Maple Questions and Posts

These are Posts and Questions associated with the product, Maple

I want to define recursive matrix P.

You can find my try in the following code. The code includes a special matrix H.

quest.mw

 

If you interest full paper, you can check the following link.

paper.pdf

Q1: In place of three statments like >a:=3: b:=4; c:=5, I have found from an example in this forum that one can use >(a,b,c):=(3,4,5). And I find this useful in some applications. Anyone know what version of Maple introduced this? I can find not refernces in the Maple books I have

Q2: Maple someimes gives 'naked' decimals when I use Numeric formatting. Any way of avoind this. I would  like 0.25 not .25

Many thanks


 

`~`[int](convert(convert(series(x^x, x), polynom), list), x = 0 .. 1)

Can this sequence (produced above in list form) be displayed as 1, -1/2^2, 1/3^3, -1/4^4, 1/5^5 -1/6^6 etc.

That is with the powers unevaluated.

Hello,

What are the methods for writing code to the recursive matrix A  as follows?

Thanks.

 

When i am running a code in maple worksheet , one error is shown by maple. My code and error (in bold) is below


Instructional workheet for the FracSym package
G. F. Jefferson and J. Carminati


Read in accompanying packages: ASP, DESOLVII and initialise using the with command:

read `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.

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 in FracSym and initialise using the with command:
read `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]


BASIC OPERATORS

The Riemann-Liouville fractional derivatives is expressed in "inert" form using the FracSym routine Rfracdiff.
The explicit formula for the form of these fractional derivatives may be found in I. Podlubny, Fractional differential equations: An introduction to fractional derivatives, fractional differential equations, some methods of their solution and some of their applications, San Diego, 1999.)

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

If the fractional derivative is taken for a product, the generalised Leibnitz rule is used to express the result (the product operator used is &* and is non-commutative). 
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                                                            

Fractional derivatives of integer order revert to the MAPLE diff routine.

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

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


The FracSym rouine TotalD may also be used to find total derivatives. evalTotalD is then used to evaluate the result (in jet notation). For example, 

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

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

EXAMPLE -  FINDING SYMMETRIES FOR A FRACTIONAL DE

Consider the fractional PDE from: R. Sahadevan, T. Bakkyaraj, Invariant analysis of time fractional generalized Burgers and Korteweg-de Vries equations, J. Math. Anal. Appl. 393 (2012) 341-347.

We use the Rfracdiff routine to express the 
                                    alpha
 fractional derivative with respect to t:
fde1:=Rfracdiff(u(x, t),t,alpha) = (diff(u(x, t), x,x))+n*(u(x, t))^p*(diff(u(x, t),  x));
        alpha             / d  / d         \\            p / d         \
     D[t     ](u(x, t)) = |--- |--- u(x, t)|| + n u(x, t)  |--- u(x, t)|
                          \ dx \ dx        //              \ dx        /

sys1:=[Rfracdiff(u(x, t),t,alpha) = (diff(v(x, t), x)), Rfracdiff(v(x, t),t,alpha) = -u(x, t)*diff(u(x, t),x)];
[   alpha              d              alpha                      / d         \]
[D[t     ](u(x, t)) = --- v(x, t), D[t     ](v(x, t)) = -u(x, t) |--- u(x, t)|]
[                      dx                                        \ dx        /]

We use the the FracSym routine fracDet to find the determining equations for the symmetry for fde1. 
NOTE: The fourth argument (some integer at least 1) corresponds to the number of terms to be "peeled off" from the sums which occur in the extended infintesimal function for the fractional derivative. A value of 2 provides a good balance between information for solution of determining equations and speed.

deteqs:=fracDet([sys1], [u, v],[x, t], 2, alpha=(0.1)..1);
Error, (in desolv/PickLHSDerivative) Cannot pick out the left hand side derivatives

Please suggest what problem it may be?
 

Hi everyone, I'm doing a thesis about a solar panel and to extract some parameters from measured data I woudl have to solve 

a set of 3 non-lineair equations. This is de code that I use to (try to) solve the equations.

restart;

;
q := 0.16021e-18;
k := 0.13865e-22;


NULL;
Ns := 28;
T := 273+27.82;
Isc := 2.07;
Voc := 19.45;
Impp := 1.88;
Vmpp := 15.32;
                           Rsh := 326
dvdi := -1.52;


Vt := n*k*T*Ns/q;

NULL;
f1 := Rs = -dvdi-Vt/(Io*exp(Voc/Vt));
f2 := Io = (Isc-Voc/Rsh)/(exp(Voc/Vt)-1);
                            /Impp Rs + Vmpp\   Impp Rs + Vmpp
   f3 := Impp = Isc - Io exp|--------------| - --------------
                            \      Vt      /        Rsh      

fsolve({f1, f2, f3}, {Io, Rs, n});

Though running this doesn't give me a solution. 

I do have a working extraction though which is the same equations but with other variables: 

restart;

NULL;
q := 0.16021e-18;
k := 0.13865e-22;


NULL;
Ns := 72;
T := 298;
Isc := 8.53;
Voc := 44.9;
Impp := 8.04;
Vmpp := 36.1;
Rsh := 401.934;
dvdi := -.48766;


Vt := n*k*T*Ns/q;

NULL;
f1 := Rs = -dvdi-Vt/(Io*exp(Voc/Vt));
f2 := Io = (Isc-Voc/Rsh)/(exp(Voc/Vt)-1);
f3 := Impp = Isc-Io*(exp((Impp*Rs+Vmpp)/Vt)-1)-(Impp*Rs+Vmpp)/Rsh;

fsolve({f1, f2, f3}, {Io, Rs, n});

I'm am wondering why the first code doesn't give me a solution? I would guess that there is certainly a solution. Also when I slightly increase /  decrease a certain variable it can suddenly give/find a solution.

Could someone clear this out ?

 

Kind regards, Sven!

Why does the implicit plot return empty?

plots:-implicitplot((x^2+y^2 = 1)^2, x = -3 .. 3, y = -3 .. 3);# plots
   plots:-implicitplot((x^2+y^2-1)^2, x = -3 .. 3, y = -3 .. 3) # empty plot

 

I kind of work on generat asample from  Adiscret uniform distribution with pdf (P(x)=1/k+1  x=0..k). 
but i couldn't insert the PDF to generate asample is there any way to insert this pdf in maple then generata asample

So I currently have:
with(DifferentialGeometry); with(Tensor);
DGsetup([r, theta], pol);
g1 := evalDG(drdr+r^2d(theta)d(theta))
C1 := Christoffel(g1);
However its coming back saying that g1 is not of metric form, am i missing something? Thanks

Dear Maple users

I am trying to test how well data from a real throw with a ball comply with the usual model, in which the air resistance is proportional to the square of the velocity. I succeeded in solving the ODE system numericallly using the rkf45 method and plottet the solutioncurve (see attached file). I am however unsure how I can retrieve the data from the model in the most convenient way in order to compare them to the data from the real throw. The latter I have as (t, x(t), y(t)) data in three columns in an Excel file. Of course I can import the x og y columns into Maple and create a plot containing both the (x,y) data from Excel and the (x,y) data from the model. The problem is however that even if the (x,y) curves are rather close, if may not be a good model. I need to take into account the time variabel as well! The data from the Excel file contains data for every 1/30 second. What I like is to be able to compute the Root Mean Square of all (xexperiment(t)-xmodel(t), yexperiment(t)-ymodel(t)) data - or would the Root Mean Square of the (Euclid) distances between the points be better?

Now back to my question on how to retrieve data from the ODE system in the most convenient way. I have read the help page for the dsolve command. There is however several options, that I am unsure about, for example the output option (listprocedure, etc). I hope someone can help. 

NB! Excel data are imported column by column into Maple as n x 1 matrices.

 

Regards,

Erik V. 

 

Throw_with_air_resistance_1.mw
 

Say I have three (3d if it matters) plot objects, which I will call A,B,C.

I need to plot A and B on the same graph and C on a different graph.

To plot objects on different graphs I would normally use an array of plots, and to plot objects on the same graph, I would use a set of plots. So what comes natural to me is this:

V:=Array(1..2):

V[1]:={A,B}:
V[2]:=C:

display(V)

However, this results in

Error, (in plots:-display) element 1 of the rtable is not a valid plot structure

 The problem is in the first element V[1] - Maple wants a plot, and not a set of plots, as each element of the array.

Another attempt which fails is the following:
 

display({A,B},C)

Here Maple will only plot {A,B} and ignore C.

I have had limited success with

 
display({A,B}), display(C)

which in fact works for the purpose stated above - it will produce the plots of {A,B} and C side by side.

However, when I try to put the above command within a procedure depending on some parameter, and use the Explore parameter to visualize the plots in dependence of the parameter, this does not work anymore. Maple will not produce any plot and will produce a wall of text within the Explore display.

 

For istance, 

with(plots); with(plottools)
display(circle([0, 0], 1)), display(circle([0, 0], 1))


Will produce the pictures side by side as desired. But:

P := proc (a)
display(circle([0, 0], 1)), display(circle([0, a], 1))
end proc:
Explore(P(a), parameters = [a = -1 .. 1])


Will result in a wall of text within the Explore window that begins like this:

 

 

So, is there a way to produce the plots I need which is compatible with the Explore command for a procedure? Ideally I need the two graphs ({A,B} and C) side by side within the same Explore window so that when I vary the parameters, both plots change accordingly. 

Thanks in advance.

can maple do a real time update graph by for loop read file data?

i can only think that use for loop and read file and draw a sequence of graph,

but memory will be accumulated to consume

just want to make a dashboard to display a multiple of graphs

How do I save these fonts as my default ones?                                

"Maple Input: Arial 24, Red"

and "2D Output: Arial 18, Blue".

I am using Maple 13.

Thank you!

 

would like to point to graph then it highlight graph with virtical line

and mark 1 in one of row in one of column in table like data 

just like define feature manually for machine learning but using graph

By default Maple labels vertices 1, 2, ...  and places these numbers within a circle making the position of the vertex.  Can one change the labels to, say, v1, v2, ... and place these outside the circles?  ..................Edgar

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