Symbolic products are currently broken.

[charpent]

The symbolic product is currently broken in Sage :

• It cannot be created in Sage :

  sage: var("j,p", domain="integer")
  sage: X,Y=function("X,Y")
  sage: prod(X(j),j,1,p)
  ---------------------------------------------------------------------------
  TypeError                                 Traceback (most recent call last)
  <ipython-input-5-85e69544cbe9> in <module>()
  ----> 1 prod(X(j),j,Integer(1),p)
  
  /usr/local/sage-8/src/sage/misc/misc_c.pyx in sage.misc.misc_c.prod (/usr/local/sage-8/src/build/cythonized/sage/misc/misc_c.c:1596)()
       69 
       70 
  ---> 71 def prod(x, z=None, Py_ssize_t recursion_cutoff=5):
       72     """
       73     Return the product of the elements in the list x.
  
  TypeError: prod() takes at most 3 positional arguments (4 given)
  sage: product(X(j),j,1,p)
  ---------------------------------------------------------------------------
  NameError                                 Traceback (most recent call last)
  <ipython-input-6-4d04d74c7489> in <module>()
  ----> 1 product(X(j),j,Integer(1),p)
  
  NameError: name 'product' is not defined
  

• Creatnig it it by casting a Maxima expression via the library interface gives nonsense :

  sage: X(j).maxima_methods().prod(j,1,p)
  X(j)^p
  sage: X(j).maxima_methods().product(j,1,p)
  X(j)^p
  

(Note : similar nonsense also happens with sums :

sage: X(j).maxima_methods().sum(j,1,p)
p*X(j)

)

• But something (what ?) can be created via the Maxima pexpect interface :

  sage: maxima("prod(X(j),j,1,p)").sage().log().log_expand()
  sum(log(X(j)), j, 1, p)