Closed kcrisman closed 11 years ago
as prime_powers(m)
works, an easy workaround is to re-implement prime_powers(m,n)
as the difference of
prime_powers(n)
and prime_powers(m-1)
.
Description changed:
---
+++
@@ -28,5 +28,8 @@
IndexError: list index out of range
+Yeah, this seems problematic. The code in question is old, too, so perhaps there is a more efficient way to do it in the meantime...
-Yeah, this seems problematic. The code in question is old, too, so perhaps there is a more efficient way to do it in the meantime... +Apply + +1. [attachment: 13516_primepowers.patch]
I found the code to be riddled with errors, so I decided to completely rework it. Also, I have qualms about calling 1 a prime power, but did so because the old function did. If you think its fine to drop this, let me know.
Thanks for your work - hopefully someone will review it soon. You can put your real name in the author area.
Also, I have qualms about calling 1 a prime power, but did so because the old function did. If you think its fine to drop this, let me know.
Well, John Horton Conway does call -1 a prime, in which case every nonzero integer (not just positive) is a unique product of prime powers - not a unique product of primes, note, nor of the exponents, but of the prime powers themselves (I can't find a link for this right now, my apologies) in which case positives get the power 1 and and negatives -1. I think that's right... anyway, maybe they were thinking this?
I would prefer to leave 1 as a prime power because it is listed in Sloane's tables as a prime power: http://oeis.org/A000961
There he says "Since 1 = p^0 does not have a well defined prime base p, it is sometimes not regarded as a prime power.", which might be where your misgivings come from.
If by "prime power" one thinks of "power of a prime", the only question is in what set are we considering the prime powers. If we take the natural numbers, then the number 1 is definitely a power of a prime.
If by "prime power" one thinks "power of a specific canonical prime", then 1 is not such a thing.
In this case, the best thing to do is stick with what is there (to avoid introducing bugs in other people's code!) and clearly document/define what a prime power is in Sage.
Author: Kevin Halasz
I just updated the docstring to make the fact that 1 is a prime power explicit.
Could you speed this up slightly by making s = stop.sqrt()
or something so that it's not computed for each prime. In fact, even that is a more expensive comparison each time because stop.sqrt()
is likely a symbolic element, so maybe even stop.sqrt().n()
would be appropriate... Also, once p >stop.sqrt()
, presumably all remaining p
are beyond it as well, so maybe there could be some speedup there too. Just some ideas.
I've changed the patch so that s=stop.sqrt() is calculated outside of the for loop. After some tests, I saw that this was faster than setting s=stop.sqrt().n().
Also, note that when p>s, the content of that if loop is a break command, meaning that the entire for loop ends. Thus, once a single p>s, no more p values are tried.
The comment on line 708 in sage/rings/arith.py
needs to be fixed, too - it talks about primes rather than prime powers.
I also think that the following:
sage: prime_powers(10,7)
761 Traceback (most recent call last):
762 ...
763 ValueError: the first input must be less than the second input, however, 10 > 7
i.e. the corresponding implementation logic is not right, in the sense that it should just return empty lists rather than throwing exceptions. And negative start
should be allowed too (cf. the semantics of range()
).
Then, in the following fragment
783 output = prime_range(start,stop)
784 if start == 1:
785 output.append(1)
786
787 s = stop.sqrt()
788 for p in prime_range(stop):
prime_range()
, which is not cheap, is basically called two times instead of one.
One can do with one call to prime_range(stop)
just fine.
Dimpase, I've addressed all of your suggestions. Let me know what you think of these changes/if you have other suggestions.
Description changed:
---
+++
@@ -32,4 +32,4 @@
**Apply**
-1. [attachment: 13516_primepowers.patch]
+1. [attachment: https://github.com/sagemath/sage/files/ticket13516/13516_primepowers.patch.gz]
Description changed:
---
+++
@@ -32,4 +32,4 @@
**Apply**
-1. [attachment: https://github.com/sagemath/sage/files/ticket13516/13516_primepowers.patch.gz]
+1. [patch](https://github.com/sagemath/sage/files/ticket13516/13516_primepowers.patch.gz)
You always should coerce stop
into Integer. Indeed, currently one gets:
sage: prime_powers(1,int(9))
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
/usr/local/src/sage/sage-5.4.rc0/devel/sage-main/<ipython console> in <module>()
/usr/local/src/sage/sage-5.4.rc0/local/lib/python2.7/site-packages/sage/rings/arith.pyc in prime_powers(start, stop)
761 from sage.rings.integer import is_Integer
762 if not (is_Integer(start) and (is_Integer(stop) or stop == None)):
--> 763 raise TypeError, "both inputs must be integers, but your inputs were %s and %s"%(start,stop)
764
765 # deal with the case in which only one input is given
TypeError: both inputs must be integers, but your inputs were 1 and 9
This is because taking sqrt(int(9))
does not work too well in Sage...
Second issue: the comment # check that all inputs are positive integers
on line 760 is misleading!
In the documentation please write `start`, `stop`
with double backticks. The single backticks will make them be formatted as latex, which is not what is desired.
Dimpase,
I'm not sure if I understand what you're suggesting I do. Should I replace the check that the inputs are Integers with a coercion of the inputs into Integers? Once I coerce the elements the check is redundant, as either it raises an error in and of itself (say, if it was passed a string it will raise a TypeError), or will fix the problem.
Replying to @sagetrac-khalasz:
Dimpase,
I'm not sure if I understand what you're suggesting I do. Should I replace the check that the inputs are Integers with a coercion of the inputs into Integers? Once I coerce the elements the check is redundant, as either it raises an error in and of itself (say, if it was passed a string it will raise a TypeError), or will fix the problem.
I think I would prefer the input of type int
to be coerced into Integer
, and throw an error if it's neither int
nor Integer
. The reason is that one could potentially try to apply this function to different from ZZ
rings, with strange results, if one just blindly coerces stuff into Integer
.
I think you can write it like this
from sage.rings.integer import Integer
if not isinstance(start, (int, Integer)):
raise TypeError("start must be an integer")
if stop is not None and not isinstance(stop, (int, Integer)):
raise TypeError("stop must be an integer")
I've made the changes. Let me know what you think!
Replying to @sagetrac-khalasz:
I've made the changes. Let me know what you think!
I think there is a bug in the code, coming from the fact that
sage: Integer(None)==None
False
You also should have test cases (doctests) for all the different combinations of start/stop, and test them, too. You know that you can run Sage so that it tests doctests in a particular file, right?
E.g. the bug above would have been caught by the proper doctest.
Also, for some reason you removed the test sage: v = prime_powers(10)
, but it was there for good reason.
I forgot to rebuild sage before doctesting before posting this patch. Sorry for putting it up with such a stupid mistake. I've fixed it, and added back the test sage: v = prime_powers(1)
.
I think I've covered all the possible basic scenarios in the doctests, in both the EXAMPLES and the TESTS, do you disagree?
Some more nitpicks. :)
==
or !=
when comparing against None
. See PEP 8.start
and stop
, then describe the default value too. - ``start`` - an integer. If two inputs are given, ....
- ``stop`` - an integer (default: ``None``). An upper bound for ....
sage: type(v[0]) # trac #922
TypeError
in python 3 style? Every small bit will help in the migration to python 3 later. raise TypeError("start must be an integer, %s is not an integer"%start)
raise TypeError("stop must be an integer, %s is not an integer"%stop)
Sorry for the delay. I've addressed the small comments.
Thanks a lot for addressing my concerns. I have made some changes to your patch.
prime_powers(-1, positive integer)
works.TypeError
.The changes can be seen in attachment: 13516_reviewer.patch. All these changes have been merged with your patch and the new patch is now attachment: 13516_primepowers.2.patch.
Aside from the above corrections, the changes introduced by your patch has positive review from my side. If you think my changes are ok, feel free to change the ticket to positive review.
Reviewer: Punarbasu Purkayastha
Description changed:
---
+++
@@ -30,6 +30,4 @@
Yeah, this seems problematic. The code in question is old, too, so perhaps there is a more efficient way to do it in the meantime...
-1. patch
+Apply to devel/sage
: attachment: 13516_reviewer.2.patch.
Changed reviewer from Punarbasu Purkayastha to Dmitrii Pasechnik, Punarbasu Purkayastha
Argggh! Uploaded the wrong patch earlier X(
Patchbot: apply 13516_primepowers.2.patch
Description changed:
---
+++
@@ -30,4 +30,4 @@
Yeah, this seems problematic. The code in question is old, too, so perhaps there is a more efficient way to do it in the meantime...
-Apply to devel/sage
: attachment: 13516_reviewer.2.patch.
+Apply to devel/sage
: attachment: 13516_primepowers.2.patch.
Looks good to me. Thanks for your help/review!
Nice work. Below, things almost certainly not worth addressing now that ppurka and khalasz have worked so hard to get this in, but I'll still point them out if ppurka is really bored and wants to fix them:
# inserted to prevent an error from occuring
:trac:
thingie@kcrisman - fixed. Thanks. :)
Ah, I knew I shouldn't have asked about this, because now of course I have to keep following up... you can't do
sage: type(v[0]) # :trac:`922`
and have it formatted, because it's in a literal block, it would have to be
TESTS:
Check :trac:`922`is fixed::
sage: v = prime_powers(10)
sage: type(v[0])
<type 'sage.rings.integer.Integer'>
or something like that. But I don't know if that's worth it...
apply only this to devel/sage
Attachment: 13516_primepowers.2.patch.gz
Yes, you are right. I have reverted the last change.
Yes, you are right. I have reverted the last change.
Sorry to be so picky, anyway nice work by both of you!
Changed reviewer from Dmitrii Pasechnik, Punarbasu Purkayastha to Dmitrii Pasechnik, Punarbasu Purkayastha, Karl-Dieter Crisman
Sorry to be so picky, anyway nice work by both of you!
No problem. But you do deserve to be in the reviewers list! ;)
Merged: sage-5.6.beta1
See this sage-support thread.
Yeah, this seems problematic. The code in question is old, too, so perhaps there is a more efficient way to do it in the meantime...
Apply to
devel/sage
: attachment: 13516_primepowers.2.patch.CC: @williamstein
Component: number theory
Author: Kevin Halasz
Reviewer: Dmitrii Pasechnik, Punarbasu Purkayastha, Karl-Dieter Crisman
Merged: sage-5.6.beta1
Issue created by migration from https://trac.sagemath.org/ticket/13516