Allow Sympy conversion sign/sgn

[kcrisman]

From ​this thread on sage-support:

Hi, 
Sage uses a dictionary to translate Sage function names to SymPy ones 
when they are different. 
Signal function is called "sgn" in Sage and "sign" in Sympy but the 
respective translation is not in the dictionary, and a error is issued 
if one tries to do something like: 
   x = var('x'); sgn(x)._sympy_() 
To fix it, it is just a matter of adding 
                "sgn": "sign", 
to the dictionary. 
Such dictionary is called "translation_table" and it is inside 
function "composition" from class "SympyConverter" of file "sage/ 
symbolic/expression_conversions.py". 
I would like to know how can I submit a patch, or ask someone to do 
it, and if it is necessary to include something in a unit test (like I 
did for Sympy for the inverse translation). 
? 

Apply:

• attachment:trac_11921-sympy_conversion.patch​
• attachment:trac_11921_conversionsDictionary.patch​
• attachment:trac_11921-doctest.patch​
• attachment:trac_11921-reviewer.patch​

[burcin]

The conversions should be specified with the conversions argument to the BuiltinFunction constructor. Having the conversion near the function definition is easier to maintain than that table.

In this case, the constructor for sage.functions.generalized.FunctionSignum? should be changed to include 'sympy': 'sign' in the conversions argument.

[jdemeyer]

Milestone sage-4.7.3 deleted

[peter.story]

I performed the addition to the conversions argument as requested by burcin.
However, x = var('x'); sgn(x)._sympy_() still fails.

[burcin]

I was wrong. For some reason, SympyConverter.composition() method defined a translation table of its own. attachment:trac_11921-sympy_conversion.patch​ fixes it to go through the standard mechanism. Your patch should work now.

We still need doctests to switch this to needs_review.

[burcin]

I attached a new patch that adds a doctest as well. This is ready for review now.

[kcrisman]

I like everything here, good simplification and clarification of all this.

I'd like a different example, though!

sage: from sage.symbolic.function import SymbolicFunction 
sage: f = SymbolicFunction('f', conversions=dict(sympy='ff'))
sage: f(x)
f(x)
sage: f(x)._sympy_()
<snip>
ValueError: Function FallingFactorial expects 2 argument(s), got 1.

Well! That was a surprise.

So I'm adding a reviewer patch that just swaps g for f and then documents the less surprising error that sympy has no gg function.

[kcrisman]

For patchbot:

Apply:

• attachment:trac_11921-sympy_conversion.patch​
• attachment:trac_11921_conversionsDictionary.patch​
• attachment:trac_11921-doctest.patch​
• attachment:trac_11921-reviewer.patch​