• Relatively prime integers in NumPy

    From Popov, Dmitry Yu@21:1/5 to All on Mon Jul 8 19:09:45 2024
    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

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  • From Paul Rubin@21:1/5 to [email protected] on Thu Jul 11 11:35:44 2024
    <[email protected]> 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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  • From Lawrence D'Oliveiro@21:1/5 to Paul Rubin on Thu Jul 11 21:43:47 2024
    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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  • From Paul Rubin@21:1/5 to [email protected] on Thu Jul 11 18:51:57 2024
    <[email protected]> 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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  • From Peter J. Holzer@21:1/5 to Dmitry Yu via Python-list on Fri Jul 12 11:14:11 2024
    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://numpy.org/doc/stable/reference/generated/numpy.gcd.html

    hp

    --
    _ | Peter J. Holzer | Story must make more sense than reality.
    |_|_) | |
    | | | [email protected] | -- Charles Stross, "Creative writing
    __/ | http://www.hjp.at/ | challenge!"

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  • From Popov, Dmitry Yu@21:1/5 to All on Thu Jul 11 19:25:37 2024
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  • From Popov, Dmitry Yu@21:1/5 to All on Fri Jul 12 17:12:59 2024
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    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Popov, Dmitry Yu@21:1/5 to All on Sat Jul 13 03:10:12 2024
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    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)