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Color Error in plot ...

Asked by: Najibeh Borhani 50
plot
June 09 2022
1  4

Hi.

What wrong could be there with the color line?

> 

restart:
> 

with(plots):
> 

equ1 := BesselJ(sqrt(17)/2, 10*sqrt(t)*sqrt(2))/t^(1/4) + BesselY(sqrt(17)/2, 10*sqrt(t)*sqrt(2))/t^(1/4):
> 

equ2 := BesselJ(sqrt(17)/2, 10*sqrt(t)*sqrt(2))/t^(1/4) + 5*BesselY(sqrt(17)/2, 10*sqrt(t)*sqrt(2))/t^(1/4):
> 

equ3 := BesselJ(sqrt(17)/2, 10*sqrt(t))/t^(1/4) + 5*BesselY(sqrt(17)/2, 10*sqrt(t))/t^(1/4):
> 

tmax   := 30:
colors := ["Red", "Violet", "Blue"]:

p1 := plot([equ1, equ2, equ3], t = 0 .. tmax, labels = [t, T[2](t)], tickmarks = [0, 0], labelfont = [TIMES, ITALIC, 12], axes = boxed, color = colors):

ymin := min(op~(1, op~(2, op~(2, [plottools:-getdata(p1)])))):
ymax := max(op~(2, op~(2, op~(2, [plottools:-getdata(p1)])))):
dy   := 2*ymax:
> 

legend1 := typeset(C[3] = 1, ` , `, C[4] = 1, ` , `, Omega^2 = 50):
legend2 := typeset(C[3] = 1, ` , `, C[4] = 5, ` , `, Omega^2 = 50):
legend3 := typeset(C[3] = 1, ` , `, C[4] = 5, ` , `, Omega^2 = 25):

p2 := seq(textplot([tmax-2, ymax-k*dy/20, legend||k], align=left), k=1..3):
> 

p3 := seq(plot([[tmax-2, ymax-k*dy/20], [tmax-1, ymax-k*dy/20]], color=colors[k]), k=1..3):
display(p1, p2, p3, view=[default, -ymax..ymax], size=[800, 500])

Error, (in plot) invalid color specification: colors[1]

  

display(p1, p2, p3, view = [default, -ymax .. ymax], size = [800, 500])

 (1)
> 

 

Download Legend_Inside.mw

How to speed up the calculation of the double inte...

Asked by: mehdibgh 235
performance integration legendrep
June 03 2022
1  1

I want to calculate the double integral of the following expression which includes sum of several Legendre polynomial terms, but the speed is so low. Any suggestion to speed up the calculation?

NULL

> 

Restart:
> 

NULL
> 

II := 9:
> 

JJ := 9:
> 

M := 9:
> 

NULL
> 

`ΔP1` := add(add(add(add(add(add(add(-(LegendreP(i, zeta__1)*LegendreP(j, eta__1)*(diff(diff(tau[r](t), t), t))+LegendreP(m, zeta__1)*LegendreP(j, eta__1)*(diff(tau[r](t), t))+LegendreP(m, zeta__1)*LegendreP(j, eta__1)*tau[r](t))/sqrt(LegendreP(m, zeta__1)*LegendreP(j, eta__1)+LegendreP(i, zeta__1)*LegendreP(l, eta__1)), i = 1 .. II), j = 1 .. JJ), k = 1 .. II), m = 1 .. II), l = 1 .. JJ), n = 1 .. JJ), r = 1 .. M):
> 

A := int(int(`ΔP1`, zeta__1 = -1 .. 1), eta__1 = -1 .. 1):
> 

A

``

Download Soal.mw

CompositionSeries just work in transitive group?...

Asked by: jud 145
group-theory
May 31 2022
1  3

When I run this code, I will get a error information:

CompositionSeries(SmallGroup(336, 209))

It's mean this function just work in transitive group? But IsTransitive(SmallGroup(336, 209)) will get true. Is it a bug of maple? Or do I have any misunderstandings?

densityplot legend...

Asked by: omkardpd 35
densityplot plotting colorbar
May 30 2022
1  1

Hi,

I am using the following (dummy) code to generate a density plot.

densityplot(x-y^2, x=-5..5, y=-5..5, axes=boxed, style=patchnogrid, numpoints=1000, legendstyle=[location=bottom], labels=[x, y]);

While this command does generate x vs y plots with varying color shared, I cannot figure out where the function (x-y^2) value by looking at the color shades. Is there a way to produce a legend along with the plot that will demonstrate how the function is taking different values with parameters? 

I found a similar post, dated 2005, that suggests using the "s_tyle=" command. However, it does not work for some reasons. I would appreciate help in this regard. 

Thank you,

Omkar

How to solve the given BVP using differential tran...

Asked by: Madhukesh J K 140
ode homework dsolve
May 29 2022
2  1

HI, I have numerically solved the given problem using the dsolve command But I want to solve the same problem using the Differential transformation method.
Can anyone help me to get the series solution for the given problem using DTM.

I want to compare the numerical results with DTM results when lambda =0.5.

eqn1 := diff(f(eta), `$`(eta, 3))+f(eta)*(diff(f(eta), `$`(eta, 2)))-(diff(f(eta), eta))^2-lambda*(diff(f(eta), eta)) = 0.

eqn2 := diff(theta(eta), `$`(eta, 2))+f(eta)*(diff(theta(eta), eta))*Pr = 0

Bcs := (D(f))(0) = 1, f(0) = 0, (D(f))(infinity) = 0, theta(0) = 1, theta(infinity) = 0;

[lambda = .5, Pr = 6.3]

package of Fractional Symmetry ASPv4.6.3.mpl...

Asked by: shaban1362 5
differential-equations
May 26 2022
2  2

restart;
read "C:/Program Files/Maple 2020/lib/ASP v4.6.3.txt";

    DESOLVII_V5R5 (March 2011)(c), by Dr. K. T. Vu, Dr. J.

       Carminati and Miss G. Jefferson

 

The authors kindly request that this software be referenced, if

   it is used in work eventuating in a publication, by citing

   the article:


  K.T. Vu, G.F. Jefferson, J. Carminati, Finding generalised

     symmetries of differential equations


  using the MAPLE package DESOLVII,Comput. Phys. Commun. 183

     (2012) 1044-1054.

 

                         -------------

 ASP (November 2011), by Miss G. Jefferson and Dr. J. Carminati


The authors kindly request that this software be referenced, if

   it is used in work eventuating in a publication, by citing

   the article:


     G.F. Jefferson, J. Carminati, ASP: Automated Symbolic

        Computation of Approximate Symmetries


   of Differential Equations, Comput. Phys. Comm. 184 (2013)

      1045-1063.

 

 [classify, comtab, defeqn, deteq_split, extgenerator, gendef,

   genvec, icde_cons, liesolve, mod_eq, originalVar, pdesolv,

   reduceVar, reduceVargen, symmetry, varchange]


                     ASP := _m2229977204928

with(ASP);
       [ApproximateSymmetry, applygenerator, commutator]

with(desolv);
 [classify, comtab, defeqn, deteq_split, extgenerator, gendef,

   genvec, icde_cons, liesolve, mod_eq, originalVar, pdesolv,

   reduceVar, reduceVargen, symmetry, varchange]


read "C:/Program Files/Maple 2020/lib/FracSym.v1.16.txt";
FracSym (April 2013), by Miss G. Jefferson and Dr. J. Carminati


The authors kindly request that this software be referenced, if

   it is used in work eventuating in a publication, by citing:


   G.F. Jefferson, J. Carminati, FracSym: Automated symbolic

      computation of Lie symmetries


   of fractional differential equations, Comput. Phys. Comm.

      Submitted May 2013.

 

with(FracSym);
[Rfracdiff, TotalD, applyFracgen, evalTotalD, expandsum, fracDet,

  fracGen, split]


Rfracdiff(u(x, t), t, alpha);
                          alpha          
                       D[t     ](u(x, t))

Rfracdiff(u(x, t) &* v(x, t), t, alpha);
infinity                                                          
 -----                                                            
  \                                                               
   )                          (alpha - n)              n          
  /     binomial(alpha, n) D[t           ](u(x, t)) D[t ](v(x, t))
 -----                                                            
 n = 0                                                            

Rfracdiff(v(x, t) &* u(x, t), t, alpha);
infinity                                                          
 -----                                                            
  \                                                               
   )                          (alpha - n)              n          
  /     binomial(alpha, n) D[t           ](v(x, t)) D[t ](u(x, t))
 -----                                                            
 n = 0                                                            

Rfracdiff(u(x, t) &* v(x, t), t, 2);
     /  2         \                                        
     | d          |             / d         \ / d         \
     |---- u(x, t)| v(x, t) + 2 |--- u(x, t)| |--- v(x, t)|
     |   2        |             \ dt        / \ dt        /
     \ dt         /                                        

                  /  2         \
                  | d          |
        + u(x, t) |---- v(x, t)|
                  |   2        |
                  \ dt         /


TotalD(xi[x](x, y), x, 2);
                          2              
                       D[x ](xi[x](x, y))

evalTotalD([%], [y], [x]);
     [     /  2             \     /   2              \    
     [   2 | d              |     |  d               |    
     [y_x  |---- xi[x](x, y)| + 2 |------ xi[x](x, y)| y_x
     [     |   2            |     \ dy dx            /    
     [     \ dy             /                             

                                   /  2             \]
               / d             \   | d              |]
        + y_xx |--- xi[x](x, y)| + |---- xi[x](x, y)|]
               \ dy            /   |   2            |]
                                   \ dx             /]


fde1 := Rfracdiff(u(x, t), t, alpha) = -u(x, t)*diff(u(x, t), x) - diff(u(x, t), x, x) - diff(u(x, t), x, x, x) - diff(u(x, t), x, x, x, x);
                alpha                      / d         \
     fde1 := D[t     ](u(x, t)) = -u(x, t) |--- u(x, t)|
                                           \ dx        /

          /  2         \   /  3         \   /  4         \
          | d          |   | d          |   | d          |
        - |---- u(x, t)| - |---- u(x, t)| - |---- u(x, t)|
          |   2        |   |   3        |   |   4        |
          \ dx         /   \ dx         /   \ dx         /


deteqs := fracDet([fde1], [u], [x, t], 2);
  Intervals/values considered for the fractional derivative/s:

                     {0 < alpha, alpha < 1}

          [                                           
          [                                           
          [[  2                                       
          [[ d                     d                  
deteqs := [[---- eta[u](x, t, u), --- xi[t](x, t, u),
          [[   2                   du                 
          [[ du                                       

   d                   d                   d                  
  --- xi[t](x, t, u), --- xi[t](x, t, u), --- xi[x](x, t, u),
   du                  dx                  du                 

                        2                    2                  
   d                   d                    d                   
  --- xi[x](x, t, u), ---- xi[t](x, t, u), ---- xi[t](x, t, u),
   du                    2                    2                 
                       du                   du                  

    2                                              
   d                         / d                \  
  ---- xi[t](x, t, u), alpha |--- xi[x](x, t, u)|,
     2                       \ dt               /  
   du                                              

                                2                  
        / d                \   d                   
  alpha |--- xi[x](x, t, u)|, ---- xi[t](x, t, u),
        \ du               /     2                 
                               du                  

    2                    2                    3                  
   d                    d                    d                   
  ---- xi[x](x, t, u), ---- xi[x](x, t, u), ---- xi[t](x, t, u),
     2                    2                    3                 
   du                   du                   du                  

    3                    3                    4                  
   d                    d                    d                   
  ---- xi[t](x, t, u), ---- xi[x](x, t, u), ---- xi[t](x, t, u),
     3                    3                    4                 
   du                   du                   du                  

    4                  
   d                   
  ---- xi[x](x, t, u),
     4                 
   du                  

     /  2                \                           
     | d                 |     / d                \  
  -6 |---- xi[t](x, t, u)| - 3 |--- xi[t](x, t, u)|,
     |   2               |     \ dx               /  
     \ dx                /                           

        / d                \     / d                \  
  alpha |--- xi[t](x, t, u)| - 4 |--- xi[x](x, t, u)|,
        \ dt               /     \ dx               /  

  / d                \              
  |--- xi[t](x, t, u)| (alpha - 1),
  \ du               /              

                               /   2                 \  
     / d                \      |  d                  |  
  -3 |--- xi[t](x, t, u)| - 12 |------ xi[t](x, t, u)|,
     \ du               /      \ dx du               /  

        / d                \              
  alpha |--- xi[t](x, t, u)| (alpha - 1),
        \ du               /              

        / d                \              
  alpha |--- xi[x](x, t, u)| (alpha - 1),
        \ du               /              

     /  2                \      /   3                  \  
     | d                 |      |  d                   |  
  -3 |---- xi[t](x, t, u)| - 12 |------- xi[t](x, t, u)|,
     |   2               |      |      2               |  
     \ du                /      \ dx du                /  

        /   2                 \              
        |  d                  |              
  alpha |------ xi[t](x, t, u)| (alpha - 1),
        \ du dt               /              

        /   2                 \              
        |  d                  |              
  alpha |------ xi[x](x, t, u)| (alpha - 1),
        \ du dt               /              

        /  2                \              
        | d                 |              
  alpha |---- xi[t](x, t, u)| (alpha - 1),
        |   2               |              
        \ du                /              

        /  2                \              
        | d                 |              
  alpha |---- xi[x](x, t, u)| (alpha - 1),
        |   2               |              
        \ dt                /              

        /  2                \              
        | d                 |              
  alpha |---- xi[x](x, t, u)| (alpha - 1),
        |   2               |              
        \ du                /              

   /  3                \     /   4                  \  
   | d                 |     |  d                   |  
  -|---- xi[t](x, t, u)| - 4 |------- xi[t](x, t, u)|,
   |   3               |     |      3               |  
   \ du                /     \ dx du                /  
                          /   2                 \
 / d                \     |  d                  |
-|--- xi[t](x, t, u)| - 4 |------ xi[t](x, t, u)|
 \ du               /     \ dx du               /

           / d                \     / d                \
   + alpha |--- xi[t](x, t, u)|, -4 |--- xi[x](x, t, u)|
           \ du               /     \ du               /

       /  2                 \      /   2                 \  
       | d                  |      |  d                  |  
   + 4 |---- eta[u](x, t, u)| - 16 |------ xi[x](x, t, u)|,
       |   2                |      \ dx du               /  
       \ du                 /                               
                            /  2                 \
   / d                \     | d                  |
-3 |--- xi[x](x, t, u)| + 3 |---- eta[u](x, t, u)|
   \ du               /     |   2                |
                            \ du                 /

        /   2                 \     /  3                \
        |  d                  |     | d                 |
   - 12 |------ xi[x](x, t, u)|, -4 |---- xi[t](x, t, u)|
        \ dx du               /     |   3               |
                                    \ dx                /

                                /  2                \  
       / d                \     | d                 |  
   - 2 |--- xi[t](x, t, u)| - 3 |---- xi[t](x, t, u)|,
       \ dx               /     |   2               |  
                                \ dx                /  
   /   2                 \      /   3                  \
   |  d                  |      |  d                   |
-6 |------ xi[t](x, t, u)| - 12 |------- xi[t](x, t, u)|
   \ dx du               /      |   2                  |
                                \ dx  du               /

       / d                \  
   - 2 |--- xi[t](x, t, u)|,
       \ du               /  

        / d                \                          
  alpha |--- xi[t](x, t, u)| (alpha - 1) (alpha - 2),
        \ du               /                          
   /  2                \     /  3                 \
   | d                 |     | d                  |
-6 |---- xi[x](x, t, u)| + 6 |---- eta[u](x, t, u)|
   |   2               |     |   3                |
   \ du                /     \ du                 /

        /   3                  \     /   3                  \
        |  d                   |     |  d                   |
   - 24 |------- xi[x](x, t, u)|, -3 |------- xi[t](x, t, u)|
        |      2               |     |      2               |
        \ dx du                /     \ dx du                /

       /    4                  \   /  2                \         
       |   d                   |   | d                 |        /
   - 6 |-------- xi[t](x, t, u)| - |---- xi[t](x, t, u)|, alpha |
       |   2   2               |   |   2               |        \
       \ dx  du                /   \ du                /         

   d                \     / d                \
  --- xi[t](x, t, u)| - 3 |--- xi[x](x, t, u)|
   dt               /     \ dx               /

       /   2                  \     /  2                \  
       |  d                   |     | d                 |  
   + 4 |------ eta[u](x, t, u)| - 6 |---- xi[x](x, t, u)|,
       \ dx du                /     |   2               |  
                                    \ dx                /  

        /   2                 \                          
        |  d                  |                          
  alpha |------ xi[t](x, t, u)| (alpha - 1) (alpha - 2),
        \ du dt               /                          

        /  2                \                          
        | d                 |                          
  alpha |---- xi[t](x, t, u)| (alpha - 1) (alpha - 2),
        |   2               |                          
        \ du                /                          
   /   2                 \     /   3                  \
   |  d                  |     |  d                   |
-3 |------ xi[t](x, t, u)| - 6 |------- xi[t](x, t, u)|
   \ dx du               /     |   2                  |
                               \ dx  du               /

                                                              /
     / d                \         / d                \        |
   - |--- xi[t](x, t, u)| + alpha |--- xi[t](x, t, u)|, alpha |
     \ du               /         \ du               /        |
                                                              \
       /  2                \     /   2                  \
       | d                 |     |  d                   |
-alpha |---- xi[t](x, t, u)| + 2 |------ eta[u](x, t, u)|
       |   2               |     \ du dt                /
       \ dt                /                             

     /  2                \\   /  3                \
     | d                 ||   | d                 |
   + |---- xi[t](x, t, u)||, -|---- xi[x](x, t, u)|
     |   2               ||   |   3               |
     \ dt                //   \ du                /

       /   4                  \   /  4                 \  
       |  d                   |   | d                  |  
   - 4 |------- xi[x](x, t, u)| + |---- eta[u](x, t, u)|,
       |      3               |   |   4                |  
       \ dx du                /   \ du                 /  
                          /  2                \
   / d                \   | d                 |
-u |--- xi[t](x, t, u)| - |---- xi[t](x, t, u)|
   \ dx               /   |   2               |
                          \ dx                /

     /  3                \   /  4                \  
     | d                 |   | d                 |  
   - |---- xi[t](x, t, u)| - |---- xi[t](x, t, u)|,
     |   3               |   |   4               |  
     \ dx                /   \ dx                /  

        /   3                  \                          
        |  d                   |                          
  alpha |------- xi[t](x, t, u)| (alpha - 1) (alpha - 2),
        |      2               |                          
        \ du dt                /                          

        /   3                  \                          
        |  d                   |                          
  alpha |------- xi[t](x, t, u)| (alpha - 1) (alpha - 2),
        |   2                  |                          
        \ du  dt               /                          

        /  3                \                          
        | d                 |                          
  alpha |---- xi[t](x, t, u)| (alpha - 1) (alpha - 2),
        |   3               |                          
        \ du                /                          
                            /  2                 \
   / d                \     | d                  |
-3 |--- xi[x](x, t, u)| + 3 |---- eta[u](x, t, u)|
   \ du               /     |   2                |
                            \ du                 /

       /   2                 \      /   3                   \
       |  d                  |      |  d                    |
   - 9 |------ xi[x](x, t, u)| + 12 |------- eta[u](x, t, u)|
       \ dx du               /      |      2                |
                                    \ dx du                 /

        /   3                  \                              
        |  d                   |        / d                \  
   - 18 |------- xi[x](x, t, u)|, alpha |--- xi[t](x, t, u)| u
        |   2                  |        \ du               /  
        \ dx  du               /                              

       /   3                  \     /   4                  \
       |  d                   |     |  d                   |
   - 3 |------- xi[t](x, t, u)| - 4 |------- xi[t](x, t, u)|
       |   2                  |     |   3                  |
       \ dx  du               /     \ dx  du               /

       /   2                 \                                  
       |  d                  |   / d                \          /
   - 2 |------ xi[t](x, t, u)| - |--- xi[t](x, t, u)| u, alpha |
       \ dx du               /   \ du               /          \

                          /  3                \
   d                \     | d                 |
  --- xi[t](x, t, u)| - 4 |---- xi[x](x, t, u)|
   dt               /     |   3               |
                          \ dx                /

       /  2                \                         
       | d                 |     / d                \
   - 3 |---- xi[x](x, t, u)| - 2 |--- xi[x](x, t, u)|
       |   2               |     \ dx               /
       \ dx                /                         

       /   3                   \     /   2                  \  
       |  d                    |     |  d                   |  
   + 6 |------- eta[u](x, t, u)| + 3 |------ eta[u](x, t, u)|,
       |   2                   |     \ dx du                /  
       \ dx  du                /                               
 /  2                \   /  3                 \
 | d                 |   | d                  |
-|---- xi[x](x, t, u)| + |---- eta[u](x, t, u)|
 |   2               |   |   3                |
 \ du                /   \ du                 /

       /   3                  \     /   4                   \
       |  d                   |     |  d                    |
   - 3 |------- xi[x](x, t, u)| + 4 |------- eta[u](x, t, u)|
       |      2               |     |      3                |
       \ dx du                /     \ dx du                 /

       /    4                  \              /
       |   d                   |              |
   - 6 |-------- xi[x](x, t, u)|, (alpha - 1) |
       |   2   2               |              |
       \ dx  du                /              \
       /  3                \     /   3                   \
       | d                 |     |  d                    |
-alpha |---- xi[t](x, t, u)| + 3 |------- eta[u](x, t, u)|
       |   3               |     |      2                |
       \ dt                /     \ du dt                 /

       /  3                \\                               
       | d                 ||           / d                \
   + 2 |---- xi[t](x, t, u)|| alpha, -u |--- xi[x](x, t, u)|
       |   3               ||           \ du               /
       \ dt                //                               

     /  2                 \     /   2                 \
     | d                  |     |  d                  |
   + |---- eta[u](x, t, u)| - 2 |------ xi[x](x, t, u)|
     |   2                |     \ dx du               /
     \ du                 /                            

       /   3                   \     /   3                  \
       |  d                    |     |  d                   |
   + 3 |------- eta[u](x, t, u)| - 3 |------- xi[x](x, t, u)|
       |      2                |     |   2                  |
       \ dx du                 /     \ dx  du               /

       /   4                  \     /    4                   \  
       |  d                   |     |   d                    |  
   - 4 |------- xi[x](x, t, u)| + 6 |-------- eta[u](x, t, u)|,
       |   3                  |     |   2   2                |  
       \ dx  du               /     \ dx  du                 /  
   / d                \                  
-u |--- xi[x](x, t, u)| + eta[u](x, t, u)
   \ dx               /                  

                                      /   2                  \
           / d                \       |  d                   |
   + alpha |--- xi[t](x, t, u)| u + 2 |------ eta[u](x, t, u)|
           \ dt               /       \ dx du                /

     /  2                \     /   3                   \
     | d                 |     |  d                    |
   - |---- xi[x](x, t, u)| + 3 |------- eta[u](x, t, u)|
     |   2               |     |   2                   |
     \ dx                /     \ dx  du                /

     /  3                \     /   4                   \
     | d                 |     |  d                    |
   - |---- xi[x](x, t, u)| + 4 |------- eta[u](x, t, u)|
     |   3               |     |   3                   |
     \ dx                /     \ dx  du                /

                             [                          
                             [                          
     /  4                \]  [                          
     | d                 |]  [                          
   - |---- xi[x](x, t, u)|], [xi[t](x, 0, u) = 0, (Diff(
     |   4               |]  [                          
     \ dx                /]  [                          

                                   / d                 \
  eta[u](x, t, u), t $ alpha)) + u |--- eta[u](x, t, u)|
                                   \ dx                /

       /    / d                            \\
   - u |Diff|--- eta[u](x, t, u), t $ alpha||
       \    \ du                           //

     /  3                 \   /  4                 \
     | d                  |   | d                  |
   + |---- eta[u](x, t, u)| + |---- eta[u](x, t, u)|
     |   3                |   |   4                |
     \ dx                 /   \ dx                 /

                             /infinity                             
                             | -----                               
     /  2                 \  |  \                                  
     | d                  |  |   )    /    1   /                   
   + |---- eta[u](x, t, u)|, |  /     |- ----- |binomial(alpha, n)
     |   2                |  | -----  \  n + 1 \                   
     \ dx                 /  \ n = 3                               

  /   (alpha - n)              (n + 1)                       
  |D[t           ](u(x, t)) D[t       ](xi[t](x, t, u)) alpha
  \                                                          

        (alpha - n)              (n + 1)                   
   - D[t           ](u(x, t)) D[t       ](xi[t](x, t, u)) n

        (alpha - n) / d         \    n                   
   + D[t           ]|--- u(x, t)| D[t ](xi[x](x, t, u)) n
                    \ dx        /                        

                                                          \   /Sum(
                                                          |   |    
                                                          |   |    
        (alpha - n) / d         \    n                 \\\|   |    
   + D[t           ]|--- u(x, t)| D[t ](xi[x](x, t, u))|||| + |    
                    \ dx        /                      ///|   |    
                                                          /   \    

                     /    / d                        \\
  binomial(alpha, n) |Diff|--- eta[u](x, t, u), t $ n||
                     \    \ du                       //

     (alpha - n) (u(x, t)), n = 3 .. infinity)\]  
  D[t           ]                             |]  
                                              |]  
                                              |]  
                                              |],
                                              |]  
                                              /]  

                                                              ]
                                                              ]
                                                              ]
                                                              ]
  [xi[x](x, t, u), xi[t](x, t, u), eta[u](x, t, u)], [x, t, u]]
                                                              ]
                                                              ]


sol1 := pdesolv(expand(deteqs[1]), deteqs[3], deteqs[4]);
Error, (in desolv/lderivx) cannot determine if this expression is true or false: 1 < x |C:/Program Files/Maple 2020/lib/ASP v4.6.3.txt:4312|

 

Maple and Matlab2022a...

Asked by: tomleslie 13771
matlab toolbox installation
May 24 2022
3  2
  1. I use both Maple and Matlab
  2. I also install (a stripped down version of) Maple as the "symbolic toolbox" for Matlab using the executable MapleToolbox2022.0WindowsX64Installer.exe, which lives in C:\Program Files\Maple 2022. This gives me acces to (some) symbolic computation capability from within Matlab.
  3. This installation process has been working for as long as I remember, certainly more than 10 years
  4. With Maple 2022 and Matlab R2022a, this installation process ran with no problems and I can perform symbolic computation within Matlab
  5. However, although the Matlab help lists the Maple toolbox as supplemental software (as in all previous releases), I can no longer acces help for Maple from within Matlab - I just get a "Page not found" message
  6. The relevant Maple "help" is at the same place within the Matlab folder structure which is C:\Program Files\MATLAB\R2022a\toolbox\maple\html
  7. I have just spoken to support at Matlab and they claim tha this must be a Maple (or Maple toolbox installer issue) - so nothing to do with them!
  8. Has anyone else had a similar problem andd found a workaround?

Arial makes sign disappear in MathContainer...

Asked by: Anthrazit 750
font mathcontainer
May 20 2022
3  3

Switching font to Arial apparently makes the sign disappear in MathContainers.

Vorzeichen.mw

How do I do mathematical modelling of planetary mo...

Asked by: aashni 10
modeling
May 20 2022
1  0

If i want to do mathematical modelling for planetary motion, how can maple help me with it?

Maple 2021 slow...

Asked by: Christopher2222 5785
performance 2dmath worksheet
May 16 2022
4  14

Anyone experience a delay in typing as the screen fills with text/math etc.?

I'm using Maple 2021 and as the space is filled typing slows. I can finish typing and watch the last 4 keys enter on the screen.

I have a problem with the "Diff" command....

Asked by: RLessard 90
differentiation diff inert
May 16 2022
2  1


Hi !

Looks like there is a bug in the inert "Diff" command.

I have Maple 2018 on Windows 10 ,64 bits.

Does Maple consider Diff(f(x),x) to be equal to Diff(f(x),[x]) ?

It should be the same.

Maple displays  that it is equal but keeps in memory something else.

In the attached file, I give a very simple example.

I don't like to say this but my old version of Maple V Release V (1997) is more consistent i.e.

this version shows it's different and  keeps in memory that difference.

diff-problem.mw

 

I wonder if newer versions have this problem ?


Best regards !

How does fsolve work?...

Asked by: kirillsor11 10
fsolve incomplete-question
May 16 2022
2  1

When using the built-in fsolve function to find the roots of a polynomial, how does exponentiation occur? For example, x3 is found​​​​​​first, and then to find x4, will he start again from the beginning, that is, x*x*x*x, or will he take the value of x3​​​​​​ and multiply by x? The teacher is interested in finding out this, but I don't know how to find out myself. 

Solve command Issue due to Computational Cost...

Asked by: Tamour_Zubair 80
solve fsolve
May 13 2022
1  0

Hello Everyone;

Hope you are fine. I am solving system of odes using rk-4 method. For this purpose I formulate the "residual" (on maple file) which is further function of "x" and "y". With the help of discritization point further I convert "residual" into system of ode's. Then i used "sys111 := solve(odes_Combine, `~`[diff](var, t))" to simplify the system. Finnally i applied RK-1. Code is pasted and attached. This all process is for "N=4". When i increase the value of "N", number of Odes increase accordingly. With increasing value of "N" the comand "sys111 := solve(odes_Combine, `~`[diff](var, t))" taking a lot of time due to heavy computation. Is that any way to proceed without this comand for rk-1?

Question1.mw

 


 

> 

restart; with(PDEtools, Solve); with(LinearAlgebra); with(plots); DD := 30; Digits := DD; N := 4; nu := 1.0; t0, tf := 0, 1; Ntt := 10; h := evalf((tf-t0)/(Ntt-1)); xmin := 0; xmax := Pi; `&Delta;xx` := 1.0*xmax/N; ymin := 0; ymax := xmax; `&Delta;yy` := 1.0*ymax/N

0, 1

  

.111111111111111111111111111111

  

.785398163397448309615660845820

  

.785398163397448309615660845820

 (1)
> 

residual := 1.000000000*(diff(A[0, 0](t), t))-32.00000000*A[2, 0](t)-32.00000002*A[0, 2](t)+(diff(A[1, 1](t), t))*(4.000000001-8.000000003*y-8.000000003*x+16.00000000*x*y)+(diff(A[1, 0](t), t))*(-2.000000000+4.000000000*x)+(diff(A[0, 3](t), t))*(-4.000000000+40.00000000*y-95.99999994*y^2+64.00000001*y^3)+(diff(A[0, 2](t), t))*(3.000000000-16.00000001*y+16.00000001*y^2)+(diff(A[0, 1](t), t))*(-2.000000001+4.000000000*y)-A[3, 3](t)*(768.0000000-7680.000000*y+18432.00000*y^2-12288.00000*y^3-1536.000000*x+15360.00000*x*y-36863.99998*x*y^2+24576.00000*x*y^3)-A[3, 2](t)*(-576.0000002+3072.000000*y-3072.000000*y^2+1152.000000*x-6144.000000*x*y+6144.000000*x*y^2)-A[3, 1](t)*(384.0000000-768.0000000*y-768.0000006*x+1536.000000*x*y)-A[3, 0](t)*(-192.0000000+384.0000000*x)-A[2, 3](t)*(-128.0000000+1280.000000*y-3072.000000*y^2+2048.000000*y^3)-A[2, 2](t)*(96.00000000-512.0000002*y+512.0000002*y^2)-A[2, 1](t)*(-64.00000002+128.0000000*y)-A[3, 3](t)*(767.9999998-1536.000000*y-7679.999998*x+15360.00000*x*y+18432.00000*x^2-36864.00000*x^2*y-12288.00000*x^3+24576.00000*x^3*y)-A[2, 3](t)*(-575.9999998+1152.000000*y+3072.000000*x-6144.000000*x*y-3072.000000*x^2+6144.000000*x^2*y)-A[3, 2](t)*(-128.0000000+1280.000000*x-3072.000000*x^2+2048.000000*x^3)-A[1, 2](t)*(-64.00000002+128.0000000*x)-A[1, 3](t)*(384.0000000-768.0000000*y-767.9999998*x+1536.000000*x*y)-A[2, 2](t)*(96.00000004-512.0000002*x+512.0000002*x^2)+(diff(A[3, 3](t), t))*(16.00000000-160.0000000*y+383.9999999*y^2-256.0000000*y^3-160.0000000*x+1600.000000*x*y-3839.999999*x*y^2+2560.000000*x*y^3+384.0000000*x^2-3840.000000*x^2*y+9215.999998*x^2*y^2-6144.000001*x^2*y^3-256.0000000*x^3+2560.000000*x^3*y-6143.999998*x^3*y^2+4096.000000*x^3*y^3)+(diff(A[3, 2](t), t))*(-12.00000000+64.00000002*y-64.00000002*y^2+120.0000000*x-640.0000002*x*y+640.0000002*x*y^2-288.0000001*x^2+1536.000000*x^2*y-1536.000000*x^2*y^2+192.0000000*x^3-1024.000000*x^3*y+1024.000000*x^3*y^2)+(diff(A[3, 1](t), t))*(8.000000003-16.00000000*y-80.00000003*x+160.0000000*x*y+192.0000000*x^2-384.0000000*x^2*y-128.0000001*x^3+256.0000000*x^3*y)-A[0, 3](t)*(-191.9999999+384.0000000*y)+(diff(A[3, 0](t), t))*(-4.000000000+40.00000000*x-96.00000002*x^2+64.00000001*x^3)+(diff(A[2, 3](t), t))*(-12.00000000+120.0000000*y-287.9999999*y^2+192.0000000*y^3+64.00000000*x-640.0000000*x*y+1536.000000*x*y^2-1024.000000*x*y^3-64.00000000*x^2+640.0000000*x^2*y-1536.000000*x^2*y^2+1024.000000*x^2*y^3)+(diff(A[2, 2](t), t))*(8.999999999-48.00000002*y+48.00000002*y^2-48.00000000*x+256.0000001*x*y-256.0000001*x*y^2+48.00000000*x^2-256.0000001*x^2*y+256.0000001*x^2*y^2)+(diff(A[2, 1](t), t))*(-6.000000002+12.00000000*y+32.00000001*x-64.00000000*x*y-32.00000001*x^2+64.00000000*x^2*y)+(diff(A[2, 0](t), t))*(3.000000000-16.00000000*x+16.00000000*x^2)+(diff(A[1, 3](t), t))*(8.000000003-80.00000003*y+192.0000000*y^2-128.0000000*y^3-16.00000000*x+160.0000000*x*y-383.9999999*x*y^2+256.0000000*x*y^3)+(diff(A[1, 2](t), t))*(-6.000000000+32.00000001*y-32.00000001*y^2+12.00000000*x-64.00000002*x*y+64.00000002*x*y^2):
> 

for i2 from 0 while i2 <= N-1 do odes11[0, i2] := simplify(eval(residual, [x = 0, y = i2*ymax/(N-1)])) = 0; odes11[N-1, i2] := simplify(eval(residual, [x = xmax, y = i2*ymax/(N-1)])) = 0 end do:

8

 (2)
> 

odes_Combine := {seq(seq(odes11[i, j], i = 0 .. N-1), j = 0 .. N-1)}:
> 

sys111 := solve(odes_Combine, `~`[diff](var, t)):
> 

ICS1 := {A[0, 0](0) = .444104979341173495851499233536, A[0, 1](0) = .198590961107083475045046921568, A[0, 2](0) = -0.167999146492673347540059075790e-1, A[0, 3](0) = -0.869171705198864625153083083786e-3, A[1, 0](0) = .198590961107083475045046921567, A[1, 1](0) = 0.888041604305848495880917177172e-1, A[1, 2](0) = -0.751243816645416714455046298805e-2, A[1, 3](0) = -0.388668563362181391196975707953e-3, A[2, 0](0) = -0.167999146492673347540059075793e-1, A[2, 1](0) = -0.751243816645416714455046298835e-2, A[2, 2](0) = 0.635518954643030408055028178047e-3, A[2, 3](0) = 0.328796368925226898150257328603e-4, A[3, 0](0) = -0.869171705198864625153083083734e-3, A[3, 1](0) = -0.388668563362181391196975707910e-3, A[3, 2](0) = 0.328796368925226898150257328592e-4, A[3, 3](0) = 0.170108305076655667148638268230e-5}:
> 

f, diffs := eval(GenerateMatrix(`~`[`-`](`~`[rhs](sys222), `~`[lhs](sys222)), var1))

f, diffs := Matrix(16, 16, {(1, 1) = 0, (1, 2) = 0, (1, 3) = 32., (1, 4) = 0.494812294492356575865153049102e-27, (1, 5) = 0, (1, 6) = 0, (1, 7) = 0.120000000000000000001649374315e-7, (1, 8) = -0.107999999927999999998854228220e-6, (1, 9) = 32.0000000200000000000000000000, (1, 10) = -0.199999999999999999998350625685e-7, (1, 11) = 0.249999999859375000081951230025e-7, (1, 12) = -0.700000000203125000132933066388e-7, (1, 13) = 0.196000000000000000000494812294e-6, (1, 14) = 0.292000000072000000001204420404e-6, (1, 15) = -0.458000000726562499721923065316e-6, (1, 16) = 0.682900000453875000014432471170e-5, (2, 1) = 0, (2, 2) = 0, (2, 3) = 0, (2, 4) = -0.377561971763063776372092766396e-27, (2, 5) = 0, (2, 6) = 0, (2, 7) = 32.0000000000000000000000000000, (2, 8) = 0.719999999999999999998878327317e-7, (2, 9) = 0, (2, 10) = -0.125853990587687925457364255465e-27, (2, 11) = 0.906355783222184042180194163758e-27, (2, 12) = 0.135077431625990682476379737660e-25, (2, 13) = 96.0000000000000000000000000001, (2, 14) = 0.719999999999999999989394464730e-7, (2, 15) = -0.549999999914062500010607576813e-6, (2, 16) = 0.202000000048749999997617654955e-5, (3, 1) = 0, (3, 2) = 0, (3, 3) = 0, (3, 4) = 0.855583965847405137008732798371e-28, (3, 5) = 0, (3, 6) = 0, (3, 7) = -0.257808598553160159742093659020e-28, (3, 8) = -0.377264825438544618607975742790e-27, (3, 9) = 0, (3, 10) = 0.285194655282468379002910932790e-28, (3, 11) = 31.9999999925000000046874999970, (3, 12) = 0.326865301360930805043812804544e-26, (3, 13) = -0.773425795659480479226280977060e-28, (3, 14) = -0.313579545661510489918366218529e-27, (3, 15) = -0.149999999882812500075601322065e-6, (3, 16) = 0.324999999796875000093151106353e-6, (4, 1) = 0, (4, 2) = 0, (4, 3) = 0, (4, 4) = -0.384112032581666751703476763000e-29, (4, 5) = 0, (4, 6) = 0, (4, 7) = 0.265935771387910529598689301718e-29, (4, 8) = 0.399754551928273029196600976861e-28, (4, 9) = 0, (4, 10) = -0.128037344193888917234492254333e-29, (4, 11) = 0.173718566046259004921454811253e-28, (4, 12) = -0.553232882345597286403223410199e-27, (4, 13) = 0.797807314163731588796067905154e-29, (4, 14) = 0.427742792008362106477653509643e-28, (4, 15) = 31.9999999950000000007812499996, (4, 16) = 0.583137134641934297089284679036e-26, (5, 1) = 0, (5, 2) = 0, (5, 3) = 0, (5, 4) = 96.0000000000000000000000000001, (5, 5) = 0, (5, 6) = 0, (5, 7) = -0.125853990576278889372664086359e-27, (5, 8) = -0.780000000000000000003341913398e-7, (5, 9) = 0, (5, 10) = 32.0000000000000000000000000000, (5, 11) = 0.155215894719877680168982772333e-28, (5, 12) = 0.179999999957812500011610427218e-6, (5, 13) = -0.377561971728836668117992259076e-27, (5, 14) = 0.121999999999999999999928850210e-6, (5, 15) = 0.957742348838601502120463181878e-26, (5, 16) = 0.413250000106171874986265224797e-5, (6, 1) = 0, (6, 2) = 0, (6, 3) = 0, (6, 4) = -0.821348457439978150891092618719e-28, (6, 5) = 0, (6, 6) = 0, (6, 7) = -0.273782819058452669879599110853e-28, (6, 8) = 95.9999999999999999999999999997, (6, 9) = 0, (6, 10) = -0.273782819146659383630364206240e-28, (6, 11) = 0.294057068291966163490658104104e-27, (6, 12) = -0.253498333196688505804635565222e-27, (6, 13) = -0.821348457175358009638797332558e-28, (6, 14) = 95.9999999999999999999999999997, (6, 15) = 0.212121033252676198558579131631e-28, (6, 16) = 0.649999999999999999980740836208e-6, (7, 1) = 0, (7, 2) = 0, (7, 3) = 0, (7, 4) = 0.186123768597305842557431955743e-28, (7, 5) = 0, (7, 6) = 0, (7, 7) = 0.214460223691860703703477959545e-28, (7, 8) = 0.317673924810187018756335641686e-28, (7, 9) = 0, (7, 10) = 0.620412561991019475191439852476e-29, (7, 11) = 0.753895620987131323747484439705e-28, (7, 12) = 95.9999999700000000093749999970, (7, 13) = 0.643380671075582111110433878635e-28, (7, 14) = 0.348244413167432788858088750543e-30, (7, 15) = -0.195081345734130085456007896310e-26, (7, 16) = 0.162499999949218750020914346448e-6, (8, 1) = 0, (8, 2) = 0, (8, 3) = 0, (8, 4) = -0.835597462589282450911924283887e-30, (8, 5) = 0, (8, 6) = 0, (8, 7) = -0.168983990754200234313642237958e-29, (8, 8) = 0.255518912827614707211229660888e-30, (8, 9) = 0, (8, 10) = -0.278532487529760816970641427962e-30, (8, 11) = -0.912041057783558505972445866734e-29, (8, 12) = 0.152862192823148604497047654434e-28, (8, 13) = -0.506951972262600702940926713875e-29, (8, 14) = 0.212025424265299406832408057357e-29, (8, 15) = 0.158222957859551043617221056103e-27, (8, 16) = 96.0000000000000000000000000002, (9, 1) = 0, (9, 2) = 0, (9, 3) = 0, (9, 4) = -0.773425795970180636575593526265e-28, (9, 5) = 0, (9, 6) = 0, (9, 7) = 0.285194655390087477280223771532e-28, (9, 8) = -0.241100887243597349107036806234e-27, (9, 9) = 0, (9, 10) = -0.257808598656726878858531175422e-28, (9, 11) = 32.0000000125000000000000000004, (9, 12) = 0.999999999843750000174507862823e-8, (9, 13) = 0.855583966170262431840671314596e-28, (9, 14) = -0.104420360226003256663758222866e-27, (9, 15) = 0.600000000000000000027497059897e-7, (9, 16) = 0.900000000046874999977170328969e-6, (10, 1) = 0, (10, 2) = 0, (10, 3) = 0, (10, 4) = 0.643380671224932994877201196193e-28, (10, 5) = 0, (10, 6) = 0, (10, 7) = 0.620412562284547562356437593923e-29, (10, 8) = -0.782971264706294608812923943602e-28, (10, 9) = 0, (10, 10) = 0.214460223741644331625733732064e-28, (10, 11) = -0.117716452160171050903010422567e-27, (10, 12) = -0.324249553007268016939337229307e-26, (10, 13) = 0.186123768685364268706931278177e-28, (10, 14) = 0.210791990319339808396292213890e-27, (10, 15) = 95.9999999999999999999999999990, (10, 16) = 0.601289924118833452883693495332e-26, (11, 1) = 0, (11, 2) = 0, (11, 3) = 0, (11, 4) = -0.145794923079456919867181504653e-28, (11, 5) = 0, (11, 6) = 0, (11, 7) = -0.485983076931523066223938348837e-29, (11, 8) = 0.703045314344404024740114826873e-28, (11, 9) = 0, (11, 10) = -0.485983076931523066223938348844e-29, (11, 11) = 0.154061910958820937154327251969e-28, (11, 12) = 0.586431085917646726477197552134e-27, (11, 13) = -0.145794923079456919867181504651e-28, (11, 14) = 0.327116591013740734656854347967e-28, (11, 15) = 0.186427448215109472676159333906e-27, (11, 16) = 0.727156843809743343593213639608e-26, (12, 1) = 0, (12, 2) = 0, (12, 3) = 0, (12, 4) = 0.654542236344866764687318521378e-30, (12, 5) = 0, (12, 6) = 0, (12, 7) = 0.382930495785563772474113758933e-30, (12, 8) = -0.765771840140216030924576968705e-29, (12, 9) = 0, (12, 10) = 0.218180745448288921562439507126e-30, (12, 11) = -0.591357855581324858104400230586e-30, (12, 12) = 0.164090126078907967224367765176e-28, (12, 13) = 0.114879148735669131742234127680e-29, (12, 14) = -0.733606589050003370341598338138e-29, (12, 15) = 0.279365514914751130455040418258e-28, (12, 16) = -0.138821502091830040436688448298e-26, (13, 1) = 0, (13, 2) = 0, (13, 3) = 0, (13, 4) = 0.797807313447167969819086050522e-29, (13, 5) = 0, (13, 6) = 0, (13, 7) = -0.128037344212226672551029214969e-29, (13, 8) = 0.262885403001488132812902903311e-28, (13, 9) = 0, (13, 10) = 0.265935771149055989939695350174e-29, (13, 11) = -0.349411324204567081081722661297e-28, (13, 12) = 31.9999999950000000007812499995, (13, 13) = -0.384112032636680017653087644907e-29, (13, 14) = 0.119403167752948354510697994999e-28, (13, 15) = -0.452504513537780686847551220204e-27, (13, 16) = 0.149999999976562500006592455374e-6, (14, 1) = 0, (14, 2) = 0, (14, 3) = 0, (14, 4) = -0.506951972202161632959380608780e-29, (14, 5) = 0, (14, 6) = 0, (14, 7) = -0.278532487328297250365487744273e-30, (14, 8) = 0.100313589069551339782957918087e-28, (14, 9) = 0, (14, 10) = -0.168983990734053877653126869593e-29, (14, 11) = 0.876003797684675659527198447426e-29, (14, 12) = 0.309396538522635365039103628797e-27, (14, 13) = -0.835597461984891751096463232820e-30, (14, 14) = -0.169500948608311509445295032991e-28, (14, 15) = 0.104005614175784513152332127959e-27, (14, 16) = 95.9999999999999999999999999996, (15, 1) = 0, (15, 2) = 0, (15, 3) = 0, (15, 4) = 0.114879148750778899237620653952e-29, (15, 5) = 0, (15, 6) = 0, (15, 7) = 0.218180745498654813213727928025e-30, (15, 8) = -0.867251219227502985269662069579e-29, (15, 9) = 0, (15, 10) = 0.382930495835929664125402179841e-30, (15, 11) = -0.267864188359583543656192185112e-29, (15, 12) = -0.387791753042961333529856694716e-28, (15, 13) = 0.654542236495964439641183784074e-30, (15, 14) = -0.523627245808308931882255033583e-29, (15, 15) = 0.369199231034048272468531636165e-28, (15, 16) = -0.123439611085554953594747603640e-26, (16, 1) = 0, (16, 2) = 0, (16, 3) = 0, (16, 4) = -0.515746730509193430144544493936e-31, (16, 5) = 0, (16, 6) = 0, (16, 7) = -0.171915576836397810048181497977e-31, (16, 8) = 0.857347676859656256220355661580e-30, (16, 9) = 0, (16, 10) = -0.171915576836397810048181497979e-31, (16, 11) = 0.182597096197097886514765184582e-30, (16, 12) = -0.370616214664321329971866697584e-29, (16, 13) = -0.515746730509193430144544493932e-31, (16, 14) = 0.865925397235117524875431212196e-30, (16, 15) = -0.750058451906403875595888288641e-29, (16, 16) = 0.183460376006651920829411996611e-27}), Vector(16, {(1) = diff(A[0, 0](t), t), (2) = diff(A[0, 1](t), t), (3) = diff(A[0, 2](t), t), (4) = diff(A[0, 3](t), t), (5) = diff(A[1, 0](t), t), (6) = diff(A[1, 1](t), t), (7) = diff(A[1, 2](t), t), (8) = diff(A[1, 3](t), t), (9) = diff(A[2, 0](t), t), (10) = diff(A[2, 1](t), t), (11) = diff(A[2, 2](t), t), (12) = diff(A[2, 3](t), t), (13) = diff(A[3, 0](t), t), (14) = diff(A[3, 1](t), t), (15) = diff(A[3, 2](t), t), (16) = diff(A[3, 3](t), t)})

 (3)
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npts := Ntt:
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Download Question1.mw

 

Maxima of the given equation...

Asked by: madhav123 30
optimization maximum
May 10 2022
1  1

Let say, 

A= A1+A2+.....................+An

B=B1+B2+.....................+Bn,

C=C1+C2+.....................+Cn

And all the values of A1 to Cn may be both positive or Negative.

Then, how to program to find the Maximum Value of  (A^2+B^2+C^2+A.B+B.C+C.A)^(1/2).

What can block the import of data from Excel?...

Asked by: MapleUser2017 170
excel import
May 04 2022
1  2

I have a student who then she uses tools/assistent/import data and then the file then Maple claims the Excel file is empty? She uses Maple 2021.2. File works on other my and other student computers. 

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