Plot surface of constraints: Possibly via Apply or Map Reduce over a list of equations












2












$begingroup$


I have a function f(A,B,C) where for specific A and B values I can use Reduce to determine the constraint on C for my problem using a constraint on f. I want to plot the resulting surface.



To illustrate, consider



f = A^5 + B^3 + C^2


If A and B vary between 1 and 3 then I get the list of constraints (with f<20)



constraints = {{1, 1, C < 18}, {2, 1, C < -13}, {3, 1, C < -224}, {1, 2, C < 11}, {2, 2, C < -20}, {3, 2, C < -231}, {1, 3, C < -8}, {2, 3, C < -39}, {3, 3, C < -250}}


I then want to plot the surface given by



surf = {{1, 1, 18}, {2, 1, -13}, {3, 1, -224}, {1, 2, 

  11}, {2, 2, -20}, {3, 2, -231}, {1, 3,  -8}, {2, 3, 

   -39}, {3, 3, -250}}



ListPlot3D[surf,Mesh->All]


I can form the list of constraints using For loops



constraints = {};

For[B = 1, B <= 3, B++,

 For[A = 1, A <= 3, A++,

  f = (A)^5 + B^3 + p;

  sol  = Reduce[f < 20, p];

  constraints = Append[constraints, {A, B, sol}]

  ]

 ]

constraints


However I am not sure how to get from the list of constraints to the max permitted value for C and therefore get to the surf expression.



I also expect that For loops are not an ideal approach, and that I should be able to form lists of the A and B values and use another approach (Map, or Thread, or Apply maybe) with Reduce. I find these methods confusing though, and don't really understand anything but the most basic examples (so possibly similar questions have not helped me figure this out).






list-manipulation equation-solving







share|improve this question









$endgroup$












  • $begingroup$
    Are A and B constrained to be integers?
    $endgroup$
    – Chris K
    17 hours ago










  • $begingroup$
    No they aren't - my actual function is quite complex so this is just a simple example. @Henrik Schumacher's solution works wonderfully, but I'd still like to know how to map across the list if anyone has a solution that works that way (just for general development of skills)
    $endgroup$
    – Esme_
    17 hours ago
















2












$begingroup$


I have a function f(A,B,C) where for specific A and B values I can use Reduce to determine the constraint on C for my problem using a constraint on f. I want to plot the resulting surface.



To illustrate, consider



f = A^5 + B^3 + C^2


If A and B vary between 1 and 3 then I get the list of constraints (with f<20)



constraints = {{1, 1, C < 18}, {2, 1, C < -13}, {3, 1, C < -224}, {1, 2, C < 11}, {2, 2, C < -20}, {3, 2, C < -231}, {1, 3, C < -8}, {2, 3, C < -39}, {3, 3, C < -250}}


I then want to plot the surface given by



surf = {{1, 1, 18}, {2, 1, -13}, {3, 1, -224}, {1, 2, 

  11}, {2, 2, -20}, {3, 2, -231}, {1, 3,  -8}, {2, 3, 

   -39}, {3, 3, -250}}



ListPlot3D[surf,Mesh->All]


I can form the list of constraints using For loops



constraints = {};

For[B = 1, B <= 3, B++,

 For[A = 1, A <= 3, A++,

  f = (A)^5 + B^3 + p;

  sol  = Reduce[f < 20, p];

  constraints = Append[constraints, {A, B, sol}]

  ]

 ]

constraints


However I am not sure how to get from the list of constraints to the max permitted value for C and therefore get to the surf expression.



I also expect that For loops are not an ideal approach, and that I should be able to form lists of the A and B values and use another approach (Map, or Thread, or Apply maybe) with Reduce. I find these methods confusing though, and don't really understand anything but the most basic examples (so possibly similar questions have not helped me figure this out).






list-manipulation equation-solving







share|improve this question









$endgroup$












  • $begingroup$
    Are A and B constrained to be integers?
    $endgroup$
    – Chris K
    17 hours ago










  • $begingroup$
    No they aren't - my actual function is quite complex so this is just a simple example. @Henrik Schumacher's solution works wonderfully, but I'd still like to know how to map across the list if anyone has a solution that works that way (just for general development of skills)
    $endgroup$
    – Esme_
    17 hours ago














2












2








2





$begingroup$


I have a function f(A,B,C) where for specific A and B values I can use Reduce to determine the constraint on C for my problem using a constraint on f. I want to plot the resulting surface.



To illustrate, consider



f = A^5 + B^3 + C^2


If A and B vary between 1 and 3 then I get the list of constraints (with f<20)



constraints = {{1, 1, C < 18}, {2, 1, C < -13}, {3, 1, C < -224}, {1, 2, C < 11}, {2, 2, C < -20}, {3, 2, C < -231}, {1, 3, C < -8}, {2, 3, C < -39}, {3, 3, C < -250}}


I then want to plot the surface given by



surf = {{1, 1, 18}, {2, 1, -13}, {3, 1, -224}, {1, 2, 

  11}, {2, 2, -20}, {3, 2, -231}, {1, 3,  -8}, {2, 3, 

   -39}, {3, 3, -250}}



ListPlot3D[surf,Mesh->All]


I can form the list of constraints using For loops



constraints = {};

For[B = 1, B <= 3, B++,

 For[A = 1, A <= 3, A++,

  f = (A)^5 + B^3 + p;

  sol  = Reduce[f < 20, p];

  constraints = Append[constraints, {A, B, sol}]

  ]

 ]

constraints


However I am not sure how to get from the list of constraints to the max permitted value for C and therefore get to the surf expression.



I also expect that For loops are not an ideal approach, and that I should be able to form lists of the A and B values and use another approach (Map, or Thread, or Apply maybe) with Reduce. I find these methods confusing though, and don't really understand anything but the most basic examples (so possibly similar questions have not helped me figure this out).






list-manipulation equation-solving







share|improve this question









$endgroup$




I have a function f(A,B,C) where for specific A and B values I can use Reduce to determine the constraint on C for my problem using a constraint on f. I want to plot the resulting surface.



To illustrate, consider



f = A^5 + B^3 + C^2


If A and B vary between 1 and 3 then I get the list of constraints (with f<20)



constraints = {{1, 1, C < 18}, {2, 1, C < -13}, {3, 1, C < -224}, {1, 2, C < 11}, {2, 2, C < -20}, {3, 2, C < -231}, {1, 3, C < -8}, {2, 3, C < -39}, {3, 3, C < -250}}


I then want to plot the surface given by



surf = {{1, 1, 18}, {2, 1, -13}, {3, 1, -224}, {1, 2, 

  11}, {2, 2, -20}, {3, 2, -231}, {1, 3,  -8}, {2, 3, 

   -39}, {3, 3, -250}}



ListPlot3D[surf,Mesh->All]


I can form the list of constraints using For loops



constraints = {};

For[B = 1, B <= 3, B++,

 For[A = 1, A <= 3, A++,

  f = (A)^5 + B^3 + p;

  sol  = Reduce[f < 20, p];

  constraints = Append[constraints, {A, B, sol}]

  ]

 ]

constraints


However I am not sure how to get from the list of constraints to the max permitted value for C and therefore get to the surf expression.



I also expect that For loops are not an ideal approach, and that I should be able to form lists of the A and B values and use another approach (Map, or Thread, or Apply maybe) with Reduce. I find these methods confusing though, and don't really understand anything but the most basic examples (so possibly similar questions have not helped me figure this out).






list-manipulation equation-solving




list-manipulation equation-solving






share|improve this question













share|improve this question











share|improve this question




share|improve this question










asked 20 hours ago









Esme_Esme_

24916




24916












  • $begingroup$
    Are A and B constrained to be integers?
    $endgroup$
    – Chris K
    17 hours ago










  • $begingroup$
    No they aren't - my actual function is quite complex so this is just a simple example. @Henrik Schumacher's solution works wonderfully, but I'd still like to know how to map across the list if anyone has a solution that works that way (just for general development of skills)
    $endgroup$
    – Esme_
    17 hours ago


















  • $begingroup$
    Are A and B constrained to be integers?
    $endgroup$
    – Chris K
    17 hours ago










  • $begingroup$
    No they aren't - my actual function is quite complex so this is just a simple example. @Henrik Schumacher's solution works wonderfully, but I'd still like to know how to map across the list if anyone has a solution that works that way (just for general development of skills)
    $endgroup$
    – Esme_
    17 hours ago
















$begingroup$
Are A and B constrained to be integers?
$endgroup$
– Chris K
17 hours ago




$begingroup$
Are A and B constrained to be integers?
$endgroup$
– Chris K
17 hours ago












$begingroup$
No they aren't - my actual function is quite complex so this is just a simple example. @Henrik Schumacher's solution works wonderfully, but I'd still like to know how to map across the list if anyone has a solution that works that way (just for general development of skills)
$endgroup$
– Esme_
17 hours ago




$begingroup$
No they aren't - my actual function is quite complex so this is just a simple example. @Henrik Schumacher's solution works wonderfully, but I'd still like to know how to map across the list if anyone has a solution that works that way (just for general development of skills)
$endgroup$
– Esme_
17 hours ago










1 Answer
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$begingroup$

f = a^5 + b^3 + c^2

RegionPlot3D[f <= 20, {a, 1, 3}, {b, 1, 3}, {c, -5, 5}, 

 AxesLabel -> {"a", "b", "c"}]


enter image description here






share|improve this answer











$endgroup$













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    $begingroup$

    f = a^5 + b^3 + c^2
    
RegionPlot3D[f <= 20, {a, 1, 3}, {b, 1, 3}, {c, -5, 5}, 
    
 AxesLabel -> {"a", "b", "c"}]


    enter image description here






    share|improve this answer











    $endgroup$


















      4












      $begingroup$

      f = a^5 + b^3 + c^2
      
RegionPlot3D[f <= 20, {a, 1, 3}, {b, 1, 3}, {c, -5, 5}, 
      
 AxesLabel -> {"a", "b", "c"}]


      enter image description here






      share|improve this answer











      $endgroup$
















        4












        4








        4





        $begingroup$

        f = a^5 + b^3 + c^2
        
RegionPlot3D[f <= 20, {a, 1, 3}, {b, 1, 3}, {c, -5, 5}, 
        
 AxesLabel -> {"a", "b", "c"}]


        enter image description here






        share|improve this answer











        $endgroup$



        f = a^5 + b^3 + c^2
        
RegionPlot3D[f <= 20, {a, 1, 3}, {b, 1, 3}, {c, -5, 5}, 
        
 AxesLabel -> {"a", "b", "c"}]


        enter image description here







        share|improve this answer














        share|improve this answer



        share|improve this answer








        edited 19 hours ago

























        answered 20 hours ago









        Henrik SchumacherHenrik Schumacher

        57.9k579159




        57.9k579159






























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