Hi
I'm trying to do some computations with Bessel functions using Sage.
Unfortunately, they don't seem to behave like other functions. For example:
to get the plot of the sine function over the interval (0,100)
plot(sin(x),(x,0,100))
works. However,
plot(bessel_J(0,x),(x,0,100))
does not. Gives the following error messages:
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
/home/pablo/sage/sage-4.0.rc0/<ipython console> in <module>()
/home/pablo/sage/sage-4.0.rc0/local/lib/python2.5/site-packages/sage/functions/special.pyc
in bessel_J(nu, z, algorithm, prec)
753 C = ComplexField(prec)
754 nu = C(nu)
--> 755 z = C(z)
756 K = C
757 if nu == 0:
/home/pablo/sage/sage-4.0.rc0/local/lib/python2.5/site-packages/sage/rings/complex_field.pyc
in __call__(self, x, im)
256 if im is not None:
257 x = x, im
--> 258 return Parent.__call__(self, x)
259
260 def _element_constructor_(self, x):
/home/pablo/sage/sage-4.0.rc0/local/lib/python2.5/site-packages/sage/structure/parent.so
in sage.structure.parent.Parent.__call__
(sage/structure/parent.c:4121)()
/home/pablo/sage/sage-4.0.rc0/local/lib/python2.5/site-packages/sage/structure/coerce_maps.so
in sage.structure.coerce_maps.DefaultConvertMap_unique._call_
(sage/structure/coerce_maps.c:3064)()
/home/pablo/sage/sage-4.0.rc0/local/lib/python2.5/site-packages/sage/structure/coerce_maps.so
in sage.structure.coerce_maps._call_
(sage/structure/coerce_maps.c:2955)()
/home/pablo/sage/sage-4.0.rc0/local/lib/python2.5/site-packages/sage/rings/complex_field.pyc
in _element_constructor_(self, x)
280
281 try:
--> 282 return x._complex_mpfr_field_( self )
283 except AttributeError:
284 pass
/home/pablo/sage/sage-4.0.rc0/local/lib/python2.5/site-packages/sage/symbolic/expression.so
in sage.symbolic.expression.Expression._complex_mpfr_field_
(sage/symbolic/expression.cpp:5573)()
/home/pablo/sage/sage-4.0.rc0/local/lib/python2.5/site-packages/sage/symbolic/expression.so
in sage.symbolic.expression.Expression._eval_self
(sage/symbolic/expression.cpp:5027)()
TypeError: Cannot evaluate symbolic expression to a numeric value.
In a similar way, you can for example compute the derivative of the
sine function by
sage: f(x)=sin(x)
sage: f.diff()
x |--> cos(x)
but if you try to define a function by
f(x)=bessel_J(0,x)
you get a similar error:
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
/home/pablo/sage/sage-4.0.rc0/<ipython console> in <module>()
/home/pablo/sage/sage-4.0.rc0/local/lib/python2.5/site-packages/sage/functions/special.pyc
in bessel_J(nu, z, algorithm, prec)
753 C = ComplexField(prec)
754 nu = C(nu)
--> 755 z = C(z)
756 K = C
757 if nu == 0:
/home/pablo/sage/sage-4.0.rc0/local/lib/python2.5/site-packages/sage/rings/complex_field.pyc
in __call__(self, x, im)
256 if im is not None:
257 x = x, im
--> 258 return Parent.__call__(self, x)
259
260 def _element_constructor_(self, x):
/home/pablo/sage/sage-4.0.rc0/local/lib/python2.5/site-packages/sage/structure/parent.so
in sage.structure.parent.Parent.__call__
(sage/structure/parent.c:4121)()
/home/pablo/sage/sage-4.0.rc0/local/lib/python2.5/site-packages/sage/structure/coerce_maps.so
in sage.structure.coerce_maps.DefaultConvertMap_unique._call_
(sage/structure/coerce_maps.c:3064)()
/home/pablo/sage/sage-4.0.rc0/local/lib/python2.5/site-packages/sage/structure/coerce_maps.so
in sage.structure.coerce_maps._call_
(sage/structure/coerce_maps.c:2955)()
/home/pablo/sage/sage-4.0.rc0/local/lib/python2.5/site-packages/sage/rings/complex_field.pyc
in _element_constructor_(self, x)
280
281 try:
--> 282 return x._complex_mpfr_field_( self )
283 except AttributeError:
284 pass
/home/pablo/sage/sage-4.0.rc0/local/lib/python2.5/site-packages/sage/symbolic/expression.so
in sage.symbolic.expression.Expression._complex_mpfr_field_
(sage/symbolic/expression.cpp:5573)()
/home/pablo/sage/sage-4.0.rc0/local/lib/python2.5/site-packages/sage/symbolic/expression.so
in sage.symbolic.expression.Expression._eval_self
(sage/symbolic/expression.cpp:5027)()
TypeError: Cannot evaluate symbolic expression to a numeric value.
=========================================================
I think it would be important to provide some uniform interfase for all
functions.
regards
Pablo
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