#15354: Make elliptic_j function symbolic
-------------------------------------------------+-------------------------
Reporter: davidamadore | Owner:
Type: defect | Status: new
Priority: major | Milestone: sage-6.4
Component: symbolics | Resolution:
Keywords: special function, elliptic, | Merged in:
modular | Reviewers:
Authors: | Work issues:
Report Upstream: N/A | Commit:
Branch: | Stopgaps:
Dependencies: |
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Changes (by rws):
* keywords: special function => special function, elliptic, modular
* priority: minor => major
Old description:
> Sage's elliptic_j function does not behave similarly to the other
> standard or special functions: it tries to numerically evaluate instead
> of building a symbolic expression:
>
> {{{
> sage: elliptic_j(I)
> 1728.00000000000
> sage: elliptic_j(x)
> ---------------------------------------------------------------------------
> TypeError Traceback (most recent call
> last)
> <ipython-input-5-b3ba173d2e63> in <module>()
> ----> 1 elliptic_j(x)
>
> /usr/src/local/sage-5.12/local/lib/python2.7/site-
> packages/sage/functions/special.pyc in elliptic_j(z)
> 803 CC = ComplexField()
> 804 try:
> --> 805 z = CC(z)
> 806 except ValueError:
> 807 raise ValueError, "elliptic_j only defined for complex
> arguments."
>
> /usr/src/local/sage-5.12/local/lib/python2.7/site-
> packages/sage/rings/complex_field.pyc in __call__(self, x, im)
> 345 if im is not None:
> 346 x = x, im
> --> 347 return Parent.__call__(self, x)
> 348
> 349 def _element_constructor_(self, x):
>
> /usr/src/local/sage-5.12/local/lib/python2.7/site-
> packages/sage/structure/parent.so in
> sage.structure.parent.Parent.__call__ (sage/structure/parent.c:8372)()
>
> /usr/src/local/sage-5.12/local/lib/python2.7/site-
> packages/sage/structure/coerce_maps.so in
> sage.structure.coerce_maps.DefaultConvertMap_unique._call_
> (sage/structure/coerce_maps.c:3856)()
>
> /usr/src/local/sage-5.12/local/lib/python2.7/site-
> packages/sage/structure/coerce_maps.so in
> sage.structure.coerce_maps.DefaultConvertMap_unique._call_
> (sage/structure/coerce_maps.c:3757)()
>
> /usr/src/local/sage-5.12/local/lib/python2.7/site-
> packages/sage/rings/complex_field.pyc in _element_constructor_(self, x)
> 375 pass
> 376 try:
> --> 377 return x._complex_mpfr_field_( self )
> 378 except AttributeError:
> 379 pass
>
> /usr/src/local/sage-5.12/local/lib/python2.7/site-
> packages/sage/symbolic/expression.so in
> sage.symbolic.expression.Expression._complex_mpfr_field_
> (sage/symbolic/expression.cpp:7534)()
>
> /usr/src/local/sage-5.12/local/lib/python2.7/site-
> packages/sage/symbolic/expression.so in
> sage.symbolic.expression.Expression._eval_self
> (sage/symbolic/expression.cpp:6913)()
>
> TypeError: Cannot evaluate symbolic expression to a numeric value.
> }}}
>
> This is very weird: it means, for example, that
> plot(real(elliptic_j(x+I)), (x,0,1)) will fail (instead, one must use
> plot(lambda t: real(elliptic_j(t+I)), (0,1)))
New description:
Sage's elliptic_j function does not behave similarly to the other standard
or special functions: it tries to numerically evaluate instead of building
a symbolic expression:
{{{
sage: elliptic_j(I)
1728.00000000000
sage: elliptic_j(x)
---------------------------------------------------------------------------
TypeError Traceback (most recent call
last)
...
TypeError: Cannot evaluate symbolic expression to a numeric value.
}}}
This is very weird: it means, for example, that
plot(real(elliptic_j(x+I)), (x,0,1)) will fail (instead, one must use
plot(lambda t: real(elliptic_j(t+I)), (0,1)))
*
http://mpmath.googlecode.com/svn/tags/0.15/doc/build/functions/elliptic.html#kleinj
* https://en.wikipedia.org/wiki/J-invariant
--
--
Ticket URL: <http://trac.sagemath.org/ticket/15354#comment:5>
Sage <http://www.sagemath.org>
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and MATLAB
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