Opened 10 years ago
Last modified 9 years ago
#12737 closed enhancement
Remove simplify_radical() from simplify_full() — at Version 25
Reported by: | mjo | Owned by: | mjo |
---|---|---|---|
Priority: | major | Milestone: | sage-5.12 |
Component: | symbolics | Keywords: | |
Cc: | jvkersch, navigium | Merged in: | |
Authors: | Michael Orlitzky | Reviewers: | Karl-Dieter Crisman, Beni Keller |
Report Upstream: | N/A | Work issues: | |
Branch: | Commit: | ||
Dependencies: | Stopgaps: |
Description (last modified by )
There are a number of tickets open due to the use of simplify_radical()
in simplify_full()
.
Removing it would fix at least,
- Ask Sage 767
- #3520 - inconsistency in simplify_radical
- #11934 - Symbolic simplification error
- #12322 - invalid simplification of complex logarithm
- Ask Sage 1983
And maybe more. Here are some related tickets.
- #11912 is related, though about
simplify_radical
specifically. - #11668 -
abs(a+b)^2 == (a+b)^2
is now fixed by #12780 - #14305 and #14630 are tangentially related
Apply sage-trac_12737-rebased.patch and trac_12737-de.patch
Change History (29)
Changed 10 years ago by
comment:1 Changed 10 years ago by
- Status changed from new to needs_review
comment:2 follow-up: ↓ 3 Changed 10 years ago by
It's not entirely clear to me which simplifications are "safe" and which are not. Simplifying x^2/x
to x
is also not "safe" in the sense that equality does not hold for x=0
. In many computer algebra systems, acceptable simplifications are not "safe" in this respect. By including a default unsafe=False
I'm afraid you'll be raising expectations to a level that Sage does not attain (yet?).
comment:3 in reply to: ↑ 2 ; follow-up: ↓ 4 Changed 10 years ago by
Replying to nbruin:
It's not entirely clear to me which simplifications are "safe" and which are not. Simplifying
x^2/x
tox
is also not "safe" in the sense that equality does not hold forx=0
. In many computer algebra systems, acceptable simplifications are not "safe" in this respect. By including a defaultunsafe=False
I'm afraid you'll be raising expectations to a level that Sage does not attain (yet?).
It's completely heuristic: the four I chose nobody seems to have a problem with. simplify_radical
, on the other hand, wreaks havoc on trivial functions and has been the cause of numerous bug reports and mailing list discussions.
In simplify
, after #12650, I say that a safe simplification is one "for which we are reasonably sure that the input will be considered equivalent to the output." That's probably the best we can do for now, and I'm reasonably sure that most people would consider x^2/x
equivalent to x
.
As it stands, I think full_simplify
sounds safe so people will assume that anyway. This fix, while not perfect, at least improves things.
comment:4 in reply to: ↑ 3 ; follow-up: ↓ 5 Changed 10 years ago by
It's not entirely clear to me which simplifications are "safe" and which are not. Simplifying
x^2/x
tox
is also not "safe" in the sense that equality does not hold forx=0
. In many computer algebra systems, acceptable simplifications are not "safe" in this respect. By including a defaultunsafe=False
I'm afraid you'll be raising expectations to a level that Sage does not attain (yet?).It's completely heuristic: the four I chose nobody seems to have a problem with.
Only in that we couldn't find Trac tickets about them.
simplify_radical
, on the other hand, wreaks havoc on trivial functions and has been the cause of numerous bug reports and mailing list discussions.In
simplify
, after #12650, I say that a safe simplification is one "for which we are reasonably sure that the input will be considered equivalent to the output." That's probably the best we can do for now, and I'm reasonably sure that most people would considerx^2/x
equivalent tox
.
I'm reasonably sure that no mathematician would consider them equivalent unless you add "almost everywhere". Simplification simplifies, hence makes it not actually the same (at least potentially). This shouldn't be controversial.
As it stands, I think
full_simplify
sounds safe so people will assume that anyway. This fix, while not perfect, at least improves things.
Well, everything sounds safe unless you put in the word "unsafe".
I'm pretty confused as to the relation of this to #12650. See my comments there.
I'm sympathetic to doing something about radcan
, but simplification is simplification, not identity.
Doesn't it make more sense to either document fully what can go wrong with simplify_full
, or to add a flag simplify_radicals
or something? I think that changing behavior in this case is probably the best compromise, but probably unsafe
is sending the wrong message. There isn't anything unsafe about radcan
, it's just a different point of view than ours - symbolic expressions versus functions. Spend some time on the Maxima list :)
comment:5 in reply to: ↑ 4 Changed 10 years ago by
Replying to kcrisman:
It's not entirely clear to me which simplifications are "safe" and which are not. Simplifying
x^2/x
tox
is also not "safe" in the sense that equality does not hold forx=0
. In many computer algebra systems, acceptable simplifications are not "safe" in this respect. By including a defaultunsafe=False
I'm afraid you'll be raising expectations to a level that Sage does not attain (yet?).It's completely heuristic: the four I chose nobody seems to have a problem with.
Only in that we couldn't find Trac tickets about them.
simplify_radical
, on the other hand, wreaks havoc on trivial functions and has been the cause of numerous bug reports and mailing list discussions.In
simplify
, after #12650, I say that a safe simplification is one "for which we are reasonably sure that the input will be considered equivalent to the output." That's probably the best we can do for now, and I'm reasonably sure that most people would considerx^2/x
equivalent tox
.I'm reasonably sure that no mathematician would consider them equivalent unless you add "almost everywhere". Simplification simplifies, hence makes it not actually the same (at least potentially). This shouldn't be controversial.
Before our discussion on another one of these tickets, I had assumed it was not controversial that simplification had to return an equivalent expression. So it is at least a little controversial.
As it stands, I think
full_simplify
sounds safe so people will assume that anyway. This fix, while not perfect, at least improves things.Well, everything sounds safe unless you put in the word "unsafe".
I'm pretty confused as to the relation of this to #12650. See my comments there.
I'm sympathetic to doing something about
radcan
, but simplification is simplification, not identity.Doesn't it make more sense to either document fully what can go wrong with
simplify_full
, or to add a flagsimplify_radicals
or something? I think that changing behavior in this case is probably the best compromise, but probablyunsafe
is sending the wrong message. There isn't anything unsafe aboutradcan
, it's just a different point of view than ours - symbolic expressions versus functions. Spend some time on the Maxima list :)
All expressions in sage are callable like functions, so if you have both radicals and a variable in an expression, simplify_radical()
is unsafe. I.e. you're probably gonna get the wrong answer. I think marking it as unsafe is more likely to catch someone's attention than asking him to read the documentation. I almost certainly used full_simplify()
for years without doing so, since I thought I knew what it was doing and had used similar functions in e.g. Mathematica. I think the problem is that it's called "simplification," not that it exists.
Either way, f.full_simplify(simplify_radicals=True)
is not much better than f.full_simplify().simplify_radical()
... the keyword argument is the easy way out, but I feel like it should control more than one method call if we do it. And if we remove the unsafe simplifications from full_simplify()
, that seems to make simplify()
redundant, too. That's the dual situation to what we'd have after #12650, but at least we could add more stuff to full_simplify()
in the future to change that.
comment:6 Changed 10 years ago by
- Status changed from needs_review to needs_info
There is not consensus that this is even a good idea, so I'll leave it alone until we can discuss it further.
comment:7 Changed 10 years ago by
- Dependencies #12650 deleted
- Description modified (diff)
- Status changed from needs_info to needs_review
- Summary changed from Add an `unsafe` argument to Expression.simplify_full() to Remove simplify_radical() from simplify_full()
This should be a more straight-forward proposal. I just removed simplify_radical()
from simplify_full()
and fixed a few doctests (details in the commit message).
One of the doctest fixes is duplicated in #12780; the doctest is wrong (missing assumptions) but we're masking that fact at the moment.
comment:8 Changed 10 years ago by
- Dependencies set to #12845
I moved the common doctest to #12845 and removed it from this patch.
comment:9 Changed 10 years ago by
- Description modified (diff)
Lest it seem weird that I'm adding to the list in the description, let it be known that I haven't necessarily changed my mind here, but fairness dictates that I point this additional example out!
comment:10 Changed 9 years ago by
- Description modified (diff)
comment:11 Changed 9 years ago by
- Description modified (diff)
comment:12 Changed 9 years ago by
- Description modified (diff)
comment:13 follow-up: ↓ 14 Changed 9 years ago by
Burcin agrees here at SD that this should be done. I concur with him that probably we should solve #11912 (perhaps even deprecating the simplify name?) at the same time. What do you think?
comment:14 in reply to: ↑ 13 ; follow-up: ↓ 15 Changed 9 years ago by
Replying to kcrisman:
Burcin agrees here at SD that this should be done. I concur with him that probably we should solve #11912 (perhaps even deprecating the simplify name?) at the same time. What do you think?
Once it's gone from simplify_full(), personally I would deprecate simplify_radical()
and rename it to radcan()
. It's probably impossible to clearly explain what radcan does, but we can try to fix the docs and add many more examples.
comment:15 in reply to: ↑ 14 Changed 9 years ago by
Burcin agrees here at SD that this should be done. I concur with him that probably we should solve #11912 (perhaps even deprecating the simplify name?) at the same time. What do you think?
Once it's gone from simplify_full(), personally I would deprecate
simplify_radical()
and rename it toradcan()
. It's probably impossible to clearly explain what radcan does, but we can try to fix the docs and add many more examples.
Do you mind putting that on #11912, as the architect of this set of changes?
comment:16 follow-up: ↓ 20 Changed 9 years ago by
Here's another example of unexpected behavior introduced by using simplify_radical as a part of simplify_full: https://groups.google.com/forum/?fromgroups=#!topic/sage-devel/Pq9hyOTzrL8.
comment:17 Changed 9 years ago by
- Cc jvkersch added
comment:18 Changed 9 years ago by
I think there's consensus to remove it now, but this will need rebasing. There are also a ton of related tickets which will all need to be coordinated so that the patches apply cleanly.
As soon as I get time I'll start by updating this patch.
comment:19 Changed 9 years ago by
I just put up a new patch that should apply cleanly. There are some failing tests in doc/de/thematische_anleitungen/sage_gymnasium.rst, but I don't know what the surrounding context is and so I'm not sure how best to fix them. Will need some attention from the Germans.
comment:20 in reply to: ↑ 16 ; follow-up: ↓ 21 Changed 9 years ago by
Here's another example of unexpected behavior introduced by using simplify_radical as a part of simplify_full: https://groups.google.com/forum/?fromgroups=#!topic/sage-devel/Pq9hyOTzrL8.
In that same thread: Robert D. of Maxima reports
> sage: u, v = var('u, v', domain='real') > sage: sqrt(-1/(u^2+v^2-1)).simplify_radical() # This will hang This is a bug in Maxima: (%i2) radcan (sqrt (-1 / (u^2 + v^2 - 1))), domain=complex; It waits apparently forever here -- but it is actually looping over *ALPHA (not sure why) which is a large prime number (8388593). (%i3) :lisp (setq *alpha 17) 17 (%i3) radcan(sqrt(-1/(u^2+v^2-1))), domain=complex; (%o3) 1/sqrt(-v^2-u^2+1) I've reported this as bug # 2605.
E.g. Maxima 2605. We may want to open a ticket for this or something, maybe along with #11912.
I'll take a look at the failures in the new German tutorial at some point today, it's probably not a big deal.
comment:21 in reply to: ↑ 20 Changed 9 years ago by
- Cc navigium added
- Dependencies #12845 deleted
- Reviewers set to Karl-Dieter Crisman
- Status changed from needs_review to needs_work
I'll take a look at the failures in the new German tutorial at some point today, it's probably not a big deal.
sage -t doc/de/thematische_anleitungen/sage_gymnasium.rst ********************************************************************** File "doc/de/thematische_anleitungen/sage_gymnasium.rst", line 397, in doc.de.thematische_anleitungen.sage_gymnasium Failed example: (log(8)/log(2)).simplify_full() Expected: 3 Got: log(8)/log(2) ********************************************************************** File "doc/de/thematische_anleitungen/sage_gymnasium.rst", line 703, in doc.de.thematische_anleitungen.sage_gymnasium Failed example: log(10^5).simplify_full() Expected: 5*log(5) + 5*log(2) Got: log(100000) **********************************************************************
Well, unfortunately the context is that the authors of the tutorial really really like using just one simplification command. In particular, they advertise simplify_full
as providing log addition rules "for free". Which I don't really see as "simplification in the latter example! (Which is some of what you've been saying earlier.) However, it does mean it would be interesting to see whether it might be worth adding canonicalize_exp
or canonicalize_log
at #11912 as aliases...
Anyway, I can fix this, but I don't have time right now, because I would have to think about how best to preserve the authors' intentions. I assume it would be annoying to all of a sudden point out that there are multiple "simplification" options. I've cc:ed the author of #14550 to see if he has any suggestions.
@navigium - man könnte behaupten, dass log(10^5) = > 5*log(5) + 5*log(2)
nicht eine Vereinfachung, sondern eine ... "Gezetzeseinsetzung" ist. Im jeden Fall sieht es nicht einfacher aus! Dennoch wollen wir die Einleitung nicht einfach so ohne weiteres zerlegen. Vorausgesetzt, dass simplify_radical
von simplify_full
verschwindet, wie wäre es am Besten (d. Hinsicht nach) simplify_radical
im Gymnasialkontext zu erwähnen?
comment:22 follow-up: ↓ 23 Changed 9 years ago by
I'm at the moment unsure how to fix this. I guess the first example that fails could just be removed since it can be numerically evaluated. But I think the second example should remain in the tutorial and should be fixed. At the moment I don't have the time to look into it. I won't be around till mid August.
@kcrisman Ich habe es vor allem als Vereinfachung bezeichnet, da es die notwendige Umformung ist, welche man für das Lösen von Exponentialgleichungen benötigt. Aus diesem Grund halte ich es auch für wichtig, dass man erwähnt, wie man eine solche Umformung machen kann.
Man könnte es aber natürlich umbennen. Ich würde es als "Zerlegung durch Benutzen der Logarithmengesetze" oder ähnlich nennen.
Natürlich wäre es schon, wenn man simplify_radical nicht separat aufführen muss, um die Sache einfach zu halten. Wenn es aber aus simplify_full fliegt, müsste man es wohl erwähnen.
comment:23 in reply to: ↑ 22 Changed 9 years ago by
@kcrisman Ich habe es vor allem als Vereinfachung bezeichnet, da es die notwendige Umformung ist, welche man für das Lösen von Exponentialgleichungen benötigt. Aus diesem Grund halte ich es auch für wichtig, dass man erwähnt, wie man eine solche Umformung machen kann.
Man könnte es aber natürlich umbennen. Ich würde es als "Zerlegung durch Benutzen der Logarithmengesetze" oder ähnlich nennen.
Eigentlich genügt das!
Natürlich wäre es schon, wenn man simplify_radical nicht separat aufführen muss, um die Sache einfach zu halten. Wenn es aber aus simplify_full fliegt, müsste man es wohl erwähnen.
Tja...
Michael, I'll try to keep this on the front burner for finding a good fix - navigium has a good phrase we can use, and I don't really see any other way to fix this, since it does happen to be very convenient that we can use radcan in some cases to do log expansion.
comment:24 Changed 9 years ago by
It is regrettable that there's no other way to get log simplification of things like log(8)/log(2)
, but simplify_radical()
will do the same thing even when the argument to the log function is a complex function of, say, z
.
It'd be nice to have something that worked for constants at least, but avoided e.g. #12322.
comment:25 Changed 9 years ago by
- Description modified (diff)
- Reviewers changed from Karl-Dieter Crisman to Karl-Dieter Crisman, Beni Keller
- Status changed from needs_work to needs_review
I'd appreciate a quick review from navigium as to whether my German syntax is 100% correct, but this should take care of it, and conforms to what he suggested as a solution.
Patchbot, apply sage-trac_12737-rebased.patch and trac_12737-de.patch
Add the flag and update doctests.