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asked 2022-06-21 21:55:55 +0200

cav24 gravatar image

Limit of piecewise function

This exact question has been asked before (8 years ago, 2 years ago). So here goes, perhaps things have changed?

f(x) = piecewise([[(0,1),x],[[1,2],x/2]])
limit(f(x),x=0)

I'd expect some output along the lines "limit is undefined". Instead I get the following error message

    ---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
/var/folders/mt/4xjm_x515mxdjkm49zmplt240000gq/T/ipykernel_84420/3147669555.py in <module>
----> 1 limit(f(x),x=Integer(0))

/private/var/tmp/sage-9.6-current/local/var/lib/sage/venv-python3.10.3/lib/python3.10/site-packages/sage/calculus/calculus.py in limit(ex, dir, taylor, algorithm, **argv)
   1409     if algorithm == 'maxima':
   1410         if dir is None:
-> 1411             l = maxima.sr_limit(ex, v, a)
   1412         elif dir in dir_plus:
   1413             l = maxima.sr_limit(ex, v, a, 'plus')

/private/var/tmp/sage-9.6-current/local/var/lib/sage/venv-python3.10.3/lib/python3.10/site-packages/sage/interfaces/maxima_lib.py in sr_limit(self, expr, v, a, dir)
    985             elif dir == "minus":
    986                 L.append(max_minus)
--> 987             return max_to_sr(maxima_eval(([max_limit], L)))
    988         except RuntimeError as error:
    989             s = str(error)

/private/var/tmp/sage-9.6-current/local/var/lib/sage/venv-python3.10.3/lib/python3.10/site-packages/sage/interfaces/maxima_lib.py in max_to_sr(expr)
   1708             op=max_op_dict[op_max]
   1709         max_args=cdr(expr)
-> 1710         args=[max_to_sr(a) for a in max_args]
   1711         return op(*args)
   1712     elif expr.symbolp():

/private/var/tmp/sage-9.6-current/local/var/lib/sage/venv-python3.10.3/lib/python3.10/site-packages/sage/interfaces/maxima_lib.py in <listcomp>(.0)
   1708             op=max_op_dict[op_max]
   1709         max_args=cdr(expr)
-> 1710         args=[max_to_sr(a) for a in max_args]
   1711         return op(*args)
   1712     elif expr.symbolp():

/private/var/tmp/sage-9.6-current/local/var/lib/sage/venv-python3.10.3/lib/python3.10/site-packages/sage/interfaces/maxima_lib.py in max_to_sr(expr)
   1709         max_args=cdr(expr)
   1710         args=[max_to_sr(a) for a in max_args]
-> 1711         return op(*args)
   1712     elif expr.symbolp():
   1713         if not(expr in max_sym_dict):

TypeError: PiecewiseFunction.__call__() takes 2 positional arguments but 3 were given

Limit of piecewise function

This exact question has been asked before (8 years ago, 2 years ago). So here goes, perhaps things have changed?

f(x) = piecewise([[(0,1),x],[[1,2],x/2]])
limit(f(x),x=0)

I'd expect some output along the lines "limit is undefined". Instead I get the following error message

    ---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
/var/folders/mt/4xjm_x515mxdjkm49zmplt240000gq/T/ipykernel_84420/3147669555.py in <module>
----> 1 limit(f(x),x=Integer(0))

/private/var/tmp/sage-9.6-current/local/var/lib/sage/venv-python3.10.3/lib/python3.10/site-packages/sage/calculus/calculus.py in limit(ex, dir, taylor, algorithm, **argv)
   1409     if algorithm == 'maxima':
   1410         if dir is None:
-> 1411             l = maxima.sr_limit(ex, v, a)
   1412         elif dir in dir_plus:
   1413             l = maxima.sr_limit(ex, v, a, 'plus')

/private/var/tmp/sage-9.6-current/local/var/lib/sage/venv-python3.10.3/lib/python3.10/site-packages/sage/interfaces/maxima_lib.py in sr_limit(self, expr, v, a, dir)
    985             elif dir == "minus":
    986                 L.append(max_minus)
--> 987             return max_to_sr(maxima_eval(([max_limit], L)))
    988         except RuntimeError as error:
    989             s = str(error)

/private/var/tmp/sage-9.6-current/local/var/lib/sage/venv-python3.10.3/lib/python3.10/site-packages/sage/interfaces/maxima_lib.py in max_to_sr(expr)
   1708             op=max_op_dict[op_max]
   1709         max_args=cdr(expr)
-> 1710         args=[max_to_sr(a) for a in max_args]
   1711         return op(*args)
   1712     elif expr.symbolp():

/private/var/tmp/sage-9.6-current/local/var/lib/sage/venv-python3.10.3/lib/python3.10/site-packages/sage/interfaces/maxima_lib.py in <listcomp>(.0)
   1708             op=max_op_dict[op_max]
   1709         max_args=cdr(expr)
-> 1710         args=[max_to_sr(a) for a in max_args]
   1711         return op(*args)
   1712     elif expr.symbolp():

/private/var/tmp/sage-9.6-current/local/var/lib/sage/venv-python3.10.3/lib/python3.10/site-packages/sage/interfaces/maxima_lib.py in max_to_sr(expr)
   1709         max_args=cdr(expr)
   1710         args=[max_to_sr(a) for a in max_args]
-> 1711         return op(*args)
   1712     elif expr.symbolp():
   1713         if not(expr in max_sym_dict):

TypeError: PiecewiseFunction.__call__() takes 2 positional arguments but 3 were given

Limit of piecewise function

This exact question has been asked before (8 years ago, 2 years ago). So here goes, perhaps things have changed?

f(x) = piecewise([[(0,1),x],[[1,2],x/2]])
limit(f(x),x=0)

I'd expect some output along (Note that I'm not even looking at the lines "limit is undefined". Instead point where the discontinuity occurs.)

I get the following error message

    ---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
/var/folders/mt/4xjm_x515mxdjkm49zmplt240000gq/T/ipykernel_84420/3147669555.py in <module>
----> 1 limit(f(x),x=Integer(0))

/private/var/tmp/sage-9.6-current/local/var/lib/sage/venv-python3.10.3/lib/python3.10/site-packages/sage/calculus/calculus.py in limit(ex, dir, taylor, algorithm, **argv)
   1409     if algorithm == 'maxima':
   1410         if dir is None:
-> 1411             l = maxima.sr_limit(ex, v, a)
   1412         elif dir in dir_plus:
   1413             l = maxima.sr_limit(ex, v, a, 'plus')

/private/var/tmp/sage-9.6-current/local/var/lib/sage/venv-python3.10.3/lib/python3.10/site-packages/sage/interfaces/maxima_lib.py in sr_limit(self, expr, v, a, dir)
    985             elif dir == "minus":
    986                 L.append(max_minus)
--> 987             return max_to_sr(maxima_eval(([max_limit], L)))
    988         except RuntimeError as error:
    989             s = str(error)

/private/var/tmp/sage-9.6-current/local/var/lib/sage/venv-python3.10.3/lib/python3.10/site-packages/sage/interfaces/maxima_lib.py in max_to_sr(expr)
   1708             op=max_op_dict[op_max]
   1709         max_args=cdr(expr)
-> 1710         args=[max_to_sr(a) for a in max_args]
   1711         return op(*args)
   1712     elif expr.symbolp():

/private/var/tmp/sage-9.6-current/local/var/lib/sage/venv-python3.10.3/lib/python3.10/site-packages/sage/interfaces/maxima_lib.py in <listcomp>(.0)
   1708             op=max_op_dict[op_max]
   1709         max_args=cdr(expr)
-> 1710         args=[max_to_sr(a) for a in max_args]
   1711         return op(*args)
   1712     elif expr.symbolp():

/private/var/tmp/sage-9.6-current/local/var/lib/sage/venv-python3.10.3/lib/python3.10/site-packages/sage/interfaces/maxima_lib.py in max_to_sr(expr)
   1709         max_args=cdr(expr)
   1710         args=[max_to_sr(a) for a in max_args]
-> 1711         return op(*args)
   1712     elif expr.symbolp():
   1713         if not(expr in max_sym_dict):

TypeError: PiecewiseFunction.__call__() takes 2 positional arguments but 3 were given

Limit of piecewise function

This exact question has been asked before (8 years ago, 2 years ago). So here goes, perhaps things have changed?

f(x) = piecewise([[(0,1),x],[[1,2],x/2]])
limit(f(x),x=0)
limit(f(x),x=1/2)

(Note that I'm not even looking at the point where the discontinuity occurs.)

I get the following error message

 ---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
/var/folders/mt/4xjm_x515mxdjkm49zmplt240000gq/T/ipykernel_84420/3147669555.py /var/folders/mt/4xjm_x515mxdjkm49zmplt240000gq/T/ipykernel_84420/3847661288.py in <module>
----> 1 limit(f(x),x=Integer(0))
limit(f(x),x=Integer(1)/Integer(2))

/private/var/tmp/sage-9.6-current/local/var/lib/sage/venv-python3.10.3/lib/python3.10/site-packages/sage/calculus/calculus.py in limit(ex, dir, taylor, algorithm, **argv)
   1409     if algorithm == 'maxima':
   1410         if dir is None:
-> 1411             l = maxima.sr_limit(ex, v, a)
   1412         elif dir in dir_plus:
   1413             l = maxima.sr_limit(ex, v, a, 'plus')

/private/var/tmp/sage-9.6-current/local/var/lib/sage/venv-python3.10.3/lib/python3.10/site-packages/sage/interfaces/maxima_lib.py in sr_limit(self, expr, v, a, dir)
    985             elif dir == "minus":
    986                 L.append(max_minus)
--> 987             return max_to_sr(maxima_eval(([max_limit], L)))
    988         except RuntimeError as error:
    989             s = str(error)

/private/var/tmp/sage-9.6-current/local/var/lib/sage/venv-python3.10.3/lib/python3.10/site-packages/sage/interfaces/maxima_lib.py in max_to_sr(expr)
   1708             op=max_op_dict[op_max]
   1709         max_args=cdr(expr)
-> 1710         args=[max_to_sr(a) for a in max_args]
   1711         return op(*args)
   1712     elif expr.symbolp():

/private/var/tmp/sage-9.6-current/local/var/lib/sage/venv-python3.10.3/lib/python3.10/site-packages/sage/interfaces/maxima_lib.py in <listcomp>(.0)
   1708             op=max_op_dict[op_max]
   1709         max_args=cdr(expr)
-> 1710         args=[max_to_sr(a) for a in max_args]
   1711         return op(*args)
   1712     elif expr.symbolp():

/private/var/tmp/sage-9.6-current/local/var/lib/sage/venv-python3.10.3/lib/python3.10/site-packages/sage/interfaces/maxima_lib.py in max_to_sr(expr)
   1709         max_args=cdr(expr)
   1710         args=[max_to_sr(a) for a in max_args]
-> 1711         return op(*args)
   1712     elif expr.symbolp():
   1713         if not(expr in max_sym_dict):

TypeError: PiecewiseFunction.__call__() takes 2 positional arguments but 3 were given
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