f(expr,hold).n() fails for all generalized functions

[rwst]

sage: M = sgn((3/2),hold=True); M.n()
...
TypeError: cannot evaluate symbolic expression numerically

The original problem is now resolved, it was reported in http://ask.sagemath.org/question/8535/problem-with-sign-sgn-and-n/ by Louis Cypher:

sage: M = sgn(cos(3/2))
sage: M.n()
TypeError                                 Traceback (most recent call last)
<ipython-input-5-0f11e9bd1e87> in <module>()
----> 1 M.n()

/home/ralf/sage/local/lib/python2.7/site-packages/sage/symbolic/expression.so in sage.symbolic.expression.Expression._numerical_approx (build/cythonized/sage/symbolic/expression.cpp:24086)()

TypeError: cannot evaluate symbolic expression numerically

kcrisman:

Problem seems to be that in M.n?? we see that it's looking for is_a_numeric(x._gobj) but apparently that fails, as does the constant, so it thinks we are looking at evaluating sgn(cos(x)) instead of sgn(cos(3/2)).

Depends on #17130
Depends on #17285

CC: @kcrisman

Component: symbolics

Keywords: sgn, evaluation

Author: Ralf Stephan

Branch/Commit: e7880b7

Reviewer: Paul Masson

Issue created by migration from https://trac.sagemath.org/ticket/16587

[kcrisman]

comment:1

You can always feel free to cc: me on any ticket coming from something I was involved in :)

[rwst]

comment:3

Actually all functions in generalized.py show this problem. Moreover, the cos can be left out:

sage: M = sgn((3/2),hold=True); M.n()
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
<ipython-input-18-b9940d9ad473> in <module>()
----> 1 M = sgn((Integer(3)/Integer(2)),hold=True); M.n()

/home/ralf/sage/local/lib/python2.7/site-packages/sage/symbolic/expression.so in sage.symbolic.expression.Expression._numerical_approx (build/cythonized/sage/symbolic/expression.cpp:27093)()

TypeError: cannot evaluate symbolic expression numerically

All the generalized functions have this code in _eval_() and I believe the bug to be there:

        try:
            approx_x = ComplexIntervalField()(x)
            if bool(approx_x.imag() == 0):      # x is real
                if bool(approx_x.real() == 0):  # x is zero
                    return ...
                else:
                    return ...
            else:
                return ...            # x is complex
        except Exception:                     # x is symbolic
            pass
        return None

[jdemeyer]

comment:4

Isn't the problem simply that these functions are missing an _evalf_() method?

[rwst]

comment:5

Thanks. This begs for a subclass of BuiltinFunction.

[jdemeyer]

comment:6

Replying to @rwst:

Thanks. This begs for a subclass of BuiltinFunction.

I don't see why.

[jdemeyer]

comment:7

Let me also mention that this ticket touches on similar issues as #17130. So if you make a patch, I would prefer it to be based on #17130 (although that ticket is still in needs_review).

[rwst]

Branch: u/rws/f_expr__n___fails_for_all_generalized_functions

[rwst]

Commit: 44ca3ad