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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

asked yesterday

Esme_Esme_

24917

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Are A and B constrained to be integers?
  $endgroup$
  – Chris K
  yesterday
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  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_
  yesterday
  

  
  
  
  

add a comment | 

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

asked yesterday

Esme_Esme_

24917

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Are A and B constrained to be integers?
  $endgroup$
  – Chris K
  yesterday
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  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_
  yesterday
  

  
  
  
  

add a comment | 

$begingroup$

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

asked yesterday

Esme_Esme_

24917

$endgroup$

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

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

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]

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

share|improve this question

asked yesterday

Esme_Esme_

24917

share|improve this question

asked yesterday

Esme_Esme_

24917

asked yesterday

Esme_Esme_

24917

asked yesterday

Esme_Esme_

24917

1 Answer
1

active

oldest

votes

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"]

share|improve this answer

edited yesterday

answered yesterday

Henrik SchumacherHenrik Schumacher

58.1k580160

$endgroup$

add a comment | 

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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"]

share|improve this answer

edited yesterday

answered yesterday

Henrik SchumacherHenrik Schumacher

58.1k580160

$endgroup$

add a comment | 

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"]

share|improve this answer

edited yesterday

answered yesterday

Henrik SchumacherHenrik Schumacher

58.1k580160

$endgroup$

add a comment | 

$begingroup$

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

share|improve this answer

edited yesterday

answered yesterday

Henrik SchumacherHenrik Schumacher

58.1k580160

$endgroup$

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

share|improve this answer

edited yesterday

answered yesterday

Henrik SchumacherHenrik Schumacher

58.1k580160

answered yesterday

Henrik SchumacherHenrik Schumacher

58.1k580160

answered yesterday

Henrik SchumacherHenrik Schumacher

58.1k580160