:
Dear Sirs.

Does NumPy provide a simple mechanism to identify relatively prime integers=
, i.e. integers which don't have a common factor other than +1 or -1? For e= xample, in case of this array:
[[1,5,8],
[2,4,8],
[3,3,9]]
I can imagine a function which would return array of common factors along a= xis 0: [1,2,3]. Those triples of numbers along axis 1 with the factor of1 o=
r -1 would be relatively prime integers.

Regards,
Dmitry Popov

Argonne, IL
USA


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=E4=CD=C9=D4=D2=C9=CA,

You may think you explained what you wanted but I do not see what result =
you
expect from your examples.

Your request is a bit too esoteric to be a great candidate for being =
built
into a module like numpy for general purpose se but I can imagine it =
could
be available in modules build on top of numpy.

Is there a reason you cannot solve this mostly outside numpy?

It looks like you could use numpy to select the numbers you want to =
compare,
then call one of many methods you can easily search for to see how to =
use
python to make some list or other data structure for divisors of each =
number
involved and then use standard methods to compare the lists and exact =
common
divisors. If needed, you could then put the results back into your =
original
data structure using numpy albeit the number of matches can vary.

Maybe a better explanation is needed as I cannot see what your latter =
words
about -1 and 1 are about. Perhaps someone else knows.




-----Original Message-----
From: Python-list =
<python-list-bounces+avi.e.gross=3Dgmail.com@python.org> On
Behalf Of Popov, Dmitry Yu via Python-list
Sent: Monday, July 8, 2024 3:10 PM
To: Popov, Dmitry Yu via Python-list <python-list@python.org>
Subject: Relatively prime integers in NumPy

Dear Sirs.

Does NumPy provide a simple mechanism to identify relatively prime =
integers,
i.e. integers which don't have a common factor other than +1 or -1? For example, in case of this array:
[[1,5,8],
[2,4,8],
[3,3,9]]
I can imagine a function which would return array of common factors =
along
axis 0: [1,2,3]. Those triples of numbers along axis 1 with the factor =
of1
or -1 would be relatively prime integers.

Regards,
Dmitry Popov

Argonne, IL
USA

--=20
https://mail.python.org/mailman/listinfo/python-list


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<avi.e.gross@gmail.com> writes:

python to make some list or other data structure for divisors of each number involved

Two numbers a and b are coprime if math.gcd(a,b) == 1, I am pretty sure.
That is true by definition(?) when a and b are both > 0. Experiment
indicates it seems to work even when one or both of a and b are
negative, but I don't have a proof and haven't examined the
implementation. I don't know how gcd is mathematically defined in that situation.

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(posting on-list this time)

On Thu, 11 Jul 2024 at 15:18, Popov, Dmitry Yu via Python-list <python-list@python.org> wrote:

Dear Sirs.

Does NumPy provide a simple mechanism to identify relatively prime integers, i.e. integers which don't have a common factor other than +1 or -1? For example, in case of this array:
[[1,5,8],
[2,4,8],
[3,3,9]]
I can imagine a function which would return array of common factors along axis 0: [1,2,3]. Those triples of numbers along axis 1 with the factor of1 or -1 would be relatively prime integers.

It sounds like you want the gcd (greatest common divisor) of each row.
The math module can do this:

In [1]: a = [[1,5,8],
...: [2,4,8],
...: [3,3,9]]

In [2]: import math

In [3]: [math.gcd(*row) for row in a]
Out[3]: [1, 2, 3]

NumPy can also do it apparently:

In [10]: np.gcd.reduce(np.transpose(a))
Out[10]: array([1, 2, 3])

https://en.wikipedia.org/wiki/Greatest_common_divisor

--
Oscar

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On Thu, 11 Jul 2024 11:35:44 -0700, Paul Rubin wrote:

Two numbers a and b are coprime if math.gcd(a,b) == 1, I am pretty sure.
That is true by definition(?) when a and b are both > 0. Experiment indicates it seems to work even when one or both of a and b are
negative, but I don't have a proof and haven't examined the
implementation. I don't know how gcd is mathematically defined in that situation.

You can derive the answer quite trivially by observing that negative
numbers are smaller (less than, not greater than) positive numbers.

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<avi.e.gross@gmail.com> writes:

make some list or other data structure for divisors of each number
involved and then use standard methods to compare the lists and exact
common divisors.

You don't need to find divisors (factor the numbers) to find the gcd. Factorization can be very slow. Gcd on the other hand is very fast,
using the Euclidean GCD algorithm. You should be able to find info
about this easily. Factorization would be a terrible way to compute
gcd's.

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On 2024-07-08 19:09:45 +0000, Popov, Dmitry Yu via Python-list wrote:

Does NumPy provide a simple mechanism to identify relatively prime
integers, i.e. integers which don't have a common factor other than +1
or -1?

Typing "numpy gcd" into my favourite search engine brings me to https://num= py.org/doc/stable/reference/generated/numpy.gcd.html

hp

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_ | Peter J. Holzer | Story must make more sense than reality.
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| | | hjp@hjp.at | -- Charles Stross, "Creative writing
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--- MBSE BBS v1.0.8.4 (Linux-x86_64)
* Origin: ---:- FTN<->UseNet Gate -:--- (3:633/280.2@fidonet)

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--- MBSE BBS v1.0.8.4 (Linux-x86_64)
* Origin: ---:- FTN<->UseNet Gate -:--- (3:633/280.2@fidonet)

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--- MBSE BBS v1.0.8.4 (Linux-x86_64)
* Origin: ---:- FTN<->UseNet Gate -:--- (3:633/280.2@fidonet)

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--- MBSE BBS v1.0.8.4 (Linux-x86_64)
* Origin: ---:- FTN<->UseNet Gate -:--- (3:633/280.2@fidonet)

Dmitry,

=20

Efficiency of several kinds is hotly debated and sometimes it depends a =
lot on what is done within loops.

=20

Many suggest a mild speed up of some comprehensions over loops but the =
loops are not gone but somewhat hidden and perhaps some aspects are =
faster for having been written in C carefully and not interpreted.

=20

Comprehensions (and there are other versions that generate dictionaries =
and tuples and sets) may also be sped up a bit for other reasons like =
your fairly expensive APPPEND that has to keep finding the end o f a =
growing list and is not done the same way in a comprehension.

=20

If you do a search, you find many opinions including on using functional = programming techniques such as map/reduce. There are also=20

=20

Your particular case is interesting because it just makes all =
combination of three variables. Some languages, like R, have functions =
that do this for you, like expand.grd. Python has many modules, like = itertools that do things including combinations but perhaps not designed =
for your case.=20

=20

Here is a version of your scenario:

=20

import itertools

a =3D range(3)

b =3D range(4)

c =3D range(5)

=20

list(itertools.product(a,b,c))

=20

The result comes as tuples but as you are moving the result into numpy, =
does it matter:

=20

list(itertools.product(a,b,c))

[(0, 0, 0), (0, 0, 1), (0, 0, 2), (0, 0, 3), (0, 0, 4), (0, 1, 0), (0, =
1, 1), (0, 1, 2), (0, 1, 3), (0, 1, 4), (0, 2, 0), (0, 2, 1), (0, 2, 2), =
(0, 2, 3), (0, 2, 4), (0, 3, 0), (0, 3, 1), (0, 3, 2), (0, 3, 3), (0, 3, =
4), (1, 0, 0), (1, 0, 1), (1, 0, 2), (1, 0, 3), (1, 0, 4), (1, 1, 0), =
(1, 1, 1), (1, 1, 2), (1, 1, 3), (1, 1, 4), (1, 2, 0), (1, 2, 1), (1, 2, =
2), (1, 2, 3), (1, 2, 4), (1, 3, 0), (1, 3, 1), (1, 3, 2), (1, 3, 3), =
(1, 3, 4), (2, 0, 0), (2, 0, 1), (2, 0, 2), (2, 0, 3), (2, 0, 4), (2, 1, =
0), (2, 1, 1), (2, 1, 2), (2, 1, 3), (2, 1, 4), (2, 2, 0), (2, 2, 1), =
(2, 2, 2), (2, 2, 3), (2, 2, 4), (2, 3, 0), (2, 3, 1), (2, 3, 2), (2, 3, =
3), (2, 3, 4)]

=20

Or a atd easier to read pretty printed:

=20

import pprint

pprint.pprint(list(itertools.product(a,b,c)))

[(0, 0, 0),

(0, 0, 1),

(0, 0, 2),

(0, 0, 3),

(0, 0, 4),

(0, 1, 0),

(0, 1, 1),

(0, 1, 2),

(0, 1, 3),

(0, 1, 4),

(0, 2, 0),

(0, 2, 1),

(0, 2, 2),

(0, 2, 3),

(0, 2, 4),

(0, 3, 0),

(0, 3, 1),

(0, 3, 2),

(0, 3, 3),

(0, 3, 4),

(1, 0, 0),

(1, 0, 1),

(1, 0, 2),

(1, 0, 3),

(1, 0, 4),

(1, 1, 0),

(1, 1, 1),

(1, 1, 2),

(1, 1, 3),

(1, 1, 4),

(1, 2, 0),

(1, 2, 1),

(1, 2, 2),

(1, 2, 3),

(1, 2, 4),

(1, 3, 0),

(1, 3, 1),

(1, 3, 2),

(1, 3, 3),

(1, 3, 4),

(2, 0, 0),

(2, 0, 1),

(2, 0, 2),

(2, 0, 3),

(2, 0, 4),

(2, 1, 0),

(2, 1, 1),

(2, 1, 2),

(2, 1, 3),

(2, 1, 4),

(2, 2, 0),

(2, 2, 1),

(2, 2, 2),

(2, 2, 3),

(2, 2, 4),

(2, 3, 0),

(2, 3, 1),

(2, 3, 2),

(2, 3, 3),

(2, 3, 4)]

=20

I think that is close enough to what you want but is it faster? You can =
try a benchmarking method on alternatives.

=20

=20

=20

=20

From: Popov, Dmitry Yu <dpopov@anl.gov>=20
Sent: Friday, July 12, 2024 11:10 PM
To: avi.e.gross@gmail.com; 'Popov, Dmitry Yu via Python-list' = <python-list@python.org>; oscar.j.benjamin@gmail.com
Subject: Re: Relatively prime integers in NumPy

=20

Thank you very much. List comprehensions make code much more concise =
indeed. Do list comprehensions also improve the speed of calculations?

_____ =20

From: avi.e.gross@gmail.com <mailto:avi.e.gross@gmail.com> = <avi.e.gross@gmail.com <mailto:avi.e.gross@gmail.com> >
Sent: Friday, July 12, 2024 6:57 PM
To: Popov, Dmitry Yu <dpopov@anl.gov <mailto:dpopov@anl.gov> >; 'Popov, = Dmitry Yu via Python-list' <python-list@python.org = <mailto:python-list@python.org> >; oscar.j.benjamin@gmail.com = <mailto:oscar.j.benjamin@gmail.com> <oscar.j.benjamin@gmail.com = <mailto:oscar.j.benjamin@gmail.com> >
Subject: RE: Relatively prime integers in NumPy=20

=20

Dmitry, I clearly did not understand what you wanted earlier as you had =
not made clear that in your example, you already had progressed to some =
level where you had the data and were now doing a second step. So, I =
hesitate to say much until=20

ZjQcmQRYFpfptBannerStart

This Message Is From an External Sender=20

This message came from outside your organization.=20

=20

ZjQcmQRYFpfptBannerEnd

Dmitry,

=20

I clearly did not understand what you wanted earlier as you had not made = clear that in your example, you already had progressed to some level =
where you had the data and were now doing a second step. So, I hesitate =
to say much until either nobody else addressed the issue (as clearly =
some have) or you explain well enough.

Ditr

I am guessing you have programming experience in other languages and are =
not as =E2=80=9Cpythonic=E2=80=9D as some. The code you show may not be =
quite how others might do it. Some may write mch of your code as a =
single line of python using a list comprehension such as:

=20

hkl_list =3D [ [h, k, l] for SOMETHING in RANGE for SOMETHING2 in =
RANGE2 for SOMETHING3 in RANGE3] =20

=20

Where h, k. l come from the somethings.

=20

Back to the real world.

=20

=20

From: Popov, Dmitry Yu <dpopov@anl.gov <mailto:dpopov@anl.gov> >=20
Sent: Friday, July 12, 2024 1:13 PM
To: avi.e.gross@gmail.com <mailto:avi.e.gross@gmail.com> ; 'Popov, =
Dmitry Yu via Python-list' <python-list@python.org = <mailto:python-list@python.org> >; oscar.j.benjamin@gmail.com = <mailto:oscar.j.benjamin@gmail.com> ; Popov, Dmitry Yu <dpopov@anl.gov = <mailto:dpopov@anl.gov> >
Subject: Re: Relatively prime integers in NumPy

=20

Thank you very much, Oscar.=20

=20

Using the following code looks like a much better solution than my =
current Python code indeed.

np.gcd.reduce(np.transpose(a))=20
or=20
np.gcd.reduce(a,1) =20
=20
The next question is how I can generate ndarray of h,k,l indices. This =
can be easily done from a Python list by using the following code.
=20
import numpy as np
hkl_list=3D[]
for h in range(0, max_h): =E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82for k in range(0, = max_k): =E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2= =80=82=E2=80=82=E2=80=82=E2=80=82for l in range(0, max_l): =E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2= =80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80= =82=E2=80=82hkl_local=3D[] =E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2= =80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80= =82=E2=80=82hkl_local.append(h) =E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2= =80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80= =82=E2=80=82hkl_local.append(k) =E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2= =80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80= =82=E2=80=82hkl_local.append(l) =E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2= =80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80= =82=E2=80=82hkl_list.append(hkl_local)
hkl=3Dnp.array(hkl_list, dtype=3Dnp.int64)
This code will generate a two-dimensional ndarray of h,k,l indices but =
is it possible to make a faster routine with NumPy?=20
=20
Regards,
Dmitry
=20
=20
=20
_____ =20


From: Python-list <python-list-bounces+dpopov=3Danl.gov@python.org = <mailto:python-list-bounces+dpopov=3Danl.gov@python.org> > on behalf of = Popov, Dmitry Yu via Python-list <python-list@python.org = <mailto:python-list@python.org> >
Sent: Thursday, July 11, 2024 2:25 PM
To: avi.e.gross@gmail.com <mailto:avi.e.gross@gmail.com> = <avi.e.gross@gmail.com <mailto:avi.e.gross@gmail.com> >; 'Popov, Dmitry =
Yu via Python-list' <python-list@python.org =
<mailto:python-list@python.org> >
Subject: Re: Relatively prime integers in NumPy=20

=20

Thank you for your interest. My explanation is too concise indeed, =
sorry. So far, I have used Python code with three enclosed 'for' loops =
for this purpose which is pretty time consuming. I'm trying to develop a = NumPy based code to make this=20

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Thank you for your interest. My explanation is too concise indeed, =
sorry. So far, I have used Python code with three enclosed 'for' loops =
for this purpose which is pretty time consuming. I'm trying to develop a = NumPy based code to make this procedure faster. This routine is kind of = 'heart' of the algorithm to index of X-ray Laue diffraction patterns. In =
our group we have to process huge amount of such patterns. They are =
collected at a synchrotron radiation facility. Faster indexation routine = would help a lot.
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This is the code I'm currently using. Any prompts how to implement it in = NumPy would be highly appreciated.
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for h in range(0, max_h): =E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82for k in range(0, = max_k): =E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2= =80=82=E2=80=82=E2=80=82=E2=80=82for l in range(0, max_l): =E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2= =80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80= =82=E2=80=82chvec=3D1 =E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2= =80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80= =82=E2=80=82maxmult=3D2 =E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2= =80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80= =82=E2=80=82if h > = 1:=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82= =E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2= =80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82 =E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2= =80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80= =82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82maxmult=
=3Dh =E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2= =80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80= =82=E2=80=82if k > 1: =E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2= =80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80= =82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82maxmult=
=3Dk =E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2= =80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80= =82=E2=80=82if l > 1: =E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2= =80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80= =82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82maxmult=
=3Dl =E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2= =80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80= =82=E2=80=82if h > 1: =E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2= =80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80= =82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82if =
maxmult > h: =E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2= =80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80= =82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82= =E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82maxmult=3Dh =E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2= =80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80= =82=E2=80=82if k > 1: =E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2= =80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80= =82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82if =
maxmult > k: =E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2= =80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80= =82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82= =E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82maxmult=3Dk =E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2= =80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80= =82=E2=80=82if l > 1: =E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2= =80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80= =82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82if =
maxmult > l: =E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2= =80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80= =82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82= =E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82maxmult=3Dl =E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2= =80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80= =82=E2=80=82maxmult=3Dmaxmult+1 =E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2= =80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80= =82=E2=80=82for innen in range(2, maxmult): =E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2= =80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80= =82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82if h =
in range(0, (max_h+1), innen): =E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2= =80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80= =82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82= =E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82if k in range(0, (max_k+1), = innen): =E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2= =80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80= =82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82= =E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2= =80=82=E2=80=82=E2=80=82if l in range(0, (max_l+1), innen): =E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2= =80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80= =82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82= =E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2= =80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80= =82chvec=3D0 =E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2= =80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80= =82=E2=80=82if chvec=3D=3D1: =E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2= =80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80= =82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82=E2=80=82# Only = relatively prime integers h,k,l pass to this block of the code
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________________________________
From: avi.e.gross@gmail.com <mailto:avi.e.gross@gmail.com> = <avi.e.gross@gmail.com <mailto:avi.e.gross@gmail.com> >
Sent: Thursday, July 11, 2024 1:22 PM
To: Popov, Dmitry Yu <dpopov@anl.gov <mailto:dpopov@anl.gov> >; 'Popov, = Dmitry Yu via Python-list' <python-list@python.org = <mailto:python-list@python.org> >
Subject: RE: Relatively prime integers in NumPy
=20
=D0=94=D0=BC=D0=B8=D1=82=D1=80=D0=B8=D0=B9, You may think you explained =
what you wanted but I do not see what result you expect from your =
examples. Your request is a bit too esoteric to be a great candidate for = being built into a module like numpy for general purpose se but ZjQcmQRYFpfptBannerStart
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=D0=94=D0=BC=D0=B8=D1=82=D1=80=D0=B8=D0=B9,
=20
You may think you explained what you wanted but I do not see what result =
you
expect from your examples.
=20
Your request is a bit too esoteric to be a great candidate for being =
built
into a module like numpy for general purpose se but I can imagine it =
could
be available in modules build on top of numpy.
=20
Is there a reason you cannot solve this mostly outside numpy?
=20
It looks like you could use numpy to select the numbers you want to =
compare,
then call one of many methods you can easily search for to see how to =
use
python to make some list or other data structure for divisors of each =
number
involved and then use standard methods to compare the lists and exact =
common
divisors. If needed, you could then put the results back into your =
original
data structure using numpy albeit the number of matches can vary.
=20
Maybe a better explanation is needed as I cannot see what your latter =
words
about -1 and 1 are about. Perhaps someone else knows.
=20
=20
=20
=20
-----Original Message-----
From: Python-list =
<python-list-bounces+avi.e.gross=3Dgmail.com@python.org = <mailto:python-list-bounces+avi.e.gross=3Dgmail.com@python.org> > On
Behalf Of Popov, Dmitry Yu via Python-list
Sent: Monday, July 8, 2024 3:10 PM
To: Popov, Dmitry Yu via Python-list <python-list@python.org = <mailto:python-list@python.org> >
Subject: Relatively prime integers in NumPy
=20
Dear Sirs.
=20
Does NumPy provide a simple mechanism to identify relatively prime =
integers,
i.e. integers which don't have a common factor other than +1 or -1? For example, in case of this array:
[[1,5,8],
[2,4,8],
[3,3,9]]
I can imagine a function which would return array of common factors =
along
axis 0: [1,2,3]. Those triples of numbers along axis 1 with the factor =
of1
or -1 would be relatively prime integers.
=20
Regards,
Dmitry Popov
=20
Argonne, IL
USA
=20
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