Is there a term for 'complementary factor'?












4












$begingroup$


Please forgive this incredibly lame question, but if I have factor $n$ of $x,$ and I find its complementary factor $y= frac xn$, does that complementary factor $y$ have a specific name?



I haven't been able to find one.



EDIT: As I mention in a comment below, I'm not trying to understand the concept; I'm looking for a piece of jargon that will make it easier to write a terse but descriptive function identifier.



EDIT 2: As @timtfj indicates in their comment directly beneath this question, I'm talking about a symmetrical term, not a unidirectional term such as "quotient". It seems (again based on comments) that "complementary factor" is acceptable, but I'm leery of writing my own answer to this question.






terminology arithmetic factoring







share|cite|improve this question











$endgroup$








  • 4




    $begingroup$
    I don’t think we have a name for this, but the terminology you suggest is fine
    $endgroup$
    – Randall
    Jan 16 at 19:24






  • 3




    $begingroup$
    Complementary factor seems clear and accurate—in particular it's nicely symmetrical (if $xy=n$ then $x$ and $y$ form a complementary pair of factors of $n$, and both have the same status).
    $endgroup$
    – timtfj
    Jan 16 at 19:54








  • 1




    $begingroup$
    @timtfj Oh oh, okay this is very helpful. Thank you very much!
    $endgroup$
    – crisis.sheep
    Jan 16 at 20:03






  • 1




    $begingroup$
    You should feel free to post your own answer. As with the other commenters, I think your terminology is fine. The only advice I have regarding your naming convention is to perhaps avoid cofactor as it might make one think of matrices (though Wikipedia does have an entry with precisely your desired definition).
    $endgroup$
    – Clayton
    Jan 16 at 22:51






  • 1




    $begingroup$
    @Clayton Much obliged for this! I actually considered cofactor for the reason you mention, but it's interesting that Wikipedia defines it as such. In fact it seems that "co-", as a prefix, is simply shorthand for "complement" in this sense. But I think I shall follow your advice and stick with the expanded "complementary factor" for the sake of resolving a potential ambiguity. Thanks again :)
    $endgroup$
    – crisis.sheep
    Jan 17 at 7:58
















4












$begingroup$


Please forgive this incredibly lame question, but if I have factor $n$ of $x,$ and I find its complementary factor $y= frac xn$, does that complementary factor $y$ have a specific name?



I haven't been able to find one.



EDIT: As I mention in a comment below, I'm not trying to understand the concept; I'm looking for a piece of jargon that will make it easier to write a terse but descriptive function identifier.



EDIT 2: As @timtfj indicates in their comment directly beneath this question, I'm talking about a symmetrical term, not a unidirectional term such as "quotient". It seems (again based on comments) that "complementary factor" is acceptable, but I'm leery of writing my own answer to this question.






terminology arithmetic factoring







share|cite|improve this question











$endgroup$








  • 4




    $begingroup$
    I don’t think we have a name for this, but the terminology you suggest is fine
    $endgroup$
    – Randall
    Jan 16 at 19:24






  • 3




    $begingroup$
    Complementary factor seems clear and accurate—in particular it's nicely symmetrical (if $xy=n$ then $x$ and $y$ form a complementary pair of factors of $n$, and both have the same status).
    $endgroup$
    – timtfj
    Jan 16 at 19:54








  • 1




    $begingroup$
    @timtfj Oh oh, okay this is very helpful. Thank you very much!
    $endgroup$
    – crisis.sheep
    Jan 16 at 20:03






  • 1




    $begingroup$
    You should feel free to post your own answer. As with the other commenters, I think your terminology is fine. The only advice I have regarding your naming convention is to perhaps avoid cofactor as it might make one think of matrices (though Wikipedia does have an entry with precisely your desired definition).
    $endgroup$
    – Clayton
    Jan 16 at 22:51






  • 1




    $begingroup$
    @Clayton Much obliged for this! I actually considered cofactor for the reason you mention, but it's interesting that Wikipedia defines it as such. In fact it seems that "co-", as a prefix, is simply shorthand for "complement" in this sense. But I think I shall follow your advice and stick with the expanded "complementary factor" for the sake of resolving a potential ambiguity. Thanks again :)
    $endgroup$
    – crisis.sheep
    Jan 17 at 7:58














4












4








4





$begingroup$


Please forgive this incredibly lame question, but if I have factor $n$ of $x,$ and I find its complementary factor $y= frac xn$, does that complementary factor $y$ have a specific name?



I haven't been able to find one.



EDIT: As I mention in a comment below, I'm not trying to understand the concept; I'm looking for a piece of jargon that will make it easier to write a terse but descriptive function identifier.



EDIT 2: As @timtfj indicates in their comment directly beneath this question, I'm talking about a symmetrical term, not a unidirectional term such as "quotient". It seems (again based on comments) that "complementary factor" is acceptable, but I'm leery of writing my own answer to this question.






terminology arithmetic factoring







share|cite|improve this question











$endgroup$




Please forgive this incredibly lame question, but if I have factor $n$ of $x,$ and I find its complementary factor $y= frac xn$, does that complementary factor $y$ have a specific name?



I haven't been able to find one.



EDIT: As I mention in a comment below, I'm not trying to understand the concept; I'm looking for a piece of jargon that will make it easier to write a terse but descriptive function identifier.



EDIT 2: As @timtfj indicates in their comment directly beneath this question, I'm talking about a symmetrical term, not a unidirectional term such as "quotient". It seems (again based on comments) that "complementary factor" is acceptable, but I'm leery of writing my own answer to this question.






terminology arithmetic factoring




terminology arithmetic factoring






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Jan 16 at 20:19







crisis.sheep

















asked Jan 16 at 18:52









crisis.sheepcrisis.sheep

16110




16110








  • 4




    $begingroup$
    I don’t think we have a name for this, but the terminology you suggest is fine
    $endgroup$
    – Randall
    Jan 16 at 19:24






  • 3




    $begingroup$
    Complementary factor seems clear and accurate—in particular it's nicely symmetrical (if $xy=n$ then $x$ and $y$ form a complementary pair of factors of $n$, and both have the same status).
    $endgroup$
    – timtfj
    Jan 16 at 19:54








  • 1




    $begingroup$
    @timtfj Oh oh, okay this is very helpful. Thank you very much!
    $endgroup$
    – crisis.sheep
    Jan 16 at 20:03






  • 1




    $begingroup$
    You should feel free to post your own answer. As with the other commenters, I think your terminology is fine. The only advice I have regarding your naming convention is to perhaps avoid cofactor as it might make one think of matrices (though Wikipedia does have an entry with precisely your desired definition).
    $endgroup$
    – Clayton
    Jan 16 at 22:51






  • 1




    $begingroup$
    @Clayton Much obliged for this! I actually considered cofactor for the reason you mention, but it's interesting that Wikipedia defines it as such. In fact it seems that "co-", as a prefix, is simply shorthand for "complement" in this sense. But I think I shall follow your advice and stick with the expanded "complementary factor" for the sake of resolving a potential ambiguity. Thanks again :)
    $endgroup$
    – crisis.sheep
    Jan 17 at 7:58














  • 4




    $begingroup$
    I don’t think we have a name for this, but the terminology you suggest is fine
    $endgroup$
    – Randall
    Jan 16 at 19:24






  • 3




    $begingroup$
    Complementary factor seems clear and accurate—in particular it's nicely symmetrical (if $xy=n$ then $x$ and $y$ form a complementary pair of factors of $n$, and both have the same status).
    $endgroup$
    – timtfj
    Jan 16 at 19:54








  • 1




    $begingroup$
    @timtfj Oh oh, okay this is very helpful. Thank you very much!
    $endgroup$
    – crisis.sheep
    Jan 16 at 20:03






  • 1




    $begingroup$
    You should feel free to post your own answer. As with the other commenters, I think your terminology is fine. The only advice I have regarding your naming convention is to perhaps avoid cofactor as it might make one think of matrices (though Wikipedia does have an entry with precisely your desired definition).
    $endgroup$
    – Clayton
    Jan 16 at 22:51






  • 1




    $begingroup$
    @Clayton Much obliged for this! I actually considered cofactor for the reason you mention, but it's interesting that Wikipedia defines it as such. In fact it seems that "co-", as a prefix, is simply shorthand for "complement" in this sense. But I think I shall follow your advice and stick with the expanded "complementary factor" for the sake of resolving a potential ambiguity. Thanks again :)
    $endgroup$
    – crisis.sheep
    Jan 17 at 7:58








4




4




$begingroup$
I don’t think we have a name for this, but the terminology you suggest is fine
$endgroup$
– Randall
Jan 16 at 19:24




$begingroup$
I don’t think we have a name for this, but the terminology you suggest is fine
$endgroup$
– Randall
Jan 16 at 19:24




3




3




$begingroup$
Complementary factor seems clear and accurate—in particular it's nicely symmetrical (if $xy=n$ then $x$ and $y$ form a complementary pair of factors of $n$, and both have the same status).
$endgroup$
– timtfj
Jan 16 at 19:54






$begingroup$
Complementary factor seems clear and accurate—in particular it's nicely symmetrical (if $xy=n$ then $x$ and $y$ form a complementary pair of factors of $n$, and both have the same status).
$endgroup$
– timtfj
Jan 16 at 19:54






1




1




$begingroup$
@timtfj Oh oh, okay this is very helpful. Thank you very much!
$endgroup$
– crisis.sheep
Jan 16 at 20:03




$begingroup$
@timtfj Oh oh, okay this is very helpful. Thank you very much!
$endgroup$
– crisis.sheep
Jan 16 at 20:03




1




1




$begingroup$
You should feel free to post your own answer. As with the other commenters, I think your terminology is fine. The only advice I have regarding your naming convention is to perhaps avoid cofactor as it might make one think of matrices (though Wikipedia does have an entry with precisely your desired definition).
$endgroup$
– Clayton
Jan 16 at 22:51




$begingroup$
You should feel free to post your own answer. As with the other commenters, I think your terminology is fine. The only advice I have regarding your naming convention is to perhaps avoid cofactor as it might make one think of matrices (though Wikipedia does have an entry with precisely your desired definition).
$endgroup$
– Clayton
Jan 16 at 22:51




1




1




$begingroup$
@Clayton Much obliged for this! I actually considered cofactor for the reason you mention, but it's interesting that Wikipedia defines it as such. In fact it seems that "co-", as a prefix, is simply shorthand for "complement" in this sense. But I think I shall follow your advice and stick with the expanded "complementary factor" for the sake of resolving a potential ambiguity. Thanks again :)
$endgroup$
– crisis.sheep
Jan 17 at 7:58




$begingroup$
@Clayton Much obliged for this! I actually considered cofactor for the reason you mention, but it's interesting that Wikipedia defines it as such. In fact it seems that "co-", as a prefix, is simply shorthand for "complement" in this sense. But I think I shall follow your advice and stick with the expanded "complementary factor" for the sake of resolving a potential ambiguity. Thanks again :)
$endgroup$
– crisis.sheep
Jan 17 at 7:58










1 Answer
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$begingroup$

In line with some of the comments I've received, I'm going to stick with "complementary factor".



As @Clayton points out in one such comment, "cofactor" has an entry on Wikipedia congruent with my requirement. In fact, it seems "co-" as a prefix is a common shortening of "complementary" in this regard.



However – again, as @Clayton points out – "cofactor" tends to evoke matrices, so to avoid any potential ambiguity I will use the full form.



Many thanks to everybody who weighed in!






share|cite|improve this answer









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    $begingroup$

    In line with some of the comments I've received, I'm going to stick with "complementary factor".



    As @Clayton points out in one such comment, "cofactor" has an entry on Wikipedia congruent with my requirement. In fact, it seems "co-" as a prefix is a common shortening of "complementary" in this regard.



    However – again, as @Clayton points out – "cofactor" tends to evoke matrices, so to avoid any potential ambiguity I will use the full form.



    Many thanks to everybody who weighed in!






    share|cite|improve this answer









    $endgroup$


















      3












      $begingroup$

      In line with some of the comments I've received, I'm going to stick with "complementary factor".



      As @Clayton points out in one such comment, "cofactor" has an entry on Wikipedia congruent with my requirement. In fact, it seems "co-" as a prefix is a common shortening of "complementary" in this regard.



      However – again, as @Clayton points out – "cofactor" tends to evoke matrices, so to avoid any potential ambiguity I will use the full form.



      Many thanks to everybody who weighed in!






      share|cite|improve this answer









      $endgroup$
















        3












        3








        3





        $begingroup$

        In line with some of the comments I've received, I'm going to stick with "complementary factor".



        As @Clayton points out in one such comment, "cofactor" has an entry on Wikipedia congruent with my requirement. In fact, it seems "co-" as a prefix is a common shortening of "complementary" in this regard.



        However – again, as @Clayton points out – "cofactor" tends to evoke matrices, so to avoid any potential ambiguity I will use the full form.



        Many thanks to everybody who weighed in!






        share|cite|improve this answer









        $endgroup$



        In line with some of the comments I've received, I'm going to stick with "complementary factor".



        As @Clayton points out in one such comment, "cofactor" has an entry on Wikipedia congruent with my requirement. In fact, it seems "co-" as a prefix is a common shortening of "complementary" in this regard.



        However – again, as @Clayton points out – "cofactor" tends to evoke matrices, so to avoid any potential ambiguity I will use the full form.



        Many thanks to everybody who weighed in!







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered Jan 17 at 8:09









        crisis.sheepcrisis.sheep

        16110




        16110






























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