Maple 18 Questions and Posts

These are Posts and Questions associated with the product, Maple 18

How to simplify the product of 4x4 matrices and how can we take out the expression that appears in each entry of the matrix?

MLM-1.mw

Hi, dear community,
I have a Maple package "rath" for finding the traveling wave solution of differential equations. But I am not able to loading in Maple 18. Please see this attached zip folder and need help in this regard.
Kind regard

inform.txt,

PaperExp.mws

rath.txt

How to plot u(t)= z'(t) with respect to x, y, z?

  Here,  z(t)=y'(t), y(t)=x'(t).

where, x(t)= z^3(t), y(t)= z^3(t)/2, z(t) = (a- b), a, b are time interval.

Trajectories.mw

How to solve the matrix for u(t) and plot phase trajector?

I have the following expresion:

G_{ik}=|u_{i} - u_{k}|-(u_{i}-u_{k})^2

 

Where i, k=1,2,3,4. How can I write this expresion in maple? I want to be able to write G_{1 2} and in the RHS

How to solve this differential equation numerically

eq:=diff(f(tau), tau) =Af(tau) +Lf(tau) +C+Bf(tau)


 

restart

R := .46+9.1625*t^alpha/(GAMMA*(alpha+1))+8.8318*t^(2*alpha)/(GAMMA*(2*alpha+1))+11.6888*t^(3*alpha)/(GAMMA*(3*alpha+1));

.46+9.1625*t^alpha/(GAMMA*(alpha+1))+8.8318*t^(2*alpha)/(GAMMA*(2*alpha+1))+11.6888*t^(3*alpha)/(GAMMA*(3*alpha+1))

 

.32+0.9282e-1*t^alpha/(GAMMA*(alpha+1))+2.1126*t^(2*alpha)/(GAMMA*(2*alpha+1))+3.9028*t^(3*alpha)/(GAMMA*(3*alpha+1))

 

.52+0.569e-1*t^alpha/(GAMMA*(alpha+1))+0.243e-1*t^(2*alpha)/(GAMMA*(2*alpha+1))+1.3102*t^(3*alpha)/(GAMMA*(3*alpha+1))

 

.46+9.1625*t^alpha/(GAMMA*(alpha+1))+8.8137*t^(2*alpha)/(GAMMA*(2*alpha+1))+8.8450*t^(3*alpha)/(GAMMA*(3*alpha+1))

 

.32+0.9282e-1*t^alpha/(GAMMA*(alpha+1))+2.1126*t^(2*alpha)/(GAMMA*(2*alpha+1))+1.9472*t^(3*alpha)/(GAMMA*(3*alpha+1))

 

.46+0.569e-1*t^alpha/(GAMMA*(alpha+1))+0.243e-1*t^(2*alpha)/(GAMMA*(2*alpha+1))+.6551*t^(3*alpha)/(GAMMA*(3*alpha+1))

(1)

``


 

 

Hi everybody, I want to find 

the second-order derivative according to alpha. Since the computer could not calculate in this way, I took the derivative twice in a row.

assume(alpha <= 1)

additionally(0 < alpha)

then output is

again using the fracdiff 

then output is 

but I want to see

after the last command. Should alpha be defined specifically for this?

Hello!

I have a difficulty with a function used in procedure. The procedure uses a multivariable function and if the specific choice of the function is not made the procedure seems to give proper result, but In case I make a specific choice of the function and then try use this procedure gives me incorrect result.

To be more exact I use Physics package (there is a need to calcute combinations of covariant derivates ). The calculations are performed in a curved space with a defined metric.

So here is the procedure:

SD2 := proc (psi) SumOverRepeatedIndices(g_[`~kappa`, `~lambda`]*(d_[kappa](d_[lambda](psi(X)))-Christoffel[`~sigma`, kappa, lambda]*d_[sigma](psi(X))))^2-SumOverRepeatedIndices(g_[`~kappa`, `~rho`]*(d_[kappa](d_[lambda](psi(X)))-Christoffel[`~sigma`, kappa, lambda]*d_[sigma](psi(X)))*g_[`~lambda`, `~tau`]*(d_[rho](d_[tau](psi(X)))-Christoffel[`~gamma`, rho, tau]*d_[gamma](psi(X)))) end proc;

If I turn to the procedure :

SD2(psi);

the result is  correct.

But  then I specify a psi function:

psi:=(t,r,x,y,z)->chi(r)+q*t;(here q is supposed to be a constant)

and turn to the procedure once again:

SD2(psi);

It gives me a wrong result.

I don't know what is the reason.

Thank you.

 

 

I make a maple worksheet for generating Pythagorean Triples Ternary Tree :

Around 10,000 records in the matrix currently !

You can set your desire size or export the Matrix as text ...

But yet ! I wish to understand from you better techniques If you have some suggestion ?

the mapleprimes Don't load my worksheet for preview so i put a screenshot !

Pythagoras_ternary.mw

Pythagoras_ternary_data.mw

Pythagoras_ternary_maple.mw

 

 

 

Dear maple users,

Greeting for the day.

I have some data in an excel file. How to plot the excel data in contours with labels.

Also, how to show the x-axis range =-1.5..1.5 and y-axis range = -0.5..1 with the contour sequence -2..2.

XLdat.xlsx

waiting for your reply.

Please see the figure for the model plot.

Can this equation has four integer solutions? 
I am consider the equation a^2*x^2/(x-a)^2+x^2 = m/n and trying to find the integer numbers a, m, n so that the given equation has integer solutions?

Four_integer_solutions.mw

Hi everyone how can I plot like a graphic? 

How to plot the phase portrait of the system of fractional DEs?

0< nu<1

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