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
    44 mins ago






  • 1




    $begingroup$
    @gaganso Precisely so.
    $endgroup$
    – bbgodfrey
    43 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











$endgroup$













    Your Answer





    StackExchange.ifUsing("editor", function () {
    return StackExchange.using("mathjaxEditing", function () {
    StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
    StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
    });
    });
    }, "mathjax-editing");

    StackExchange.ready(function() {
    var channelOptions = {
    tags: "".split(" "),
    id: "387"
    };
    initTagRenderer("".split(" "), "".split(" "), channelOptions);

    StackExchange.using("externalEditor", function() {
    // Have to fire editor after snippets, if snippets enabled
    if (StackExchange.settings.snippets.snippetsEnabled) {
    StackExchange.using("snippets", function() {
    createEditor();
    });
    }
    else {
    createEditor();
    }
    });

    function createEditor() {
    StackExchange.prepareEditor({
    heartbeatType: 'answer',
    autoActivateHeartbeat: false,
    convertImagesToLinks: false,
    noModals: true,
    showLowRepImageUploadWarning: true,
    reputationToPostImages: null,
    bindNavPrevention: true,
    postfix: "",
    imageUploader: {
    brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
    contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
    allowUrls: true
    },
    onDemand: true,
    discardSelector: ".discard-answer"
    ,immediatelyShowMarkdownHelp:true
    });


    }
    });














    draft saved

    draft discarded


















    StackExchange.ready(
    function () {
    StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmathematica.stackexchange.com%2fquestions%2f192764%2ffind-maximum-of-the-output-from-reduce%23new-answer', 'question_page');
    }
    );

    Post as a guest















    Required, but never shown

























    2 Answers
    2






    active

    oldest

    votes








    2 Answers
    2






    active

    oldest

    votes









    active

    oldest

    votes






    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
      44 mins ago






    • 1




      $begingroup$
      @gaganso Precisely so.
      $endgroup$
      – bbgodfrey
      43 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
      44 mins ago






    • 1




      $begingroup$
      @gaganso Precisely so.
      $endgroup$
      – bbgodfrey
      43 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 47 mins ago

























    answered 52 mins 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
      44 mins ago






    • 1




      $begingroup$
      @gaganso Precisely so.
      $endgroup$
      – bbgodfrey
      43 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
      44 mins ago






    • 1




      $begingroup$
      @gaganso Precisely so.
      $endgroup$
      – bbgodfrey
      43 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
    44 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
    44 mins ago




    1




    1




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




    $begingroup$
    @gaganso Precisely so.
    $endgroup$
    – bbgodfrey
    43 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 5 mins ago

























        answered 36 mins ago









        kglrkglr

        187k10203421




        187k10203421






























            draft saved

            draft discarded




















































            Thanks for contributing an answer to Mathematica Stack Exchange!


            • Please be sure to answer the question. Provide details and share your research!

            But avoid …



            • Asking for help, clarification, or responding to other answers.

            • Making statements based on opinion; back them up with references or personal experience.


            Use MathJax to format equations. MathJax reference.


            To learn more, see our tips on writing great answers.




            draft saved


            draft discarded














            StackExchange.ready(
            function () {
            StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmathematica.stackexchange.com%2fquestions%2f192764%2ffind-maximum-of-the-output-from-reduce%23new-answer', 'question_page');
            }
            );

            Post as a guest















            Required, but never shown





















































            Required, but never shown














            Required, but never shown












            Required, but never shown







            Required, but never shown

































            Required, but never shown














            Required, but never shown












            Required, but never shown







            Required, but never shown







            -

            Popular posts from this blog

            Сан-Квентин

            Image
            Сан-Квентин Местоположение Сан-Квентин, Калифорния Координаты 37°56′13″ с. ш. 122°29′20″ з. д. H G Я O L Текущий статус Действует Режим безопасности минимальный и максимальный Количество мест 3 302 Открытие Июнь 1852 Находится в ведомстве California Department of Corrections and Rehabilitation Начальник Mike Martel, начальник  Сан-Квентин на Викискладе Сан-Квентин (англ.  San Quentin ) — тюрьма, располагающаяся на 432 акрах (около 1,7 км²), на мысе Сан-Квентин, в округе Марин, штат Калифорния, США. Тюрьма штата Калифорния Сан-Квентин была открыта в июле 1852 года и является старейшей в штате. Она была построена заключёнными, которые проживали в течение строительства на тюремном судне Вабан. В Сан-Квентине отбывали наказание и мужчины, и женщины до 1934 года, когда построили женскую тюрьму в Техачапи и туда перевели всех заключённых женщин. В Сан-Квентине приводятся в исполнение смертные казни, для этого имеется газовая камера, но
            Read more

            Алькесар

            Image
            Муниципалитет Алькесар Alquézar Герб 42°10′16″ с. ш. 0°01′27″ в. д. H G Я O L Страна Испания   Испания Автономное сообщество Арагон Провинция Уэска Комарка Сомонтано-де-Барбастро Алькальд Хосе Марияно Альтемир Ласкорс (ИСРП) История и география Площадь 32,36 км² Высота НУМ 660 м Часовой пояс UTC+1, летом UTC+2 Население Население 313 человек ( 2010 ) Плотность 9,92 чел./км² Этнохороним alquezarano/-a Цифровые идентификаторы Телефонный код +34 974 Почтовые индексы 22112 Автомобильный код HU alquezar.org   (исп.) Показать/скрыть карты Алькесар Алькесар Алькесар  Аудио, фото и видео на Викискладе Алькесар (исп.  Alquézar ) — муниципалитет в Испании, входит в провинцию Уэска, в составе автономного сообщества Арагон. Муниципалитет находится в составе района (комарки) Сомонтано-де-Барбастро. Занимает площадь 32,36 км². Население — 321 челове
            Read more

            Josef Freinademetz

            Image
            San Ujöp (Giuseppe/Josef) Freinademetz Josef Freinademetz in abiti cinesi   Religioso e missionario   Nascita 15 aprile 1852 Morte 28 gennaio 1908 Venerato da Chiesa cattolica Beatificazione 1975 Canonizzazione 5 ottobre 2003 Ricorrenza 28 gennaio Manuale Ujöp Freinademetz noto anche come Giuseppe o Josef Freinademetz (Oies, 15 aprile 1852 – Taikia, 28 gennaio 1908) è stato un presbitero austriaco, membro della Società del Verbo Divino, fu missionario in Cina; è venerato come santo dalla Chiesa cattolica. .mw-parser-output .citazione-table{margin-bottom:.5em;font-size:95%}.mw-parser-output .citazione-table td{padding:0 1.2em 0 2.4em}.mw-parser-output .citazione-lang{vertical-align:top}.mw-parser-output .citazione-lang td{width:50%}.mw-parser-output .citazione-lang td:first-child{padding:0 0 0 2.4em}.mw-parser-output .citazione-lang td:nth-child(2){padding:0 1.2em} «Io amo la Cina e i cinesi; voglio morire in mezzo a loro, e tra loro
            Read more