List of invertible congruence classes












2












$begingroup$


I am attempting to create a list of the invertible congruence classes $bmod 120$.



The code I have is Table[If[{ModularInverse[i, 120]} = {}, 120, ModularInverse[i, 120]], {i,
0, 119}]



If the modular inverse does not exist, it should return $120$. If it does exist, it should return the integer that corresponds to the inverse congruence class.



The code is not working how I expected it to. If the modular inverse does not exists, it gives me a list with the unevaluated code, for example, ModularInverse[0, 120].










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  • $begingroup$
    Not the only problem, but one thing to note: Equality is tested with a double-equals ==.
    $endgroup$
    – Michael E2
    4 hours ago
















2












$begingroup$


I am attempting to create a list of the invertible congruence classes $bmod 120$.



The code I have is Table[If[{ModularInverse[i, 120]} = {}, 120, ModularInverse[i, 120]], {i,
0, 119}]



If the modular inverse does not exist, it should return $120$. If it does exist, it should return the integer that corresponds to the inverse congruence class.



The code is not working how I expected it to. If the modular inverse does not exists, it gives me a list with the unevaluated code, for example, ModularInverse[0, 120].










share|improve this question









$endgroup$












  • $begingroup$
    Not the only problem, but one thing to note: Equality is tested with a double-equals ==.
    $endgroup$
    – Michael E2
    4 hours ago














2












2








2





$begingroup$


I am attempting to create a list of the invertible congruence classes $bmod 120$.



The code I have is Table[If[{ModularInverse[i, 120]} = {}, 120, ModularInverse[i, 120]], {i,
0, 119}]



If the modular inverse does not exist, it should return $120$. If it does exist, it should return the integer that corresponds to the inverse congruence class.



The code is not working how I expected it to. If the modular inverse does not exists, it gives me a list with the unevaluated code, for example, ModularInverse[0, 120].










share|improve this question









$endgroup$




I am attempting to create a list of the invertible congruence classes $bmod 120$.



The code I have is Table[If[{ModularInverse[i, 120]} = {}, 120, ModularInverse[i, 120]], {i,
0, 119}]



If the modular inverse does not exist, it should return $120$. If it does exist, it should return the integer that corresponds to the inverse congruence class.



The code is not working how I expected it to. If the modular inverse does not exists, it gives me a list with the unevaluated code, for example, ModularInverse[0, 120].







table modular-arithmetic






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asked 5 hours ago









pmacpmac

182




182












  • $begingroup$
    Not the only problem, but one thing to note: Equality is tested with a double-equals ==.
    $endgroup$
    – Michael E2
    4 hours ago


















  • $begingroup$
    Not the only problem, but one thing to note: Equality is tested with a double-equals ==.
    $endgroup$
    – Michael E2
    4 hours ago
















$begingroup$
Not the only problem, but one thing to note: Equality is tested with a double-equals ==.
$endgroup$
– Michael E2
4 hours ago




$begingroup$
Not the only problem, but one thing to note: Equality is tested with a double-equals ==.
$endgroup$
– Michael E2
4 hours ago










1 Answer
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$begingroup$

Note what happens when i does not have an inverse:



ModularInverse[2, 120]



ModularInverse::ninv: 2 is not invertible modulo 120.




(*  Out=  ModularInverse[2, 120]  *)


The output is the same as the input (it returns "unevaluated" in Mma jargon).
You can use FreeQ to see if the inverse returned unevaluated:



Table[With[{inv = Quiet@ModularInverse[i, 120]}, 
If[FreeQ[inv, ModularInverse], inv, 120]], {i, 0, 119}]





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    1 Answer
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    1 Answer
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    $begingroup$

    Note what happens when i does not have an inverse:



    ModularInverse[2, 120]



    ModularInverse::ninv: 2 is not invertible modulo 120.




    (*  Out=  ModularInverse[2, 120]  *)


    The output is the same as the input (it returns "unevaluated" in Mma jargon).
    You can use FreeQ to see if the inverse returned unevaluated:



    Table[With[{inv = Quiet@ModularInverse[i, 120]}, 
    If[FreeQ[inv, ModularInverse], inv, 120]], {i, 0, 119}]





    share|improve this answer









    $endgroup$


















      3












      $begingroup$

      Note what happens when i does not have an inverse:



      ModularInverse[2, 120]



      ModularInverse::ninv: 2 is not invertible modulo 120.




      (*  Out=  ModularInverse[2, 120]  *)


      The output is the same as the input (it returns "unevaluated" in Mma jargon).
      You can use FreeQ to see if the inverse returned unevaluated:



      Table[With[{inv = Quiet@ModularInverse[i, 120]}, 
      If[FreeQ[inv, ModularInverse], inv, 120]], {i, 0, 119}]





      share|improve this answer









      $endgroup$
















        3












        3








        3





        $begingroup$

        Note what happens when i does not have an inverse:



        ModularInverse[2, 120]



        ModularInverse::ninv: 2 is not invertible modulo 120.




        (*  Out=  ModularInverse[2, 120]  *)


        The output is the same as the input (it returns "unevaluated" in Mma jargon).
        You can use FreeQ to see if the inverse returned unevaluated:



        Table[With[{inv = Quiet@ModularInverse[i, 120]}, 
        If[FreeQ[inv, ModularInverse], inv, 120]], {i, 0, 119}]





        share|improve this answer









        $endgroup$



        Note what happens when i does not have an inverse:



        ModularInverse[2, 120]



        ModularInverse::ninv: 2 is not invertible modulo 120.




        (*  Out=  ModularInverse[2, 120]  *)


        The output is the same as the input (it returns "unevaluated" in Mma jargon).
        You can use FreeQ to see if the inverse returned unevaluated:



        Table[With[{inv = Quiet@ModularInverse[i, 120]}, 
        If[FreeQ[inv, ModularInverse], inv, 120]], {i, 0, 119}]






        share|improve this answer












        share|improve this answer



        share|improve this answer










        answered 4 hours ago









        Michael E2Michael E2

        148k12198475




        148k12198475






























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