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
    46 mins ago






  • 1




    $begingroup$
    @gaganso Precisely so.
    $endgroup$
    – bbgodfrey
    45 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
      46 mins ago






    • 1




      $begingroup$
      @gaganso Precisely so.
      $endgroup$
      – bbgodfrey
      45 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
      46 mins ago






    • 1




      $begingroup$
      @gaganso Precisely so.
      $endgroup$
      – bbgodfrey
      45 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 48 mins ago

























    answered 54 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
      46 mins ago






    • 1




      $begingroup$
      @gaganso Precisely so.
      $endgroup$
      – bbgodfrey
      45 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
      46 mins ago






    • 1




      $begingroup$
      @gaganso Precisely so.
      $endgroup$
      – bbgodfrey
      45 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
    46 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
    46 mins ago




    1




    1




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




    $begingroup$
    @gaganso Precisely so.
    $endgroup$
    – bbgodfrey
    45 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 7 mins ago

























        answered 38 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

            الفوسفات في المغرب

            Image
            قطار ينقل فوسفات من منطقة خريبكة متجه نحو الدار البيضاء. ديار عمال بمصانع الفوسفات بمدينة آسفي. المحتوى هنا ينقصه الاستشهاد بمصادر. يرجى إيراد مصادر موثوق بها. أي معلومات غير موثقة يمكن التشكيك بها وإزالتها. (أغسطس 2015) الفوسفات في المغرب هو ثالث مصدر عالمي للفوسفات، ويتوفر المغرب على %75 من الاحتياطي العالمي  [بحاجة لمصدر] ويتوزع بنسب متفاوتة بين عدة مناطق أساسية وهي: وادي زم بن جرير بوكراع خريبكة اليوسفية أولاد عبدون كنتور واد الذهب مستقلة. هذه الأخيرة لم تفتح بعد للاستغلال. الصادرات الحامض الفوسفوري P205 تمتص الهند %50 من ا لصادرات الإجمالية آسيا (دون روسيا)%59 أوروبا %30 أمريكا اللاتينية %11 أسمدة صلبة أوروبا 38 % أمريكا اللاتينية %30 آسيا (دون روسيا) 22 % أستراليا 9 % بوابة المغرب هذه بذرة مقالة عن علم الاقتصاد أو موضوع متعلق به بحاجة للتوسيع. شارك في تحريرها. This page is only for reference, If you need detailed information, please check here
            Read more

            Four equal circles intersect: What is the area of the small shaded portion and its height

            Image
            3 $begingroup$ In terms of $R$ which is the radius of all four circles, what is the area of the intersection region of these four equal circles and the height of the marked arrow in the figure? The marked arrow is along the line CD, also the midpoint of all the circles are points A, B, C and D. Looking for a very short intuitive solution. I have checked similar questions on this site for example this and this. geometry circle share | cite | improve this question edited 2 hours ago Abdulhameed asked 2 hours ago ...
            Read more

            جامعة ليفربول

            Image
            جامعة ليفربول University of Liverpool الأسماء السابقة كلية ليفربول الجامعية (1882-1884) جامعة فيكتوريا في ليفربول (1884-1903) معلومات التأسيس 1882 (منذ 137 سنة) الإنتماءات رابطة الجامعات الأوروبية مجموعة راسل جامعات القرميد الأحمر المنحة المالية 143.5 مليون £ النوع جامعة عامة الكليات 6 الموقع الجغرافي إحداثيات 53°24′22″N 2°58′01″W  /  53.406°N 2.967°W  / 53.406; -2.967   المدينة ليفربول المكان   إنجلترا البلد   المملكة المتحدة رقم الهاتف 7942000 151 (44+) إحصاءات الطلاب 17,405 (سنة 2008) عضوية مجموعة رسل [1] أورسيد [2]   طلاب الدراسات العليا 3,860 الموقع www.liverpool.ac.uk تعديل   جامعة ليفربول مبنى فكتوريا جامعة ليفربول (بالإنجليزية: The University of Liverpool )) إحدى الجامعات البريطانية العريقة، تقع في مدينة ليفربول على الساحل الشمالي الغربي من أنجلترا . وهي عضو في مجموعة راسل للجامعات وتعتبر من ضمن جامعات الطوب الأحمر الستة. محتويات ...
            Read more