implement symbolic product

[rwst]

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

At the moment anonymous functions named product can be created via the Maxima pexpect interface and they even behave as products in specific cases:

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

The present ticket aims at creating a Sage function/method either evaluating the sum, or correctly creating a unevaluted symbolic product object.

For evaluation the ticket would have to decide which of (Maxima,SymPy) would be used as default for this.

sage: import sympy
sage: x = sympy.Symbol('x')
sage: n = sympy.Symbol('n')
sage: sympy.product(x, (x, 1, n))
factorial(n)
sage: sympy.product(sin(x), (x, 1, n))
Product(sin(x), (x, 1, n))

Creating products by casting a Maxima expression via the library interface gives nonsense, see #17502.

CC: @EmmanuelCharpentier

Component: symbolics

Author: Ralf Stephan

Branch/Commit: u/rws/implement_symbolic_product @ 5779423

Reviewer: Emmanuel Charpentier

Issue created by migration from https://trac.sagemath.org/ticket/17505

[rwst]

Description changed:

--- 
+++ 
@@ -6,6 +6,8 @@
 sage: n = sympy.Symbol('n')
 sage: sympy.product(x, (x, 1, n))
 factorial(n)
+sage: sympy.product(sin(x), (x, 1, n))
+Product(sin(x), (x, 1, n))
 ```
 
 Any Maxima implementation likely depends on #17502.

[rwst]

comment:3

Note that if #20179 is implemented it has to be adapted when symbolic products are made available.

[EmmanuelCharpentier]

Description changed:

--- 
+++ 
@@ -1,3 +1,55 @@
+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)
+```
+
+The part of the problem bound to the Maxima library interface is the object of #22920. The present ticket aims at creating a Sage function/method correctly creating a symbolic product object.
+
 The ticket would have to decide which of (Maxima,SymPy) would be used as default for this. 
 
 ```

[EmmanuelCharpentier]

comment:5

Cut'n paste of the description of #22914 (duplicate ticket), at the request of the present ticket's author.

Note : Couldn't we cut'n'paste the recent code for symbolic sums (#21645) ?

[rwst]

comment:6

Replying to @EmmanuelCharpentier:

Note : Couldn't we cut'n'paste the recent code for symbolic sums (#21645) ?

Yes, but as you can see with #22844 it may not work 100%.

[rwst]

Description changed:

--- 
+++ 
@@ -26,31 +26,17 @@
 
 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 :
+At the moment anonymous functions named `product` can be created via the Maxima `pexpect` interface and they even behave as products in specific cases:
 
 ```
 sage: maxima("prod(X(j),j,1,p)").sage().log().log_expand()
 sum(log(X(j)), j, 1, p)
 ```
 
-The part of the problem bound to the Maxima library interface is the object of #22920. The present ticket aims at creating a Sage function/method correctly creating a symbolic product object.
+The present ticket aims at creating a Sage function/method either evaluating the sum, or correctly creating a unevaluted symbolic product object.
 
-The ticket would have to decide which of (Maxima,SymPy) would be used as default for this. 
+For evaluation the ticket would have to decide which of (Maxima,SymPy) would be used as default for this. 
 
 ```
 sage: import sympy
@@ -62,4 +48,5 @@
 Product(sin(x), (x, 1, n))
 ```
 
-Any Maxima implementation likely depends on #17502.
+Creating products by casting a Maxima expression via the library interface gives nonsense, see #17502.
+

[rwst]

Branch: u/rws/implement_symbolic_product