broken translation of polylog from Maxima

[Robert Marik]

Maixma's li[2](x) translates to polylog2(x) which is not defined in Sage

sage: maxima('li[1](x)').sage().subs(x=2).n() 
-3.14159265358979*I
sage: maxima('li[2](x)').sage().subs(x=2).n()
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)

/opt/sage-4.3.3-i686-Linux/<ipython console> in <module>()

/opt/sage/local/lib/python2.6/site-packages/sage/symbolic/expression.so in sage.symbolic.expression.Expression.n (sage/symbolic/expression.cpp:17036)()

TypeError: cannot evaluate symbolic expresssion numerically

sage: f(x)= integrate(log(1-x^2)/x, x); f(2).n()
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)

/opt/sage-4.3.3-i686-Linux/<ipython console> in <module>()

/opt/sage/local/lib/python2.6/site-packages/sage/symbolic/expression.so in sage.symbolic.expression.Expression.n (sage/symbolic/expression.cpp:17036)()

TypeError: cannot evaluate symbolic expresssion numerically

sage: maxima('li[2](x)').sage()
polylog2(x)
sage: polylog2?
Object `polylog2` not found.

patch comes soon

[Robert Marik]

apply only this patch

[Robert Marik]

The patch is attached. Still have behavior which I do not understand: log(-x^{2 + 1)*log(x) + 1/2*polylog(2, -x}2 + 1) evaluates numerically at x=1/2 only if it is obtained from direct input and not from Maxima.

----------------------------------------------------------------------
| Sage Version 4.3.3, Release Date: 2010-02-21                       |
| Type notebook() for the GUI, and license() for information.        |
----------------------------------------------------------------------
sage: f(x)=integrate(ln(1-x^2)/x,x)                       
sage: f
x |--> log(-x^2 + 1)*log(x) + 1/2*polylog(2, -x^2 + 1)
sage: g(x)=log(-x^2 + 1)*log(x) + 1/2*polylog(2, -x^2 + 1)
sage: g
x |--> log(-x^2 + 1)*log(x) + 1/2*polylog(2, -x^2 + 1)
sage: bool(f==g)                                          
False
sage: bool(f._repr_()==g._repr_())                        
True
sage: g(1/2).n()
0.688640713882747
sage: f(1/2).n()
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)

/opt/sage-4.3.3-i686-Linux/<ipython console> in <module>()

/opt/sage/local/lib/python2.6/site-packages/sage/symbolic/expression.so in sage.symbolic.expression.Expression.n (sage/symbolic/expression.cpp:17036)()

TypeError: cannot evaluate symbolic expresssion numerically
sage:

Any idea what happens?

[Robert Marik]

And anther issue which I do not understand:

----------------------------------------------------------------------
| Sage Version 4.3.3, Release Date: 2010-02-21                       |
| Type notebook() for the GUI, and license() for information.        |
----------------------------------------------------------------------
Loading Sage library. Current Mercurial branch is: polylog
sage: g(x)=integrate(ln(1-x^2)/x,x)
sage: g(1/2).n()
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)

/opt/sage-4.3.3/<ipython console> in <module>()

/opt/sage-4.3.3/local/lib/python2.6/site-packages/sage/symbolic/expression.so in                                              sage.symbolic.expression.Expression.n (sage/symbolic/expression.cpp:17036)()

TypeError: cannot evaluate symbolic expresssion numerically
sage: g(x)=eval(preparse(integrate(ln(1-x^2)/x,x)._repr_()))
sage: g(1/2).n()
0.688640713882747
sage: g
x |--> log(-x^2 + 1)*log(x) + 1/2*polylog(2, -x^2 + 1)
sage:

why are eval and _repr_ necessary?

[Robert Marik]

​sage-support question concerning the problem above

[Burcin Erocal]

Thank you for the patch and pointing out the conversion problem Robert.

I fixed the problems reported in comment:2 in #7661.

attachment:trac_8459-doctest.patch​ adds a doctest to sage.functions.log.Function_polylog to check if the conversion works. It also moves the compilation of the regular expression out of the symbolic_expression_from_maxima_string() function.

Patches to be applied, in this order:

• attachment:trac-8459.patch​
• attachment:trac_8459-doctest.patch​

This ticket depends on #7661.

[Robert Marik]

Thanks for improving this, Burcin.

To the release manager: Apply only the patches trac-8459* , the first patch was my mistake and it is not relevant in this ticket.

[John Palmieri]

After applying "trac-8459.patch" and "trac_8459-doctest.patch" to Sage 4.3.5, I get doctest errors for functions/log.py:

sage -t  "devel/sage/sage/functions/log.py"                 
**********************************************************************
File "/Applications/sage/devel/sage/sage/functions/log.py", line 305:
    sage: t.operator() == polylog
Expected:
    True
Got:
    False
**********************************************************************
File "/Applications/sage/devel/sage/sage/functions/log.py", line 307:
    sage: t.subs(x=.5).n()
Exception raised:
    Traceback (most recent call last):
      File "/Applications/sage/local/bin/ncadoctest.py", line 1231, in run_one_test
        self.run_one_example(test, example, filename, compileflags)
      File "/Applications/sage/local/bin/sagedoctest.py", line 38, in run_one_example
        OrigDocTestRunner.run_one_example(self, test, example, filename, compileflags)
      File "/Applications/sage/local/bin/ncadoctest.py", line 1172, in run_one_example
        compileflags, 1) in test.globs
      File "<doctest __main__.example_5[17]>", line 1, in <module>
        t.subs(x=RealNumber('.5')).n()###line 307:
    sage: t.subs(x=.5).n()
      File "expression.pyx", line 3797, in sage.symbolic.expression.Expression.n (sage/symbolic/expression.cpp:17043)
    TypeError: cannot evaluate symbolic expression numerically
**********************************************************************
1 items had failures:
   2 of  18 in __main__.example_5
***Test Failed*** 2 failures.
For whitespace errors, see the file /Users/palmieri/.sage//tmp/.doctest_log.py
	 [7.6 s]

[Burcin Erocal]

Replying to jhpalmieri:

After applying "trac-8459.patch" and "trac_8459-doctest.patch" to Sage 4.3.5, I get doctest errors for functions/log.py:

<snipped the error log>

These errors look like the patch attachment:trac_8459-doctest.patch​ was applied without #7661. That ticket was merged before this, so I have no idea what went wrong.

I applied these patches to Sage-4.4.1 and ran the tests. There were no errors. Switching this back to positive review, and keeping fingers crossed that there is no subtle bug hiding somewhere.

[Burcin Erocal]

Patches to be applied, in this order:

• attachment:trac-8459.patch​
• attachment:trac_8459-doctest.patch​

[Minh Van Nguyen]

Merged in this order:

1. ​trac-8459.patch
2. ​trac_8459-doctest.patch