Context : finding patterns of explicit forms of inverse
(hyperbolic|trigonometric) functions for simplification.
Simple solution :
reset() y=SR.var("y") IL = [] w0=SR.wild(0) L=[sin, cos, tan, csc, sec,
cot, sinh, cosh, tanh, csch, sech, coth] for f in L:
R=(f(y)==x).solve(y)[0].rhs() for s in (f(y)==x).exponentialize().solve(y):
IL += [s.rhs().subs(x==w0)==R.subs(x==w0)] # End loop
This works. But I’d like to express this list as a dictionary. Brute-force
solution fails with a mysterious TypeError: ECL says: THROW: The catch
MACSYMA-QUIT is undefined.. But calling this on *parts* of the list seems
to work (not shown).
Try a loop :
ID=dict() for s in IL: ID[s.lhs()]=s.rhs() # End loop
This fails again :
---------------------------------------------------------------------------
RuntimeError Traceback (most recent call last) File
/usr/local/sage-10/src/sage/interfaces/interface.py:749, in
InterfaceElement.__init__(self, parent, value, is_name, name) 748 try: -->
749 self._name = parent._create(value, name=name) 750 except (TypeError,
RuntimeError, ValueError) as x: File
/usr/local/sage-10/src/sage/interfaces/maxima_lib.py:632, in
MaximaLib._create(self, value, name) 631 else: --> 632 self.set(name,
value) 633 except RuntimeError as error: File
/usr/local/sage-10/src/sage/interfaces/maxima_lib.py:540, in
MaximaLib.set(self, var, value) 539 cmd = '%s : %s$' % (var,
value.rstrip(';')) --> 540 self.eval(cmd) File
/usr/local/sage-10/src/sage/interfaces/maxima_lib.py:486, in
MaximaLib._eval_line(self, line, locals, reformat, **kwds) 485 if
statement: --> 486 maxima_eval("#$%s$" % statement) 487 if not reformat:
File /usr/local/sage-10/src/sage/libs/ecl.pyx:837, in
sage.libs.ecl.EclObject.__call__() 836 """ --> 837 lispargs =
EclObject(list(args)) 838 return ecl_wrap(ecl_safe_apply(self.obj,
(<EclObject>lispargs).obj)) File
/usr/local/sage-10/src/sage/libs/ecl.pyx:698, in
sage.libs.ecl.EclObject.__init__() 697 elif len(args) == 1: --> 698
self.set_obj(python_to_ecl(args[0], True)) 699 elif len(args) == 2: File
/usr/local/sage-10/src/sage/libs/ecl.pyx:481, in
sage.libs.ecl.python_to_ecl() 480 for i in range(len(pyobj) - 1, -1, -1):
--> 481 L = cl_cons(python_to_ecl(pyobj[i], read_strings), L) 482 return L
File /usr/local/sage-10/src/sage/libs/ecl.pyx:458, in
sage.libs.ecl.python_to_ecl() 457 if read_strings: --> 458 return
ecl_safe_funcall(read_from_string_clobj, o) 459 else: File
/usr/local/sage-10/src/sage/libs/ecl.pyx:342, in
sage.libs.ecl.ecl_safe_funcall() 341 else: --> 342 raise RuntimeError("ECL
says: {}".format(message)) 343 else: RuntimeError: ECL says: THROW: The
catch MACSYMA-QUIT is undefined. During handling of the above exception,
another exception occurred: TypeError Traceback (most recent call last)
Cell In[231], line 1 ----> 1
load('/tmp/sage_shell_modeSJ8pfj/sage_shell_mode_temp.sage') File
/usr/local/sage-10/src/sage/misc/persist.pyx:175, in
sage.misc.persist.load() 173 174 if
sage.repl.load.is_loadable_filename(filename): --> 175
sage.repl.load.load(filename, globals()) 176 return 177 File
/usr/local/sage-10/src/sage/repl/load.py:277, in load(filename, globals,
attach) 275 add_attached_file(fpath) 276 with fpath.open() as f: --> 277
exec(preparse_file(f.read()) + "\n", globals) 278 elif ext in ['.spyx',
'.pyx']: 279 if attach: File <string>:5 File
/usr/local/sage-10/src/sage/symbolic/expression.pyx:3515, in
sage.symbolic.expression.Expression.__bool__() 3513 if res in (True,
False): 3514 return res -> 3515 res =
self.operator()((self.lhs()-self.rhs()).simplify_full(), 0).test_relation()
3516 if res in (True, False): 3517 return res File
/usr/local/sage-10/src/sage/symbolic/expression.pyx:10737, in
sage.symbolic.expression.Expression.simplify_full() 10735 """ 10736 x =
self > 10737 x = x.simplify_factorial() 10738 x = x.simplify_rectform()
10739 x = x.simplify_trig() File
/usr/local/sage-10/src/sage/symbolic/expression.pyx:11217, in
sage.symbolic.expression.Expression.simplify_factorial() 11215 11216 """ >
11217 return
self.parent()(self._maxima_().makefact().factcomb().minfactorial()) 11218
11219 factorial_simplify = simplify_factorial File
/usr/local/sage-10/src/sage/symbolic/expression.pyx:1227, in
sage.symbolic.expression.Expression._maxima_() 1225 # Maybe not such a
great idea because the "default" interface is another one 1226 from
sage.calculus.calculus import maxima -> 1227 return
super()._interface_(maxima) 1228 else: 1229 return
super()._interface_(session) File
/usr/local/sage-10/src/sage/structure/sage_object.pyx:724, in
sage.structure.sage_object.SageObject._interface_() 722 except Exception:
723 raise NotImplementedError("coercion of object %s to %s not
implemented:\n%s\n%s" % (repr(self), I)) --> 724 X = I(s) 725 if c: 726
try: 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:751, in
InterfaceElement.__init__(self, parent, value, is_name, name) 749
self._name = parent._create(value, name=name) 750 except (TypeError,
RuntimeError, ValueError) as x: --> 751 raise TypeError(x) TypeError: ECL
says: THROW: The catch MACSYMA-QUIT is undefined.
Diagnosis :
sage: len(IL) 24 sage: len(ID) 20
Hmm. The problem starts with :
sage: IL[len(ID)] log(-sqrt(-$0^2 + 1)/$0 + 1/$0) == arcsech($0)
which *can* be put in dictionary form :
sage: {IL[len(ID)].lhs():IL[len(ID)].rhs()} {log(-sqrt(-$0^2 + 1)/$0 +
1/$0): arcsech($0)}
But can’t be used for updating the dictionary :
sage: foo=copy(ID)|{IL[len(ID)].lhs():IL[len(ID)].rhs()}
---------------------------------------------------------------------------
RuntimeError Traceback (most recent call last) File
/usr/local/sage-10/src/sage/interfaces/interface.py:749, in
InterfaceElement.__init__(self, parent, value, is_name, name) 748 try: -->
749 self._name = parent._create(value, name=name) 750 except (TypeError,
RuntimeError, ValueError) as x: File
/usr/local/sage-10/src/sage/interfaces/maxima_lib.py:632, in
MaximaLib._create(self, value, name) 631 else: --> 632 self.set(name,
value) 633 except RuntimeError as error: File
/usr/local/sage-10/src/sage/interfaces/maxima_lib.py:540, in
MaximaLib.set(self, var, value) 539 cmd = '%s : %s$' % (var,
value.rstrip(';')) --> 540 self.eval(cmd) File
/usr/local/sage-10/src/sage/interfaces/maxima_lib.py:486, in
MaximaLib._eval_line(self, line, locals, reformat, **kwds) 485 if
statement: --> 486 maxima_eval("#$%s$" % statement) 487 if not reformat:
File /usr/local/sage-10/src/sage/libs/ecl.pyx:837, in
sage.libs.ecl.EclObject.__call__() 836 """ --> 837 lispargs =
EclObject(list(args)) 838 return ecl_wrap(ecl_safe_apply(self.obj,
(<EclObject>lispargs).obj)) File
/usr/local/sage-10/src/sage/libs/ecl.pyx:698, in
sage.libs.ecl.EclObject.__init__() 697 elif len(args) == 1: --> 698
self.set_obj(python_to_ecl(args[0], True)) 699 elif len(args) == 2: File
/usr/local/sage-10/src/sage/libs/ecl.pyx:481, in
sage.libs.ecl.python_to_ecl() 480 for i in range(len(pyobj) - 1, -1, -1):
--> 481 L = cl_cons(python_to_ecl(pyobj[i], read_strings), L) 482 return L
File /usr/local/sage-10/src/sage/libs/ecl.pyx:458, in
sage.libs.ecl.python_to_ecl() 457 if read_strings: --> 458 return
ecl_safe_funcall(read_from_string_clobj, o) 459 else: File
/usr/local/sage-10/src/sage/libs/ecl.pyx:342, in
sage.libs.ecl.ecl_safe_funcall() 341 else: --> 342 raise RuntimeError("ECL
says: {}".format(message)) 343 else: RuntimeError: ECL says: THROW: The
catch MACSYMA-QUIT is undefined. During handling of the above exception,
another exception occurred: TypeError Traceback (most recent call last)
Cell In[243], line 1 ----> 1
foo=copy(ID)|{IL[len(ID)].lhs():IL[len(ID)].rhs()} File
/usr/local/sage-10/src/sage/symbolic/expression.pyx:3515, in
sage.symbolic.expression.Expression.__bool__() 3513 if res in (True,
False): 3514 return res -> 3515 res =
self.operator()((self.lhs()-self.rhs()).simplify_full(), 0).test_relation()
3516 if res in (True, False): 3517 return res File
/usr/local/sage-10/src/sage/symbolic/expression.pyx:10737, in
sage.symbolic.expression.Expression.simplify_full() 10735 """ 10736 x =
self > 10737 x = x.simplify_factorial() 10738 x = x.simplify_rectform()
10739 x = x.simplify_trig() File
/usr/local/sage-10/src/sage/symbolic/expression.pyx:11217, in
sage.symbolic.expression.Expression.simplify_factorial() 11215 11216 """ >
11217 return
self.parent()(self._maxima_().makefact().factcomb().minfactorial()) 11218
11219 factorial_simplify = simplify_factorial File
/usr/local/sage-10/src/sage/symbolic/expression.pyx:1227, in
sage.symbolic.expression.Expression._maxima_() 1225 # Maybe not such a
great idea because the "default" interface is another one 1226 from
sage.calculus.calculus import maxima -> 1227 return
super()._interface_(maxima) 1228 else: 1229 return
super()._interface_(session) File
/usr/local/sage-10/src/sage/structure/sage_object.pyx:724, in
sage.structure.sage_object.SageObject._interface_() 722 except Exception:
723 raise NotImplementedError("coercion of object %s to %s not
implemented:\n%s\n%s" % (repr(self), I)) --> 724 X = I(s) 725 if c: 726
try: 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:751, in
InterfaceElement.__init__(self, parent, value, is_name, name) 749
self._name = parent._create(value, name=name) 750 except (TypeError,
RuntimeError, ValueError) as x: --> 751 raise TypeError(x) TypeError: ECL
says: THROW: The catch MACSYMA-QUIT is undefined.
I’m stymied… Any idea ?
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