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Find maximum of the output from reduce


How Can I use Solve/Reduce OutputFailure message from ReduceExtract desired solutions from ReduceFinding the least positive integer satisfying a quantified statementhow do I control the output of Reduce function?Using the output of ReduceIncomplete and weird output from ReduceUsing Solve returns unnecessary Root, overcomplicated formula, and erroneous negative valueHow to analyse huge output from Reduce systematically?Make Reduce produce nicer output













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










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










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










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






share|improve this question















share|improve this question













share|improve this question




share|improve this question








edited 1 hour ago







gaganso

















asked 2 hours 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
    1 hour ago






  • 1




    $begingroup$
    @gaganso Precisely so.
    $endgroup$
    – bbgodfrey
    1 hour 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

    votes






    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
      1 hour ago






    • 1




      $begingroup$
      @gaganso Precisely so.
      $endgroup$
      – bbgodfrey
      1 hour 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
      1 hour ago






    • 1




      $begingroup$
      @gaganso Precisely so.
      $endgroup$
      – bbgodfrey
      1 hour 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 1 hour 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
      1 hour ago






    • 1




      $begingroup$
      @gaganso Precisely so.
      $endgroup$
      – bbgodfrey
      1 hour 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
      1 hour ago






    • 1




      $begingroup$
      @gaganso Precisely so.
      $endgroup$
      – bbgodfrey
      1 hour 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
    1 hour 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
    1 hour ago




    1




    1




    $begingroup$
    @gaganso Precisely so.
    $endgroup$
    – bbgodfrey
    1 hour ago




    $begingroup$
    @gaganso Precisely so.
    $endgroup$
    – bbgodfrey
    1 hour 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 49 mins ago

























        answered 1 hour ago









        kglrkglr

        187k10203421




        187k10203421






























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