#16697: implement symbolic lower incomplete gamma function
-------------------------------------+-------------------------------------
       Reporter:  rws                |        Owner:
           Type:  defect             |       Status:  needs_work
       Priority:  major              |    Milestone:  sage-pending
      Component:  symbolics          |   Resolution:
       Keywords:  gamma,             |    Merged in:
  incomplete, special, functions     |    Reviewers:  Buck Evan
        Authors:  Ralf Stephan       |  Work issues:
Report Upstream:  N/A                |       Commit:
         Branch:                     |  5f4a7fbd8598ef3fb22d8cb61d199dfffea23a8c
  public/ticket/16697                |     Stopgaps:
   Dependencies:  #17130,            |
  sympy-0.7.7                        |
-------------------------------------+-------------------------------------

Comment (by buck):

 Merged and attempted to run the doctests, and got this result:

 {{{
 ./sage -t src/sage/functions/other.py
 ⬆ ✱ ◼
 too few successful tests, not using stored timings
 Running doctests with ID 2015-07-26-17-39-51-10ac5315.
 Git branch: master
 Using --optional=mpir,python2,sage,scons
 Doctesting 1 file.
 sage -t src/sage/functions/other.py
 **********************************************************************
 File "src/sage/functions/other.py", line 1076, in
 sage.functions.other.Function_gamma_inc_lower._eval_
 Failed example:
     gamma_inc_lower(1/2,2)
 Exception raised:
     Traceback (most recent call last):
       File "/home/buck/trees/mine/sage/local/lib/python2.7/site-
 packages/sage/doctest/forker.py", line 496, in _run
         self.compile_and_execute(example, compiler, test.globs)
       File "/home/buck/trees/mine/sage/local/lib/python2.7/site-
 packages/sage/doctest/forker.py", line 858, in compile_and_execute
         exec(compiled, globs)
       File "<doctest
 sage.functions.other.Function_gamma_inc_lower._eval_[2]>", line 1, in
 <module>
         gamma_inc_lower(Integer(1)/Integer(2),Integer(2))
       File "sage/symbolic/function.pyx", line 994, in
 sage.symbolic.function.BuiltinFunction.__call__
 
(/home/buck/trees/mine/sage/src/build/cythonized/sage/symbolic/function.cpp:10875)
         res = super(BuiltinFunction, self).__call__(
       File "sage/symbolic/function.pyx", line 507, in
 sage.symbolic.function.Function.__call__
 
(/home/buck/trees/mine/sage/src/build/cythonized/sage/symbolic/function.cpp:6887)
         res = g_function_eval2(self._serial, (<Expression>args[0])._gobj,
       File "sage/symbolic/pynac.pyx", line 185, in
 sage.symbolic.pynac.pyExpression_to_ex
 (/home/buck/trees/mine/sage/src/build/cythonized/sage/symbolic/pynac.cpp:3934)
         t = ring.SR.coerce(res)
       File "sage/structure/parent.pyx", line 1310, in
 sage.structure.parent.Parent.coerce
 (/home/buck/trees/mine/sage/src/build/cythonized/sage/structure/parent.c:10682)
         cpdef coerce(self, x):
       File "sage/structure/parent.pyx", line 1339, in
 sage.structure.parent.Parent.coerce
 (/home/buck/trees/mine/sage/src/build/cythonized/sage/structure/parent.c:10628)
         return (<map.Map>mor)._call_(x)
       File "sage/symbolic/ring.pyx", line 927, in
 sage.symbolic.ring.UnderscoreSageMorphism._call_
 (/home/buck/trees/mine/sage/src/build/cythonized/sage/symbolic/ring.cpp:10428)
         return self.codomain()(a._sage_())
       File "/home/buck/trees/mine/sage/local/lib/python2.7/site-
 packages/sympy/core/mul.py", line 1467, in _sage_
         s *= x._sage_()
     AttributeError: 'erf' object has no attribute '_sage_'
 **********************************************************************
 File "src/sage/functions/other.py", line 1078, in
 sage.functions.other.Function_gamma_inc_lower._eval_
 Failed example:
     gamma_inc_lower(1/2,1)
 Exception raised:
     Traceback (most recent call last):
       File "/home/buck/trees/mine/sage/local/lib/python2.7/site-
 packages/sage/doctest/forker.py", line 496, in _run
         self.compile_and_execute(example, compiler, test.globs)
       File "/home/buck/trees/mine/sage/local/lib/python2.7/site-
 packages/sage/doctest/forker.py", line 858, in compile_and_execute
         exec(compiled, globs)
       File "<doctest
 sage.functions.other.Function_gamma_inc_lower._eval_[3]>", line 1, in
 <module>
         gamma_inc_lower(Integer(1)/Integer(2),Integer(1))
       File "sage/symbolic/function.pyx", line 994, in
 sage.symbolic.function.BuiltinFunction.__call__
 
(/home/buck/trees/mine/sage/src/build/cythonized/sage/symbolic/function.cpp:10875)
         res = super(BuiltinFunction, self).__call__(
       File "sage/symbolic/function.pyx", line 507, in
 sage.symbolic.function.Function.__call__
 
(/home/buck/trees/mine/sage/src/build/cythonized/sage/symbolic/function.cpp:6887)
         res = g_function_eval2(self._serial, (<Expression>args[0])._gobj,
       File "sage/symbolic/pynac.pyx", line 185, in
 sage.symbolic.pynac.pyExpression_to_ex
 (/home/buck/trees/mine/sage/src/build/cythonized/sage/symbolic/pynac.cpp:3934)
         t = ring.SR.coerce(res)
       File "sage/structure/parent.pyx", line 1310, in
 sage.structure.parent.Parent.coerce
 (/home/buck/trees/mine/sage/src/build/cythonized/sage/structure/parent.c:10682)
         cpdef coerce(self, x):
       File "sage/structure/parent.pyx", line 1339, in
 sage.structure.parent.Parent.coerce
 (/home/buck/trees/mine/sage/src/build/cythonized/sage/structure/parent.c:10628)
         return (<map.Map>mor)._call_(x)
       File "sage/symbolic/ring.pyx", line 927, in
 sage.symbolic.ring.UnderscoreSageMorphism._call_
 (/home/buck/trees/mine/sage/src/build/cythonized/sage/symbolic/ring.cpp:10428)
         return self.codomain()(a._sage_())
       File "/home/buck/trees/mine/sage/local/lib/python2.7/site-
 packages/sympy/core/mul.py", line 1467, in _sage_
         s *= x._sage_()
     AttributeError: 'erf' object has no attribute '_sage_'
 **********************************************************************
 File "src/sage/functions/other.py", line 1092, in
 sage.functions.other.Function_gamma_inc_lower._eval_
 Failed example:
     gamma_inc_lower(9/2,37/7)
 Exception raised:
     Traceback (most recent call last):
       File "/home/buck/trees/mine/sage/local/lib/python2.7/site-
 packages/sage/doctest/forker.py", line 496, in _run
         self.compile_and_execute(example, compiler, test.globs)
       File "/home/buck/trees/mine/sage/local/lib/python2.7/site-
 packages/sage/doctest/forker.py", line 858, in compile_and_execute
         exec(compiled, globs)
       File "<doctest
 sage.functions.other.Function_gamma_inc_lower._eval_[10]>", line 1, in
 <module>
         gamma_inc_lower(Integer(9)/Integer(2),Integer(37)/Integer(7))
       File "sage/symbolic/function.pyx", line 994, in
 sage.symbolic.function.BuiltinFunction.__call__
 
(/home/buck/trees/mine/sage/src/build/cythonized/sage/symbolic/function.cpp:10875)
         res = super(BuiltinFunction, self).__call__(
       File "sage/symbolic/function.pyx", line 507, in
 sage.symbolic.function.Function.__call__
 
(/home/buck/trees/mine/sage/src/build/cythonized/sage/symbolic/function.cpp:6887)
         res = g_function_eval2(self._serial, (<Expression>args[0])._gobj,
       File "sage/symbolic/pynac.pyx", line 185, in
 sage.symbolic.pynac.pyExpression_to_ex
 (/home/buck/trees/mine/sage/src/build/cythonized/sage/symbolic/pynac.cpp:3934)
         t = ring.SR.coerce(res)
       File "sage/structure/parent.pyx", line 1310, in
 sage.structure.parent.Parent.coerce
 (/home/buck/trees/mine/sage/src/build/cythonized/sage/structure/parent.c:10682)
         cpdef coerce(self, x):
       File "sage/structure/parent.pyx", line 1339, in
 sage.structure.parent.Parent.coerce
 (/home/buck/trees/mine/sage/src/build/cythonized/sage/structure/parent.c:10628)
         return (<map.Map>mor)._call_(x)
       File "sage/symbolic/ring.pyx", line 927, in
 sage.symbolic.ring.UnderscoreSageMorphism._call_
 (/home/buck/trees/mine/sage/src/build/cythonized/sage/symbolic/ring.cpp:10428)
         return self.codomain()(a._sage_())
       File "/home/buck/trees/mine/sage/local/lib/python2.7/site-
 packages/sympy/core/add.py", line 732, in _sage_
         s += x._sage_()
       File "/home/buck/trees/mine/sage/local/lib/python2.7/site-
 packages/sympy/core/mul.py", line 1467, in _sage_
         s *= x._sage_()
     AttributeError: 'erf' object has no attribute '_sage_'
 **********************************************************************
 1 item had failures:
    3 of  12 in sage.functions.other.Function_gamma_inc_lower._eval_
     [509 tests, 3 failures, 3.90 s]
 ----------------------------------------------------------------------
 sage -t src/sage/functions/other.py  # 3 doctests failed
 ----------------------------------------------------------------------
 Total time for all tests: 4.1 seconds
     cpu time: 2.5 seconds
     cumulative wall time: 3.9 seconds
 }}}

--
Ticket URL: <http://trac.sagemath.org/ticket/16697#comment:51>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
and MATLAB

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