## Explore a surface...

Dear all,

I'd like to explore graphically a polynomial surface depending on two parameters a and b.

The problem is that, as soon as I start playing with the sliders, Maple freezes and I have to 'force quit'.

Can you please tell me if you have the same problem with this example?

Thanks.

 > restart:
 > with(plots):
 > K := 1 - y*x - (1 - x)*(b*x^3 + a*x^2 + x + 1)*(1 - y)*(b*y^3 + a*y^2 + y + 1)
 (1)
 > Explore(plot3d(K, x=0..1, y=0..1,  font= [Times, bold, 20], labels= ['x', 'y','z'],   labelfont= [Times, bold, 40],  title = "K(x,y)"), b = 0..1., a=0..1.);
 >

Hello Dear Professional users,

I have a question regarding the "fsolve" command and also the "assign" command in Maple.

In my previous codes, I just used one time from "fsolve" and then "assign" command.

Today, I want to use "fsolve" and "assign" in a for loop. But, I can not get the results correctly.

For example, previously I reach a system of algebraic equations and the solve my problem easily:

N:=8:
y:=sum(a[n]*t^n,n=0..N):
y:=unapply(y,t):
*****some calculations with a[n] coefficients *****
A:={a set of nonlinear algebraic equations in terms of a[n]}%The number of equations is N+1 (same as the number of a[n] for n=0..N)
sol:=fsolve(A):
assign(sol)
plot(y(t),t=0..1)

****************************************************************************************************
****************************************************************************************************
****************************************************************************************************

Today, my problem is:

N:=8:
M:=4:
for i from 1 to M do
y[i]:=sum(a[i,n]*t^n,n=0..N):
y[i]:=unapply(y[i],t):
end do
for i from 1 to M do
*****some calculations with a[n] coefficients *****
@A[i]:={a set of nonlinear algebraic equations in terms of a[i,n]}%The number of equations is N+1 (same as the number of a[n] for n=0..N)
@sol[i]:=fsolve(A[i]):
@assign(sol[i])
@plot(y[i](t),t=0..1)
end do
****************************************************************************************************
****************************************************************************************************
****************************************************************************************************

What I should write instead of "A[i]", "sol[i]", and "assign(sol[i])" the lines started with
@A[i],....
@sol[i],...
@assign(sol[i]),....

With kind regards,
Emran

## Given that the solution of a PDE is known, how can...

Hello

I am trying to understand how to use Maple to solve a PDE.  Below it is a problem (Henon-Heilles system) where the answer is known.

with(PDEtools);

infolevel[pdsolve]:=3:

declare(Hamil(x,y,u,v));

PDEHamil := u*diff(Hamil(x, y, u, v), x) + v*diff(Hamil(x, y, u, v), y) + (-2*x*y - x)*diff(Hamil(x, y, u, v), u) + (-x^2 + y^2 - y)*diff(Hamil(x, y, u, v), v) = 0;

pdsolve(PDEHamil)


Maple returns no solution, but one solution is:

sH:=1/2*(u^2+v^2)+1/2*(x^2+y^2-2/3*y^3)+x^2*y;

simplify(eval(subs(Hamil(x,y,u,v)=sH,PDEHamil)));
0=0


What am I missing?

Many thanks.

## trouble installing Syrup...

I am trying to install Syrup in my home computer (I have it installed in my work computer).  I followed the instructions in the Readme file:

From Standard Maple:
Open the file Syrup-Installer.mla.
To do so, use File -> Open, choose file type
"Maple Library Archive (.mla)", select the file, and
click "Open".

Everything seemed to work and the help page opened up:  But, it is not the syrup help page.  furthermore, when I type ?Syrup, it doesn't open it either.

When I try to run a worksheet that uses Syrup (that works on my work computer), I get these errors:

I"m going to reboot now and try again.

Jorge

## How to change datatype of multiple columns in data...

I was working with a Dataframe when I wanted to change the datatype of multiple columns at the same time as this is quite a large dataframe. I found in the helpfile that I can change datatype by the following command:

SubsDatatype(Data, plts, float) which then change the datatype of "plts" into float. I had hoped that using multiple columns in the command would work in this way: SubsDatatype(Data, [plts, act], float)  but apparently not. Is there a way to do this or do I have to do it column by column?

Additionally I have another question about dataframes. I would like to replace "0" in the dataframe by a "blank" as you can do in excel. How do you do this in a dataframe?

Thanks in advance for any help given!

## How find list of solution for ordinary differentia...

restart;
with(DEtools);
ode := diff(y(x), x) = epsilon - y(x)^2;
d                       2
ode := --- y(x) = epsilon - y(x)
dx

sol := dsolve(ode);
/           (1/2)            (1/2)\        (1/2)
sol := y(x) = tanh\_C1 epsilon      + x epsilon     / epsilon

P := particularsol(ode);
(1/2)                 (1/2)
P := y(x) = epsilon     , y(x) = -epsilon     ,

/    y(x)    \            (1/2)
arctanh|------------| - x epsilon      + _C1 = 0
|       (1/2)|
\epsilon     /



i am looking for finding all solution of this equation like this picture below

## Covariant Derivative of Einstein Tensor for specif...

Dear all,

I would like to find how I can calculate covariant derivative of Einstein tensor for an arbitrary metric ds_2=-A(r)*dt^2+B(r)*dr^2+dtheta^2+sin(theta)^2*dphi^2

with best

## Error with minimize/maximize...

Dear all,

I have this polynomial function

G(x, y) := (-0.14*y^3 + 1.20000000000000*y^2 - 1.26000000000000*y + 0.200000000000000)*x^3 + (1.20*y^3 - 10.0800000000000*y^2 + 10.0800000000000*y - 1.20000000000000)*x^2 + (-8.82*y + 10.08*y^2 - 1.26*y^3)*x + 1. - 1.2*y^2 + 0.2*y^3

I don't understand why the command

minimize(G(x,y),x=0..1,y=0..1);

produces the error

Error, (in RootOf/RootOf:-algnum_in_range) invalid input: RootOf/RootOf:-rootof_in_range expects its 1st argument, rt, to be of type ('RootOf')(polynom(rational,_Z),identical(index) = posint), but received RootOf(7*_Z^3-93*_Z^2+327*_Z-187)

## Adding H-type error bars to a plot of 2d points...

Using ScatterPlot (or ErrorPlot), one can add error bars to a 2d point plot of data. However, the bars are single lines. I wish to create a plot with H-type error bars in both the horizontal and vertical directions.  Below is an example showing how the bars should appear. (This image is taken from a previous question about adding error bars.)

I do not need to reproduce this figure exactly. The location of the data points and the size of the error bars are irrelevant. The closest I have seen is using BoxPlot.

Has this question been asked and answered? If so, I cannot find it.

## define conformable fractional derivative for calcu...

there is any way for define conformable fractional derivative in partial differential equation

restart;
with(PDEtools);
pde := a*diff(psi(x, t), x $2) + (b*abs(psi(x, t))^(-2*n) + c*abs(psi(x, t))^(-n) + d*abs(psi(x, t))^n + f*abs(psi(x, t))^(2*n))*psi(x, t) = 0; pde + i*diff(u(x, t), [t$ beta]) = 0;


how define a  fractional derivative in sense of conformable derivative

## where does the csgn(L) come from in the solution, ...

I don't understand where the the csgn(L) comes from in the solution below:

all the variables are defined as real:

coupled_network_vbat.mw

Thanks in advance for any help.

Jorge

## gcd for large degree polynomials...

I notice that the command gcd(a,b), if a and b are large degree polynomials, takes too much time and often crashes Windows (not only Maple).

As the euclidean algorithm is very efficient even for large numbers,why not for polynomials?

And how could I calculate the gcd between polynomials with a large degree?

Thanks Michele

## Iteration of string in print command...

Hi everyone:

I watn to create expressions like below expressions in "printf" command:

%15s

%15s%15s

%15s%15s%15s

%15s%15s%15s%15s

...........................................

Can I write these form expressions with "for' command for i=1..n or "seq" command? infact I need those in print command so that I do not type manually.