Opened 9 years ago

# Sage is missing the lambert_w function conversion from Maxima — at Version 3

Reported by: Owned by: benjaminfjones burcin minor sage-5.1 symbolics lambert_w symbolics conversion maxima sd35.5 sd40.5 kcrisman, ktkohl Benjamin Jones N/A

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. trac_11888.patch to `\$SAGE_ROOT/devel/sage`
2. trac_11888-doctests.patch to `\$SAGE_ROOT/devel/sage`

### comment:2 Changed 9 years ago by benjaminfjones

• Authors set to Benjamin Jones
• Status changed from new to needs_review

Preliminary patch needs review. The function has been added using the template developed as part of #11143. The issue described in the description is addressed in one of the doctests.

### Changed 9 years ago by kini

apply to \$SAGE_ROOT/devel/sage

### comment:3 Changed 9 years ago by kini

• Description modified (diff)

Running `make ptestlong` now. I fixed a couple of doctests that broke, and fixed some typos and rST syntax problems in your docstring.

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