Find maximum of the output from reduce












3












$begingroup$


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
    3 hours ago










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
















3












$begingroup$


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
    3 hours ago










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














3












3








3





$begingroup$


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 3 hours ago







gaganso

















asked 3 hours ago









gagansogaganso

1257




1257








  • 1




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










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














  • 1




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










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




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












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




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






  • 1




    $begingroup$
    @gaganso Precisely so.
    $endgroup$
    – bbgodfrey
    3 hours 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

    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
      3 hours ago






    • 1




      $begingroup$
      @gaganso Precisely so.
      $endgroup$
      – bbgodfrey
      3 hours 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
      3 hours ago






    • 1




      $begingroup$
      @gaganso Precisely so.
      $endgroup$
      – bbgodfrey
      3 hours 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 3 hours ago

























    answered 3 hours 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
      3 hours ago






    • 1




      $begingroup$
      @gaganso Precisely so.
      $endgroup$
      – bbgodfrey
      3 hours 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
      3 hours ago






    • 1




      $begingroup$
      @gaganso Precisely so.
      $endgroup$
      – bbgodfrey
      3 hours 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
    3 hours 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
    3 hours ago




    1




    1




    $begingroup$
    @gaganso Precisely so.
    $endgroup$
    – bbgodfrey
    3 hours ago




    $begingroup$
    @gaganso Precisely so.
    $endgroup$
    – bbgodfrey
    3 hours 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 2 hours ago

























        answered 2 hours ago









        kglrkglr

        187k10203421




        187k10203421






























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            19世紀

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            この記事は検証可能な参考文献や出典が全く示されていないか、不十分です。 出典を追加して記事の信頼性向上にご協力ください。 （ 2012年3月 ） 千年紀: 2千年紀 世紀: 18世紀 - 19世紀 - 20世紀 十年紀: 1800年代 1810年代 1820年代 1830年代 1840年代 1850年代 1860年代 1870年代 1880年代 1890年代 19世紀に君臨した大英帝国。 19世紀 （じゅうきゅうせいき）は、西暦1801年から西暦1900年までの100年間を指す世紀。 目次 1 19世紀の歴史 1.1 国民国家の成立 1.2 帝国主義の興隆 1.3 列強の植民地争奪戦 2 できごと 2.1 1800年代 2.2 1810年代 2.3 1820年代 2.4 1830年代 2.5 1840年代 2.6 1850年代 2.7 1860年代 2.8 1870年代 2.9 1880年代 2.10 1890年代 2.11 1900年代 3 文化 3.1 文学 3.2 音楽 3.3 思想 3.4 科学 3.5 技術 4 人物 4.1 ヨーロッパ 4.1.1 政治家・王族 4.1.1.1 フランス 4.1.1.2 オーストリア＝ハンガリー 4.1.1.3 ロシア 4.1.1.4 イギリス 4.1.1.5 ドイツ（プロイセンほかドイツ領邦を含む） 4.1.1.6 北欧 4.1.1.7 イタリア 4.1.1.8 スペイン 4.1.1.9 ベルギー 4.1.1.10 ギリシア 4.1.2 軍人 4.1.3 実業家 4.1.4 科学と技術 4.1.5 思想と哲学・人文諸学 4.1.6 宗教 4.1.7 文学 4.1.8 美術 4.1.9 音楽 4.1.10 社会事業家 4.1.11 探検家・旅行家 4.1.12 料
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