#11888: Sage is missing the lambert_w function conversion from Maxima
------------------------------+---------------------------------------------
Reporter: benjaminfjones | Owner: burcin
Type: defect | Status: needs_review
Priority: minor | Milestone: sage-4.8
Component: symbolics | Keywords: lambert_w symbolics conversion
maxima sd35.5
Work_issues: | Upstream: N/A
Reviewer: | Author: Benjamin Jones
Merged: | Dependencies:
------------------------------+---------------------------------------------
Old description:
> Maxima returns solutions to some exponential equations in terms of the
> `lambert_w` function. Sage is missing a conversion for this function:
>
> {{{
>
> sage: solve(e^(5*x)+x==0, x, to_poly_solve=True)
> [x == -1/5*lambert_w(5)]
> sage: S = solve(e^(5*x)+x==0, x, to_poly_solve=True)
> sage: z = S[0].rhs()
> sage: z
> -1/5*lambert_w(5)
> sage: N(z)
> ---------------------------------------------------------------------------
> TypeError Traceback (most recent call
> last)
>
> /Users/jonesbe/sage/sage-4.7.2.alpha2/devel/sage-test/sage/<ipython
> console> in <module>()
>
> /Users/jonesbe/sage/latest/local/lib/python2.6/site-
> packages/sage/misc/functional.pyc in numerical_approx(x, prec, digits)
> 1264 prec = int((digits+1) * 3.32192) + 1
> 1265 try:
> -> 1266 return x._numerical_approx(prec)
> 1267 except AttributeError:
> 1268 from sage.rings.complex_double import
> is_ComplexDoubleElement
>
> /Users/jonesbe/sage/latest/local/lib/python2.6/site-
> packages/sage/symbolic/expression.so in
> sage.symbolic.expression.Expression._numerical_approx
> (sage/symbolic/expression.cpp:17950)()
>
> TypeError: cannot evaluate symbolic expression numerically
> sage: lambert_w(5)
> ---------------------------------------------------------------------------
> NameError Traceback (most recent call
> last)
>
> /Users/jonesbe/sage/sage-4.7.2.alpha2/devel/sage-test/sage/<ipython
> console> in <module>()
>
> NameError: name 'lambert_w' is not defined
> sage:
> }}}
>
> `mpmath` can evaluate the `lambert_w` function, so it should be easy to
> add a new symbolic function to Sage that will fix this issue.
New description:
Maxima returns solutions to some exponential equations in terms of the
`lambert_w` function. Sage is missing a conversion for this function:
{{{
sage: solve(e^(5*x)+x==0, x, to_poly_solve=True)
[x == -1/5*lambert_w(5)]
sage: S = solve(e^(5*x)+x==0, x, to_poly_solve=True)
sage: z = S[0].rhs()
sage: z
-1/5*lambert_w(5)
sage: N(z)
---------------------------------------------------------------------------
TypeError Traceback (most recent call
last)
/Users/jonesbe/sage/sage-4.7.2.alpha2/devel/sage-test/sage/<ipython
console> in <module>()
/Users/jonesbe/sage/latest/local/lib/python2.6/site-
packages/sage/misc/functional.pyc in numerical_approx(x, prec, digits)
1264 prec = int((digits+1) * 3.32192) + 1
1265 try:
-> 1266 return x._numerical_approx(prec)
1267 except AttributeError:
1268 from sage.rings.complex_double import
is_ComplexDoubleElement
/Users/jonesbe/sage/latest/local/lib/python2.6/site-
packages/sage/symbolic/expression.so in
sage.symbolic.expression.Expression._numerical_approx
(sage/symbolic/expression.cpp:17950)()
TypeError: cannot evaluate symbolic expression numerically
sage: lambert_w(5)
---------------------------------------------------------------------------
NameError Traceback (most recent call
last)
/Users/jonesbe/sage/sage-4.7.2.alpha2/devel/sage-test/sage/<ipython
console> in <module>()
NameError: name 'lambert_w' is not defined
sage:
}}}
`mpmath` can evaluate the `lambert_w` function, so it should be easy to
add a new symbolic function to Sage that will fix this issue.
----
Apply:
1. [attachment:trac_11888.patch] to `$SAGE_ROOT/devel/sage`
1. [attachment:trac_11888-doctests.patch] to `$SAGE_ROOT/devel/sage`
--
Comment(by kini):
Running `make ptestlong` now. I fixed a couple of doctests that broke, and
fixed some typos and rST syntax problems in your docstring.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11888#comment:3>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
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