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,
>>>
>>>
>>
>
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