How I can obtain system (21) in the following pdf file?
In the first step several changes of variables are done to obtain the system (20),
then changes the variables again repeated in the neighborhood (w1 *, w2 *) to gain Eq 21.
I have 3 questuin:
1-The change of variables performed in the neighborhood (w1 *, w2 *)
for system (20) or for system (7) ???
2-What does it mean in the neighborhood (w1 *, w2 *)?
3- How did obtaun Eq (21)?

[paperhub.ir]10.1016@j.neucom.2010.06.023.pdf

Could you please help me at the solution of my problem?

Let us consider the following list:

A := [x[1, 1]*(a*x[1, 1] + E[1, 1]) + x[2, 1]*(a*x[1, 2] + E[1, 2]) + x[3, 1]*(a*x[1, 3] + E[1, 3]), x[1, 2]*(a*x[1, 1] + E[1, 1]) + x[2, 2]*(a*x[1, 2] + E[1, 2]) + x[3, 2]*(a*x[1, 3] + E[1, 3]), x[1, 3]*(a*x[1, 1] + E[1, 1]) + x[2, 3]*(a*x[1, 2] + E[1, 2]) + x[3, 3]*(a*x[1, 3] + E[1, 3]), x[1, 1]*(a*x[2, 1] + E[2, 1]) + x[2, 1]*(a*x[2, 2] + E[2, 2]) + x[3, 1]*(a*x[2, 3] + E[2, 3]), x[1, 2]*(a*x[2, 1] + E[2, 1]) + x[2, 2]*(a*x[2, 2] + E[2, 2]) + x[3, 2]*(a*x[2, 3] + E[2, 3]), x[1, 3]*(a*x[2, 1] + E[2, 1]) + x[2, 3]*(a*x[2, 2] + E[2, 2]) + x[3, 3]*(a*x[2, 3] + E[2, 3]), x[1, 1]*(a*x[3, 1] + E[3, 1]) + x[2, 1]*(a*x[3, 2] + E[3, 2]) + x[3, 1]*(a*x[3, 3] + E[3, 3]), x[1, 2]*(a*x[3, 1] + E[3, 1]) + x[2, 2]*(a*x[3, 2] + E[3, 2]) + x[3, 2]*(a*x[3, 3] + E[3, 3]), x[1, 3]*(a*x[3, 1] + E[3, 1]) + x[2, 3]*(a*x[3, 2] + E[3, 2]) + x[3, 3]*(a*x[3, 3] + E[3, 3])]

I want to subs E[k,k]=1 when there is "a*x[k,k]+E[k,k]" as a part of polynomial in the above list.

Thank you so much in advance

In the following Solution_3.3_page_103.mw, after equation (15), I would like to use the clickable functionality to obtain the equations A, B, C, and D. I had to manually use copy-paste to obtain those equations. Because when I used the equation manipulator to square both sides, it started to be a mess.  After that, I was able to continue for (16) and the rest to obtain finally the speed of the muon neutrino.

P.S. If you see something wrong in the calculation, I am always interested to correct them.

Thank you in advance.

Hi,

I was able to get Procedure 2 to work using a for - do loop. I was wondering if it is possible to speed up the calculation by using map to find the number of roots? I do not fully understand map and passing data.

tgf := proc(a, b, c, d, t, m, n)

          local X;

          X := [solve(abs(a*x + b) + abs(c*x + d) - t*x^2 + m*x - n = 0)]; 

          return nops(X);

end proc;

res := CodeTools:-Usage(map(tgf, L));
Error, (in CodeTools:-Usage) invalid input: tgf uses a 2nd argument, b, which is missing

The L Array is tripping me up, here is a partial display of the array:

Array(1..262, 1..7, [[5,2,3,9,1,1,1],[5,2,3,9,2,1,1],[5,4,3,7,1,1,1],[5,4,3,7,2,1,1],[5,5,3,6,1,1,1],[5,5,3,6,2,1,1],[5,5,4,8,1,1,2],[5,5,4,8,2,1,2], ... ,[10,10,5,10,2,2,2]], datatype = integer[4]).

I made L Array into a list of list, R. Somewhat works.

Here is the script:

Roots_with_map.mw 

Thanks for any help.

Hi Maple community. How to find the any real root of the complex equation which has been mention in my worksheet.

Real_root.mw

Hi. is there a site for using maple online?

How to solve this integral equation?

rho:=1/(2);

mu:=1/(2);

T:=1/(4)*(t-x)^(1/(2));

E[rho,mu](T):=Sum((T^(k))/(GAMMA(k*rho+ mu)),k=0..5);
                       
eq1 := h(t) = (8/3)*(int((t-x)^(1/2)*E[rho, mu](T)*(1/(sqrt(Pi)*x^(1/2))-(3/32)*x^2+(3/16)*exp(-x)-1), t = -1 .. 1));       

 

Download 1.mw

Hi.

I have 7 polynomials r[9], r[6, 6], r[7, 9], r[8, 6], r[9, 6], r[6, 9, 7], r[6, 9, 6] each of 7 variables a[3],...,a[9] and I generate an ideal QQ usinig these polynomials. What Maple tells me quite fast is the follows:

IdealMembership(a[3], QQ) 

true

Also using Groebner as follows
F := [r[9], r[6, 6], r[7, 9], r[8, 6], r[9, 6], r[6, 9, 7], r[6, 9, 6]];
G := Basis(F, tdeg(a[3], a[4], a[5], a[6], a[7], a[8], a[9]));
provides me with the basis quite fast and a[3] is part of it. 

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

However, Mathematica is stuck and I have noticed that if I change a[3],...,a[9] to x,y,z,,v,w,t then Maple with the same polynomials is evaluating very long time. 

My question is: what am I doing wrong with subscripts a[3],...,a[9] in Maple? Does Maple 2019 have a problem with it?

I have attached my worksheet. 
Maple_Problem.mw
Would appreciate any help.

BRINKMAN_TRIAL.mw

Maple Worksheet - Error

Failed to load the worksheet /maplenet/convert/BRINKMAN_TRIAL.mw .
 

Download BRINKMAN_TRIAL.mw

Maple Worksheet - Error

Failed to load the worksheet /maplenet/convert/BRINKMAN_TRIAL.mw .
 

Download BRINKMAN_TRIAL.mw

Maple Worksheet - Error

Failed to load the worksheet /maplenet/convert/BRINKMAN_TRIAL.mw .
 

Download BRINKMAN_TRIAL.mw

hi, can anyone help me?

i am trying to solve a set of boundary layer equation.  when i executed the file, the following message appear.

Suppose I specify a metric in say the differential geometry package or Physics package that has an arbitary function f(x,y) of some of the coordinates as a component. Can I specify Maple to treat the function as real valued when Maple is asked to compute curvature etc for the metric? In some examples I have performed Maple sometimes returns expressions in f(x,y) for components that are in fact zero once one treats f(x,y) as real valued. It would be preferable to have Maple actually return '0' in such cases.

I tried the 'assume' command but Maple complained it was being applied to a protected name and I tried using

use RealDomain in simplify (5) end use

after Maple's computations, where (5) lablled Maple's output, but Maple didn't perform any simplification.

Hi, see above image, how do I get maple to do the chain rule automatically, for example, if I simply put in the alias V(h), instead of V(h(x)), this last command generates zero. 

Also, what is D(V)(h) ? is this equivalent to dV/dh, and if so how would I get maple to present it in this form?

Many thanks for your help ! 

I am using code edit region for parameters but getting this error, can someone help me to solve this issue.

Can anyone correct me, what's wrong with it.

Help_solution.mw

Hello.

I have the ode 

x' = 4 * lambda * x^4 - x^6

and I want to plot the phase portrait with x be the horizontal axis and lambda be the vertical axis.

Also, I want to plot the arrows showing the stability of the fixed points as lambda is changing values.

Thanks !

I have two functions, f1(x,y,z) and f2(x,y). I want to use Grid package to parallelize the runs of two functions. I have tried Grid:-Seq() but this way the maple does not seem to finish the computation.

Another thing I have tried so far was using Grid:-Run(), like so:

Grid:-Setup("local", numnodes=2):

Grid:-Run(0, f1, [x,y,z]):

Grid:-Run(1, f2, [x,y]):

It seems that this way i create background processes but I never see them finish. On their own the functions f1 and f2 work fine if used sequentially.

Is there any way to run time in parallel?