Thats amazing! Thx a lot for providing this documents! :)

I can learn a lot from you guys. I never used embeded components yet, as they weren't included in Maple 11, which I had till I upgraded to 15 now. But it looks like they are enormously useful and flexible to use! Also I never have written a proc yet - so guess it's getting time for me to learn that and do so 8).

Thx again acer! Your approach really gives a result like I always wanted it to look like and work! :)

Also thx again pagan for your help and information to the use of 'animate' and 'Explore'! :)

Thats amazing! Thx a lot for providing this documents! :)

I can learn a lot from you guys. I never used embeded components yet, as they weren't included in Maple 11, which I had till I upgraded to 15 now. But it looks like they are enormously useful and flexible to use! Also I never have written a proc yet - so guess it's getting time for me to learn that and do so 8).

Thx again acer! Your approach really gives a result like I always wanted it to look like and work! :)

Also thx again pagan for your help and information to the use of 'animate' and 'Explore'! :)

@pagan 

Here is the Document i promised: animation_on_B.mw

I'd also have one more question on Explore: Can I also explore more outputs at once? In my case for example: The plot of the flow + the coordinates of a fixed point that is moving around with varying the parameters?

thx again!

@pagan 

Here is the Document i promised: animation_on_B.mw

I'd also have one more question on Explore: Can I also explore more outputs at once? In my case for example: The plot of the flow + the coordinates of a fixed point that is moving around with varying the parameters?

thx again!

Hi pagan! :)

"…, you'll be able to see a new dialogue box which has editable entry fields for the width and height of that Component."

That works, thx! :)

"…, if you change either of the two range end-points for any of the Explore parameters to a float (eg, 2.0 instead of 2, or 0.0 instead of 0) then that slider will take on many more values between the major ticks"

Yes, I already know that. The reason why my graph doesn't change fluently is because the computation seems to be too expensive for that.

" Does that mean that you're calling DEplot with a new ode system, for each parameter value change?"

Yes thats basically it. I will upload the file tomorrow from Uni, containing only a plot and this animation, and some text for explanation. (The file has 13MB, and with the upload of my home internet that doesn't seem to work.. so please drop by again tomorrow for the file ;) )

The file works fine for me as it is with the standard number of 25 frames. When I however change to 50 frames by adding "frames=50" to the animate options, I get the saving problem described.

kernelopts(bytesalloc) = 205745360 for the 25 frames version

kernelopts(bytesalloc) = 345311480 for the 50 frames version

Thx a lot, you are a great help! :)

Hi pagan! :)

"…, you'll be able to see a new dialogue box which has editable entry fields for the width and height of that Component."

That works, thx! :)

"…, if you change either of the two range end-points for any of the Explore parameters to a float (eg, 2.0 instead of 2, or 0.0 instead of 0) then that slider will take on many more values between the major ticks"

Yes, I already know that. The reason why my graph doesn't change fluently is because the computation seems to be too expensive for that.

" Does that mean that you're calling DEplot with a new ode system, for each parameter value change?"

Yes thats basically it. I will upload the file tomorrow from Uni, containing only a plot and this animation, and some text for explanation. (The file has 13MB, and with the upload of my home internet that doesn't seem to work.. so please drop by again tomorrow for the file ;) )

The file works fine for me as it is with the standard number of 25 frames. When I however change to 50 frames by adding "frames=50" to the animate options, I get the saving problem described.

kernelopts(bytesalloc) = 205745360 for the 25 frames version

kernelopts(bytesalloc) = 345311480 for the 50 frames version

Thx a lot, you are a great help! :)

That was very usefull, thanks! It works indeed :)

Maybe you can help me out more:

In the new Document where the plot is explored, the plot is presented in standard size. Usually I then click on the plot and adjust the size with the mouse as big as I want it to be, but within that interface I can't. How can I do it? Is there a plot-option for that? I didn't find one so far.

One thing that would speak for using animate instead of Explore is, that it calculates everything in advance. So it takes a bit longer till I see the result, but then it runs all fluent.

However with animate I have the problem stated above. Do you maybe know why I cant save my Document or quit Maple after I run an "expensive" animation?

Further, is there a way to animate more than one parameter in advance? In another topic people told me I could simply use animate within animate. This works indeed, but parameters aren't changeable independently with two sliders then.

Is animate and Explore the only ways? Can I tell Explore to calculate everything in advance, instead of calculating life?

Thx :)

That was very usefull, thanks! It works indeed :)

Maybe you can help me out more:

In the new Document where the plot is explored, the plot is presented in standard size. Usually I then click on the plot and adjust the size with the mouse as big as I want it to be, but within that interface I can't. How can I do it? Is there a plot-option for that? I didn't find one so far.

One thing that would speak for using animate instead of Explore is, that it calculates everything in advance. So it takes a bit longer till I see the result, but then it runs all fluent.

However with animate I have the problem stated above. Do you maybe know why I cant save my Document or quit Maple after I run an "expensive" animation?

Further, is there a way to animate more than one parameter in advance? In another topic people told me I could simply use animate within animate. This works indeed, but parameters aren't changeable independently with two sliders then.

Is animate and Explore the only ways? Can I tell Explore to calculate everything in advance, instead of calculating life?

Thx :)

Here is the Document with the issue. Thx a lot! :)

case_and_assumptions.mw

Here is the Document with the issue. Thx a lot! :)

case_and_assumptions.mw

Hi Doug!

I thought of this solution already, but it didn't want to work. Maple sometimes decided to give me the output, and two minutes later it decided to give me a spinning ball of death.

But something is fishy with this anyway. In my opinion the output maple is giving me for a simple solve command is wrong! Maybe you can tell me if I am doing something wrong here:

All I wanted to do is this:

> fb := proc (H, Sigma) options operator, arrow; -(1-H^2)*(2*Sigma^2+(1/2+(3/2)*w)*(1-Sigma^2)-H*Sigma), -(2-2*Sigma^2-(1/2+(3/2)*w)*(1-Sigma^2))*H*Sigma-(1-H^2)*(1-Sigma^2)-(1/2)*(3-3*Sigma^2)*(-w+1)*beta end proc;
print(`output redirected...`); # input placeholder
  (H, Sigma) -> 

     /     2\ /       2   /1   3  \ /         2\          \  
    -\1 - H / |2 Sigma  + |- + - w| \1 - Sigma / - H Sigma|, 
              \           \2   2  /                       /  
   /           2   /1   3  \ /         2\\        
  -|2 - 2 Sigma  - |- + - w| \1 - Sigma /| H Sigma
   \               \2   2  /             /        

       /     2\ /         2\   1 /           2\              
     - \1 - H / \1 - Sigma / - - \3 - 3 Sigma / (-w + 1) beta
                               2                             

> `assuming`([solve({fb(H, Sigma)[1] = 0, fb(H, Sigma)[2] = 0}, [H, Sigma], useassumptions)], [H > 0]);
print(`output redirected...`); # input placeholder
         /                                    /             
         |                 1                  |             
piecewise|----------------------------------- \(3 beta w - 2
         |              2                                   
         |-1 + 6 w - 9 w  - 6 beta + 6 beta w               
         \                                                  

                                                 (1/2)\      [[    
             /             2                    \     |      [[    
   - 3 beta) \1 - 6 w + 9 w  + 6 beta - 6 beta w/     / < 0, [[H = 
                                                             [[    
                                                             [[    
                                                             [[    

                                        /                        
                     1                  |                        
  - ----------------------------------- \(3 beta w - 2 - 3 beta) 
                  2                                              
    -1 + 6 w - 9 w  - 6 beta + 6 beta w                          

                                      (1/2)\  
  /             2                    \     |  
  \1 - 6 w + 9 w  + 6 beta - 6 beta w/     /, 

                                                     ]  
                             1 + 3 w                 ]  
  Sigma = - -----------------------------------------], 
                                                (1/2)]  
            /             2                    \     ]  
            \1 - 6 w + 9 w  + 6 beta - 6 beta w/     ]  

  [H = 1, Sigma = 1], [H = 1, Sigma = -1], 

                                            ]      
                                            ]      
  [H = 1, Sigma = -beta], [H = 2, Sigma = 1]], 0 < 
                                            ]      
                                            ]      
                                            ]      

                                      /                        
                   1                  |                        
  ----------------------------------- \(3 beta w - 2 - 3 beta) 
                2                                              
  -1 + 6 w - 9 w  - 6 beta + 6 beta w                          

                                      (1/2)\  [[    
  /             2                    \     |  [[    
  \1 - 6 w + 9 w  + 6 beta - 6 beta w/     /, [[H = 
                                              [[    
                                              [[    
                                              [[    

                                      /                        
                   1                  |                        
  ----------------------------------- \(3 beta w - 2 - 3 beta) 
                2                                              
  -1 + 6 w - 9 w  - 6 beta + 6 beta w                          

                                      (1/2)\  
  /             2                    \     |  
  \1 - 6 w + 9 w  + 6 beta - 6 beta w/     /, 

                                                   ]  
                           1 + 3 w                 ]  
  Sigma = -----------------------------------------], 
                                              (1/2)]  
          /             2                    \     ]  
          \1 - 6 w + 9 w  + 6 beta - 6 beta w/     ]  

  [H = 1, Sigma = 1], [H = 1, Sigma = -1], 

                                            ]    \
                                            ]    |
  [H = 1, Sigma = -beta], [H = 2, Sigma = 1]], []|
                                            ]    |
                                            ]    |
                                            ]    /

And in my opinion this output is wrong in the following sense: When looking at the equations one sees by naked eye that (1,±1), (2,1) and (1,-beta) are solutions in any case. But they aren't listed in the last case! Further I think I once took a closer look on the first case, and found that it is a contradiction on its own, as in this case H and Sigma of the first solution get complex, but H is assumed to be >0. (But I didn't write the latter down properly, and can't remember for sure).

Do you have an idea whats going on here? -.^

Hi Doug!

I thought of this solution already, but it didn't want to work. Maple sometimes decided to give me the output, and two minutes later it decided to give me a spinning ball of death.

But something is fishy with this anyway. In my opinion the output maple is giving me for a simple solve command is wrong! Maybe you can tell me if I am doing something wrong here:

All I wanted to do is this:

> fb := proc (H, Sigma) options operator, arrow; -(1-H^2)*(2*Sigma^2+(1/2+(3/2)*w)*(1-Sigma^2)-H*Sigma), -(2-2*Sigma^2-(1/2+(3/2)*w)*(1-Sigma^2))*H*Sigma-(1-H^2)*(1-Sigma^2)-(1/2)*(3-3*Sigma^2)*(-w+1)*beta end proc;
print(`output redirected...`); # input placeholder
  (H, Sigma) -> 

     /     2\ /       2   /1   3  \ /         2\          \  
    -\1 - H / |2 Sigma  + |- + - w| \1 - Sigma / - H Sigma|, 
              \           \2   2  /                       /  
   /           2   /1   3  \ /         2\\        
  -|2 - 2 Sigma  - |- + - w| \1 - Sigma /| H Sigma
   \               \2   2  /             /        

       /     2\ /         2\   1 /           2\              
     - \1 - H / \1 - Sigma / - - \3 - 3 Sigma / (-w + 1) beta
                               2                             

> `assuming`([solve({fb(H, Sigma)[1] = 0, fb(H, Sigma)[2] = 0}, [H, Sigma], useassumptions)], [H > 0]);
print(`output redirected...`); # input placeholder
         /                                    /             
         |                 1                  |             
piecewise|----------------------------------- \(3 beta w - 2
         |              2                                   
         |-1 + 6 w - 9 w  - 6 beta + 6 beta w               
         \                                                  

                                                 (1/2)\      [[    
             /             2                    \     |      [[    
   - 3 beta) \1 - 6 w + 9 w  + 6 beta - 6 beta w/     / < 0, [[H = 
                                                             [[    
                                                             [[    
                                                             [[    

                                        /                        
                     1                  |                        
  - ----------------------------------- \(3 beta w - 2 - 3 beta) 
                  2                                              
    -1 + 6 w - 9 w  - 6 beta + 6 beta w                          

                                      (1/2)\  
  /             2                    \     |  
  \1 - 6 w + 9 w  + 6 beta - 6 beta w/     /, 

                                                     ]  
                             1 + 3 w                 ]  
  Sigma = - -----------------------------------------], 
                                                (1/2)]  
            /             2                    \     ]  
            \1 - 6 w + 9 w  + 6 beta - 6 beta w/     ]  

  [H = 1, Sigma = 1], [H = 1, Sigma = -1], 

                                            ]      
                                            ]      
  [H = 1, Sigma = -beta], [H = 2, Sigma = 1]], 0 < 
                                            ]      
                                            ]      
                                            ]      

                                      /                        
                   1                  |                        
  ----------------------------------- \(3 beta w - 2 - 3 beta) 
                2                                              
  -1 + 6 w - 9 w  - 6 beta + 6 beta w                          

                                      (1/2)\  [[    
  /             2                    \     |  [[    
  \1 - 6 w + 9 w  + 6 beta - 6 beta w/     /, [[H = 
                                              [[    
                                              [[    
                                              [[    

                                      /                        
                   1                  |                        
  ----------------------------------- \(3 beta w - 2 - 3 beta) 
                2                                              
  -1 + 6 w - 9 w  - 6 beta + 6 beta w                          

                                      (1/2)\  
  /             2                    \     |  
  \1 - 6 w + 9 w  + 6 beta - 6 beta w/     /, 

                                                   ]  
                           1 + 3 w                 ]  
  Sigma = -----------------------------------------], 
                                              (1/2)]  
          /             2                    \     ]  
          \1 - 6 w + 9 w  + 6 beta - 6 beta w/     ]  

  [H = 1, Sigma = 1], [H = 1, Sigma = -1], 

                                            ]    \
                                            ]    |
  [H = 1, Sigma = -beta], [H = 2, Sigma = 1]], []|
                                            ]    |
                                            ]    |
                                            ]    /

And in my opinion this output is wrong in the following sense: When looking at the equations one sees by naked eye that (1,±1), (2,1) and (1,-beta) are solutions in any case. But they aren't listed in the last case! Further I think I once took a closer look on the first case, and found that it is a contradiction on its own, as in this case H and Sigma of the first solution get complex, but H is assumed to be >0. (But I didn't write the latter down properly, and can't remember for sure).

Do you have an idea whats going on here? -.^

thanks a lot : )

thanks a lot : )

Thanks for the detailed description! :)