implement symbolic product #17505

rwst · 2014-12-15T07:20:23Z

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

The text was updated successfully, but these errors were encountered:

rwst · 2017-02-22T14:11:18Z

comment:3

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

EmmanuelCharpentier · 2017-05-02T06:41:34Z

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 · 2017-05-02T07:10:03Z

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 · 2017-05-05T08:45:10Z

Branch: u/rws/implement_symbolic_product

mforets · 2017-05-07T09:15:41Z

comment:9

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`

mforets · 2017-05-07T09:15:41Z

Commit: 647ff39

sagetrac-git · 2017-05-08T08:48:29Z

Changed commit from 647ff39 to e4769b5

sagetrac-git · 2017-05-08T08:48:29Z

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

`e4769b5`	`17505: symbolic product`

rwst · 2017-05-08T08:55:44Z

comment:11

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?

rwst · 2017-05-08T08:55:44Z

Author: Ralf Stephan

EmmanuelCharpentier · 2017-05-08T13:40:25Z

comment:12

Replying to @rwst:

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 Implement a "distribute" method #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

sagetrac-git · 2017-05-11T06:57:46Z

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

`58119b0`	`17505: fix doctests`

sagetrac-git · 2017-05-11T06:57:46Z

Changed commit from e4769b5 to 58119b0

rwst · 2017-05-11T06:59:06Z

comment:15

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

rwst · 2017-05-12T07:23:01Z

comment:30

Replying to @EmmanuelCharpentier:

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?

EmmanuelCharpentier · 2017-05-12T08:52:53Z

comment:31

Replying to @rwst:

Replying to @EmmanuelCharpentier:

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.

EmmanuelCharpentier · 2017-05-12T09:52:42Z

comment:32

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)

sagetrac-git · 2017-05-12T12:55:58Z

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

`5779423`	`17505: fix doctests`

sagetrac-git · 2017-05-12T12:55:58Z

Changed commit from d420ec4 to 5779423

rwst · 2017-05-12T12:57:06Z

comment:34

Hopefully my reviewers keep their patience. Thanks.

EmmanuelCharpentier · 2017-05-12T13:04:41Z

comment:35

Replying to @rwst:

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.

EmmanuelCharpentier · 2017-05-12T14:06:03Z

comment:36

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 · 2017-05-12T14:15:51Z

comment:37

sr_prod is missing a doctest.

rwst · 2017-05-13T06:01:49Z

comment:38

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.

EmmanuelCharpentier · 2017-05-13T06:25:50Z

comment:39

Replying to @rwst:

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 :

Implement a "distribute" method #22937 should no longer depend on implement symbolic product #17505
Doctest: Remaining issues with symbolic product #22989 should depend on Implement a "distribute" method #22937
Am I right ?

vbraun · 2017-05-13T10:34:26Z

comment:40

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

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rwst mentioned this issue Nov 15, 2016

Full symbolic sum function #21645

Closed

This was referenced Dec 29, 2022

Maxima library interface is broken for symbolic sums #22920

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Implement a "distribute" method #22937

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rwst mentioned this issue Jun 12, 2017

Doctest: Remaining issues with symbolic product #22989

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implement symbolic product #17505

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