implement symbolic product

[rws]

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.

[rws]

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

[charpent]

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) ?

[rws]

Replying to charpent:

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%.

[mforets]

do you mind adding giac='product' ?

since:

sage: giac('product(x, x, 1, n)')
n!
sage: _.sage()
factorial(n)

---

New commits:

​647ff39

17505: unevaluated symbolic product

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​e4769b5

17505: symbolic product

[rws]

This doesn't have the prod interface (other ticket) and some docs are missing but everything should work. Question: where does SymPy differ from Maxima?

[charpent]

Replying to rws:

This doesn't have the prod interface (other ticket) and some docs are missing but everything should work. Question: where does SymPy differ from Maxima?

First of all, thank you very much for this addition, which should enhance Sage's usefulness fo high-school/undergrad levels.

However, ptestlong gives three failures :

----------------------------------------------------------------------
sage -t --long src/sage/calculus/calculus.py  # 5 doctests failed
sage -t --long src/sage/combinat/posets/posets.py  # 1 doctest failed
sage -t --long src/sage/homology/simplicial_complex.py  # 1 doctest failed
----------------------------------------------------------------------

The second and third ones have been ​reported for 8.0.beta4 and are seen again in 8.0beta5. Nothing new here, so probably not related.

The third one is new :

charpent@asus16-ec:/usr/local/sage-8$ sage -t --long src/sage/calculus/calculus.py
too many failed tests, not using stored timings
Running doctests with ID 2017-05-08-14-44-39-93705f01.
Git branch: t/17505/implement_symbolic_product
Using --optional=database_gap,giacpy_sage,git_trac,mpir,python2,sage
Doctesting 1 file.
sage -t --long src/sage/calculus/calculus.py
**********************************************************************
File "src/sage/calculus/calculus.py", line 843, in sage.calculus.calculus.symbolic_prod
Failed example:
    symbolic_prod(x + i*(i+1)/2, i, 1, 4)
Exception raised:
    Traceback (most recent call last):
      File "/usr/local/sage-8/local/lib/python2.7/site-packages/sage/doctest/forker.py", line 509, in _run
        self.compile_and_execute(example, compiler, test.globs)
      File "/usr/local/sage-8/local/lib/python2.7/site-packages/sage/doctest/forker.py", line 872, in compile_and_execute
        exec(compiled, globs)
      File "<doctest sage.calculus.calculus.symbolic_prod[3]>", line 1, in <module>
        symbolic_prod(x + i*(i+Integer(1))/Integer(2), i, Integer(1), Integer(4))
      File "/usr/local/sage-8/local/lib/python2.7/site-packages/sage/calculus/calculus.py", line 860, in symbolic_prod
        raise TypeError("need a multiplication variable")
    TypeError: need a multiplication variable
**********************************************************************
File "src/sage/calculus/calculus.py", line 845, in sage.calculus.calculus.symbolic_prod
Failed example:
    symbolic_prod(i^2, i, 1, 7)
Exception raised:
    Traceback (most recent call last):
      File "/usr/local/sage-8/local/lib/python2.7/site-packages/sage/doctest/forker.py", line 509, in _run
        self.compile_and_execute(example, compiler, test.globs)
      File "/usr/local/sage-8/local/lib/python2.7/site-packages/sage/doctest/forker.py", line 872, in compile_and_execute
        exec(compiled, globs)
      File "<doctest sage.calculus.calculus.symbolic_prod[4]>", line 1, in <module>
        symbolic_prod(i**Integer(2), i, Integer(1), Integer(7))
      File "/usr/local/sage-8/local/lib/python2.7/site-packages/sage/calculus/calculus.py", line 860, in symbolic_prod
        raise TypeError("need a multiplication variable")
    TypeError: need a multiplication variable
**********************************************************************
File "src/sage/calculus/calculus.py", line 848, in sage.calculus.calculus.symbolic_prod
Failed example:
    symbolic_prod(f(i), i, 1, 7)
Exception raised:
    Traceback (most recent call last):
      File "/usr/local/sage-8/local/lib/python2.7/site-packages/sage/doctest/forker.py", line 509, in _run
        self.compile_and_execute(example, compiler, test.globs)
      File "/usr/local/sage-8/local/lib/python2.7/site-packages/sage/doctest/forker.py", line 872, in compile_and_execute
        exec(compiled, globs)
      File "<doctest sage.calculus.calculus.symbolic_prod[6]>", line 1, in <module>
        symbolic_prod(f(i), i, Integer(1), Integer(7))
      File "/usr/local/sage-8/local/lib/python2.7/site-packages/sage/calculus/calculus.py", line 860, in symbolic_prod
        raise TypeError("need a multiplication variable")
    TypeError: need a multiplication variable
**********************************************************************
File "src/sage/calculus/calculus.py", line 850, in sage.calculus.calculus.symbolic_prod
Failed example:
    symbolic_prod(f(i), i, 1, n)
Exception raised:
    Traceback (most recent call last):
      File "/usr/local/sage-8/local/lib/python2.7/site-packages/sage/doctest/forker.py", line 509, in _run
        self.compile_and_execute(example, compiler, test.globs)
      File "/usr/local/sage-8/local/lib/python2.7/site-packages/sage/doctest/forker.py", line 872, in compile_and_execute
        exec(compiled, globs)
      File "<doctest sage.calculus.calculus.symbolic_prod[7]>", line 1, in <module>
        symbolic_prod(f(i), i, Integer(1), n)
      File "/usr/local/sage-8/local/lib/python2.7/site-packages/sage/calculus/calculus.py", line 860, in symbolic_prod
        raise TypeError("need a multiplication variable")
    TypeError: need a multiplication variable
**********************************************************************
File "src/sage/calculus/calculus.py", line 1489, in sage.calculus.calculus.laplace
Failed example:
    laplace(t^n, t, s, algorithm='giac')
Expected:
    Traceback (most recent call last):
    ...
    NotImplementedError: Unable to parse Giac output: integrate(t^n*exp(-s*t),t,0,+infinity)
Got:
    integration(t^n*e^(-s*t), t, 0, +Infinity)
**********************************************************************
2 items had failures:
   1 of  39 in sage.calculus.calculus.laplace
   4 of  11 in sage.calculus.calculus.symbolic_prod
    [429 tests, 5 failures, 9.57 s]
----------------------------------------------------------------------
sage -t --long src/sage/calculus/calculus.py  # 5 doctests failed
----------------------------------------------------------------------
Total time for all tests: 9.6 seconds
    cpu time: 9.1 seconds
    cumulative wall time: 9.6 seconds

The last one is identical to one already seen in 8.0.beta4 and 8.0.beta5 ; again, nothing new, else probably not related. The four first ones seem identical : aren't they related to an undeclared variable ?

• A couple suggestions, of varying importance :

1. (major) the interface methods ("symbolic_expression.prod" (or product)) and function(s) ("symbolic_product", parallelling "symbolic_sum") are necessary for easy use of this new functionality.

2. (minor) for aesthetics and consistency, could we have for sage.functions.other.symbolic_sum (aka Function_sum) (almost) the same _print_latex_ function you defined in sage.functions.other.symbolic_product (aka Function_prod) ?

3. ((very) minor) consider a "mathematica" method, parallelling tye one in symbolic_sum (necessary for would-be Mathematica users, since mathematica.Sum(X(j), [j,1,p]) give utter nonsense currently).

• A question : can #22937 depend on this ?

• And a possible doctest, demonstrating that this formal mayhem has a mathematical sense :

  sage: var("j,p", domain="integer")
  (j, p)
  sage: X=function("X")
  sage: sage.functions.other.symbolic_product(X(j),j,1,p).log().log_expand()
  sum(log(X(j)), j, 1, p)
  

==>needs_work

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​58119b0

17505: fix doctests

[rws]

Ah sorry just a moment, I'll address your other issues ASAP.

[charpent]

Replying to rws:

Ah sorry just a moment, I'll address your other issues ASAP.

Those were just suggestions, not requests ;-)

Unless you have other suggestions, I'll implement the "symbolic product of product" case in #22937 ASAP, and depend on the present ticket.

[rws]

Replying to charpent:

1. (major) the interface methods ("symbolic_expression.prod" (or product))

Yes, but in a different ticket.

• A question : can #22937 depend on this ?

Yes you can state the dependency in the ticket form, but please wait with merging this branch, as I'll change the branch probably.

Agree to everything else.

[charpent]

Replying to rws:

Replying to charpent:

1. (major) the interface methods ("symbolic_expression.prod" (or product))

Yes, but in a different ticket.

Okay. I'll take that in mind when implementing (and doctesting) #22937.

• A question : can #22937 depend on this ?

Yes you can state the dependency in the ticket form, but please wait with merging this branch, as I'll change the branch probably.

Okay also : I'll marl the dependency before starting the implementation of the multiplicative case. Should I wait your say so before reviewing the ticket ? Or should I review it in its current state ?

Suggestion : mark it as needs_work before reworkiong it and needs_review when satisfied with (a step of) your work.

Agree to everything else.

Thanks !

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​7a56004

17505: address reviewer's suggestions

[rws]

OK, which doctests are still missing?

[rws]

Replying to charpent:

Should I wait your say so before reviewing the ticket ? Or should I review it in its current state ?

Please review now, there may only be some doctests missing.

[charpent]

Replying to rws:

Replying to charpent:

Should I wait your say so before reviewing the ticket ? Or should I review it in its current state ?

Please review now, there may only be some doctests missing.

Builds OK on top of my distribute branch. ptestlon running (needs about 1 hour : stay tuned...).

[charpent]

Passes ptestlong with the same failures already reported for 8.0.beta4 and not yet fixed.

===> positive review

Waiting your say-so to merge into #22937...

[rws]

Thanks.

Replying to charpent:

Waiting your say-so to merge into #22937...

Please go ahead.

[rws]

Your real name in the Reviewer field is missing, please add.,

[charpent]

Wups !

Done...

[charpent]

Slight issue :

sage: var("j,p", domain="integer")
(j, p)
sage: X=function("X")
sage: latex(maxima("product(X(j),j,1,p)").sage()^2)
\prod_{j=1}^{p} X(j)^{2}

which prints wrong (it should be {\prod_{j=1}^{p} X(j)}^{2} in order to position the exponent over the whole sum, not the "productand"). The same is true for sum.

Care to fix it here or should I open a new ticket (depending on this one) ?

[rws]

I'll fix it immediately.

[git]

Branch pushed to git repo; I updated commit sha1 and set ticket back to needs_review. New commits:

​d420ec4

17505: fix latex, cosmetics

[rws]

Replying to charpent:

which prints wrong (it should be {\prod_{j=1}^{p} X(j)}^{2} in order to position the exponent over the whole sum, not the "productand"). The same is true for sum.

However, isn't it the duty of power to make the braces?

[charpent]

Replying to rws:

Replying to charpent:

which prints wrong (it should be {\prod_{j=1}^{p} X(j)}^{2} in order to position the exponent over the whole sum, not the "productand"). The same is true for sum.

However, isn't it the duty of power to make the braces?

Not necessarily. \sum_{j=1}^p X(j)^2 is mathematically wrong ; however, {X_{j}}^2 is correct but ugly, whereas X_{j}^2 is also ((almost) unambiguously) correct and much more pleasant.

There is still an ambiguity, that does not concern us there : tensors. But that's another whole can of worms.

Your patch looks good. ptestlong is running and should terminate in about an hour.

[charpent]

Two new failures :

sage -t --long src/sage/functions/other.py
**********************************************************************
File "src/sage/functions/other.py", line 2617, in sage.functions.other.Function_
sum._print_latex_
Failed example:
    latex(ssum(x^2, x, 1, 10))
Expected:
    \sum_{x=1}^{10} x^2
Got:
    {\sum_{x=1}^{10} x^2}
**********************************************************************
File "src/sage/functions/other.py", line 2664, in sage.functions.other.Function_prod._print_latex_
Failed example:
    latex(sprod(x^2, x, 1, 10))
Expected:
    \prod_{x=1}^{10} x^2
Got:
    {\prod_{x=1}^{10} x^2}
**********************************************************************
2 items had failures:
   1 of   3 in sage.functions.other.Function_prod._print_latex_
   1 of   3 in sage.functions.other.Function_sum._print_latex_
    [580 tests, 2 failures, 7.13 s]

It seems that you forgot to upate your doctests... ;-)

==> needs work (pro forma)

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​5779423

17505: fix doctests

[rws]

Hopefully my reviewers keep their patience. Thanks.

[charpent]

Replying to rws:

Hopefully my reviewers keep their patience. Thanks.

sage -t --long src/sage/symbolic/expression.pyx passes with no error. ptestlong underway (again, pro forma). Stay tuned.

[charpent]

ptestlong passes with the known, supposed unrelated failure ; no whoopee cushions.

==>positive_review

Since this was tested on top of #22937, the latter is also ready for re-review. Would you mind ?

[tscrim]

sr_prod is missing a doctest.

[rws]

The ticket was merged up to a point. I'll close it and put the branch with the remaining issues in another ticket. See #22989.

[charpent]

Replying to rws:

The ticket was merged up to a point.

You mean in #22937, I suppose ?

I'll close it and put the branch with the remaining issues in another ticket. See #22989.

Hmm... Unles I'm mistaken, there are two consequences :

• #22937 should no longer depend on #17505
• #22989 should depend on #22937

Am I right ?

[vbraun]

Sorry, forgot to close this ticket. Move your new commits to a new ticket.