Hi Debian Stable's maxima 46 also shows the error:
0 jan@jan-latitude:~$dpkg -l maxima|grep ii ii maxima 5.46.0-11 amd64 Computer algebra system -- base system 0 jan@jan-latitude:~$maxima -q<test-taylor.mac (%i1) (%i2) PQUOTIENT: Quotient by a polynomial of higher degree (case 2a) -- an error. To debug this try: debugmode(true); Regards, Jan On Sun, 25 Aug 2024 at 11:25, Dima Pasechnik <dimp...@gmail.com> wrote: > > > On 25 August 2024 09:52:20 BST, Emmanuel Charpentier < > emanuel.charpent...@gmail.com> wrote: > > > > > >*Correction :* > > > > - /usr/bin/maxima, the “standalone” version of maxima provided by > Debian > > testing, runs without error : > > > >(%i3) t:taylor(g, x4, 0, 8)$ (%i4) > > > > - /usr/local/sage-10/local/bin/maxima, “our” version of Maxima, fails > to > > compute the Taylor series : > > > >(%i4) t:taylor(g, x4, 0, 8)$ PQUOTIENT: Quotient by a polynomial of > higher > >degree (case 2a) -- an error. To debug this try: debugmode(true); (%i5) > > > our Maxima version is older by one or two versions. (5.45 vs 5.47) > > Dima > > > > >Ticket underway (slowly). > > > >HTH, > > > >Le jeudi 22 août 2024 à 17:42:06 UTC+2, Nils Bruin a écrit : > > > >> By the looks of it, the place of failure is the same in both cases. In > the > >> case of using maxima_lib, the maxima error generation doesn't quite > work > >> though: as you can see, a condition RAT-ERR is not defined. That means > >> there is code that "throws" the condition, assuming there's a "catch" > set > >> up around it. maxima_lib was originally designed to provide lower > overhead > >> for maxima access as well as provide a more robust interface by > avoiding > >> string parsing as much as possible. So it tries to run maxima code in a > >> lisp environment that is as cheaply set up as possible. There is some > >> catching, but I did not trace through all of maxima to see what catches > can > >> occur. Note that maxima sets up its evaluation loop once with all its > >> catches around it, so set up is amortized. For maxima_lib, every > command > >> will exit back completely, so the stack frames holding the condition > >> catches all need to be built up and torn down for every access to > >> maxima_lib. > >> > >> That explains why you see the message about RAT-ERR rather than the > >> PQUOTIENT message (presumably, the RAT-ERR condition has some extra > data > >> hanging off it that the corresponding catch can use to generate a > message > >> with more data) > >> > >> As to why something fails when called via sage and succeeds when > executed > >> in maxima directly: that will require some drilling down. There are > >> non-standard settings that sage makes for its maxima-calculus instance, > but > >> that's unlikely to make a difference for polynomial division. There may > be > >> a small inequivalence between the code that is actually generated (note > >> that maxima_lib will be entering and exiting the maxima environment for > >> every method call, leaving the return value on ECL's heap to serve as > input > >> for the next call, whereas the maxima evaluation loop has its own way > of > >> chaining things together) > >> > >> It looks to me it could be made into a ticket/issue. > >> > >> On Thursday 22 August 2024 at 04:04:32 UTC-7 Emmanuel Charpentier wrote: > >> > >>> Inspired by this ask.sagemath.org question > >>> < > https://ask.sagemath.org/question/78686/taylor-expansion-in-sagemath-returns-error/ > > > >>> . > >>> > >>> Compare this Maxima standalone execution : > >>> (%i1) display2d:false; (%o1) false (%i2) g: > >>> 1/4*((w1^2*w3^2*x1^4*x2^6*x3^8 + 2*(w1^2*w3^2*x1^4*x2^6 + > >>> w1^2*w3*x1^3*x2^5)*x3^7 + (w1^2*w3^2*x1^4*x2^6 + 2*w1^2*w3*x1^3*x2^5 + > >>> 2*w1^2*x1^2*x2^4)*x3^6)*x4^6 + 2*((w1^2*w3^2*x1^4*x2^6 + > (w1^2*w3^2*x1^4 + > >>> (2*w1^2*w3 + w1*w3^2)*x1^3)*x2^5)*x3^7 + 2*(w1^2*w3^2*x1^4*x2^6 + > >>> (w1^2*w3^2*x1^4 + (3*w1^2*w3 + w1*w3^2)*x1^3)*x2^5 + (w1^2*w3*x1^3 + > (w1^2 > >>> + w1*w3)*x1^2)*x2^4)*x3^6 + (w1^2*w3^2*x1^4*x2^6 + (w1^2*w3^2*x1^4 + > >>> (4*w1^2*w3 + w1*w3^2)*x1^3)*x2^5 + 2*(w1^2*w3*x1^3 + (2*w1^2 + > >>> w1*w3)*x1^2)*x2^4 + 2*(w1^2*x1^2 + w1*x1)*x2^3)*x3^5)*x4^5 + > >>> ((w1^2*w3^2*x1^4*x2^6 + 2*(w1^2*w3^2*x1^4 + (3*w1^2*w3 + > >>> 2*w1*w3^2)*x1^3)*x2^5 + (w1^2*w3^2*x1^4 + 2*(3*w1^2*w3 + > 2*w1*w3^2)*x1^3 + > >>> 2*(3*w1^2 + 6*w1*w3 + w3^2)*x1^2)*x2^4)*x3^6 + 2*(w1^2*w3^2*x1^4*x2^6 > + > >>> (2*w1^2*w3^2*x1^4 + (7*w1^2*w3 + 4*w1*w3^2)*x1^3)*x2^5 + > (w1^2*w3^2*x1^4 + > >>> 4*(2*w1^2*w3 + w1*w3^2)*x1^3 + (9*w1^2 + 16*w1*w3 + 2*w3^2)*x1^2)*x2^4 > + > >>> (w1^2*w3*x1^3 + (3*w1^2 + 4*w1*w3)*x1^2 + 2*(3*w1 + w3)*x1)*x2^3)*x3^5 > + > >>> (w1^2*w3^2*x1^4*x2^6 + 2*(w1^2*w3^2*x1^4 + 2*(2*w1^2*w3 + > >>> w1*w3^2)*x1^3)*x2^5 + (w1^2*w3^2*x1^4 + 2*(5*w1^2*w3 + 2*w1*w3^2)*x1^3 > + > >>> 2*(7*w1^2 + 10*w1*w3 + w3^2)*x1^2)*x2^4 + 2*(w1^2*w3*x1^3 + (5*w1^2 + > >>> 4*w1*w3)*x1^2 + 2*(5*w1 + w3)*x1)*x2^3 + 2*(w1^2*x1^2 + 4*w1*x1 + > >>> 2)*x2^2)*x3^4)*x4^4 + 2*(((w1^2*w3 + w1*w3^2)*x1^3*x2^5 + (2*(w1^2*w3 > + > >>> w1*w3^2)*x1^3 + (3*w1^2 + 10*w1*w3 + 2*w3^2)*x1^2)*x2^4 + ((w1^2*w3 + > >>> w1*w3^2)*x1^3 + (3*w1^2 + 10*w1*w3 + 2*w3^2)*x1^2 + 4*(3*w1 + > >>> 2*w3)*x1)*x2^3)*x3^5 + (2*(w1^2*w3 + w1*w3^2)*x1^3*x2^5 + (4*(w1^2*w3 > + > >>> w1*w3^2)*x1^3 + (7*w1^2 + 22*w1*w3 + 4*w3^2)*x1^2)*x2^4 + 2*((w1^2*w3 > + > >>> w1*w3^2)*x1^3 + 2*(2*w1^2 + 6*w1*w3 + w3^2)*x1^2 + (17*w1 + > 10*w3)*x1)*x2^3 > >>> + ((w1^2 + 2*w1*w3)*x1^2 + 2*(5*w1 + 2*w3)*x1 + 8)*x2^2)*x3^4 + > ((w1^2*w3 + > >>> w1*w3^2)*x1^3*x2^5 + 2*((w1^2*w3 + w1*w3^2)*x1^3 + (2*w1^2 + 6*w1*w3 + > >>> w3^2)*x1^2)*x2^4 + ((w1^2*w3 + w1*w3^2)*x1^3 + (5*w1^2 + 14*w1*w3 + > >>> 2*w3^2)*x1^2 + 12*(2*w1 + w3)*x1)*x2^3 + ((w1^2 + 2*w1*w3)*x1^2 + > 2*(7*w1 + > >>> 2*w3)*x1 + 12)*x2^2 + 2*(w1*x1 + 2)*x2)*x3^3)*x4^3 + 24*(x2^2 + 2*x2 + > >>> 1)*x3^2 + 2*(((w1^2 + 4*w1*w3 + w3^2)*x1^2*x2^4 + 2*((w1^2 + 4*w1*w3 + > >>> w3^2)*x1^2 + (8*w1 + 7*w3)*x1)*x2^3 + ((w1^2 + 4*w1*w3 + w3^2)*x1^2 + > >>> 2*(8*w1 + 7*w3)*x1 + 20)*x2^2)*x3^4 + 2*((w1^2 + 4*w1*w3 + > w3^2)*x1^2*x2^4 > >>> + (2*(w1^2 + 4*w1*w3 + w3^2)*x1^2 + 3*(6*w1 + 5*w3)*x1)*x2^3 + ((w1^2 > + > >>> 4*w1*w3 + w3^2)*x1^2 + 4*(5*w1 + 4*w3)*x1 + 27)*x2^2 + ((2*w1 + w3)*x1 > + > >>> 7)*x2)*x3^3 + ((w1^2 + 4*w1*w3 + w3^2)*x1^2*x2^4 + 2*((w1^2 + 4*w1*w3 > + > >>> w3^2)*x1^2 + 2*(5*w1 + 4*w3)*x1)*x2^3 + ((w1^2 + 4*w1*w3 + w3^2)*x1^2 > + > >>> 6*(4*w1 + 3*w3)*x1 + 36)*x2^2 + 2*((2*w1 + w3)*x1 + 9)*x2 + > 2)*x3^2)*x4^2 + > >>> 24*x2^2 + 48*(x2^2 + 2*x2 + 1)*x3 + 12*(((w1 + w3)*x1*x2^3 + (2*(w1 + > >>> w3)*x1 + 5)*x2^2 + ((w1 + w3)*x1 + 5)*x2)*x3^3 + (2*(w1 + w3)*x1*x2^3 > + > >>> (4*(w1 + w3)*x1 + 11)*x2^2 + 2*((w1 + w3)*x1 + 6)*x2 + 1)*x3^2 + ((w1 > + > >>> w3)*x1*x2^3 + 2*((w1 + w3)*x1 + 3)*x2^2 + ((w1 + w3)*x1 + 7)*x2 + > 1)*x3)*x4 > >>> + 48*x2 + 24)*e^(-w2*x1*x2*x3*x4)/((x2^3*x3^6*e^(w5*x1*x2) + > >>> 3*x2^3*x3^5*e^(w5*x1*x2) + 3*x2^3*x3^4*e^(w5*x1*x2) + > >>> x2^3*x3^3*e^(w5*x1*x2))*x4^3*e^(w6*x1*x2*x3) + 3*((x2^3 + > >>> x2^2)*x3^5*e^(w5*x1*x2) + 3*(x2^3 + x2^2)*x3^4*e^(w5*x1*x2) + 3*(x2^3 > + > >>> x2^2)*x3^3*e^(w5*x1*x2) + (x2^3 + > >>> x2^2)*x3^2*e^(w5*x1*x2))*x4^2*e^(w6*x1*x2*x3) + 3*((x2^3 + 2*x2^2 + > >>> x2)*x3^4*e^(w5*x1*x2) + 3*(x2^3 + 2*x2^2 + x2)*x3^3*e^(w5*x1*x2) + > 3*(x2^3 > >>> + 2*x2^2 + x2)*x3^2*e^(w5*x1*x2) + (x2^3 + 2*x2^2 + > >>> x2)*x3*e^(w5*x1*x2))*x4*e^(w6*x1*x2*x3) + ((x2^3 + 3*x2^2 + 3*x2 + > >>> 1)*x3^3*e^(w5*x1*x2) + 3*(x2^3 + 3*x2^2 + 3*x2 + 1)*x3^2*e^(w5*x1*x2) > + > >>> 3*(x2^3 + 3*x2^2 + 3*x2 + 1)*x3*e^(w5*x1*x2) + (x2^3 + 3*x2^2 + 3*x2 + > >>> 1)*e^(w5*x1*x2))*e^(w6*x1*x2*x3))$ (%i3) foo:coeff(taylor(g, x4, 0, > 8), > >>> x4^7)$ > >>> > >>> which works okay, with these Sage snippets : > >>> sage: g.taylor(x4, 0, 7).coefficient(x4, 7) > >>> > --------------------------------------------------------------------------- > >>> RuntimeError Traceback (most recent call last) File > >>> /usr/local/sage-10/src/sage/interfaces/interface.py:750, in > >>> InterfaceElement.__init__(self, parent, value, is_name, name) 749 try: > --> > >>> 750 self._name = parent._create(value, name=name) 751 except > (TypeError, > >>> RuntimeError, ValueError) as x: File > >>> /usr/local/sage-10/src/sage/interfaces/maxima_lib.py:623, in > >>> MaximaLib._create(self, value, name) 622 else: --> 623 self.set(name, > >>> value) 624 except RuntimeError as error: File > >>> /usr/local/sage-10/src/sage/interfaces/maxima_lib.py:533, in > >>> MaximaLib.set(self, var, value) 532 cmd = '%s : %s$' % (var, > >>> value.rstrip(';')) --> 533 self.eval(cmd) File > >>> /usr/local/sage-10/src/sage/interfaces/maxima_lib.py:479, in > >>> MaximaLib._eval_line(self, line, locals, reformat, **kwds) 478 if > >>> statement: --> 479 maxima_eval("#$%s$" % statement) 480 if not > reformat: > >>> File /usr/local/sage-10/src/sage/libs/ecl.pyx:830, in > >>> sage.libs.ecl.EclObject.__call__() 829 lispargs = > EclObject(list(args)) --> > >>> 830 return ecl_wrap(ecl_safe_apply(self.obj, > (<EclObject>lispargs).obj)) > >>> 831 File /usr/local/sage-10/src/sage/libs/ecl.pyx:358, in > >>> sage.libs.ecl.ecl_safe_apply() 357 else: --> 358 raise > RuntimeError("ECL > >>> says: {}".format(message)) 359 else: RuntimeError: ECL says: THROW: > The > >>> catch RAT-ERR is undefined. During handling of the above exception, > another > >>> exception occurred: TypeError Traceback (most recent call last) Cell > >>> In[161], line 1 ----> 1 g.taylor(x4, Integer(0), > >>> Integer(7)).coefficient(x4, Integer(7)) File > >>> /usr/local/sage-10/src/sage/symbolic/expression.pyx:5044, in > >>> sage.symbolic.expression.Expression.taylor() 5042 except Exception: > 5043 > >>> raise NotImplementedError("Wrong arguments passed to taylor. See > taylor? > >>> for more details.") -> 5044 l = self._maxima_().taylor(B) 5045 return > >>> self.parent()(l) 5046 File > >>> /usr/local/sage-10/src/sage/interfaces/interface.py:698, in > >>> InterfaceFunctionElement.__call__(self, *args, **kwds) 697 def > >>> __call__(self, *args, **kwds): --> 698 return > >>> self._obj.parent().function_call(self._name, [self._obj] + list(args), > >>> kwds) File /usr/local/sage-10/src/sage/interfaces/interface.py:617, in > >>> Interface.function_call(self, function, args, kwds) 613 > >>> self._check_valid_function_name(function) 614 s = > >>> self._function_call_string(function, 615 [s.name() for s in args], > 616 > >>> ['%s=%s' % (key, value.name()) for key, value in kwds.items()]) --> > 617 > >>> return self.new(s) File > >>> /usr/local/sage-10/src/sage/interfaces/interface.py:386, in > >>> Interface.new(self, code) 385 def new(self, code): --> 386 return > >>> self(code) File > /usr/local/sage-10/src/sage/interfaces/interface.py:299, in > >>> Interface.__call__(self, x, name) 296 pass 298 if isinstance(x, str): > --> > >>> 299 return cls(self, x, name=name) 300 try: 301 # Special methods do > not > >>> and should not have an option to 302 # set the name directly, as the > >>> identifier assigned by the 303 # interface should stay consistent. An > >>> identifier with a 304 # user-assigned name might change its value, so > we > >>> return a 305 # new element. 306 result = > >>> self._coerce_from_special_method(x) File > >>> /usr/local/sage-10/src/sage/interfaces/interface.py:752, in > >>> InterfaceElement.__init__(self, parent, value, is_name, name) 750 > >>> self._name = parent._create(value, name=name) 751 except (TypeError, > >>> RuntimeError, ValueError) as x: --> 752 raise TypeError(x) TypeError: > ECL > >>> says: THROW: The catch RAT-ERR is undefined. > >>> > >>> Furthermore, > >>> sage: foo=maxima_calculus("coeff(taylor(%s, %s, %s, %s), > >>> %s);"%tuple(map(lambda u:u._maxima_lib_init_(), (g, x4, 0, 8, x4^7)))) > >>> > --------------------------------------------------------------------------- > >>> RuntimeError Traceback (most recent call last) File > >>> /usr/local/sage-10/src/sage/interfaces/interface.py:750, in > >>> InterfaceElement.__init__(self, parent, value, is_name, name) 749 try: > --> > >>> 750 self._name = parent._create(value, name=name) 751 except > (TypeError, > >>> RuntimeError, ValueError) as x: File > >>> /usr/local/sage-10/src/sage/interfaces/maxima_lib.py:623, in > >>> MaximaLib._create(self, value, name) 622 else: --> 623 self.set(name, > >>> value) 624 except RuntimeError as error: File > >>> /usr/local/sage-10/src/sage/interfaces/maxima_lib.py:533, in > >>> MaximaLib.set(self, var, value) 532 cmd = '%s : %s$' % (var, > >>> value.rstrip(';')) --> 533 self.eval(cmd) File > >>> /usr/local/sage-10/src/sage/interfaces/maxima_lib.py:479, in > >>> MaximaLib._eval_line(self, line, locals, reformat, **kwds) 478 if > >>> statement: --> 479 maxima_eval("#$%s$" % statement) 480 if not > reformat: > >>> File /usr/local/sage-10/src/sage/libs/ecl.pyx:830, in > >>> sage.libs.ecl.EclObject.__call__() 829 lispargs = > EclObject(list(args)) --> > >>> 830 return ecl_wrap(ecl_safe_apply(self.obj, > (<EclObject>lispargs).obj)) > >>> 831 File /usr/local/sage-10/src/sage/libs/ecl.pyx:358, in > >>> sage.libs.ecl.ecl_safe_apply() 357 else: --> 358 raise > RuntimeError("ECL > >>> says: {}".format(message)) 359 else: RuntimeError: ECL says: THROW: > The > >>> catch RAT-ERR is undefined. During handling of the above exception, > another > >>> exception occurred: TypeError Traceback (most recent call last) Cell > >>> In[165], line 1 ----> 1 foo=maxima_calculus("coeff(taylor(%s, %s, %s, > %s), > >>> %s);"%tuple(map(lambda u:u._maxima_lib_init_(), (g, x4, Integer(0), > >>> Integer(8), x4**Integer(7))))) File > >>> /usr/local/sage-10/src/sage/interfaces/interface.py:299, in > >>> Interface.__call__(self, x, name) 296 pass 298 if isinstance(x, str): > --> > >>> 299 return cls(self, x, name=name) 300 try: 301 # Special methods do > not > >>> and should not have an option to 302 # set the name directly, as the > >>> identifier assigned by the 303 # interface should stay consistent. An > >>> identifier with a 304 # user-assigned name might change its value, so > we > >>> return a 305 # new element. 306 result = > >>> self._coerce_from_special_method(x) File > >>> /usr/local/sage-10/src/sage/interfaces/interface.py:752, in > >>> InterfaceElement.__init__(self, parent, value, is_name, name) 750 > >>> self._name = parent._create(value, name=name) 751 except (TypeError, > >>> RuntimeError, ValueError) as x: --> 752 raise TypeError(x) TypeError: > ECL > >>> says: THROW: The catch RAT-ERR is undefined. > >>> > >>> Here, the maxima_lib interface does not hint at the source of problem. > >>> sage: foo=maxima("coeff(taylor(%s, %s, %s, %s), %s);"%tuple(map(lambda > >>> u:u._maxima_init_(), (g, x4, 0, 8, x4^7)))) > >>> > --------------------------------------------------------------------------- > >>> TypeError Traceback (most recent call last) Cell In[168], line 1 ----> > 1 > >>> foo=maxima("coeff(taylor(%s, %s, %s, %s), %s);"%tuple(map(lambda > >>> u:u._maxima_init_(), (g, x4, Integer(0), Integer(8), > x4**Integer(7))))) > >>> File /usr/local/sage-10/src/sage/interfaces/interface.py:299, in > >>> Interface.__call__(self, x, name) 296 pass 298 if isinstance(x, str): > --> > >>> 299 return cls(self, x, name=name) 300 try: 301 # Special methods do > not > >>> and should not have an option to 302 # set the name directly, as the > >>> identifier assigned by the 303 # interface should stay consistent. An > >>> identifier with a 304 # user-assigned name might change its value, so > we > >>> return a 305 # new element. 306 result = > >>> self._coerce_from_special_method(x) File > >>> /usr/local/sage-10/src/sage/interfaces/maxima.py:1176, in > >>> MaximaElement.__init__(self, parent, value, is_name, name) 1155 def > >>> __init__(self, parent, value, is_name=False, name=None): 1156 """ 1157 > >>> Create a Maxima element. 1158 See ``MaximaElement`` for full > documentation. > >>> (...) 1174 True 1175 """ -> 1176 ExpectElement.__init__(self, parent, > >>> value, is_name=False, name=None) File > >>> /usr/local/sage-10/src/sage/interfaces/expect.py:1518, in > >>> ExpectElement.__init__(self, parent, value, is_name, name) 1516 else: > 1517 > >>> try: -> 1518 self._name = parent._create(value, name=name) 1519 # > Convert > >>> ValueError and RuntimeError to TypeError for 1520 # coercion to work > >>> properly. 1521 except (RuntimeError, ValueError) as x: File > >>> /usr/local/sage-10/src/sage/interfaces/interface.py:517, in > >>> Interface._create(self, value, name) 515 def _create(self, value, > >>> name=None): 516 name = self._next_var_name() if name is None else name > --> > >>> 517 self.set(name, value) 518 return name File > >>> /usr/local/sage-10/src/sage/interfaces/maxima.py:1015, in > Maxima.set(self, > >>> var, value) 1013 cmd = '%s : %s$' % (var, value.rstrip(';')) 1014 if > >>> len(cmd) > self.__eval_using_file_cutoff: -> 1015 self._batch(cmd, > >>> batchload=True) 1016 else: 1017 self._eval_line(cmd) File > >>> /usr/local/sage-10/src/sage/interfaces/maxima.py:905, in > >>> Maxima._batch(self, s, batchload) 903 self._expect_expr(s) 904 out = > >>> self._before() --> 905 self._error_check(cmd, out) 906 > os.unlink(filename) > >>> 907 return out File > /usr/local/sage-10/src/sage/interfaces/maxima.py:949, > >>> in Maxima._error_check(self, cmd, out) 947 m = r.search(out) 948 if m > is > >>> not None: --> 949 self._error_msg(cmd, out) File > >>> /usr/local/sage-10/src/sage/interfaces/maxima.py:966, in > >>> Maxima._error_msg(self, cmd, out) 951 def _error_msg(self, cmd, out): > 952 > >>> """ 953 Raise error with formatted description. 954 (...) 964 > Principal > >>> Value 965 """ --> 966 raise TypeError("Error executing code in > >>> Maxima\nCODE:\n\t%s\nMaxima ERROR:\n\t%s" % (cmd, out.replace('-- an > error. > >>> To debug this try debugmode(true);', ''))) TypeError: Error executing > code > >>> in Maxima CODE: > batchload("/tmp/tmp2d0k4lw6.input-1538064300");1+915520876; > >>> Maxima ERROR: > >>> > kill(sage6)$batchload("/tmp/tmp2d0k4lw6.input-1538064300");1+915520876; > >>> PQUOTIENT: Quotient by a polynomial of higher degree (case 2a) -- an > error. > >>> To debug this try: debugmode(true); (%o47) > >>> > >>> Here, an external maxima process, *launched by Sage*, gives us an hint > >>> to the error. > >>> > >>> However, *as initialized by Sage,* this process triggers an error *not > >>> occurring in a “standalone” `maxima process.* > >>> > >>> I did not find a relevant ticket in Github. Suggestions for filing a > new > >>> issue ? > >>> > >>> HTH, > >>> > >>> > >> > > > > -- > You received this message because you are subscribed to the Google Groups > "sage-support" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to sage-support+unsubscr...@googlegroups.com. > To view this discussion on the web visit > https://groups.google.com/d/msgid/sage-support/8CB1F994-36C2-454A-8CFC-229E3E9FACB2%40gmail.com > . > -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-support/CAAg%3Dp_2hrVKv-SFrjRhpRe7BfE%3DcXu1cEn1A3XrRk_FRDj%3DUFQ%40mail.gmail.com.
