# Revision history [back]

### Confusion about integrating a string.

sagemath 8.9

Follow up based on answer here why-sagemath-can-integrate-a-string sagemath can integrate a string.

Well. Sometimes it can, and sometimes it does not. And this getting confusing. For example

sage: integrate("ln(t)",t,algorithm="fricas")
integral(ln(t), t)

But if it is not a string, it works.

sage: integrate(ln(t),t,algorithm="fricas")
t*log(t) - t

But using "log(t)" as string, instead of "ln(t)" now it works

sage: integrate("log(t)",t,algorithm="fricas")
t*log(t) - t

sage: integrate(SR("ln(t)"),t,algorithm="fricas")
integral(ln(t), t)
sage: integrate(SR("log(t)"),t,algorithm="fricas")
t*log(t) - t
sage:

Why does it fail when doing "ln(t)" but it works with "log(t)" ? I am sure there is a good reason.

Thank you --Nasser

### Confusion about integrating a string.

sagemath 8.9

Follow up based on answer here why-sagemath-can-integrate-a-string sagemath can integrate a string.

Well. Sometimes it can, and sometimes it does not. And this getting confusing. For example

sage: integrate("ln(t)",t,algorithm="fricas")
integral(ln(t), t)

But if it is not a string, it works.

sage: integrate(ln(t),t,algorithm="fricas")
t*log(t) - t

But using "log(t)" as string, instead of "ln(t)" now it works

sage: integrate("log(t)",t,algorithm="fricas")
t*log(t) - t

sage: integrate(SR("ln(t)"),t,algorithm="fricas")
integral(ln(t), t)
sage: integrate(SR("log(t)"),t,algorithm="fricas")
t*log(t) - t
sage:

Why does it fail when doing "ln(t)" but it works with "log(t)" ? I am sure there is a good reason.

And sometimes it crashes also

sage: integrate("ln(1-t)",t,algorithm="fricas")
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
----> 1 integrate("ln(1-t)",t,algorithm="fricas")

/usr/lib/python2.7/site-packages/sage/misc/functional.pyc in integral(x, *args, **kwds)
754     else:
755         from sage.symbolic.ring import SR
--> 756         return SR(x).integral(*args, **kwds)
757
758

/usr/lib/python2.7/site-packages/sage/symbolic/expression.pyx in sage.symbolic.expression.Expression.integral (build/cythonized/sage/symbolic/expression.cpp:64032)()
12360                     R = ring.SR
12361             return R(integral(f, v, a, b, **kwds))
> 12362         return integral(self, *args, **kwds)
12363
12364     integrate = integral

/usr/lib/python2.7/site-packages/sage/symbolic/integration/integral.pyc in integrate(expression, v, a, b, algorithm, hold)
910         if not integrator:
911             raise ValueError("Unknown algorithm: %s" % algorithm)
--> 912         return integrator(expression, v, a, b)
913     if a is None:
914         return indefinite_integral(expression, v, hold=hold)

/usr/lib/python2.7/site-packages/sage/symbolic/integration/external.pyc in fricas_integrator(expression, v, a, b, noPole)
381
382     from sage.interfaces.fricas import fricas
--> 383     ex = fricas(expression)
384
385     if a is None:

/usr/lib/python2.7/site-packages/sage/interfaces/interface.pyc in __call__(self, x, name)
293             # user-assigned name might change its value, so we return a
294             # new element.
--> 295             result = self._coerce_from_special_method(x)
296             return result if name is None else result.name(new_name=name)
297         except TypeError:

/usr/lib/python2.7/site-packages/sage/interfaces/interface.pyc in _coerce_from_special_method(self, x)
321             s = '_gp_'
322         try:
--> 323             return (x.__getattribute__(s))(self)
324         except AttributeError:
325             return self(x._interface_init_())

/usr/lib/python2.7/site-packages/sage/structure/sage_object.pyx in sage.structure.sage_object.SageObject._fricas_ (build/cythonized/sage/structure/sage_object.c:7272)()
744             import sage.interfaces.fricas
745             G = sage.interfaces.fricas.fricas
--> 746         return self._interface_(G)
747
748     def _fricas_init_(self):

/usr/lib/python2.7/site-packages/sage/symbolic/expression.pyx in sage.symbolic.expression.Expression._interface_ (build/cythonized/sage/symbolic/expression.cpp:7633)()
797         if is_a_constant(self._gobj):
798             return self.pyobject()._interface_(I)
--> 799         return super(Expression, self)._interface_(I)
800
801     def _maxima_(self, session=None):

/usr/lib/python2.7/site-packages/sage/structure/sage_object.pyx in sage.structure.sage_object.SageObject._interface_ (build/cythonized/sage/structure/sage_object.c:5474)()
667             except Exception:
668                 raise NotImplementedError("coercion of object %s to %s not implemented:\n%s\n%s" % (repr(self), I))
--> 669         X = I(s)
670         if c:
671             try:

/usr/lib/python2.7/site-packages/sage/interfaces/interface.pyc in __call__(self, x, name)
286
287         if isinstance(x, string_types):
--> 288             return cls(self, x, name=name)
289         try:
290             # Special methods do not and should not have an option to

/usr/lib/python2.7/site-packages/sage/interfaces/expect.pyc in __init__(self, parent, value, is_name, name)
1474             except (RuntimeError, ValueError) as x:
1475                 self._session_number = -1
-> 1476                 raise_(TypeError, TypeError(*x.args), sys.exc_info()[2])
1477             except BaseException:
1478                 self._session_number = -1

/usr/lib/python2.7/site-packages/sage/interfaces/expect.pyc in __init__(self, parent, value, is_name, name)
1469         else:
1470             try:
-> 1471                 self._name = parent._create(value, name=name)
1472             # Convert ValueError and RuntimeError to TypeError for
1473             # coercion to work properly.

/usr/lib/python2.7/site-packages/sage/interfaces/interface.pyc in _create(self, value, name)
489     def _create(self, value, name=None):
490         name = self._next_var_name() if name is None else name
--> 491         self.set(name, value)
492         return name
493

/usr/lib/python2.7/site-packages/sage/interfaces/fricas.pyc in set(self, var, value)
588         cmd = '%s%s%s;' % (var, self._assign_symbol(), value)
589         output = self.eval(cmd, reformat=False)
--> 590         self._check_errors(value, output)
591
592     def get(self, var):

/usr/lib/python2.7/site-packages/sage/interfaces/fricas.pyc in _check_errors(self, line, output)
562             for old, new in replacements:
563                 output = output.replace(old, new)
--> 564             raise RuntimeError("An error occurred when FriCAS evaluated '%s':\n%s" % (line, output))
565
566         # or even an error

TypeError: An error occurred when FriCAS evaluated 'operator("ln")(((t)*(-1))+(1))':
There are 1 exposed and 1 unexposed library operations named elt having
1 argument(s) but none was determined to be applicable. Use HyperDoc
Browse, or issue
)display op elt
package-calling the operation or using coercions on the arguments
will allow you to apply the operation.

Cannot find application of object of type BasicOperator to argument(s)
of type(s)
Polynomial(Integer)

Thank you --Nasser

### Confusion about integrating a string.

sagemath 8.9

Follow up based on answer here why-sagemath-can-integrate-a-string sagemath can integrate a string.

Well. Sometimes it can, and sometimes it does not. And this getting confusing. For example

sage: integrate("ln(t)",t,algorithm="fricas")
integral(ln(t), t)

But if it is not a string, it works.

sage: integrate(ln(t),t,algorithm="fricas")
t*log(t) - t

But using "log(t)" as string, instead of "ln(t)" now it works

sage: integrate("log(t)",t,algorithm="fricas")
t*log(t) - t

sage: integrate(SR("ln(t)"),t,algorithm="fricas")
integral(ln(t), t)
sage: integrate(SR("log(t)"),t,algorithm="fricas")
t*log(t) - t
sage:

Why does it fail when doing "ln(t)" but it works with "log(t)" ? I am sure there is a good reason.

And sometimes it crashes also

sage: integrate("ln(1-t)",t,algorithm="fricas")
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
----> 1 integrate("ln(1-t)",t,algorithm="fricas")

/usr/lib/python2.7/site-packages/sage/misc/functional.pyc in integral(x, *args, **kwds)
754     else:
755         from sage.symbolic.ring import SR
--> 756         return SR(x).integral(*args, **kwds)
757
758

/usr/lib/python2.7/site-packages/sage/symbolic/expression.pyx in sage.symbolic.expression.Expression.integral (build/cythonized/sage/symbolic/expression.cpp:64032)()
12360                     R = ring.SR
12361             return R(integral(f, v, a, b, **kwds))
> 12362         return integral(self, *args, **kwds)
12363
12364     integrate = integral

/usr/lib/python2.7/site-packages/sage/symbolic/integration/integral.pyc in integrate(expression, v, a, b, algorithm, hold)
910         if not integrator:
911             raise ValueError("Unknown algorithm: %s" % algorithm)
--> 912         return integrator(expression, v, a, b)
913     if a is None:
914         return indefinite_integral(expression, v, hold=hold)

/usr/lib/python2.7/site-packages/sage/symbolic/integration/external.pyc in fricas_integrator(expression, v, a, b, noPole)
381
382     from sage.interfaces.fricas import fricas
--> 383     ex = fricas(expression)
384
385     if a is None:

/usr/lib/python2.7/site-packages/sage/interfaces/interface.pyc in __call__(self, x, name)
293             # user-assigned name might change its value, so we return a
294             # new element.
--> 295             result = self._coerce_from_special_method(x)
296             return result if name is None else result.name(new_name=name)
297         except TypeError:

/usr/lib/python2.7/site-packages/sage/interfaces/interface.pyc in _coerce_from_special_method(self, x)
321             s = '_gp_'
322         try:
--> 323             return (x.__getattribute__(s))(self)
324         except AttributeError:
325             return self(x._interface_init_())

/usr/lib/python2.7/site-packages/sage/structure/sage_object.pyx in sage.structure.sage_object.SageObject._fricas_ (build/cythonized/sage/structure/sage_object.c:7272)()
744             import sage.interfaces.fricas
745             G = sage.interfaces.fricas.fricas
--> 746         return self._interface_(G)
747
748     def _fricas_init_(self):

/usr/lib/python2.7/site-packages/sage/symbolic/expression.pyx in sage.symbolic.expression.Expression._interface_ (build/cythonized/sage/symbolic/expression.cpp:7633)()
797         if is_a_constant(self._gobj):
798             return self.pyobject()._interface_(I)
--> 799         return super(Expression, self)._interface_(I)
800
801     def _maxima_(self, session=None):

/usr/lib/python2.7/site-packages/sage/structure/sage_object.pyx in sage.structure.sage_object.SageObject._interface_ (build/cythonized/sage/structure/sage_object.c:5474)()
667             except Exception:
668                 raise NotImplementedError("coercion of object %s to %s not implemented:\n%s\n%s" % (repr(self), I))
--> 669         X = I(s)
670         if c:
671             try:

/usr/lib/python2.7/site-packages/sage/interfaces/interface.pyc in __call__(self, x, name)
286
287         if isinstance(x, string_types):
--> 288             return cls(self, x, name=name)
289         try:
290             # Special methods do not and should not have an option to

/usr/lib/python2.7/site-packages/sage/interfaces/expect.pyc in __init__(self, parent, value, is_name, name)
1474             except (RuntimeError, ValueError) as x:
1475                 self._session_number = -1
-> 1476                 raise_(TypeError, TypeError(*x.args), sys.exc_info()[2])
1477             except BaseException:
1478                 self._session_number = -1

/usr/lib/python2.7/site-packages/sage/interfaces/expect.pyc in __init__(self, parent, value, is_name, name)
1469         else:
1470             try:
-> 1471                 self._name = parent._create(value, name=name)
1472             # Convert ValueError and RuntimeError to TypeError for
1473             # coercion to work properly.

/usr/lib/python2.7/site-packages/sage/interfaces/interface.pyc in _create(self, value, name)
489     def _create(self, value, name=None):
490         name = self._next_var_name() if name is None else name
--> 491         self.set(name, value)
492         return name
493

/usr/lib/python2.7/site-packages/sage/interfaces/fricas.pyc in set(self, var, value)
588         cmd = '%s%s%s;' % (var, self._assign_symbol(), value)
589         output = self.eval(cmd, reformat=False)
--> 590         self._check_errors(value, output)
591
592     def get(self, var):

/usr/lib/python2.7/site-packages/sage/interfaces/fricas.pyc in _check_errors(self, line, output)
562             for old, new in replacements:
563                 output = output.replace(old, new)
--> 564             raise RuntimeError("An error occurred when FriCAS evaluated '%s':\n%s" % (line, output))
565
566         # or even an error

TypeError: An error occurred when FriCAS evaluated 'operator("ln")(((t)*(-1))+(1))':
There are 1 exposed and 1 unexposed library operations named elt having
1 argument(s) but none was determined to be applicable. Use HyperDoc
Browse, or issue
)display op elt
package-calling the operation or using coercions on the arguments
will allow you to apply the operation.

Cannot find application of object of type BasicOperator to argument(s)
of type(s)
Polynomial(Integer)

But OK if not a string

sage: integrate(ln(1-t),t,algorithm="fricas")
(t - 1)*log(-t + 1) - t

ps. The whole idea of allowing a string as input to integrate is not right IMHO, but I assume it is allowed for a good reason. If it is to be allowed, it should be treated as a constant with no interpretation at all. This is what Mathematica does:

But I think Maple handles this best by rejecting a string all together

int("x^10",x)
Error, (in int) wrong number (or type) of arguments: wrong type of integrand passed to indefinite integration.

Thank you --Nasser

### Confusion about integrating a string.

sagemath 8.9

Follow up based on answer here why-sagemath-can-integrate-a-string sagemath can integrate a string.

Well. Sometimes it can, and sometimes it does not. And this getting confusing. For example

sage: integrate("ln(t)",t,algorithm="fricas")
integral(ln(t), t)

But if it is not a string, it works.

sage: integrate(ln(t),t,algorithm="fricas")
t*log(t) - t

But using "log(t)" as string, instead of "ln(t)" now it works

sage: integrate("log(t)",t,algorithm="fricas")
t*log(t) - t

sage: integrate(SR("ln(t)"),t,algorithm="fricas")
integral(ln(t), t)
sage: integrate(SR("log(t)"),t,algorithm="fricas")
t*log(t) - t
sage:

Why does it fail when doing "ln(t)" but it works with "log(t)" ? I am sure there is a good reason.

And sometimes it crashes also

sage: integrate("ln(1-t)",t,algorithm="fricas")
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
----> 1 integrate("ln(1-t)",t,algorithm="fricas")

/usr/lib/python2.7/site-packages/sage/misc/functional.pyc in integral(x, *args, **kwds)
754     else:
755         from sage.symbolic.ring import SR
--> 756         return SR(x).integral(*args, **kwds)
757
758

/usr/lib/python2.7/site-packages/sage/symbolic/expression.pyx in sage.symbolic.expression.Expression.integral (build/cythonized/sage/symbolic/expression.cpp:64032)()
12360                     R = ring.SR
12361             return R(integral(f, v, a, b, **kwds))
> 12362         return integral(self, *args, **kwds)
12363
12364     integrate = integral

/usr/lib/python2.7/site-packages/sage/symbolic/integration/integral.pyc in integrate(expression, v, a, b, algorithm, hold)
910         if not integrator:
911             raise ValueError("Unknown algorithm: %s" % algorithm)
--> 912         return integrator(expression, v, a, b)
913     if a is None:
914         return indefinite_integral(expression, v, hold=hold)

/usr/lib/python2.7/site-packages/sage/symbolic/integration/external.pyc in fricas_integrator(expression, v, a, b, noPole)
381
382     from sage.interfaces.fricas import fricas
--> 383     ex = fricas(expression)
384
385     if a is None:

/usr/lib/python2.7/site-packages/sage/interfaces/interface.pyc in __call__(self, x, name)
293             # user-assigned name might change its value, so we return a
294             # new element.
--> 295             result = self._coerce_from_special_method(x)
296             return result if name is None else result.name(new_name=name)
297         except TypeError:

/usr/lib/python2.7/site-packages/sage/interfaces/interface.pyc in _coerce_from_special_method(self, x)
321             s = '_gp_'
322         try:
--> 323             return (x.__getattribute__(s))(self)
324         except AttributeError:
325             return self(x._interface_init_())

/usr/lib/python2.7/site-packages/sage/structure/sage_object.pyx in sage.structure.sage_object.SageObject._fricas_ (build/cythonized/sage/structure/sage_object.c:7272)()
744             import sage.interfaces.fricas
745             G = sage.interfaces.fricas.fricas
--> 746         return self._interface_(G)
747
748     def _fricas_init_(self):

/usr/lib/python2.7/site-packages/sage/symbolic/expression.pyx in sage.symbolic.expression.Expression._interface_ (build/cythonized/sage/symbolic/expression.cpp:7633)()
797         if is_a_constant(self._gobj):
798             return self.pyobject()._interface_(I)
--> 799         return super(Expression, self)._interface_(I)
800
801     def _maxima_(self, session=None):

/usr/lib/python2.7/site-packages/sage/structure/sage_object.pyx in sage.structure.sage_object.SageObject._interface_ (build/cythonized/sage/structure/sage_object.c:5474)()
667             except Exception:
668                 raise NotImplementedError("coercion of object %s to %s not implemented:\n%s\n%s" % (repr(self), I))
--> 669         X = I(s)
670         if c:
671             try:

/usr/lib/python2.7/site-packages/sage/interfaces/interface.pyc in __call__(self, x, name)
286
287         if isinstance(x, string_types):
--> 288             return cls(self, x, name=name)
289         try:
290             # Special methods do not and should not have an option to

/usr/lib/python2.7/site-packages/sage/interfaces/expect.pyc in __init__(self, parent, value, is_name, name)
1474             except (RuntimeError, ValueError) as x:
1475                 self._session_number = -1
-> 1476                 raise_(TypeError, TypeError(*x.args), sys.exc_info()[2])
1477             except BaseException:
1478                 self._session_number = -1

/usr/lib/python2.7/site-packages/sage/interfaces/expect.pyc in __init__(self, parent, value, is_name, name)
1469         else:
1470             try:
-> 1471                 self._name = parent._create(value, name=name)
1472             # Convert ValueError and RuntimeError to TypeError for
1473             # coercion to work properly.

/usr/lib/python2.7/site-packages/sage/interfaces/interface.pyc in _create(self, value, name)
489     def _create(self, value, name=None):
490         name = self._next_var_name() if name is None else name
--> 491         self.set(name, value)
492         return name
493

/usr/lib/python2.7/site-packages/sage/interfaces/fricas.pyc in set(self, var, value)
588         cmd = '%s%s%s;' % (var, self._assign_symbol(), value)
589         output = self.eval(cmd, reformat=False)
--> 590         self._check_errors(value, output)
591
592     def get(self, var):

/usr/lib/python2.7/site-packages/sage/interfaces/fricas.pyc in _check_errors(self, line, output)
562             for old, new in replacements:
563                 output = output.replace(old, new)
--> 564             raise RuntimeError("An error occurred when FriCAS evaluated '%s':\n%s" % (line, output))
565
566         # or even an error

TypeError: An error occurred when FriCAS evaluated 'operator("ln")(((t)*(-1))+(1))':
There are 1 exposed and 1 unexposed library operations named elt having
1 argument(s) but none was determined to be applicable. Use HyperDoc
Browse, or issue
)display op elt
package-calling the operation or using coercions on the arguments
will allow you to apply the operation.

Cannot find application of object of type BasicOperator to argument(s)
of type(s)
Polynomial(Integer)

But OK if not a string

sage: integrate(ln(1-t),t,algorithm="fricas")
(t - 1)*log(-t + 1) - t

ps. The whole idea of allowing a string as input to integrate is not right IMHO, but I assume it is allowed for a good reason. If it is to be allowed, it should be treated as a constant with no interpretation at all. This is what Mathematica does:

But I think Maple handles this best by rejecting a string all together

int("x^10",x)
Error, (in int) wrong number (or type) of arguments: wrong type of integrand passed to indefinite integration.

Another observation: This seems to affect fricas and maxima, but not giac

sage: integrate("ln(t)",t,algorithm="fricas")
integral(ln(t), t)
sage: integrate("ln(t)",t,algorithm="giac")
t*log(t) - t
sage: integrate("ln(t)",t,algorithm="maxima")
integrate(ln(t), t)

Thank you --Nasser