have the above appear onscreen via ``xdvi``, type
+``view(s)``. (TODO: For OS X should create pdf output
+and use preview instead?)
+::
+    sage: e = maxima('sin(u + v) * cos(u)^3'); e
+    cos(u)^3*sin(v+u)
+    sage: f = e.trigexpand(); f
+    cos(u)^3*(cos(u)*sin(v)+sin(u)*cos(v))
+    sage: f.trigreduce()
+    (sin(v+4*u)+sin(v-2*u))/8+(3*sin(v+2*u)+3*sin(v))/8
+    sage: w = maxima('3 + k*%i')
+    sage: f = w^2 + maxima('%e')^w
+    sage: f.realpart()
+    %e^3*cos(k)-k^2+9
+::
+    sage: f = maxima('x^3 * %e^(k*x) * sin(w*x)'); f
+    x^3*%e^(k*x)*sin(w*x)
+    sage: f.diff('x')
+    k*x^3*%e^(k*x)*sin(w*x)+3*x^2*%e^(k*x)*sin(w*x)+w*x^3*%e^(k*x)*cos(w*x)
+    sage: f.integrate('x')
+    (((k*w^6+3*k^3*w^4+3*k^5*w^2+k^7)*x^3+(3*w^6+3*k^2*w^4-3*k^4*w^2-3*k^6)*x^2+(-18*k*w^4-12*k^3*w^2+6*k^5)*x-6*w^4+36*k^2*w^2-6*k^4)*%e^(k*x)*sin(w*x)+((-w^7-3*k^2*w^5-3*k^4*w^3-k^6*w)*x^3+(6*k*w^5+12*k^3*w^3+6*k^5*w)*x^2+(6*w^5-12*k^2*w^3-18*k^4*w)*x-24*k*w^3+24*k^3*w)*%e^(k*x)*cos(w*x))/(w^8+4*k^2*w^6+6*k^4*w^4+4*k^6*w^2+k^8)
+::
+    sage: f = maxima('1/x^2')
+    sage: f.integrate('x', 1, 'inf')
+    sage: g = maxima('f/sinh(k*x)^4')
+    sage: g.taylor('x', 0, 3)
+    f/(k^4*x^4)-2*f/(3*k^2*x^2)+11*f/45-62*k^2*f*x^2/945
+::
+    sage: maxima.taylor('asin(x)','x',0, 10)
+    x+x^3/6+3*x^5/40+5*x^7/112+35*x^9/1152
+Examples involving matrices
+---------------------------
+We illustrate computing with the matrix whose `i,j` entry
+is `i/j`, for `i,j=1,\ldots,4`.
+::
+    sage: f = maxima.eval('f[i,j] := i/j')
+    sage: A = maxima('genmatrix(f,4,4)'); A
+    matrix([1,1/2,1/3,1/4],[2,1,2/3,1/2],[3,3/2,1,3/4],[4,2,4/3,1])
+    sage: A.determinant()
+    sage: A.echelon()
+    matrix([1,1/2,1/3,1/4],[0,0,0,0],[0,0,0,0],[0,0,0,0])
+    sage: A.eigenvalues()
+    [[0,4],[3,1]]
+    sage: A.eigenvectors()
+    [[[0,4],[3,1]],[[[1,0,0,-4],[0,1,0,-2],[0,0,1,-4/3]],[[1,2,3,4]]]]
+We can also compute the echelon form in Sage::
+    sage: B = matrix(QQ, A)
+    sage: B.echelon_form()
+    [  1 1/2 1/3 1/4]
+    [  0   0   0   0]
+    [  0   0   0   0]
+    [  0   0   0   0]
+    sage: B.charpoly('x').factor()
+    (x - 4) * x^3
+Laplace Transforms
+------------------
+We illustrate Laplace transforms::
+    sage: _ = maxima.eval("f(t) := t*sin(t)")
+    sage: maxima("laplace(f(t),t,s)")
+*s/(s^2+1)^2
+::
+    sage: maxima("laplace(delta(t-3),t,s)") #Dirac delta function
+    %e^-(3*s)
+::
+    sage: _ = maxima.eval("f(t) := exp(t)*sin(t)")
+    sage: maxima("laplace(f(t),t,s)")
+/(s^2-2*s+2)
+::
+    sage: _ = maxima.eval("f(t) := t^5*exp(t)*sin(t)")
+    sage: maxima("laplace(f(t),t,s)")
+*(2*s-2)/(s^2-2*s+2)^4-480*(2*s-2)^3/(s^2-2*s+2)^5+120*(2*s-2)^5/(s^2-2*s+2)^6
+    sage: print maxima("laplace(f(t),t,s)")
+                 5
+(2 s - 2)    480 (2 s - 2)     120 (2 s - 2)
+              --------------- - --------------- + ---------------
+           4     2           5     2           6
+              (s  - 2 s + 2)    (s  - 2 s + 2)    (s  - 2 s + 2)
+::
+    sage: maxima("laplace(diff(x(t),t),t,s)")
+    s*'laplace(x(t),t,s)-x(0)
+::
+    sage: maxima("laplace(diff(x(t),t,2),t,s)")
+    -?%at('diff(x(t),t,1),t=0)+s^2*'laplace(x(t),t,s)-x(0)*s
+It is difficult to read some of these without the 2d
+representation::
+    sage: print maxima("laplace(diff(x(t),t,2),t,s)")
+                         !
+                d        !         2
+              - -- (x(t))!      + s  laplace(x(t), t, s) - x(0) s
+                dt       !
+                         !t = 0
+Even better, use
+``view(maxima("laplace(diff(x(t),t,2),t,s)"))`` to see
+a typeset version.
+Continued Fractions
+-------------------
+A continued fraction `a + 1/(b + 1/(c + \cdots))` is
+represented in maxima by the list `[a, b, c, \ldots]`.
+::
+    sage: maxima("cf((1 + sqrt(5))/2)")
+    [1,1,1,1,2]
+    sage: maxima("cf ((1 + sqrt(341))/2)")
+    [9,1,2,1,2,1,17,1,2,1,2,1,17,1,2,1,2,1,17,2]
+Special examples
+----------------
+In this section we illustrate calculations that would be awkward to
+do (as far as I know) in non-symbolic computer algebra systems like
+MAGMA or GAP.
+We compute the gcd of `2x^{n+4} - x^{n+2}` and
+`4x^{n+1} + 3x^n` for arbitrary `n`.
+::
+    sage: f = maxima('2*x^(n+4) - x^(n+2)')
+    sage: g = maxima('4*x^(n+1) + 3*x^n')
+    sage: f.gcd(g)
+    x^n
+You can plot 3d graphs (via gnuplot)::
+    sage: maxima('plot3d(x^2-y^2, [x,-2,2], [y,-2,2], [grid,12,12])')  # not tested
+    [displays a 3 dimensional graph]
+You can formally evaluate sums (note the ``nusum``
+command)::
+    sage: S = maxima('nusum(exp(1+2*i/n),i,1,n)')
+    sage: print S
+/n + 3                   2/n + 1
+                          %e                        %e
+                   ----------------------- - -----------------------
+/n         1/n           1/n         1/n
+                   (%e    - 1) (%e    + 1)   (%e    - 1) (%e    + 1)
+We formally compute the limit as `n\to\infty` of
+`2S/n` as follows::
+    sage: T = S*maxima('2/n')
+    sage: T.tlimit('n','inf')
+    %e^3-%e
+Miscellaneous
+-------------
+Obtaining digits of `\pi`::
+    sage: maxima.eval('fpprec : 100')
+    '100'
+    sage: maxima(pi).bfloat()
+.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117068b0
+Defining functions in maxima::
+    sage: maxima.eval('fun[a] := a^2')
+    'fun[a]:=a^2'
+    sage: maxima('fun[10]')
+Interactivity
+-------------
+Unfortunately maxima doesn't seem to have a non-interactive mode,
+which is needed for the Sage interface. If any Sage call leads to
+maxima interactively answering questions, then the questions can't be
+answered and the maxima session may hang. See the discussion at
+http://www.ma.utexas.edu/pipermail/maxima/2005/011061.html for some
+ideas about how to fix this problem. An example that illustrates this
+problem is ``maxima.eval('integrate (exp(a*x), x, 0, inf)')``.
+Latex Output
+------------
+To TeX a maxima object do this::
+    sage: latex(maxima('sin(u) + sinh(v^2)'))
+    \sinh v^2+\sin u
+Here's another example::
+    sage: g = maxima('exp(3*%i*x)/(6*%i) + exp(%i*x)/(2*%i) + c')
+    sage: latex(g)
+    -{{i\,e^{3\,i\,x}}\over{6}}-{{i\,e^{i\,x}}\over{2}}+c
+Long Input
+----------
+The MAXIMA interface reads in even very long input (using files) in
+a robust manner, as long as you are creating a new object.
+.. note::
+   Using ``maxima.eval`` for long input is much less robust, and is
+   not recommended.
+::
+    sage: t = '"%s"'%10^10000   # ten thousand character string.
+    sage: a = maxima(t)
+TESTS: This working tests that a subtle bug has been fixed::
+    sage: f = maxima.function('x','gamma(x)')
+    sage: g = f(1/7)
+    sage: g
+    gamma(1/7)
+    sage: del f
+    sage: maxima(sin(x))
+    sin(x)
+This tests to make sure we handle the case where Maxima asks if an
+expression is positive or zero.
+::
+    sage: var('Ax,Bx,By')
+    (Ax, Bx, By)
+    sage: t = -Ax*sin(sqrt(Ax^2)/2)/(sqrt(Ax^2)*sqrt(By^2 + Bx^2))
+    sage: t.limit(Ax=0,dir='above')
+A long complicated input expression::
+    sage: maxima._eval_line('((((((((((0) + ((1) / ((n0) ^ (0)))) + ((1) / ((n1) ^ (1)))) + ((1) / ((n2) ^ (2)))) + ((1) / ((n3) ^ (3)))) + ((1) / ((n4) ^ (4)))) + ((1) / ((n5) ^ (5)))) + ((1) / ((n6) ^ (6)))) + ((1) / ((n7) ^ (7)))) + ((1) / ((n8) ^ (8)))) + ((1) / ((n9) ^ (9)));')
+    '1/n9^9+1/n8^8+1/n7^7+1/n6^6+1/n5^5+1/n4^4+1/n3^3+1/n2^2+1/n1+1'
+"""
+#*****************************************************************************
+#       Copyright (C) 2005 William Stein <wstein@gmail.com>
+#
+#  Distributed under the terms of the GNU General Public License (GPL)
+#
+#    This code is distributed in the hope that it will be useful,
+#    but WITHOUT ANY WARRANTY; without even the implied warranty of
+#    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+#    General Public License for more details.
+#
+#  The full text of the GPL is available at:
+#
+#                  http://www.gnu.org/licenses/
+#*****************************************************************************
+from __future__ import with_statement
+import os, re, sys, subprocess
+import pexpect
+cygwin = os.uname()[0][:6]=="CYGWIN"
+from expect import Expect, ExpectElement, FunctionElement, ExpectFunction, gc_disabled, AsciiArtString
+from pexpect import EOF
+from random import randrange
+##import sage.rings.all
+import sage.rings.complex_number
+from sage.misc.misc import verbose, DOT_SAGE, SAGE_ROOT
+from sage.misc.multireplace import multiple_replace
+COMMANDS_CACHE = '%s/maxima_commandlist_cache.sobj'%DOT_SAGE
+import sage.server.support
+# The Maxima "apropos" command, e.g., apropos(det) gives a list
+# of all identifiers that begin in a certain way.  This could
+# maybe be useful somehow... (?)  Also maxima has a lot for getting
+# documentation from the system -- this could also be useful.
+class Maxima(Expect):
+    """
+    Interface to the Maxima interpreter.
+    """
+    def __init__(self, script_subdirectory=None, logfile=None, server=None,
+                 init_code = None):
+        """
+        Create an instance of the Maxima interpreter.
+        TESTS::
+            sage: maxima == loads(dumps(maxima))
+            True
+        We make sure labels are turned off (see trac 6816)::
+            sage: 'nolabels:true' in maxima._Expect__init_code
+            True
+        """
+        # TODO: Input and output prompts in maxima can be changed by
+        # setting inchar and outchar..
+        eval_using_file_cutoff = 256
+        self.__eval_using_file_cutoff = eval_using_file_cutoff
+        STARTUP = '%s/local/bin/sage-maxima.lisp'%SAGE_ROOT
+        if not os.path.exists(STARTUP):
+            raise RuntimeError, 'You must get the file local/bin/sage-maxima.lisp'
+        if init_code is None:
+            # display2d -- no ascii art output
+            # keepfloat -- don't automatically convert floats to rationals
+            init_code = ['display2d : false', 'keepfloat : true']
+        # Turn off the prompt labels, since computing them *very
+        # dramatically* slows down the maxima interpret after a while.
+        # See the function makelabel in suprv1.lisp.
+        # Many thanks to andrej.vodopivec@gmail.com and also
+        # Robert Dodier for figuring this out!
+        # See trac # 6818.
+        init_code.append('nolabels:true')
+        Expect.__init__(self,
+                        name = 'maxima',
+                        prompt = '\(\%i[0-9]+\)',
+                        command = 'maxima-noreadline -p "%s"'%STARTUP,
+                        maxread = 10000,
+                        script_subdirectory = script_subdirectory,
+                        restart_on_ctrlc = False,
+                        verbose_start = False,
+                        init_code = init_code,
+                        logfile = logfile,
+                        eval_using_file_cutoff=eval_using_file_cutoff)
+        self._display_prompt = '<sage-display>'  # must match what is in the file local/ibn/sage-maxima.lisp!!
+        self._output_prompt_re = re.compile('\(\%o[0-9]+\)')
+        self._ask = ['zero or nonzero?', 'an integer?', 'positive, negative, or zero?',
+                     'positive or negative?', 'positive or zero?']
+        self._prompt_wait = [self._prompt] + [re.compile(x) for x in self._ask] + \
+                            ['Break [0-9]+'] #note that you might need to change _expect_expr if you
+                                             #change this
+        self._error_re = re.compile('(Principal Value|debugmode|Incorrect syntax|Maxima encountered a Lisp error)')
+        self._display2d = False
+    def _quit_string(self):
+        """
+        EXAMPLES::
+            sage: maxima._quit_string()
+            'quit();'
+        """
+        return 'quit();'
+    def _crash_msg(self):
+        """
+        EXAMPLES::
+            sage: maxima._crash_msg()
+            Maxima crashed -- automatically restarting.
+        """
+        print "Maxima crashed -- automatically restarting."
+    def _batch(self, s, batchload=True):
+        filename = '%s-%s'%(self._local_tmpfile(),randrange(2147483647))
+        F = open(filename, 'w')
+        F.write(s)
+        F.close()
+        if self.is_remote():
+            self._send_tmpfile_to_server(local_file=filename)
+            tmp_to_use = self._remote_tmpfile()
+        tmp_to_use = filename
+        if batchload:
+            cmd = 'batchload("%s");'%tmp_to_use
+        else:
+            cmd = 'batch("%s");'%tmp_to_use
+        r = randrange(2147483647)
+        s = str(r+1)
+        cmd = "%s1+%s;\n"%(cmd,r)
+        self._sendline(cmd)
+        self._expect_expr(s)
+        out = self._before()
+        self._error_check(str, out)
+        os.unlink(filename)
+        return out
+    def _error_check(self, str, out):
+        r = self._error_re
+        m = r.search(out)
+        if not m is None:
+            self._error_msg(str, out)
+    def _error_msg(self, str, out):
+        raise TypeError, "Error executing code in Maxima\nCODE:\n\t%s\nMaxima ERROR:\n\t%s"%(str, out.replace('-- an error.  To debug this try debugmode(true);',''))
+    ###########################################
+    # System -- change directory, etc
+    ###########################################
+    def chdir(self, dir):
+        """
+        Change Maxima's current working directory.
+        EXAMPLES::
+            sage: maxima.chdir('/')
+        """
+        self.lisp('(ext::cd "%s")'%dir)
+    ###########################################
+    # Interactive help
+    ###########################################
+    def help(self, s):
+        """
+        EXAMPLES::
+            sage: maxima.help('gcd')
+            -- Function: gcd (<p_1>, <p_2>, <x_1>, ...)
+            ...
+        """
+        return self._command_runner("describe", s)
+    def example(self, s):
+        """
+        EXAMPLES::
+            sage: maxima.example('arrays')
+            a[n]:=n*a[n-1]
+                                            a  := n a
+                                             n       n - 1
+            a[0]:1
+            a[5]
+            a[n]:=n
+            a[6]
+            a[4]
+                                                 done
+        """
+        return self._command_runner("example", s)
+    describe = help
+    def demo(self, s):
+        """
+        EXAMPLES::
+            sage: maxima.demo('array') # not tested
+            batching /opt/sage/local/share/maxima/5.16.3/demo/array.dem
+        At the _ prompt, type ';' followed by enter to get next demo
+        subscrmap : true _
+        """
+        return self._command_runner("demo", s, redirect=False)
+    def completions(self, s, verbose=True):
+        """
+        Return all commands that complete the command starting with the
+        string s. This is like typing s[tab] in the Maxima interpreter.
+        EXAMPLES::
+            sage: sorted(maxima.completions('gc', verbose=False))
+            ['gcd', 'gcdex', 'gcfactor', 'gcprint', 'gctime']
+        """
+        if verbose:
+            print s,
+            sys.stdout.flush()
+        # in Maxima 5.19.1, apropos returns all commands that contain
+        # the given string, instead of all commands that start with
+        # the given string
+        cmd_list = self._eval_line('apropos("%s")'%s, error_check=False).replace('\\ - ','-')
+        cmd_list = [x for x in cmd_list[1:-1].split(',') if x[0] != '?']
+        return [x for x in cmd_list if x.find(s) == 0]
+    def _commands(self, verbose=True):
+        """
+        Return list of all commands defined in Maxima.
+        EXAMPLES::
+            sage: sorted(maxima._commands(verbose=False))
+            ['Alpha',
+             'Beta',
+             ...
+             'zunderflow']
+        """
+        try:
+            return self.__commands
+        except AttributeError:
+            self.__commands = sum(
+                [self.completions(chr(65+n), verbose=verbose)+
+                 self.completions(chr(97+n), verbose=verbose)
+                 for n in range(26)], [])
+        return self.__commands
+    def trait_names(self, verbose=True, use_disk_cache=True):
+        """
+        Return all Maxima commands, which is useful for tab completion.
+        EXAMPLES::
+            sage: t = maxima.trait_names(verbose=False)
+            sage: 'gcd' in t
+            True
+            sage: len(t)    # random output
+        """
+        try:
+            return self.__trait_names
+        except AttributeError:
+            import sage.misc.persist
+            if use_disk_cache:
+                try:
+                    self.__trait_names = sage.misc.persist.load(COMMANDS_CACHE)
+                    return self.__trait_names
+                except IOError:
+                    pass
+            if verbose:
+                print "\nBuilding Maxima command completion list (this takes"
+                print "a few seconds only the first time you do it)."
+                print "To force rebuild later, delete %s."%COMMANDS_CACHE
+            v = self._commands(verbose=verbose)
+            if verbose:
+                print "\nDone!"
+            self.__trait_names = v
+            sage.misc.persist.save(v, COMMANDS_CACHE)
+            return v
+    def _true_symbol(self):
+        """
+        Return the true symbol in Maxima.
+        EXAMPLES::
+            sage: maxima._true_symbol()
+            'true'
+            sage: maxima.eval('is(2 = 2)')
+            'true'
+        """
+        return 'true'
+    def _false_symbol(self):
+        """
+        Return the false symbol in Maxima.
+        EXAMPLES::
+            sage: maxima._false_symbol()
+            'false'
+            sage: maxima.eval('is(2 = 4)')
+            'false'
+        """
+        return 'false'
+    def _equality_symbol(self):
+        """
+        Returns the equality symbol in Maxima.
+        EXAMPLES::
+             sage: maxima._equality_symbol()
+             '='
+        """
+        return '='
+    def _inequality_symbol(self):
+        """
+        Returns the equality symbol in Maxima.
+        EXAMPLES::
+             sage: maxima._inequality_symbol()
+             '#'
+             sage: maxima((x != 1))
+             x#1
+        """
+        return '#'
+    def console(self):
+        r"""
+        Start the interactive Maxima console. This is a completely separate
+        maxima session from this interface. To interact with this session,
+        you should instead use ``maxima.interact()``.
+        EXAMPLES::
+            sage: maxima.console()             # not tested (since we can't)
+            Maxima 5.13.0 http://maxima.sourceforge.net
+            Using Lisp CLISP 2.41 (2006-10-13)
+            Distributed under the GNU Public License. See the file COPYING.
+            Dedicated to the memory of William Schelter.
+            This is a development version of Maxima. The function bug_report()
+            provides bug reporting information.
+            (%i1)
+        ::
+            sage: maxima.interact()     # this is not tested either
+              --> Switching to Maxima <--
+            maxima: 2+2
+            maxima:
+              --> Exiting back to Sage <--
+        """
+        maxima_console()
+    def cputime(self, t=None):
+        r"""
+        Returns the amount of CPU time that this Maxima session has used.
+        If \var{t} is not None, then it returns the difference between
+        the current CPU time and \var{t}.
+        EXAMPLES:
+            sage: t = maxima.cputime()
+            sage: _ = maxima.de_solve('diff(y,x,2) + 3*x = y', ['x','y'], [1,1,1])
+            sage: maxima.cputime(t) # output random
+.568913
+        """
+        if t:
+            return float(self.eval('elapsed_run_time()')) - t
+        else:
+            return float(self.eval('elapsed_run_time()'))
+##     def display2d(self, flag=True):
+##         """
+##         Set the flag that determines whether Maxima objects are
+##         printed using their 2-d ASCII art representation.  When the
+##         maxima interface starts the default is that objects are not
+##         represented in 2-d.
+##         INPUT:
+##             flag -- bool (default: True)
+##         EXAMPLES
+##             sage: maxima('1/2')
+##             1/2
+##             sage: maxima.display2d(True)
+##             sage: maxima('1/2')
+##                                            1
+##                                            -
+##                                            2
+##             sage: maxima.display2d(False)
+##         """
+##         self._display2d = bool(flag)
+    def plot2d(self, *args):
+        r"""
+        Plot a 2d graph using Maxima / gnuplot.
+        maxima.plot2d(f, '[var, min, max]', options)
+        INPUT:
+        -  ``f`` - a string representing a function (such as
+           f="sin(x)") [var, xmin, xmax]
+        -  ``options`` - an optional string representing plot2d
+           options in gnuplot format
+        EXAMPLES::
+            sage: maxima.plot2d('sin(x)','[x,-5,5]')   # not tested
+            sage: opts = '[gnuplot_term, ps], [gnuplot_out_file, "sin-plot.eps"]'
+            sage: maxima.plot2d('sin(x)','[x,-5,5]',opts)    # not tested
+        The eps file is saved in the current directory.
+        """
+        self('plot2d(%s)'%(','.join([str(x) for x in args])))
+    def plot2d_parametric(self, r, var, trange, nticks=50, options=None):
+        r"""
+        Plots r = [x(t), y(t)] for t = tmin...tmax using gnuplot with
+        options
+        INPUT:
+        -  ``r`` - a string representing a function (such as
+           r="[x(t),y(t)]")
+        -  ``var`` - a string representing the variable (such
+           as var = "t")
+        -  ``trange`` - [tmin, tmax] are numbers with tmintmax
+        -  ``nticks`` - int (default: 50)
+        -  ``options`` - an optional string representing plot2d
+           options in gnuplot format
+        EXAMPLES::
+            sage: maxima.plot2d_parametric(["sin(t)","cos(t)"], "t",[-3.1,3.1])   # not tested
+        ::
+            sage: opts = '[gnuplot_preamble, "set nokey"], [gnuplot_term, ps], [gnuplot_out_file, "circle-plot.eps"]'
+            sage: maxima.plot2d_parametric(["sin(t)","cos(t)"], "t", [-3.1,3.1], options=opts)   # not tested
+        The eps file is saved to the current working directory.
+        Here is another fun plot::
+            sage: maxima.plot2d_parametric(["sin(5*t)","cos(11*t)"], "t", [0,2*pi()], nticks=400)    # not tested
+        """
+        tmin = trange[0]
+        tmax = trange[1]
+        cmd = "plot2d([parametric, %s, %s, [%s, %s, %s], [nticks, %s]]"%( \
+                   r[0], r[1], var, tmin, tmax, nticks)
+        if options is None:
+            cmd += ")"
+        else:
+            cmd += ", %s)"%options
+        self(cmd)
+    def plot3d(self, *args):
+        r"""
+        Plot a 3d graph using Maxima / gnuplot.
+        maxima.plot3d(f, '[x, xmin, xmax]', '[y, ymin, ymax]', '[grid, nx,
+        ny]', options)
+        INPUT:
+        -  ``f`` - a string representing a function (such as
+           f="sin(x)") [var, min, max]
+        EXAMPLES::
+            sage: maxima.plot3d('1 + x^3 - y^2', '[x,-2,2]', '[y,-2,2]', '[grid,12,12]')    # not tested
+            sage: maxima.plot3d('sin(x)*cos(y)', '[x,-2,2]', '[y,-2,2]', '[grid,30,30]')   # not tested
+            sage: opts = '[gnuplot_term, ps], [gnuplot_out_file, "sin-plot.eps"]'
+            sage: maxima.plot3d('sin(x+y)', '[x,-5,5]', '[y,-1,1]', opts)    # not tested
+        The eps file is saved in the current working directory.
+        """
+        self('plot3d(%s)'%(','.join([str(x) for x in args])))
+    def plot3d_parametric(self, r, vars, urange, vrange, options=None):
+        r"""
+        Plot a 3d parametric graph with r=(x,y,z), x = x(u,v), y = y(u,v),
+        z = z(u,v), for u = umin...umax, v = vmin...vmax using gnuplot with
+        options.
+        INPUT:
+        -  ``x, y, z`` - a string representing a function (such
+           as ``x="u2+v2"``, ...) vars is a list or two strings
+           representing variables (such as vars = ["u","v"])
+        -  ``urange`` - [umin, umax]
+        -  ``vrange`` - [vmin, vmax] are lists of numbers with
+           umin umax, vmin vmax
+        -  ``options`` - optional string representing plot2d
+           options in gnuplot format
+        OUTPUT: displays a plot on screen or saves to a file
+        EXAMPLES::
+            sage: maxima.plot3d_parametric(["v*sin(u)","v*cos(u)","v"], ["u","v"],[-3.2,3.2],[0,3])     # not tested
+            sage: opts = '[gnuplot_term, ps], [gnuplot_out_file, "sin-cos-plot.eps"]'
+            sage: maxima.plot3d_parametric(["v*sin(u)","v*cos(u)","v"], ["u","v"],[-3.2,3.2],[0,3],opts)      # not tested
+        The eps file is saved in the current working directory.
+        Here is a torus::
+            sage: _ = maxima.eval("expr_1: cos(y)*(10.0+6*cos(x)); expr_2: sin(y)*(10.0+6*cos(x)); expr_3: -6*sin(x);")  # optional
+            sage: maxima.plot3d_parametric(["expr_1","expr_2","expr_3"], ["x","y"],[0,6],[0,6])   # not tested
+        Here is a Mobius strip::
+            sage: x = "cos(u)*(3 + v*cos(u/2))"
+            sage: y = "sin(u)*(3 + v*cos(u/2))"
+            sage: z = "v*sin(u/2)"
+            sage: maxima.plot3d_parametric([x,y,z],["u","v"],[-3.1,3.2],[-1/10,1/10])   # not tested
+        """
+        umin = urange[0]
+        umax = urange[1]
+        vmin = vrange[0]
+        vmax = vrange[1]
+        cmd = 'plot3d([%s, %s, %s], [%s, %s, %s], [%s, %s, %s]'%(
+            r[0], r[1], r[2], vars[0], umin, umax, vars[1], vmin, vmax)
+        if options is None:
+            cmd += ')'
+        else:
+            cmd += ', %s)'%options
+        self(cmd)
+    def de_solve(self, de, vars, ics=None):
+        """
+        Solves a 1st or 2nd order ordinary differential equation (ODE) in
+        two variables, possibly with initial conditions.
+        INPUT:
+        -  ``de`` - a string representing the ODE
+        -  ``vars`` - a list of strings representing the two
+           variables.
+        -  ``ics`` - a triple of numbers [a,b1,b2] representing
+           y(a)=b1, y'(a)=b2
+        EXAMPLES::
+            sage: maxima.de_solve('diff(y,x,2) + 3*x = y', ['x','y'], [1,1,1])
+            y=3*x-2*%e^(x-1)
+            sage: maxima.de_solve('diff(y,x,2) + 3*x = y', ['x','y'])
+            y=%k1*%e^x+%k2*%e^-x+3*x
+            sage: maxima.de_solve('diff(y,x) + 3*x = y', ['x','y'])
+            y=(%c-3*(-x-1)*%e^-x)*%e^x
+            sage: maxima.de_solve('diff(y,x) + 3*x = y', ['x','y'],[1,1])
+            y=-%e^-1*(5*%e^x-3*%e*x-3*%e)
+        """
+        if not isinstance(vars, str):
+            str_vars = '%s, %s'%(vars[1], vars[0])
+        else:
+            str_vars = vars
+        self.eval('depends(%s)'%str_vars)
+        m = self(de)
+        a = 'ode2(%s, %s)'%(m.name(), str_vars)
+        if ics != None:
+            if len(ics) == 3:
+                cmd = "ic2("+a+",%s=%s,%s=%s,diff(%s,%s)=%s);"%(vars[0],ics[0], vars[1],ics[1], vars[1], vars[0], ics[2])
+                return self(cmd)
+            if len(ics) == 2:
+                return self("ic1("+a+",%s=%s,%s=%s);"%(vars[0],ics[0], vars[1],ics[1]))
+        return self(a+";")
+    def de_solve_laplace(self, de, vars, ics=None):
+        """
+        Solves an ordinary differential equation (ODE) using Laplace
+        transforms.
+        INPUT:
+        -  ``de`` - a string representing the ODE (e.g., de =
+           "diff(f(x),x,2)=diff(f(x),x)+sin(x)")
+        -  ``vars`` - a list of strings representing the
+           variables (e.g., vars = ["x","f"])
+        -  ``ics`` - a list of numbers representing initial
+           conditions, with symbols allowed which are represented by strings
+           (eg, f(0)=1, f'(0)=2 is ics = [0,1,2])
+        EXAMPLES::
+            sage: maxima.clear('x'); maxima.clear('f')
+            sage: maxima.de_solve_laplace("diff(f(x),x,2) = 2*diff(f(x),x)-f(x)", ["x","f"], [0,1,2])
+            f(x)=x*%e^x+%e^x
+        ::
+            sage: maxima.clear('x'); maxima.clear('f')
+            sage: f = maxima.de_solve_laplace("diff(f(x),x,2) = 2*diff(f(x),x)-f(x)", ["x","f"])
+            sage: f
+            f(x)=x*%e^x*('at('diff(f(x),x,1),x=0))-f(0)*x*%e^x+f(0)*%e^x
+            sage: print f
+                                               !
+                                   x  d        !                  x          x
+                        f(x) = x %e  (-- (f(x))!     ) - f(0) x %e  + f(0) %e
+                                      dx       !
+                                               !x = 0
+        .. note::
+           The second equation sets the values of `f(0)` and
+           `f'(0)` in Maxima, so subsequent ODEs involving these
+           variables will have these initial conditions automatically
+           imposed.
+        """
+        if not (ics is None):
+            d = len(ics)
+            for i in range(0,d-1):
+                ic = 'atvalue(diff(%s(%s), %s, %s), %s = %s, %s)'%(
+                    vars[1], vars[0], vars[0], i, vars[0], ics[0], ics[1+i])
+                self.eval(ic)
+        return self('desolve(%s, %s(%s))'%(de, vars[1], vars[0]))
+    def solve_linear(self, eqns,vars):
+        """
+        Wraps maxima's linsolve.
+        INPUT: eqns is a list of m strings, each representing a linear
+        question in m = n variables vars is a list of n strings, each
+        representing a variable
+        EXAMPLES::
+            sage: eqns = ["x + z = y","2*a*x - y = 2*a^2","y - 2*z = 2"]
+            sage: vars = ["x","y","z"]
+            sage: maxima.solve_linear(eqns, vars)
+            [x=a+1,y=2*a,z=a-1]
+        """
+        eqs = "["
+        for i in range(len(eqns)):
+            if i<len(eqns)-1:
+                eqs = eqs + eqns[i]+","
+            if  i==len(eqns)-1:
+                eqs = eqs + eqns[i]+"]"
+        vrs = "["
+        for i in range(len(vars)):
+            if i<len(vars)-1:
+                vrs = vrs + vars[i]+","
+            if  i==len(vars)-1:
+                vrs = vrs + vars[i]+"]"
+        return self('linsolve(%s, %s)'%(eqs, vrs))
+    def unit_quadratic_integer(self, n):
+        r"""
+        Finds a unit of the ring of integers of the quadratic number field
+        `\QQ(\sqrt{n})`, `n>1`, using the qunit maxima
+        command.
+        EXAMPLES::
+            sage: u = maxima.unit_quadratic_integer(101); u
+            a + 10
+            sage: u.parent()
+            Number Field in a with defining polynomial x^2 - 101
+            sage: u = maxima.unit_quadratic_integer(13)
+            sage: u
+*a + 18
+            sage: u.parent()
+            Number Field in a with defining polynomial x^2 - 13
+        """
+        from sage.rings.all import QuadraticField, Integer
+        # Take square-free part so sqrt(n) doesn't get simplified further by maxima
+        # (The original version of this function would yield wrong answers if
+        # n is not squarefree.)
+        n = Integer(n).squarefree_part()
+        if n < 1:
+            raise ValueError, "n (=%s) must be >= 1"%n
+        s = repr(self('qunit(%s)'%n)).lower()
+        r = re.compile('sqrt\(.*\)')
+        s = r.sub('a', s)
+        a = QuadraticField(n, 'a').gen()
+        return eval(s)
+    def plot_list(self, ptsx, ptsy, options=None):
+        r"""
+        Plots a curve determined by a sequence of points.
+        INPUT:
+        -  ``ptsx`` - [x1,...,xn], where the xi and yi are
+           real,
+        -  ``ptsy`` - [y1,...,yn]
+        -  ``options`` - a string representing maxima plot2d
+           options.
+        The points are (x1,y1), (x2,y2), etc.
+        This function requires maxima 5.9.2 or newer.
+        .. note::
+           More that 150 points can sometimes lead to the program
+           hanging. Why?
+        EXAMPLES::
+            sage: zeta_ptsx = [ (pari(1/2 + i*I/10).zeta().real()).precision(1) for i in range (70,150)]
+            sage: zeta_ptsy = [ (pari(1/2 + i*I/10).zeta().imag()).precision(1) for i in range (70,150)]
+            sage: maxima.plot_list(zeta_ptsx, zeta_ptsy)         # not tested
+            sage: opts='[gnuplot_preamble, "set nokey"], [gnuplot_term, ps], [gnuplot_out_file, "zeta.eps"]'
+            sage: maxima.plot_list(zeta_ptsx, zeta_ptsy, opts)      # not tested
+        """
+        cmd = 'plot2d([discrete,%s, %s]'%(ptsx, ptsy)
+        if options is None:
+            cmd += ')'
+        else:
+            cmd += ', %s)'%options
+        self(cmd)
+    def plot_multilist(self, pts_list, options=None):
+        r"""
+        Plots a list of list of points pts_list=[pts1,pts2,...,ptsn],
+        where each ptsi is of the form [[x1,y1],...,[xn,yn]] x's must be
+        integers and y's reals options is a string representing maxima
+        plot2d options.
+        Requires maxima 5.9.2 at least.
+        .. note::
+           More that 150 points can sometimes lead to the program
+           hanging.
+        EXAMPLES::
+            sage: xx = [ i/10.0 for i in range (-10,10)]
+            sage: yy = [ i/10.0 for i in range (-10,10)]
+            sage: x0 = [ 0 for i in range (-10,10)]
+            sage: y0 = [ 0 for i in range (-10,10)]
+            sage: zeta_ptsx1 = [ (pari(1/2+i*I/10).zeta().real()).precision(1) for i in range (10)]
+            sage: zeta_ptsy1 = [ (pari(1/2+i*I/10).zeta().imag()).precision(1) for i in range (10)]
+            sage: maxima.plot_multilist([[zeta_ptsx1,zeta_ptsy1],[xx,y0],[x0,yy]])       # not tested
+            sage: zeta_ptsx1 = [ (pari(1/2+i*I/10).zeta().real()).precision(1) for i in range (10,150)]
+            sage: zeta_ptsy1 = [ (pari(1/2+i*I/10).zeta().imag()).precision(1) for i in range (10,150)]
+            sage: maxima.plot_multilist([[zeta_ptsx1,zeta_ptsy1],[xx,y0],[x0,yy]])      # not tested
+            sage: opts='[gnuplot_preamble, "set nokey"]'
+            sage: maxima.plot_multilist([[zeta_ptsx1,zeta_ptsy1],[xx,y0],[x0,yy]],opts)    # not tested
+        """
+        n = len(pts_list)
+        cmd = '['
+        for i in range(n):
+            if i < n-1:
+                cmd = cmd+'[discrete,'+str(pts_list[i][0])+','+str(pts_list[i][1])+'],'
+            if i==n-1:
+                cmd = cmd+'[discrete,'+str(pts_list[i][0])+','+str(pts_list[i][1])+']]'
+        #print cmd
+        if options is None:
+            self('plot2d('+cmd+')')
+        else:
+            self('plot2d('+cmd+','+options+')')
+class MaximaElement(ExpectElement):
+    def __str__(self):
+        """
+        Printing an object explicitly gives ASCII art:
+        EXAMPLES::
+            sage: f = maxima('1/(x-1)^3'); f
+/(x-1)^3
+            sage: print f
+                                               --------
+                                               (x - 1)
+        """
+        return self.display2d(onscreen=False)
+    def bool(self):
+        """
+        EXAMPLES::
+            sage: maxima(0).bool()
+            False
+            sage: maxima(1).bool()
+            True
+        """
+        P = self._check_valid()
+        return P.eval('is(%s = 0);'%self.name()) == P._false_symbol() # but be careful, since for relations things like is(equal(a,b)) are what Maxima needs
+    def __cmp__(self, other):
+        """
+        EXAMPLES::
+            sage: a = maxima(1); b = maxima(2)
+            sage: a == b
+            False
+            sage: a < b
+            True
+            sage: a > b
+            False
+            sage: b < a
+            False
+            sage: b > a
+            True
+        We can also compare more complicated object such as functions::
+            sage: f = maxima('sin(x)'); g = maxima('cos(x)')
+            sage: -f == g.diff('x')
+            True
+        """
+        # thanks to David Joyner for telling me about using "is".
+        # but be careful, since for relations things like is(equal(a,b)) are what Maxima needs
+        P = self.parent()
+        try:
+            if P.eval("is (%s < %s)"%(self.name(), other.name())) == P._true_symbol():
+                return -1
+            elif P.eval("is (%s > %s)"%(self.name(), other.name())) == P._true_symbol():
+                return 1
+            elif P.eval("is (%s = %s)"%(self.name(), other.name())) == P._true_symbol():
+                return 0
+        except TypeError:
+            pass
+        return cmp(repr(self),repr(other))
+                   # everything is supposed to be comparable in Python, so we define
+                   # the comparison thus when no comparable in interfaced system.
+    def _sage_(self):
+        """
+        Attempt to make a native Sage object out of this maxima object.
+        This is useful for automatic coercions in addition to other
+        things.
+        EXAMPLES::
+            sage: a = maxima('sqrt(2) + 2.5'); a
+            sqrt(2)+2.5
+            sage: b = a._sage_(); b
+            sqrt(2) + 2.5
+            sage: type(b)
+            <type 'sage.symbolic.expression.Expression'>
+        We illustrate an automatic coercion::
+            sage: c = b + sqrt(3); c
+            sqrt(2) + sqrt(3) + 2.5
+            sage: type(c)
+            <type 'sage.symbolic.expression.Expression'>
+            sage: d = sqrt(3) + b; d
+            sqrt(2) + sqrt(3) + 2.5
+            sage: type(d)
+            <type 'sage.symbolic.expression.Expression'>
+        """
+        from sage.calculus.calculus import symbolic_expression_from_maxima_string
+        #return symbolic_expression_from_maxima_string(self.name(), maxima=self.parent())
+        return symbolic_expression_from_maxima_string(repr(self))
+    def _symbolic_(self, R):
+        """
+        Return a symbolic expression equivalent to this maxima object.
+        EXAMPLES::
+            sage: t = sqrt(2)._maxima_()
+            sage: u = t._symbolic_(SR); u
+            sqrt(2)
+            sage: u.parent()
+            Symbolic Ring
+        This is used when converting maxima objects to the Symbolic Ring::
+            sage: SR(t)
+            sqrt(2)
+        """
+        return R(self._sage_())
+    def __complex__(self):
+        """
+        EXAMPLES::
+            sage: complex(maxima('sqrt(-2)+1'))
+            (1+1.4142135623730951j)
+        """
+        return complex(self._sage_())
+    def _complex_mpfr_field_(self, C):
+        """
+        EXAMPLES::
+            sage: CC(maxima('1+%i'))
+.00000000000000 + 1.00000000000000*I
+            sage: CC(maxima('2342.23482943872+234*%i'))
+.23482943872 + 234.000000000000*I
+            sage: ComplexField(10)(maxima('2342.23482943872+234*%i'))
+. + 230.*I
+            sage: ComplexField(200)(maxima('1+%i'))
+.0000000000000000000000000000000000000000000000000000000000 + 1.0000000000000000000000000000000000000000000000000000000000*I
+            sage: ComplexField(200)(maxima('sqrt(-2)'))
+.4142135623730950488016887242096980785696718753769480731767*I
+            sage: N(sqrt(-2), 200)
+.0751148893563733350506651837615871941533119425962889089783e-62 + 1.4142135623730950488016887242096980785696718753769480731767*I
+        """
+        return C(self._sage_())
+    def _mpfr_(self, R):
+        """
+        EXAMPLES::
+            sage: RealField(100)(maxima('sqrt(2)+1'))
+.4142135623730950488016887242
+        """
+        return R(self._sage_())
+    def _complex_double_(self, C):
+        """
+        EXAMPLES::
+            sage: CDF(maxima('sqrt(2)+1'))
+.41421356237
+        """
+        return C(self._sage_())
+    def _real_double_(self, R):
+        """
+        EXAMPLES::
+            sage: RDF(maxima('sqrt(2)+1'))
+.41421356237
+        """
+        return R(self._sage_())
+    def real(self):
+        """
+        Return the real part of this maxima element.
+        EXAMPLES::
+            sage: maxima('2 + (2/3)*%i').real()
+        """
+        return self.realpart()
+    def imag(self):
+        """
+        Return the imaginary part of this maxima element.
+        EXAMPLES::
+            sage: maxima('2 + (2/3)*%i').imag()
+/3
+        """
+        return self.imagpart()
+    def numer(self):
+        """
+        Return numerical approximation to self as a Maxima object.
+        EXAMPLES::
+            sage: a = maxima('sqrt(2)').numer(); a
+.414213562373095
+            sage: type(a)
+            <class 'sage.interfaces.maxima_abstract.MaximaElement'>
+        """
+        return self.comma('numer')
+    def str(self):
+        """
+        Return string representation of this maxima object.
+        EXAMPLES::
+            sage: maxima('sqrt(2) + 1/3').str()
+            'sqrt(2)+1/3'
+        """
+        P = self._check_valid()
+        return P.get(self._name)
+    def __repr__(self):
+        """
+        Return print representation of this object.
+        EXAMPLES::
+            sage: maxima('sqrt(2) + 1/3').__repr__()
+            'sqrt(2)+1/3'
+        """
+        P = self._check_valid()
+        try:
+            return self.__repr
+        except AttributeError:
+            pass
+        r = P.get(self._name)
+        self.__repr = r
+        return r
+    def display2d(self, onscreen=True):
+        """
+        EXAMPLES::
+            sage: F = maxima('x^5 - y^5').factor()
+            sage: F.display2d ()
+      3    2  2    3      4
+                       - (y - x) (y  + x y  + x  y  + x  y + x )
+        """
+        self._check_valid()
+        P = self.parent()
+        with gc_disabled():
+            P._eval_line('display2d : true$')
+            s = P._eval_line('disp(%s)$'%self.name(), reformat=False)
+            P._eval_line('display2d: false$')
+        s = s.strip('\r\n')
+        # if ever want to dedent, see
+        # http://mail.python.org/pipermail/python-list/2006-December/420033.html
+        if onscreen:
+            print s
+        else:
+            return s
+    def diff(self, var='x', n=1):
+        """
+        Return the n-th derivative of self.
+        INPUT:
+        -  ``var`` - variable (default: 'x')
+        -  ``n`` - integer (default: 1)
+        OUTPUT: n-th derivative of self with respect to the variable var
+        EXAMPLES::
+            sage: f = maxima('x^2')
+            sage: f.diff()
+*x
+            sage: f.diff('x')
+*x
+            sage: f.diff('x', 2)
+            sage: maxima('sin(x^2)').diff('x',4)
+*x^4*sin(x^2)-12*sin(x^2)-48*x^2*cos(x^2)
+        ::
+            sage: f = maxima('x^2 + 17*y^2')
+            sage: f.diff('x')
+*y*'diff(y,x,1)+2*x
+            sage: f.diff('y')
+*y
+        """
+        return ExpectElement.__getattr__(self, 'diff')(var, n)
+    derivative = diff
+    def nintegral(self, var='x', a=0, b=1,
+                  desired_relative_error='1e-8',
+                  maximum_num_subintervals=200):
+        r"""
+        Return a numerical approximation to the integral of self from a to
+        b.
+        INPUT:
+        -  ``var`` - variable to integrate with respect to
+        -  ``a`` - lower endpoint of integration
+        -  ``b`` - upper endpoint of integration
+        -  ``desired_relative_error`` - (default: '1e-8') the
+           desired relative error
+        -  ``maximum_num_subintervals`` - (default: 200)
+           maxima number of subintervals
+        OUTPUT:
+        -  approximation to the integral
+        -  estimated absolute error of the
+           approximation
+        -  the number of integrand evaluations
+        -  an error code:
+            -  ``0`` - no problems were encountered
+            -  ``1`` - too many subintervals were done
+            -  ``2`` - excessive roundoff error
+            -  ``3`` - extremely bad integrand behavior
+            -  ``4`` - failed to converge
+            -  ``5`` - integral is probably divergent or slowly convergent
+            -  ``6`` - the input is invalid
+        EXAMPLES::
+            sage: maxima('exp(-sqrt(x))').nintegral('x',0,1)
+            (.5284822353142306, 4.163314137883845e-11, 231, 0)
+        Note that GP also does numerical integration, and can do so to very
+        high precision very quickly::
+            sage: gp('intnum(x=0,1,exp(-sqrt(x)))')
+.5284822353142307136179049194             # 32-bit
+.52848223531423071361790491935415653021   # 64-bit
+            sage: _ = gp.set_precision(80)
+            sage: gp('intnum(x=0,1,exp(-sqrt(x)))')
+.52848223531423071361790491935415653021675547587292866196865279321015401702040079
+        """
+        from sage.rings.all import Integer
+        v = self.quad_qags(var, a, b, epsrel=desired_relative_error,
+                           limit=maximum_num_subintervals)
+        return v[0], v[1], Integer(v[2]), Integer(v[3])
+    def integral(self, var='x', min=None, max=None):
+        r"""
+        Return the integral of self with respect to the variable x.
+        INPUT:
+        -  ``var`` - variable
+        -  ``min`` - default: None
+        -  ``max`` - default: None
+        Returns the definite integral if xmin is not None, otherwise
+        returns an indefinite integral.
+        EXAMPLES::
+            sage: maxima('x^2+1').integral()
+            x^3/3+x
+            sage: maxima('x^2+ 1 + y^2').integral('y')
+            y^3/3+x^2*y+y
+            sage: maxima('x / (x^2+1)').integral()
+            log(x^2+1)/2
+            sage: maxima('1/(x^2+1)').integral()
+            atan(x)
+            sage: maxima('1/(x^2+1)').integral('x', 0, infinity)
+            %pi/2
+            sage: maxima('x/(x^2+1)').integral('x', -1, 1)
+        ::
+            sage: f = maxima('exp(x^2)').integral('x',0,1); f
+            -sqrt(%pi)*%i*erf(%i)/2
+            sage: f.numer()
+.462651745907182
+        """
+        I = ExpectElement.__getattr__(self, 'integrate')
+        if min is None:
+            return I(var)
+        else:
+            if max is None:
+                raise ValueError, "neither or both of min/max must be specified."
+            return I(var, min, max)
+    integrate = integral
+    def __float__(self):
+        """
+        Return floating point version of this maxima element.
+        EXAMPLES::
+            sage: float(maxima("3.14"))
+.1400000000000001
+            sage: float(maxima("1.7e+17"))
+.7e+17
+            sage: float(maxima("1.7e-17"))
+.6999999999999999e-17
+        """
+        try:
+            return float(repr(self.numer()))
+        except ValueError:
+            raise TypeError, "unable to coerce '%s' to float"%repr(self)
+    def __len__(self):
+        """
+        Return the length of a list.
+        EXAMPLES::
+            sage: v = maxima('create_list(x^i,i,0,5)')
+            sage: len(v)
+        """
+        P = self._check_valid()
+        return int(P.eval('length(%s)'%self.name()))
+    def dot(self, other):
+        """
+        Implements the notation self . other.
+        EXAMPLES::
+            sage: A = maxima('matrix ([a1],[a2])')
+            sage: B = maxima('matrix ([b1, b2])')
+            sage: A.dot(B)
+            matrix([a1*b1,a1*b2],[a2*b1,a2*b2])
+        """
+        P = self._check_valid()
+        Q = P(other)
+        return P('%s . %s'%(self.name(), Q.name()))
+    def __getitem__(self, n):
+        r"""
+        Return the n-th element of this list.
+        .. note::
+           Lists are 0-based when accessed via the Sage interface, not
+-based as they are in the Maxima interpreter.
+        EXAMPLES::
+            sage: v = maxima('create_list(i*x^i,i,0,5)'); v
+            [0,x,2*x^2,3*x^3,4*x^4,5*x^5]
+            sage: v[3]
+*x^3
+            sage: v[0]
+            sage: v[10]
+            Traceback (most recent call last):
+            ...
+            IndexError: n = (10) must be between 0 and 5
+        """
+        n = int(n)
+        if n < 0 or n >= len(self):
+            raise IndexError, "n = (%s) must be between %s and %s"%(n, 0, len(self)-1)
+        # If you change the n+1 to n below, better change __iter__ as well.
+        return ExpectElement.__getitem__(self, n+1)
+    def __iter__(self):
+        """
+        EXAMPLE::
+            sage: v = maxima('create_list(i*x^i,i,0,5)')
+            sage: L = list(v)
+            sage: [e._sage_() for e in L]
+            [0, x, 2*x^2, 3*x^3, 4*x^4, 5*x^5]
+        """
+        for i in range(len(self)):
+            yield self[i]
+    def subst(self, val):
+        """
+        Substitute a value or several values into this Maxima object.
+        EXAMPLES::
+            sage: maxima('a^2 + 3*a + b').subst('b=2')
+            a^2+3*a+2
+            sage: maxima('a^2 + 3*a + b').subst('a=17')
+            b+340
+            sage: maxima('a^2 + 3*a + b').subst('a=17, b=2')
+        """
+        return self.comma(val)
+    def comma(self, args):
+        """
+        Form the expression that would be written 'self, args' in Maxima.
+        EXAMPLES::
+            sage: maxima('sqrt(2) + I').comma('numer')
+            I+1.414213562373095
+            sage: maxima('sqrt(2) + I*a').comma('a=5')
+*I+sqrt(2)
+        """
+        self._check_valid()
+        P = self.parent()
+        return P('%s, %s'%(self.name(), args))
+    def _latex_(self):
+        """
+        Return Latex representation of this Maxima object.
+        This calls the tex command in Maxima, then does a little
+        post-processing to fix bugs in the resulting Maxima output.
+        EXAMPLES::
+            sage: maxima('sqrt(2) + 1/3 + asin(5)')._latex_()
+            '\\sin^{-1}\\cdot5+\\sqrt{2}+{{1}\\over{3}}'
+            sage: y,d = var('y,d')
+            sage: latex(maxima(derivative(ceil(x*y*d), d,x,x,y)))
+            d^3\,\left({{{\it \partial}^4}\over{{\it \partial}\,d^4}}\,  {\it ceil}\left(d , x , y\right)\right)\,x^2\,y^3+5\,d^2\,\left({{  {\it \partial}^3}\over{{\it \partial}\,d^3}}\,{\it ceil}\left(d , x   , y\right)\right)\,x\,y^2+4\,d\,\left({{{\it \partial}^2}\over{  {\it \partial}\,d^2}}\,{\it ceil}\left(d , x , y\right)\right)\,y
+            sage: latex(maxima(d/(d-2)))
+            {{d}\over{d-2}}
+        """
+        self._check_valid()
+        P = self.parent()
+        s = P._eval_line('tex(%s);'%self.name(), reformat=False)
+        if not '$$' in s:
+            raise RuntimeError, "Error texing maxima object."
+        i = s.find('$$')
+        j = s.rfind('$$')
+        s = s[i+2:j]
+        s = multiple_replace({'\r\n':' ',
+                              '\\%':'',
+                              '\\arcsin ':'\\sin^{-1} ',
+                              '\\arccos ':'\\cos^{-1} ',
+                              '\\arctan ':'\\tan^{-1} '}, s)
+        # Fix a maxima bug, which gives a latex representation of multiplying
+        # two numbers as a single space. This was really bad when 2*17^(1/3)
+        # gets TeXed as '2 17^{\frac{1}{3}}'
+        #
+        # This regex matches a string of spaces preceded by either a '}', a
+        # decimal digit, or a ')', and followed by a decimal digit. The spaces
+        # get replaced by a '\cdot'.
+        s = re.sub(r'(?<=[})\d]) +(?=\d)', '\cdot', s)
+        return s
+    def trait_names(self, verbose=False):
+        """
+        Return all Maxima commands, which is useful for tab completion.
+        EXAMPLES::
+            sage: m = maxima(2)
+            sage: 'gcd' in m.trait_names()
+            True
+        """
+        return self.parent().trait_names(verbose=False)
+    def _matrix_(self, R):
+        r"""
+        If self is a Maxima matrix, return the corresponding Sage matrix
+        over the Sage ring `R`.
+        This may or may not work depending in how complicated the entries
+        of self are! It only works if the entries of self can be coerced as
+        strings to produce meaningful elements of `R`.
+        EXAMPLES::
+            sage: _ = maxima.eval("f[i,j] := i/j")
+            sage: A = maxima('genmatrix(f,4,4)'); A
+            matrix([1,1/2,1/3,1/4],[2,1,2/3,1/2],[3,3/2,1,3/4],[4,2,4/3,1])
+            sage: A._matrix_(QQ)
+            [  1 1/2 1/3 1/4]
+            [  2   1 2/3 1/2]
+            [  3 3/2   1 3/4]
+            [  4   2 4/3   1]
+        You can also use the ``matrix`` command (which is
+        defined in ``sage.misc.functional``)::
+            sage: matrix(QQ, A)
+            [  1 1/2 1/3 1/4]
+            [  2   1 2/3 1/2]
+            [  3 3/2   1 3/4]
+            [  4   2 4/3   1]
+        """
+        from sage.matrix.all import MatrixSpace
+        self._check_valid()
+        P = self.parent()
+        nrows = int(P.eval('length(%s)'%self.name()))
+        if nrows == 0:
+            return MatrixSpace(R, 0, 0)(0)
+        ncols = int(P.eval('length(%s[1])'%self.name()))
+        M = MatrixSpace(R, nrows, ncols)
+        s = self.str().replace('matrix','').replace(',',"','").\
+            replace("]','[","','").replace('([',"['").replace('])',"']")
+        s = eval(s)
+        return M([R(x) for x in s])
+    def partial_fraction_decomposition(self, var='x'):
+        """
+        Return the partial fraction decomposition of self with respect to
+        the variable var.
+        EXAMPLES::
+            sage: f = maxima('1/((1+x)*(x-1))')
+            sage: f.partial_fraction_decomposition('x')
+/(2*(x-1))-1/(2*(x+1))
+            sage: print f.partial_fraction_decomposition('x')
+           1
+                             --------- - ---------
+(x - 1)   2 (x + 1)
+        """
+        return self.partfrac(var)
+    def _operation(self, operation, right):
+        r"""
+        Note that right's parent should already be Maxima since this should
+        be called after coercion has been performed.
+        If right is a ``MaximaFunction``, then we convert
+        ``self`` to a ``MaximaFunction`` that takes
+        no arguments, and let the
+        ``MaximaFunction._operation`` code handle everything
+        from there.
+        EXAMPLES::
+            sage: f = maxima.cos(x)
+            sage: f._operation("+", f)
+*cos(x)
+        """
+        P = self._check_valid()
+        if isinstance(right, MaximaFunction):
+            fself = P.function('', repr(self))
+            return fself._operation(operation, right)
+        try:
+            return P.new('%s %s %s'%(self._name, operation, right._name))
+        except Exception, msg:
+            raise TypeError, msg
+class MaximaFunctionElement(FunctionElement):
+    def _sage_doc_(self):
+        """
+        EXAMPLES::
+            sage: m = maxima(4)
+            sage: m.gcd._sage_doc_()
+            -- Function: gcd (<p_1>, <p_2>, <x_1>, ...)
+            ...
+        """
+        return self._obj.parent().help(self._name)
+class MaximaExpectFunction(ExpectFunction):
+    def _sage_doc_(self):
+        """
+        EXAMPLES::
+            sage: maxima.gcd._sage_doc_()
+            -- Function: gcd (<p_1>, <p_2>, <x_1>, ...)
+            ...
+        """
+        M = self._parent
+        return M.help(self._name)
+class MaximaFunction(MaximaElement):
+    def __init__(self, parent, name, defn, args, latex):
+        """
+        EXAMPLES::
+            sage: f = maxima.function('x,y','sin(x+y)')
+            sage: f == loads(dumps(f))
+            True
+        """
+        MaximaElement.__init__(self, parent, name, is_name=True)
+        self.__defn = defn
+        self.__args = args
+        self.__latex = latex
+    def __reduce__(self):
+        """
+        EXAMPLES::
+            sage: f = maxima.function('x,y','sin(x+y)')
+            sage: f.__reduce__()
+            (<function reduce_load_Maxima_function at 0x...>,
+             (Maxima, 'sin(x+y)', 'x,y', None))
+        """
+        return reduce_load_Maxima_function, (self.parent(), self.__defn, self.__args, self.__latex)
+    def __call__(self, *x):
+        """
+        EXAMPLES::
+            sage: f = maxima.function('x,y','sin(x+y)')
+            sage: f(1,2)
+            sin(3)
+            sage: f(x,x)
+            sin(2*x)
+        """
+        P = self._check_valid()
+        if len(x) == 1:
+            x = '(%s)'%x
+        return P('%s%s'%(self.name(), x))
+    def __repr__(self):
+        """
+        EXAMPLES::
+            sage: f = maxima.function('x,y','sin(x+y)')
+            sage: repr(f)
+            'sin(x+y)'
+        """
+        return self.definition()
+    def _latex_(self):
+        """
+        EXAMPLES::
+            sage: f = maxima.function('x,y','sin(x+y)')
+            sage: latex(f)
+            \mathrm{sin(x+y)}
+        """
+        if self.__latex is None:
+            return r'\mathrm{%s}'%self.__defn
+        else:
+            return self.__latex
+    def arguments(self, split=True):
+        r"""
+        Returns the arguments of this Maxima function.
+        EXAMPLES::
+            sage: f = maxima.function('x,y','sin(x+y)')
+            sage: f.arguments()
+            ['x', 'y']
+            sage: f.arguments(split=False)
+            'x,y'
+            sage: f = maxima.function('', 'sin(x)')
+            sage: f.arguments()
+            []
+        """
+        if split:
+            return self.__args.split(',') if self.__args != '' else []
+        else:
+            return self.__args
+    def definition(self):
+        """
+        Returns the definition of this Maxima function as a string.
+        EXAMPLES::
+            sage: f = maxima.function('x,y','sin(x+y)')
+            sage: f.definition()
+            'sin(x+y)'
+        """
+        return self.__defn
+    def integral(self, var):
+        """
+        Returns the integral of self with respect to the variable var.
+        Note that integrate is an alias of integral.
+        EXAMPLES::
+            sage: x,y = var('x,y')
+            sage: f = maxima.function('x','sin(x)')
+            sage: f.integral(x)
+            -cos(x)
+            sage: f.integral(y)
+            sin(x)*y
+        """
+        var = str(var)
+        P = self._check_valid()
+        f = P('integrate(%s(%s), %s)'%(self.name(), self.arguments(split=False), var))
+        args = self.arguments()
+        if var not in args:
+            args.append(var)
+        return P.function(",".join(args), repr(f))
+    integrate = integral
+    def _operation(self, operation, f=None):
+        r"""
+        This is a utility function which factors out much of the
+        commonality used in the arithmetic operations for
+        ``MaximaFunctions``.
+        INPUT:
+        -  ``operation`` - A string representing the operation
+           being performed. For example, '\*', or '1/'.
+        -  ``f`` - The other operand. If f is
+           ``None``, than the operation is assumed to be unary
+           rather than binary.
+        EXAMPLES::
+            sage: f = maxima.function('x,y','sin(x+y)')
+            sage: f._operation("+", f)
+*sin(y+x)
+            sage: f._operation("+", 2)
+            sin(y+x)+2
+            sage: f._operation('-')
+            -sin(y+x)
+            sage: f._operation('1/')
+/sin(y+x)
+        """
+        P = self._check_valid()
+        if isinstance(f, MaximaFunction):
+            tmp = list(sorted(set(self.arguments() + f.arguments())))
+            args = ','.join(tmp)
+            defn = "(%s)%s(%s)"%(self.definition(), operation, f.definition())
+        elif f is None:
+            args = self.arguments(split=False)
+            defn = "%s(%s)"%(operation, self.definition())
+        else:
+            args = self.arguments(split=False)
+            defn = "(%s)%s(%s)"%(self.definition(), operation, repr(f))
+        return P.function(args,P.eval(defn))
+    def _add_(self, f):
+        """
+        MaximaFunction as left summand.
+        EXAMPLES::
+            sage: x,y = var('x,y')
+            sage: f = maxima.function('x','sin(x)')
+            sage: g = maxima.function('x','-cos(x)')
+            sage: f+g
+            sin(x)-cos(x)
+            sage: f+3
+            sin(x)+3
+        ::
+            sage: (f+maxima.cos(x))(2)
+            sin(2)+cos(2)
+            sage: (f+maxima.cos(y)) # This is a function with only ONE argument!
+            cos(y)+sin(x)
+            sage: (f+maxima.cos(y))(2)
+            cos(y)+sin(2)
+        ::
+            sage: f = maxima.function('x','sin(x)')
+            sage: g = -maxima.cos(x)
+            sage: g+f
+            sin(x)-cos(x)
+            sage: (g+f)(2) # The sum IS a function
+            sin(2)-cos(2)
+            sage: 2+f
+            sin(x)+2
+        """
+        return self._operation("+", f)
+    def _sub_(self, f):
+        r"""
+        ``MaximaFunction`` as minuend.
+        EXAMPLES::
+            sage: x,y = var('x,y')
+            sage: f = maxima.function('x','sin(x)')
+            sage: g = -maxima.cos(x) # not a function
+            sage: f-g
+            sin(x)+cos(x)
+            sage: (f-g)(2)
+            sin(2)+cos(2)
+            sage: (f-maxima.cos(y)) # This function only has the argument x!
+            sin(x)-cos(y)
+            sage: _(2)
+            sin(2)-cos(y)
+        ::
+            sage: g-f
+            -sin(x)-cos(x)
+        """
+        return self._operation("-", f)
+    def _mul_(self, f):
+        r"""
+        ``MaximaFunction`` as left factor.
+        EXAMPLES::
+            sage: f = maxima.function('x','sin(x)')
+            sage: g = maxima('-cos(x)') # not a function!
+            sage: f*g
+            -cos(x)*sin(x)
+            sage: _(2)
+            -cos(2)*sin(2)
+        ::
+            sage: f = maxima.function('x','sin(x)')
+            sage: g = maxima('-cos(x)')
+            sage: g*f
+            -cos(x)*sin(x)
+            sage: _(2)
+            -cos(2)*sin(2)
+            sage: 2*f
+*sin(x)
+        """
+        return self._operation("*", f)
+    def _div_(self, f):
+        r"""
+        ``MaximaFunction`` as dividend.
+        EXAMPLES::
+            sage: f=maxima.function('x','sin(x)')
+            sage: g=maxima('-cos(x)')
+            sage: f/g
+            -sin(x)/cos(x)
+            sage: _(2)
+            -sin(2)/cos(2)
+        ::
+            sage: f=maxima.function('x','sin(x)')
+            sage: g=maxima('-cos(x)')
+            sage: g/f
+            -cos(x)/sin(x)
+            sage: _(2)
+            -cos(2)/sin(2)
+            sage: 2/f
+/sin(x)
+        """
+        return self._operation("/", f)
+    def __neg__(self):
+        r"""
+        Additive inverse of a ``MaximaFunction``.
+        EXAMPLES::
+            sage: f=maxima.function('x','sin(x)')
+            sage: -f
+            -sin(x)
+        """
+        return self._operation('-')
+    def __inv__(self):
+        r"""
+        Multiplicative inverse of a ``MaximaFunction``.
+        EXAMPLES::
+            sage: f = maxima.function('x','sin(x)')
+            sage: ~f
+/sin(x)
+        """
+        return self._operation('1/')
+    def __pow__(self,f):
+        r"""
+        ``MaximaFunction`` raised to some power.
+        EXAMPLES::
+            sage: f=maxima.function('x','sin(x)')
+            sage: g=maxima('-cos(x)')
+            sage: f^g
+/sin(x)^cos(x)
+        ::
+            sage: f=maxima.function('x','sin(x)')
+            sage: g=maxima('-cos(x)') # not a function
+            sage: g^f
+            (-cos(x))^sin(x)
+        """
+        return self._operation("^", f)
+def reduce_load_Maxima_function(parent, defn, args, latex):
+    return parent.function(args, defn, defn, latex)
+import os
+def maxima_console():
+    """
+    Spawn a new Maxima command-line session.
+    EXAMPLES::
+        sage: from sage.interfaces.maxima import maxima_console
+        sage: maxima_console()                    # not tested
+        Maxima 5.16.3 http://maxima.sourceforge.net
+        ...
+    """
+    os.system('maxima')

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