Piecewise functions are symbolic functions now; The problem is that your g
doesn't define a symbolic function, so you can't use it as input to
piecewise:
sage: g(x)
...
TypeError: unable to simplify to float approximation. You can manually
define a symbolic function whose numeric evaluation is prescribed:
sage: def gnum(self, x, **kwds):
....: var('u')
....: return numerical_integral(u^2,0,x)[0]
sage: gsym = function('gsym', nargs=1, evalf_func=gnum)
sage: gsym(x)
gsym(x)
sage: gsym(1)
gsym(1)
sage: gsym(1).n()
0.3333333333333333
Then you can use it to define a piecewise function
sage: piecewise([[(0,1), gsym(x)]])
We should probably automatically try that if g(x) raises an exception,
though there might be further implication...
On Sunday, May 22, 2016 at 1:38:06 AM UTC+2, paulmasson wrote:
>
> Another problem I've encountered concerns including numerical integrals in
> piecewise functions. This used to work in Sage 6.9:
>
> def g(x):
> var('u')
> return numerical_integral(u^2,0,x)[0]
>
> f=piecewise([ [(0,1), g ] ])
>
> but now gives the error message
>
>
> ---------------------------------------------------------------------------
> TypeError Traceback (most recent call last)
> <ipython-input-1-d490d0695d4b> in <module>()
> 4
> 5
> ----> 6 f=piecewise([ [(Integer(0),Integer(1)), g ] ])
> 7
>
> /home/sc_serv/sage/src/sage/misc/lazy_import.pyx in
> sage.misc.lazy_import.LazyImport.__call__
> (/home/sc_serv/sage/src/build/cythonized/sage/misc/lazy_import.c:3628)()
> 384 True
> 385 """
> --> 386 return self._get_object()(*args, **kwds)
> 387
> 388 def __repr__(self):
>
> /home/sc_serv/sage/local/lib/python2.7/site-packages/sage/functions/piecewise.py
> in __call__(self, function_pieces, **kwds)
> 149 function = function()
> 150 else:
> --> 151 function = function(var)
> 152 function = SR(function)
> 153 if var is None and len(function.variables()) > 0:
>
> <ipython-input-1-d490d0695d4b> in g(x)
> 1 def g(x):
> 2 var('u')
> ----> 3 return numerical_integral(u**Integer(2),Integer(0),x)[Integer(0)]
> 4
> 5
>
> /home/sc_serv/sage/src/sage/gsl/integration.pyx in
> sage.gsl.integration.numerical_integral
> (/home/sc_serv/sage/src/build/cythonized/sage/gsl/integration.c:3387)()
> 329 else:
> 330 _a=a
> --> 331 _b=b
> 332 W = <gsl_integration_workspace*>
> gsl_integration_workspace_alloc(n)
> 333 sig_on()
>
> /home/sc_serv/sage/src/sage/symbolic/expression.pyx in
> sage.symbolic.expression.Expression.__float__
> (/home/sc_serv/sage/src/build/cythonized/sage/symbolic/expression.cpp:10403)()
> 1384 return float(self._eval_self(float))
> 1385 except TypeError:
> -> 1386 raise TypeError("unable to simplify to float
> approximation")
> 1387
> 1388 def __complex__(self):
>
> TypeError: unable to simplify to float approximation
>
>
> which makes no sense since a numerical integral is already a float. Is
> there some other new behavior I'm missing?
>
>
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