Find maximum of the output from reduce












2












$begingroup$


I am trying to reduce a function in two variables($n_1$ and $n_2$) whose domain is the set of Integers. I get a long list of pairs of values for these two variables(instead of a range). This could be because the range of $n_2$ changes for each $n_1$. I just want the maximum value of $n_1$ and $n_2$. Can you please guide me?



   driftParamSet = 1.9 - 0.2 Subscript[n, 2] + Subscript[n, 1] (-0.2 + (2.91434*10^-16 Subscript[n, 1])/(1. Subscript[n, 1] + 1.5 Subscript[n, 2]));

   drift[Gamma] = 17;

   Reduce[driftParamSet> -drift[Gamma] && Subscript[n, 1]>= 0 && Subscript[n, 2]>= 0,{Subscript[n, 1],Subscript[n, 2]}, Integers];


Current output:
$n_1=0land n_2=1left|n_1=0land n_2=2right|n_1=0land n_2=3|n_1=0land n_2=4
\......\left|n_1=0land n_2=90right|n_1=0land n_2=91|\.....\
left(n_1=92land n_2=2right)lor left(n_1=93land n_2=0right)lor left(n_1=93land n_2=1right)lor left(n_1=94land n_2=0right)$



Expected output:



$n_1$=94 and $n_2=$91






equation-solving functions







share|improve this question











$endgroup$








  • 1




    $begingroup$
    Several symbols in your code are undefined. Please provide the definitions to aid the reader in answering your question.
    $endgroup$
    – bbgodfrey
    1 hour ago










  • $begingroup$
    @bbgodfrey, sorry about that. I have updated the question now.
    $endgroup$
    – gaganso
    1 hour ago
















2












$begingroup$


I am trying to reduce a function in two variables($n_1$ and $n_2$) whose domain is the set of Integers. I get a long list of pairs of values for these two variables(instead of a range). This could be because the range of $n_2$ changes for each $n_1$. I just want the maximum value of $n_1$ and $n_2$. Can you please guide me?



   driftParamSet = 1.9 - 0.2 Subscript[n, 2] + Subscript[n, 1] (-0.2 + (2.91434*10^-16 Subscript[n, 1])/(1. Subscript[n, 1] + 1.5 Subscript[n, 2]));

   drift[Gamma] = 17;

   Reduce[driftParamSet> -drift[Gamma] && Subscript[n, 1]>= 0 && Subscript[n, 2]>= 0,{Subscript[n, 1],Subscript[n, 2]}, Integers];


Current output:
$n_1=0land n_2=1left|n_1=0land n_2=2right|n_1=0land n_2=3|n_1=0land n_2=4
\......\left|n_1=0land n_2=90right|n_1=0land n_2=91|\.....\
left(n_1=92land n_2=2right)lor left(n_1=93land n_2=0right)lor left(n_1=93land n_2=1right)lor left(n_1=94land n_2=0right)$



Expected output:



$n_1$=94 and $n_2=$91






equation-solving functions







share|improve this question











$endgroup$








  • 1




    $begingroup$
    Several symbols in your code are undefined. Please provide the definitions to aid the reader in answering your question.
    $endgroup$
    – bbgodfrey
    1 hour ago










  • $begingroup$
    @bbgodfrey, sorry about that. I have updated the question now.
    $endgroup$
    – gaganso
    1 hour ago














2












2








2





$begingroup$


I am trying to reduce a function in two variables($n_1$ and $n_2$) whose domain is the set of Integers. I get a long list of pairs of values for these two variables(instead of a range). This could be because the range of $n_2$ changes for each $n_1$. I just want the maximum value of $n_1$ and $n_2$. Can you please guide me?



   driftParamSet = 1.9 - 0.2 Subscript[n, 2] + Subscript[n, 1] (-0.2 + (2.91434*10^-16 Subscript[n, 1])/(1. Subscript[n, 1] + 1.5 Subscript[n, 2]));

   drift[Gamma] = 17;

   Reduce[driftParamSet> -drift[Gamma] && Subscript[n, 1]>= 0 && Subscript[n, 2]>= 0,{Subscript[n, 1],Subscript[n, 2]}, Integers];


Current output:
$n_1=0land n_2=1left|n_1=0land n_2=2right|n_1=0land n_2=3|n_1=0land n_2=4
\......\left|n_1=0land n_2=90right|n_1=0land n_2=91|\.....\
left(n_1=92land n_2=2right)lor left(n_1=93land n_2=0right)lor left(n_1=93land n_2=1right)lor left(n_1=94land n_2=0right)$



Expected output:



$n_1$=94 and $n_2=$91






equation-solving functions







share|improve this question











$endgroup$




I am trying to reduce a function in two variables($n_1$ and $n_2$) whose domain is the set of Integers. I get a long list of pairs of values for these two variables(instead of a range). This could be because the range of $n_2$ changes for each $n_1$. I just want the maximum value of $n_1$ and $n_2$. Can you please guide me?



   driftParamSet = 1.9 - 0.2 Subscript[n, 2] + Subscript[n, 1] (-0.2 + (2.91434*10^-16 Subscript[n, 1])/(1. Subscript[n, 1] + 1.5 Subscript[n, 2]));

   drift[Gamma] = 17;

   Reduce[driftParamSet> -drift[Gamma] && Subscript[n, 1]>= 0 && Subscript[n, 2]>= 0,{Subscript[n, 1],Subscript[n, 2]}, Integers];


Current output:
$n_1=0land n_2=1left|n_1=0land n_2=2right|n_1=0land n_2=3|n_1=0land n_2=4
\......\left|n_1=0land n_2=90right|n_1=0land n_2=91|\.....\
left(n_1=92land n_2=2right)lor left(n_1=93land n_2=0right)lor left(n_1=93land n_2=1right)lor left(n_1=94land n_2=0right)$



Expected output:



$n_1$=94 and $n_2=$91






equation-solving functions




equation-solving functions






share|improve this question















share|improve this question













share|improve this question




share|improve this question








edited 1 hour ago







gaganso

















asked 1 hour ago









gagansogaganso

1207




1207








  • 1




    $begingroup$
    Several symbols in your code are undefined. Please provide the definitions to aid the reader in answering your question.
    $endgroup$
    – bbgodfrey
    1 hour ago










  • $begingroup$
    @bbgodfrey, sorry about that. I have updated the question now.
    $endgroup$
    – gaganso
    1 hour ago














  • 1




    $begingroup$
    Several symbols in your code are undefined. Please provide the definitions to aid the reader in answering your question.
    $endgroup$
    – bbgodfrey
    1 hour ago










  • $begingroup$
    @bbgodfrey, sorry about that. I have updated the question now.
    $endgroup$
    – gaganso
    1 hour ago








1




1




$begingroup$
Several symbols in your code are undefined. Please provide the definitions to aid the reader in answering your question.
$endgroup$
– bbgodfrey
1 hour ago




$begingroup$
Several symbols in your code are undefined. Please provide the definitions to aid the reader in answering your question.
$endgroup$
– bbgodfrey
1 hour ago












$begingroup$
@bbgodfrey, sorry about that. I have updated the question now.
$endgroup$
– gaganso
1 hour ago




$begingroup$
@bbgodfrey, sorry about that. I have updated the question now.
$endgroup$
– gaganso
1 hour ago










2 Answers
2






active

oldest

votes


















3












$begingroup$

Let the large result of Reduce be rs. Then the maximum of each quantity is determined by



Max@Cases[rs, Equal[Subscript[n, 1], z_] -> z, Infinity]

(* 94 *)

Max@Cases[rs, Equal[Subscript[n, 2], z_] -> z, Infinity]

(* 94 *)


not 91 as speculated in the question. The corresponding terms in rs can be obtained by



Position[rs, 94, Infinity]

(* {{94, 2, 2}, {4559, 1, 2}} *)



rs[[94]]

(* Subscript[n, 1] == 0 && Subscript[n, 2] == 94 *)



rs[[4559]]

(* Subscript[n, 1] == 94 && Subscript[n, 2] == 0 *)





share|improve this answer











$endgroup$













  • $begingroup$
    thank you! To understand this better, the Cases function with the specified parameter creates a list of values of n1/n2 and the Max function operates on this list to give the maximum?
    $endgroup$
    – gaganso
    53 mins ago






  • 1




    $begingroup$
    @gaganso Precisely so.
    $endgroup$
    – bbgodfrey
    52 mins ago



















3












$begingroup$

An alternative is to use Solve after Rationalizeing input expressions:



driftParamSet = Rationalize[1.9 - 0.2 n2 + 

  n1 (-0.2 + (2.91434*10^-16 n1)/(1. n1 + 1.5 n2)), 10^-16]

driftγ = 17;

solutions = Solve[driftParamSet > -driftγ && n1 >= 0 && n2 >= 0, {n1, n2}, Integers];



Max /@ Transpose[{n1, n2} /. solutions]



{94, 94}




Yet another approach is using ArgMax:



Extract[ArgMax[{#, driftParamSet > -driftγ && n1 >= 0 && n2 >= 0}, {n1, n2}, Integers]& /@ 

  {n1, n2}, {{1, 1}, {-1, -1}}]



{94, 94}







share|improve this answer











$endgroup$













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    2 Answers
    2






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    oldest

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    2 Answers
    2






    active

    oldest

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    active

    oldest

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    active

    oldest

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    3












    $begingroup$

    Let the large result of Reduce be rs. Then the maximum of each quantity is determined by



    Max@Cases[rs, Equal[Subscript[n, 1], z_] -> z, Infinity]
    
(* 94 *)
    
Max@Cases[rs, Equal[Subscript[n, 2], z_] -> z, Infinity]
    
(* 94 *)


    not 91 as speculated in the question. The corresponding terms in rs can be obtained by



    Position[rs, 94, Infinity]
    
(* {{94, 2, 2}, {4559, 1, 2}} *)
    

    
rs[[94]]
    
(* Subscript[n, 1] == 0 && Subscript[n, 2] == 94 *)
    

    
rs[[4559]]
    
(* Subscript[n, 1] == 94 && Subscript[n, 2] == 0 *)





    share|improve this answer











    $endgroup$













    • $begingroup$
      thank you! To understand this better, the Cases function with the specified parameter creates a list of values of n1/n2 and the Max function operates on this list to give the maximum?
      $endgroup$
      – gaganso
      53 mins ago






    • 1




      $begingroup$
      @gaganso Precisely so.
      $endgroup$
      – bbgodfrey
      52 mins ago
















    3












    $begingroup$

    Let the large result of Reduce be rs. Then the maximum of each quantity is determined by



    Max@Cases[rs, Equal[Subscript[n, 1], z_] -> z, Infinity]
    
(* 94 *)
    
Max@Cases[rs, Equal[Subscript[n, 2], z_] -> z, Infinity]
    
(* 94 *)


    not 91 as speculated in the question. The corresponding terms in rs can be obtained by



    Position[rs, 94, Infinity]
    
(* {{94, 2, 2}, {4559, 1, 2}} *)
    

    
rs[[94]]
    
(* Subscript[n, 1] == 0 && Subscript[n, 2] == 94 *)
    

    
rs[[4559]]
    
(* Subscript[n, 1] == 94 && Subscript[n, 2] == 0 *)





    share|improve this answer











    $endgroup$













    • $begingroup$
      thank you! To understand this better, the Cases function with the specified parameter creates a list of values of n1/n2 and the Max function operates on this list to give the maximum?
      $endgroup$
      – gaganso
      53 mins ago






    • 1




      $begingroup$
      @gaganso Precisely so.
      $endgroup$
      – bbgodfrey
      52 mins ago














    3












    3








    3





    $begingroup$

    Let the large result of Reduce be rs. Then the maximum of each quantity is determined by



    Max@Cases[rs, Equal[Subscript[n, 1], z_] -> z, Infinity]
    
(* 94 *)
    
Max@Cases[rs, Equal[Subscript[n, 2], z_] -> z, Infinity]
    
(* 94 *)


    not 91 as speculated in the question. The corresponding terms in rs can be obtained by



    Position[rs, 94, Infinity]
    
(* {{94, 2, 2}, {4559, 1, 2}} *)
    

    
rs[[94]]
    
(* Subscript[n, 1] == 0 && Subscript[n, 2] == 94 *)
    

    
rs[[4559]]
    
(* Subscript[n, 1] == 94 && Subscript[n, 2] == 0 *)





    share|improve this answer











    $endgroup$



    Let the large result of Reduce be rs. Then the maximum of each quantity is determined by



    Max@Cases[rs, Equal[Subscript[n, 1], z_] -> z, Infinity]
    
(* 94 *)
    
Max@Cases[rs, Equal[Subscript[n, 2], z_] -> z, Infinity]
    
(* 94 *)


    not 91 as speculated in the question. The corresponding terms in rs can be obtained by



    Position[rs, 94, Infinity]
    
(* {{94, 2, 2}, {4559, 1, 2}} *)
    

    
rs[[94]]
    
(* Subscript[n, 1] == 0 && Subscript[n, 2] == 94 *)
    

    
rs[[4559]]
    
(* Subscript[n, 1] == 94 && Subscript[n, 2] == 0 *)






    share|improve this answer














    share|improve this answer



    share|improve this answer








    edited 56 mins ago

























    answered 1 hour ago









    bbgodfreybbgodfrey

    44.8k958110




    44.8k958110












    • $begingroup$
      thank you! To understand this better, the Cases function with the specified parameter creates a list of values of n1/n2 and the Max function operates on this list to give the maximum?
      $endgroup$
      – gaganso
      53 mins ago






    • 1




      $begingroup$
      @gaganso Precisely so.
      $endgroup$
      – bbgodfrey
      52 mins ago


















    • $begingroup$
      thank you! To understand this better, the Cases function with the specified parameter creates a list of values of n1/n2 and the Max function operates on this list to give the maximum?
      $endgroup$
      – gaganso
      53 mins ago






    • 1




      $begingroup$
      @gaganso Precisely so.
      $endgroup$
      – bbgodfrey
      52 mins ago
















    $begingroup$
    thank you! To understand this better, the Cases function with the specified parameter creates a list of values of n1/n2 and the Max function operates on this list to give the maximum?
    $endgroup$
    – gaganso
    53 mins ago




    $begingroup$
    thank you! To understand this better, the Cases function with the specified parameter creates a list of values of n1/n2 and the Max function operates on this list to give the maximum?
    $endgroup$
    – gaganso
    53 mins ago




    1




    1




    $begingroup$
    @gaganso Precisely so.
    $endgroup$
    – bbgodfrey
    52 mins ago




    $begingroup$
    @gaganso Precisely so.
    $endgroup$
    – bbgodfrey
    52 mins ago











    3












    $begingroup$

    An alternative is to use Solve after Rationalizeing input expressions:



    driftParamSet = Rationalize[1.9 - 0.2 n2 + 
    
  n1 (-0.2 + (2.91434*10^-16 n1)/(1. n1 + 1.5 n2)), 10^-16]
    
driftγ = 17;
    
solutions = Solve[driftParamSet > -driftγ && n1 >= 0 && n2 >= 0, {n1, n2}, Integers];
    

    
Max /@ Transpose[{n1, n2} /. solutions]



    {94, 94}




    Yet another approach is using ArgMax:



    Extract[ArgMax[{#, driftParamSet > -driftγ && n1 >= 0 && n2 >= 0}, {n1, n2}, Integers]& /@ 
    
  {n1, n2}, {{1, 1}, {-1, -1}}]



    {94, 94}







    share|improve this answer











    $endgroup$


















      3












      $begingroup$

      An alternative is to use Solve after Rationalizeing input expressions:



      driftParamSet = Rationalize[1.9 - 0.2 n2 + 
      
  n1 (-0.2 + (2.91434*10^-16 n1)/(1. n1 + 1.5 n2)), 10^-16]
      
driftγ = 17;
      
solutions = Solve[driftParamSet > -driftγ && n1 >= 0 && n2 >= 0, {n1, n2}, Integers];
      

      
Max /@ Transpose[{n1, n2} /. solutions]



      {94, 94}




      Yet another approach is using ArgMax:



      Extract[ArgMax[{#, driftParamSet > -driftγ && n1 >= 0 && n2 >= 0}, {n1, n2}, Integers]& /@ 
      
  {n1, n2}, {{1, 1}, {-1, -1}}]



      {94, 94}







      share|improve this answer











      $endgroup$
















        3












        3








        3





        $begingroup$

        An alternative is to use Solve after Rationalizeing input expressions:



        driftParamSet = Rationalize[1.9 - 0.2 n2 + 
        
  n1 (-0.2 + (2.91434*10^-16 n1)/(1. n1 + 1.5 n2)), 10^-16]
        
driftγ = 17;
        
solutions = Solve[driftParamSet > -driftγ && n1 >= 0 && n2 >= 0, {n1, n2}, Integers];
        

        
Max /@ Transpose[{n1, n2} /. solutions]



        {94, 94}




        Yet another approach is using ArgMax:



        Extract[ArgMax[{#, driftParamSet > -driftγ && n1 >= 0 && n2 >= 0}, {n1, n2}, Integers]& /@ 
        
  {n1, n2}, {{1, 1}, {-1, -1}}]



        {94, 94}







        share|improve this answer











        $endgroup$



        An alternative is to use Solve after Rationalizeing input expressions:



        driftParamSet = Rationalize[1.9 - 0.2 n2 + 
        
  n1 (-0.2 + (2.91434*10^-16 n1)/(1. n1 + 1.5 n2)), 10^-16]
        
driftγ = 17;
        
solutions = Solve[driftParamSet > -driftγ && n1 >= 0 && n2 >= 0, {n1, n2}, Integers];
        

        
Max /@ Transpose[{n1, n2} /. solutions]



        {94, 94}




        Yet another approach is using ArgMax:



        Extract[ArgMax[{#, driftParamSet > -driftγ && n1 >= 0 && n2 >= 0}, {n1, n2}, Integers]& /@ 
        
  {n1, n2}, {{1, 1}, {-1, -1}}]



        {94, 94}








        share|improve this answer














        share|improve this answer



        share|improve this answer








        edited 14 mins ago

























        answered 45 mins ago









        kglrkglr

        187k10203421




        187k10203421






























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