#22937 closed enhancement (fixed)
Implement a "distribute" method
Reported by: | charpent | Owned by: | |
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Priority: | major | Milestone: | sage-8.0 |
Component: | symbolics | Keywords: | |
Cc: | rws, tscrim | Merged in: | |
Authors: | Emmanuel Charpentier, Ralf Stephan | Reviewers: | Travis Scrimshaw |
Report Upstream: | None of the above - read trac for reasoning. | Work issues: | |
Branch: | 7aee739 (Commits, GitHub, GitLab) | Commit: | |
Dependencies: | #17505 | Stopgaps: |
Description
Motivation : some "obvious" transformations, sometimes helpful in routine calculations, cannot be obtained via the current methods. Some (elementary,
- e. high-school- or undergrad-level) exemples : given the declarations :
var("a,b") var("j,p", domain="integer") f,g,X=function("f,g,X")
the following equalities, true under no or mild conditions, cannot be deduced currently :
sum(X(j)+Y(j),j,1,p)==sum(X(j),j,1,p)+sum(Y(j),j,1,p) ## (1) prod(X(j)*Y(j),j,1,p)==prod(X(j),j,1,p)*prod(Y(j),j,1,p) ## (2) integrate(f(x)+g(x),x,a,b)==integrate(f(x),x,a,b)+integrate(g(x),x,a,b) ## (3)
Similarly, if A, B and C are matrices over a suitable ring and of suitable dimensions, the following equalities cannot be straightforwardly obtained.
(A+B).trace()==A.trace()+B.trace() ## (4) (A*B).det()==A.det()*B.det() ## (5)
(Curiously, (f(x)+g(x)).diff(x)
does return
diff(f(x),x)+diff(g(x),x)
(and a way to return to the original
expression does not seem to exist currently)).
The ability to generate the right-hand form from the left-hand form of these various examples is sometimes useful in (low-level) examples. The examples (1) and/or (2) arise naturally when deriving the maximum-likelihood estimators of the mean and variance of a given distribution. The third one is often encountered in elementary calculus exercises.
In all cases, an operator is "distributed" over another one : (1) : symbolic_sum is distributed over addition. (2) : symbolic product is distributed over multiplication. (3) : integration is ditributed over addition. (4) : trace is distributed over (matrix) addition. (5) : determinant is distributed over (matrix) multiplication.
Implementing (1) as an extension of the expand()
method of
Expression is tempting (see #22915). However, there are situations
where this expansion is not useful. So, creating a method for such
situations seems useful.
One should note that such "distributions" are not systematically valid : we have a collection of special cases rather than a general mechanism. So this method shoud either limit itself to a few recognized cases or take keyword argument(s) specifying what should be distributed over what.
Another design choice is to know if these distributions should be recursive or run only on the top level of a given expression (possibly controlled by another keyword argument).
The present ticket aims at implementing this method for sage.symbolic.expression.Expression
, at least in cases (1) to (3) (case (2) needs an implementation of the symbolic products, see #17505). Further suggestions for other classes are welcome...
Change History (37)
comment:1 Changed 6 years ago by
comment:2 Changed 6 years ago by
Branch: | → u/charpent/distribute |
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comment:3 Changed 6 years ago by
Commit: | → c3bcef0564e154e930191471334b7c43e5637bea |
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Status: | new → needs_review |
First implementation :
- Symbolic sum of a sum ==> sum of symbolic sums
- Integral (definite or not) of a sum ==> sum of integrals.
Passes ptestlong
with the same errors as those reported for 8.0.beta4 and 8.0.beta5
==>neeeds_review
New commits:
c3bcef0 | First implementation of distribute() : sums.
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comment:4 Changed 6 years ago by
Status: | needs_review → needs_work |
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Further verifications show that this does not work in all cases.
Back to the old drawing board...
comment:5 Changed 6 years ago by
Commit: | c3bcef0564e154e930191471334b7c43e5637bea → 7f9666a22d0d290f4b3504bc1d4b61a4dcf7c455 |
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Branch pushed to git repo; I updated commit sha1. New commits:
7f9666a | Fixed recursion when non-match at toplevel.
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comment:6 Changed 6 years ago by
Status: | needs_work → needs_review |
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Passes ptestlong
with the same (unrelated) failures as before +one transient timeout :
sage -t --long src/sage/modular/modform/find_generators.py
which passes when run standalone.
==>needs_review
again.
comment:7 Changed 6 years ago by
Dependencies: | → 17505 |
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Status: | needs_review → needs_work |
Planning to implement the multiplicative case allowed by #17505.
comment:8 follow-up: 9 Changed 6 years ago by
Dependencies: | 17505 → #17505 |
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Minor comment: Instead of using map
, you can do, e.g.,
map(lambda t:treat_term(op, t, la), aa) treat_term(op, t, la) for t in aa
(with wrapping it as a list comprehension [treat_term(op, t, la) for t in aa]
when you need a list).
comment:9 Changed 6 years ago by
Replying to tscrim:
Minor comment: Instead of using
map
, you can do, e.g.,map(lambda t:treat_term(op, t, la), aa) treat_term(op, t, la) for t in aa(with wrapping it as a list comprehension
[treat_term(op, t, la) for t in aa]
when you need a list).
Indeed (my Lisp roots (and my age...) are showing).
Addendum - I feel this is cleaner and IIRC, it is faster.
I'll check that. But I'll submit first the "map" version (which works...), and re-submit the "comprehension" version afterwards if it makes a serious difference.
BTW : other enhancements are possible. For example create a local (static) dictionary of distributable operators, whose values are functions processing the corresponding case of distribution (with possible generalizations/factorizations). I didn't feel the four special cases we treat in SR so fare were worth it, but if you have other ideas, you're welcome...
Commit forthcoming. Review request after ptestlong
(sually a couple of hours...).
comment:10 Changed 6 years ago by
Commit: | 7f9666a22d0d290f4b3504bc1d4b61a4dcf7c455 → c67f95735d1f816c0255dad81985a8c98aa49757 |
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Branch pushed to git repo; I updated commit sha1. New commits:
647ff39 | 17505: unevaluated symbolic product
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e4769b5 | 17505: symbolic product
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58119b0 | 17505: fix doctests
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7a56004 | 17505: address reviewer's suggestions
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a018030 | Merge branch 'u/rws/implement_symbolic_product' of trac.sagemath.org:sage into distribute
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c67f957 | Implement distribute() in the multiplicative case.
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comment:11 Changed 6 years ago by
It's about 3x slower to use map
:
sage: %timeit [i for i in range(10000)] 1000 loops, best of 3: 265 µs per loop sage: %timeit map(lambda i: i, range(10000)) 1000 loops, best of 3: 897 µs per loop
Also in Python2, map
returns a list, which takes extra time and memory to create. Whereas for the sum
, you only need a generator object.
I cannot comment so much about the operators as it is a little beyond my expertise.
comment:12 Changed 6 years ago by
This version passes ptestlong
with the same three failure (deemed unrelated).
I'll try Travis' version before marking the better version for review.
New commits:
647ff39 | 17505: unevaluated symbolic product
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e4769b5 | 17505: symbolic product
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58119b0 | 17505: fix doctests
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7a56004 | 17505: address reviewer's suggestions
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a018030 | Merge branch 'u/rws/implement_symbolic_product' of trac.sagemath.org:sage into distribute
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c67f957 | Implement distribute() in the multiplicative case.
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comment:13 Changed 6 years ago by
Commit: | c67f95735d1f816c0255dad81985a8c98aa49757 → 687cc8ea8b0a225d81309bcfffcb3aa948afd31b |
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Branch pushed to git repo; I updated commit sha1. New commits:
687cc8e | Distribute : implement Travis Scrimshaw's suggestion for iterations.
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comment:14 Changed 6 years ago by
Authors: | → Emmanuel Charpentier, Ralf Stephan, Travis Scrimshaw |
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Cc: | tscrim added |
Report Upstream: | N/A → None of the above - read trac for reasoning. |
Status: | needs_work → needs_review |
With Travis' suggestion, passes ptestlong
with the same result as before ==> needs_review
Do you think that this enhancement should be passed to Maxima ? The algorithm seems simple to port in Maxima or Lisp.
comment:15 Changed 6 years ago by
Commit: | 687cc8ea8b0a225d81309bcfffcb3aa948afd31b → 4b6e71b471ac6747defcc0784208baea42f1da20 |
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Branch pushed to git repo; I updated commit sha1. New commits:
d420ec4 | 17505: fix latex, cosmetics
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b784a2c | Merge branch 'u/rws/implement_symbolic_product' of trac.sagemath.org:sage into distribute
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5779423 | 17505: fix doctests
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4b6e71b | Merge branch 'u/rws/implement_symbolic_product' of trac.sagemath.org:sage into distribute
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comment:17 Changed 6 years ago by
In general, it is always better to pass things to upstream. Although for now, we should do things on our side.
Some other small comments:
- There is a typo:
_ Symbolic product of a product ==> product of symbolic products.
self
is not considered as an input.- Small change to your
INPUT:
:- ``recursive`` -- (default: ``True``) the distribution proceeds along the subtrees of the expression
comment:18 follow-up: 21 Changed 6 years ago by
Authors: | Emmanuel Charpentier, Ralf Stephan, Travis Scrimshaw → Emmanuel Charpentier, Ralf Stephan |
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Reviewers: | → Travis Scrimshaw |
comment:19 Changed 6 years ago by
Commit: | 4b6e71b471ac6747defcc0784208baea42f1da20 → 2412f7a387cf0dec3a764a52a8e644d545cef5f8 |
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Branch pushed to git repo; I updated commit sha1. New commits:
2412f7a | Distribute : cosmetics on documentation.
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comment:20 Changed 6 years ago by
Cosmetic (but important) changes to the documentation. Thank you, Travis.
sage -t --long src/sage/symbolic/expression.pyx
passes without failure. Would you mind reviewing it (I probably can't ptestlong
right now...).
comment:21 Changed 6 years ago by
Replying to tscrim:
You are still listed as an author in the docstring (credit where credit is due...).
comment:22 follow-up: 27 Changed 6 years ago by
I shouldn't be because I just did some simple review changes (so please remove me). But thank you. :)
Everything else looks good.
comment:23 Changed 6 years ago by
is the word "indiced" correct or it is "indexed"? (i'm not native english speaker though..)
comment:24 Changed 6 years ago by
Commit: | 2412f7a387cf0dec3a764a52a8e644d545cef5f8 → c28097a513f90c7d4e738d6f97c1036d897b4d62 |
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Branch pushed to git repo; I updated commit sha1. New commits:
c28097a | Distribute : at his request, Travis Crimshaw removed from Author's list.
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comment:26 Changed 6 years ago by
Commit: | c28097a513f90c7d4e738d6f97c1036d897b4d62 → 7aee739cceff13c596c12e93130250f1ea1fae3f |
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Branch pushed to git repo; I updated commit sha1. New commits:
7aee739 | Distribute : one last typo (I hope...).
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comment:27 follow-up: 28 Changed 6 years ago by
RReplying to tscrim:
I shouldn't be because I just did some simple review changes
Your suggestion to do without map() was a good one (and teached me something I tend to oversee : Python is not Lisp...).
(so please remove me).
If you insist...
But thank you. :)
Everything else looks good.
So this last update (including indiced --> indexed) should be reviewed...
New commits:
7aee739 | Distribute : one last typo (I hope...).
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comment:28 follow-up: 29 Changed 6 years ago by
Status: | needs_review → positive_review |
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Replying to charpent:
RReplying to tscrim:
I shouldn't be because I just did some simple review changes
Your suggestion to do without map() was a good one (and teached me something I tend to oversee : Python is not Lisp...).
I am always learning things from my reviewers too.
(so please remove me).
If you insist...
Thank you. I didn't really author code other than give suggestions, so I don't think I should be listed as an author. :)
You will need to add a doctest in the dependency, but you don't have to merge it into this ticket explicitly (because it is a dependency and will be done by Volker in the develop branch).
comment:29 Changed 6 years ago by
Replying to tscrim:
[ Snip ... ]
You will need to add a doctest in the dependency, but you don't have to merge it into this ticket explicitly (because it is a dependency and will be done by Volker in the develop branch).
This should wait Ralf's implementation of the externally-visible product
method and function (currently, we have to either import an internal function or cast to Sage a Maxima contraption...) : that will be cleaner an probably more useful to users.
comment:30 follow-up: 31 Changed 6 years ago by
Interesting. Both branches apply but mine has a hunk that fuses two hunks into one; yours has the first of the two so my hunk cannot be applied. I'll upload a branch where the two are separated.
comment:31 follow-up: 32 Changed 6 years ago by
comment:32 Changed 6 years ago by
Replying to rws:
Replying to rws:
Interesting. Both branches apply but mine has a hunk that fuses two hunks into one; yours has the first of the two so my hunk cannot be applied. I'll upload a branch where the two are separated.
Ah that should have gone to #22989.
Go ahead. Do you need me to do anything ?
comment:33 Changed 6 years ago by
Branch: | u/charpent/distribute → 7aee739cceff13c596c12e93130250f1ea1fae3f |
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Resolution: | → fixed |
Status: | positive_review → closed |
comment:34 follow-up: 35 Changed 6 years ago by
Commit: | 7aee739cceff13c596c12e93130250f1ea1fae3f |
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WARNING
You have used here "apply()" which is not python3-compatible. Please correct this ASAP in another ticket.
Reference: www.diveintopython3.net/porting-code-to-python-3-with-2to3.html
The Python 2 builtin apply() has been removed in Python 3
comment:35 Changed 6 years ago by
Replying to chapoton:
WARNING
You have used here "apply()" which is not python3-compatible. Please correct this ASAP in another ticket.
Will do that, maybe over the coming week-end, but have to think about it I'm not much of a Python coder...).
Reference: www.diveintopython3.net/porting-code-to-python-3-with-2to3.html
Thanks for the suggestion.
The Python 2 builtin apply() has been removed in Python 3
H... right.
comment:36 Changed 6 years ago by
Do you want me to take care of that, and then be a reviewer ? Maybe this will be faster.
Discussion opened onsage-devel