In the OrthogonalExpansions package, how can I change the summation variable to be n instead of i?

doubt_1.mw

Hi, I am trying to solve two simultaneous equations (for t1) they are as follows-

eq 1

i__m2(0) = (-(-b*`#msub(mi("θ",fontstyle = "normal"),mi("m"))`+`#msub(mi("θ",fontstyle = "normal"),mi("m"))`^2-2*c)*exp(0)*a*N^alpha/`#msub(mi("θ",fontstyle = "normal"),mi("m"))`^3+(-c*t__2^2*`#msub(mi("θ",fontstyle = "normal"),mi("m"))`^2+b*t__2*`#msub(mi("θ",fontstyle = "normal"),mi("m"))`^2+2*c*t__2*`#msub(mi("θ",fontstyle = "normal"),mi("m"))`-b*`#msub(mi("θ",fontstyle = "normal"),mi("m"))`+`#msub(mi("θ",fontstyle = "normal"),mi("m"))`^2-2*c)*exp(`#msub(mi("θ",fontstyle = "normal"),mi("m"))`*t__2)*a*N^alpha/`#msub(mi("θ",fontstyle = "normal"),mi("m"))`^3)*exp(0)

eq 2

i__m1(t__1) = ((-c*t__1^2*`#msub(mi("θ",fontstyle = "normal"),mi("m"))`^2+b*t__1*`#msub(mi("θ",fontstyle = "normal"),mi("m"))`^2+2*c*t__1*`#msub(mi("θ",fontstyle = "normal"),mi("m"))`-b*`#msub(mi("θ",fontstyle = "normal"),mi("m"))`+`#msub(mi("θ",fontstyle = "normal"),mi("m"))`^2-2*c)*exp(`#msub(mi("θ",fontstyle = "normal"),mi("m"))`*t__1)*a*N^alpha*(lambda-1)/`#msub(mi("θ",fontstyle = "normal"),mi("m"))`^3-(-b*`#msub(mi("θ",fontstyle = "normal"),mi("m"))`+`#msub(mi("θ",fontstyle = "normal"),mi("m"))`^2-2*c)*a*N^alpha*(lambda-1)/`#msub(mi("θ",fontstyle = "normal"),mi("m"))`^3)*exp(-`#msub(mi("θ",fontstyle = "normal"),mi("m"))`*t__1)

rhs(i__m2(0) = (-(-b*theta__m+theta__m^2-2*c)*exp(0)*a*N^alpha/theta__m^3+(-c*t__2^2*theta__m^2+b*t__2*theta__m^2+2*c*t__2*theta__m-b*theta__m+theta__m^2-2*c)*exp(theta__m*t__2)*a*N^alpha/theta__m^3)*exp(0)) = rhs(i__m1(t__1) = ((-c*t__1^2*theta__m^2+b*t__1*theta__m^2+2*c*t__1*theta__m-b*theta__m+theta__m^2-2*c)*exp(theta__m*t__1)*a*N^alpha*(lambda-1)/theta__m^3-(-b*theta__m+theta__m^2-2*c)*a*N^alpha*(lambda-1)/theta__m^3)*exp(-theta__m*t__1))

solve({-(-b*theta__m+theta__m^2-2*c)*a*N^alpha/theta__m^3+(-c*t__2^2*theta__m^2+b*t__2*theta__m^2+2*c*t__2*theta__m-b*theta__m+theta__m^2-2*c)*exp(theta__m*t__2)*a*N^alpha/theta__m^3 = ((-c*t__1^2*theta__m^2+b*t__1*theta__m^2+2*c*t__1*theta__m-b*theta__m+theta__m^2-2*c)*exp(theta__m*t__1)*a*N^alpha*(lambda-1)/theta__m^3-(-b*theta__m+theta__m^2-2*c)*a*N^alpha*(lambda-1)/theta__m^3)*exp(-theta__m*t__1)}, [t__1]);
Warning, solutions may have been lost
 

Can someone, please help. Thanks in advance.

Any idea why a similar indexing call to an Array and a Matrix gives different "orientations"?

The indexing call [1..2,1] to a Matrix gives a a column Vector, while a similar call to an Array gives a (row) Array. So somehow the Array call gives a transpose of the original.

MatrixVsArray.mw

I have used maple to solve a system of differential equations. However, I need to do the same in R. The problem is that when I use the same parameter values as used in maple to R, I don't get the same plots. Can someone assist wrt? 

The definition 
a:=ModularSquareRoot(10,11)
returns
Error, ... because no numbers in Z11 have the square equal to 10. I need, in a procedure, to prevent the error, I mean something like this:
if a<>ERROR then b:=b+1 else c:=c+1 end if
Any suggestions? Thanks

Dear maple users,

Greetings.

JVB.mw
 

Download JVB.mw

How to obtain a solution for various values of "ax"

waiting for your reply.

how can i plot the relation betwen x and B[k] from result of itterition in this work sheetx_phi.mw

Download x_phi.mw

I can't figure out how to write a program to work out the classification of a conic and if it is a degenerate given a data file.

So far I have programed the following which reads the conic coefficients (a,h,b,f,g,c) and displays it as an equation: 

conic :=proc(a,h,b,f,g,c)
local C;
C:= a*x^2+h*x*y+b*y^2+f*x+g*y+c=0;
end proc:

Can anyone help me work this out

According to Wikipedia, Abel's first order odes have general analytical solutions, due to "Panayotounakos, Dimitrios E.; Zarmpoutis, Theodoros I. (2011)" where the claim is that, if I understand it right, all Abel ode's can be solved analytically.

https://en.wikipedia.org/wiki/Abel_equation_of_the_first_kind

"Construction of Exact Parametric or Closed Form Solutions of Some Unsolvable Classes of Nonlinear ODEs (Abel's Nonlinear ODEs of the First Kind and Relative Degenerate Equations)"

Maple is very good on solving ODE's, but some Abel ode's it can not solve. For example

restart;
ode:=diff(y(t),t)= y(t)^3+exp(-5*t);#_Abel
ode:=diff(y(x),x) = (1+x^3*y(x))*y(x)^2;#_Abel
ode:=diff(y(x),x) = y(x)^2-a*x*(1-x^(n-1))*y(x)^3;#_Abel
ode:=diff(y(x),x) = a*y(x)^2+x*y(x)^3*(b+c*x^(n-1));#_Abel
ode:=diff(y(x),x) = f0(x)+f1(x)*y(x)+f2(x)*y(x)^2+f3(x)*y(x)^3;#_Abel
ode:=(tan(x)*sec(x)-2*y(x))*diff(y(x),x)+sec(x)*(1+2*y(x)*sin(x)) = 0;#_Abel, `2nd type`, `class A`
ode:=x*(a+y(x))*diff(y(x),x)+b*x+c*y(x) = 0; #[_Abel, `2nd type`, `class B`]
ode:=(g0(x)+y(x)*g1(x))*diff(y(x),x) = f0(x)+f1(x)*y(x)+f2(x)*y(x)^2+f3(x)*y(x)^3;#_Abel, `2nd type`, `class C`

etc..

All the above Abel ode's are from Book: Ordinary differential equations and their solutions. By George Moseley Murphy. 1960

I am just asking what is the status of this. Is it true there is now a method to solve all these exactly and may be Maple's implementation is not in yet for this? 

btw, I found the description of solution methods in https://fr.maplesoft.com/support/help/Maple/view.aspx?path=odeadvisor/Abel much easier to follow to learn how to solve Abel ode's. That paper mentioned on Wikipeida, I had hard time following after the 3rd page. (need more time to study it).

Could someone please comment on the status of solving Abel's first order ODE's in Maple and if it possible now to solve them all analytically?

Dear friends, 

I have to select the last element of a remember table T from a recursive procedure. I've tried 

with(ListTools): 

SelectLast(T); 

as this command works with rtables, as it is stated in Maple's online help page. However I receive no result. 

Can you please tell me how to obtain a correct result? 

Many thanks for the help. 

How to install this old package for Maple 6 , should be trivial but turns te be out a puzzle with no result so far.

### This is the Maple initialization file created for use with the 
### LAMP modules. For Maple 6 in Windows 95, 98, 2000, or NT, this file 
### should be installed in the folder 
###
###        C:\Program Files\Maple 6\BIN.WNT
###
### The last three letters, WNT, may vary with the version of Windows.
###
### The following lines set up libname, so Maple knows to look in the
### proper folder to find the Lamp library. If you did not put the 
### Lamplib folder in C:\lamp6\lamplib, you must edit the first line.

lamppath := "C:\\lamp6\\lamplib\\":
libname := `lamppath`, libname:

### The following line enables one to use the command read(lampstart) 
### to establish the Lamp environment. It is optional.

lampstart := cat(lamppath,"lamp.txt"):

I've got a question regarding sum of matrix or arrays.

My problem is that sum of the values of the maxtrices is not calculated, but shown as a sum with the '+' sign. I have tried to recreate the problem with an easier example, but so far I have not managed to do so.

Before posting the whole program, I'd like to post it as a question, if someone has an idea about how I could get an evaluation of the matrix.

Here's a screenshot.

Why when trying to substitute a term in denominator, subs does not work, when this term is product. But it works when this term is single variable?

subs((x*y)=t,1/(x*y));

does not work. i.e. it does not return 1/t

But this works

subs(z=t,1/z);

and returns 1/t

algsubs does not work either on the first example above. 

Just wondering why, that is all.

I do not think Maple help on the subject is easy to follow as the exampels are not clear. I was hoping someone can give a very simple example.  

Now, I run long script, over say 1,000 problems. This takes long time each time I run it. Since each problem is completely independent of others, and there is no shared data at all (for each problem, its output is written to separate file), I am thinking of using the parallel programming in Maple, and hoping this will speed it up. I have an intel PC, with modern CPU. I think it has may be 10 or 16 cores, not sure now, so in theory it should be faster to complete.

For a very basic example, suppose I have this sequential program

foo:=proc(i::integer)
   return i^2;
end proc;

for i from 1 to 10 do
   foo(i);
od;

Where foo() is now called 10 times, one after the other. How would one change the above to make it run in parallel?

I know I need to call Threads:-Task:-Start and then use Threads:-Task:-Continue 

But I am not sure how to use Threads:-Task:-Continue to tell it to call foo in parallel passing each task 1,2,3,.... in turn, and wait until they are all done. This is the part not clear to me how to do even after looking at the help example under Task Programming Model

Could someone show how to do the above for this simple example?   

Since I have 1,000 problems, do I need to create 1,000 tasks at once, one for each problem and wait for them to all be done? what if I have 10,000 problems, creating 10,000 tasks at once might not work, would it? or will Maple handle this internally by queuing the creation of tasks as needed? This part is also not clear to me.

thanks

Hello!

I just want to try plot a conformal map for better understanding how it works.

For example, I want to plot a conformal map, so I do this:

restart;
assume(y, real);
assume(x, real);
f := z -> I + z*exp(1/4*I*Pi);
w := f(x + y*I);
u := Re(w);
v := Im(w);
A := array(1 .. 2);
A[1] := plots:-conformal(z, z = 0 .. 1 + I/2, grid = [16, 16], numxy = [16, 16], scaling = constrained);
A[2] := plots:-conformal(f(z), z = 0 .. 1 + I/2, grid = [16, 16], numxy = [16, 16], scaling = constrained);
plots:-display(A);

It works fine. But if I want to map more complecated region, I have lot's of problem. Could you help me please.

For example:

how to map a triangle [0,0], [1,0], [0,i] or half-plane Im z> 1, excluding the circle | z - 2i | <= 1.

Thank you!