Maxima misses an obvious simplification with sums

[rtoy]

Imported from SourceForge on 2024-07-01 18:02:27 Created by charpent on 2016-12-29 16:18:06 Original: https://sourceforge.net/p/maxima/bugs/3267

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My test system :

(%i4) bug_report();

Please report bugs to:
    http://sourceforge.net/p/maxima/bugs
To report a bug, you must have a Sourceforge account.
Please include the following information with your bug report:
-------------------------------------------------------------
Maxima version: "5.38.1"
Maxima build date: "2016-11-25 20:51:03"
Host type: "x86_64-pc-linux-gnu"
Lisp implementation type: "GNU Common Lisp (GCL)"
Lisp implementation version: "GCL 2.6.12"
-------------------------------------------------------------

The problem : I want to simplify sums of vectors of unspecified quantities, here represented as unspecified finctions with an integer argument. The simplest case is :

(%i1) display2d:false;

(%o1) false
(%i2) sumcontract(sum(X(i),i,1,n+1)+sum(X(i),i,1,n));

(%o2) X(n+1)+2*'sum(X(i),i,1,n)

So far, so good. But :

(%i3) sumcontract(sum(X(i),i,1,n+1)-sum(X(i),i,1,n));

(%o3) 'sum(X(i),i,1,n+1)-'sum(X(i),i,1,n)

(%o2) let me hope that (%o3) would be X(n+1) (the simplified result). Bit no. Ad adding ,simpsum doesn't fix the problem.

[rtoy]

Imported from SourceForge on 2024-07-01 18:02:28 Created by robert_dodier on 2016-12-30 06:55:03 Original: https://sourceforge.net/p/maxima/bugs/3267/#3abc

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I find that intosum helps sumcontract find the expected result.

(%i11) intosum (sum(X(i),i,1,n+1)-sum(X(i),i,1,n));
                          n + 1         n
                          ====         ====
                          \            \
(%o11)                     >    X(i) +  >    (- X(i))
                          /            /
                          ====         ====
                          i = 1        i = 1
(%i12) sumcontract (intosum (sum(X(i),i,1,n+1)-sum(X(i),i,1,n)));
(%o12)                             X(n + 1)

What do you think -- is this good enough? The documentation for sumcontract does mention intosum although it doesn't explain why one would do that. Certainly the documentation can be improved.

[rtoy]

Imported from SourceForge on 2024-07-01 18:02:30 Created by charpent on 2016-12-30 11:32:57 Original: https://sourceforge.net/p/maxima/bugs/3267/#3abc/8806

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On 30/12/2016 07:55, Robert Dodier wrote:

I find that |intosum| helps |sumcontract| find the expected result.

(%i11) intosum (sum(X(i),i,1,n+1)-sum(X(i),i,1,n)); n + 1 n ==== ==== \ \ (%o11) > X(i) + > (- X(i)) / / ==== ==== i = 1 i = 1 (%i12) sumcontract (intosum (sum(X(i),i,1,n+1)-sum(X(i),i,1,n))); (%o12) X(n + 1)

What do you think -- is this good enough?

Well... yes and no (see below).

The documentation for |sumcontract| does mention |intosum| although it doesn't explain why one would do that. Certainly the documentation can be improved.

Following the doc, I had tried sumcontract(intosum(sum(X(i),,i,1,n))-intosum(sum(X(i),i,1,n-1))); which was unhelpful, as you might think. An example (such as the one I used to report the bug) might clarify the sentence...

To be frank, I think that the description of intosum does not allow to understand why it should help in this case : there is no "external" factor to intern in the sum( except the sight of the operation), and the doc does not help to understand why and how sum(X(i),i,1,n+1) is interpreted as sum((=X(i),i,1,n)+X(n+1). And even less this behavior :

(%i21) sumcontract(intosum(sum(X(i),i,1,n+3)-sum(X(i),i,1,n)));
(%o21)                  X(n + 3) + X(n + 2) + X(n + 1)
(%i22) sumcontract(intosum(sum(X(i),i,4,n+3)-sum(X(i),i,1,n)));
(%o22)        X(n + 3) + X(n + 2) + X(n + 1) - X(3) - X(2) - X(1)

This kind of result is something quite easy to miss when working "manually" (i. e. with pencil, eraser and paper) ; that's where CAS are extremely valuable : these possibilities should not be missed.

More generally, that's something that could be tried by Maxima itself, possibly under the control of an option.

Something similar could (should ?) be done for products, which currently have not facilities similar to sumcontract and intosum

Finally, I note that some obvious sum-to-product and product-to-sum equalities are missed by Maxima (-that should be implemented as log() and exp() properties ; there might be other opportinities for trig functions...) :

(%i20) is(equal(log(product(X(i),i,1,n)),sum(log(X(i)),i,1,n)));
(%o20)                              unknown

"The competition" does not seem to be in better shape : neither Sympy nor Mathematica can get the result obtained in Maxima.

FYI : I note that Sage doesn't implement product and that Sage's use of Maxima's product is false. I'll file a ticket against it.

HTH,

-- Emmanuel Charpentier

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[bugs:#3267] https://sourceforge.net/p/maxima/bugs/3267/ Maxima misses an obvious simplification with sums

Status: open Group: None Labels: simplify simplify_sum sum sumcontract Created: Thu Dec 29, 2016 04:18 PM UTC by Emmanuel Charpentier Last Updated: Thu Dec 29, 2016 04:18 PM UTC Owner: nobody

My test system :

(%i4) bug_report();

Please report bugs to: http://sourceforge.net/p/maxima/bugs To report a bug, you must have a Sourceforge account. Please include the following information with your bug report:

Maxima version: "5.38.1" Maxima build date: "2016-11-25 20:51:03" Host type: "x86_64-pc-linux-gnu" Lisp implementation type: "GNU Common Lisp (GCL)" Lisp implementation version: "GCL 2.6.12"

The problem : I want to simplify sums of vectors of unspecified quantities, here represented as unspecified finctions with an integer argument. The simplest case is :

(%i1) display2d:false;

(%o1) false (%i2) sumcontract(sum(X(i),i,1,n+1)+sum(X(i),i,1,n));

(%o2) X(n+1)+2*'sum(X(i),i,1,n)

So far, so good. But :

(%i3) sumcontract(sum(X(i),i,1,n+1)-sum(X(i),i,1,n));

(%o3) 'sum(X(i),i,1,n+1)-'sum(X(i),i,1,n)

|(%o2)| let me hope that |(%o3)| would be |X(n+1)| (the simplified result). Bit no. Ad adding |,simpsum| doesn't fix the problem.

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[rtoy]

Imported from SourceForge on 2024-07-01 18:02:32 Created by robert_dodier on 2016-12-31 07:03:25 Original: https://sourceforge.net/p/maxima/bugs/3267/#f1b2

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OK, I see your point. I will think about how to get sumcontract to call intosum as necessary. (The question seems a little subtle to me. I don't know if it's possible for intosum to actually make the problem harder for sumcontract. If so, it can't be called always. Also, calling intosum might cause sumcontract to yield a different result. Which one should be returned? Is there any way to determine which result is "simpler" or preferable in some other way? It's not important to answer these questions now; these are just the thoughts going through my head.)

About analogues of sumcontract and intosum for product expressions, I agree that would be a good idea. Feel free to submit a "Feature Request" ticket for it.

About simplifying log(product(...)) to sum(log(...)), note that logexpand = all or logexpand = super enables this. I guess that's not mentioned in the documentation; I'll add a note.