Allow to take the sign of a callable symbolic expression

[rburing]

Reported in ​Ask SageMath question #55417:

sage: f(x) = x^2
sage: cos(f)
x |--> cos(x^2)
sage: log(f)
x |--> log(x^2)
sage: sign(x^2)
sgn(x^2)
sage: sign(f)
...
TypeError: cannot coerce arguments: no canonical coercion from Callable function ring with argument x to Symbolic Ring

[vdelecroix]

Moreover, one can build the object in sage

sage: sgn(x^2).function(x)
x |--> sgn(x^2)

[gh-bmlivin]

I think this can be fixed by renaming the sage.symbolics.expression.Expression.csgn method to sgn and giving it the @property decorator. I'm going to test that out and see if it breaks anything.

[gh-bmlivin]

Replying to gh-bmlivin:

I think this can be fixed by renaming the sage.symbolics.expression.Expression.csgn method to sgn and giving it the @property decorator. I'm going to test that out and see if it breaks anything.

Never mind. That broke a number of tests, and it doesn't appear to do what it should anyway. I will continue to look for other ways to do this.

[gh-bmlivin]

So I've attempted to make a sage.symbolic.expression.Expression.sgn method which returns giac.sgn(self). This causes one of the tests in src.sage.symbolic.expression to fail:

sage: unicode_art(SR(1.3 - I)) should return 1.3 - ⅈ, but it instead returns 1.3 - 1.0⋅ⅈ. I'm not sure whether this really matters, especially since there are other tests in that same method which return 1.0⋅x instead of x, but is a test that technically fails.

I have a feeling there may some other formatting tests that this may cause to fail, and I'm not sure why.

[mkoeppe]

Sage development has entered the release candidate phase for 9.3. Setting a new milestone for this ticket based on a cursory review of ticket status, priority, and last modification date.

[mkoeppe]

By the docstring, FunctionSignum seems intended to be used for real inputs only. But the various conversions also work for complex input. What's missing is a conversion to pynac's csgn (FunctionSignum is a BuiltinFunction, not a GinacFunction, for a reason unknown to me). Fixing this will likely also fix the issue on the ticket description.