## solved numerically a system of nonlinear algebraic...

Hi everyone:

How can I solve numerically the system of nonlinear algebraic equations by Newton’s method?

eq1:= (1/2)*x[0]*sqrt(3)-(1/2)*x[1]*sqrt(3) = ((1/2)*x[0]*(t+(1/3)*sqrt(3))*sqrt(3)-(1/2)*x[1]*(t-(1/3)*sqrt(3))*sqrt(3))*(1-(1/6)*y[0]*(t+(1/3)*sqrt(3))*sqrt(3)+(1/6)*y[1]*(t-(1/3)*sqrt(3))*sqrt(3)-(1/8)*y[0]*(5*sqrt(3)*(1/12)-1/4+t)*sqrt(3)+(1/8)*y[1]*(-(1/4)*sqrt(3)-1/4+t)*sqrt(3)-(1/8)*y[0]*((1/4)*sqrt(3)-1/4+t)*sqrt(3)+(1/8)*y[1]*(-5*sqrt(3)*(1/12)-1/4+t)*sqrt(3))-5*t^3*(1/2)+49*t^2*(1/12)+17*t*(1/12)-23/6;
eq2:= (1/2)*y[0]*sqrt(3)-(1/2)*y[1]*sqrt(3) = ((1/2)*y[0]*(t+(1/3)*sqrt(3))*sqrt(3)-(1/2)*y[1]*(t-(1/3)*sqrt(3))*sqrt(3))*(-2+(1/2)*x[0]*(t+(1/3)*sqrt(3))*sqrt(3)-(1/2)*x[1]*(t-(1/3)*sqrt(3))*sqrt(3)+(1/4)*(-(1/12)*sqrt(3)-3/4)*((1/2)*x[0]*(5*sqrt(3)*(1/12)-1/4+t)*sqrt(3)-(1/2)*x[1]*(-(1/4)*sqrt(3)-1/4+t)*sqrt(3))+(1/4)*((1/12)*sqrt(3)-3/4)*((1/2)*x[0]*((1/4)*sqrt(3)-1/4+t)*sqrt(3)-(1/2)*x[1]*(-5*sqrt(3)*(1/12)-1/4+t)*sqrt(3)))+15*t^3*(1/8)-(1/4)*t^2+3*t*(1/8)-1;
eq3:=(1/2)*x[0]+(1/2)*x[1] = 1;
eq4:=(1/2)*y[0]+(1/2)*y[1] = 0;

## How I find college students to create problem work...

I teach high school IB Math.

I want to find someone who can take problems I have created and enter them into Maple (problem and solution) so I can use those in my classroom.

I can keep up with the new stuff I create, but I have almost 20 years of accumulated material I'd like to move into Maple.

Does anyone know where I can find someone to enter the problem and solution so that it is proved out in Maple? Maybe an existing college student using Maple at their school for math, engineering, or education? I am willing to pay them, it is just locating them that is a problem.

Even if you know a site for maple contractor types, that would be helpful.

Thanks a ton!

Robert

## Finding a Derivative with Maple...

I have a function e^(-\lambda z \sqrt(x^2 + y^2)), is it possible to use Maple to find some sequence of derivatives wrt to x and y which could be applied to this function to get

(z/(1+2*sqrt(x^2 + y^2)*lambda))*e^(-\lambda z \sqrt(x^2 + y^2))

## Any maple built in function can find the possible ...

Any maple built-in function can find the possible numbers when modular a fixed number?

For example,

(x&^3+y) mod 124 = 123 mod 124

Find the possible values of x and y.

## Maple prints out in loop even though I tell it not...

for i from 1 to numelems(X) do
A := x:
B := C;
end;

maple will print all statements even though I use the colon to try to suppress the first line. This just seems wrong. If I suppress the entire loop I have to use prints, and if I have a lot of statements I have to do it for every one even if I just want to supress 1.

It seems maple is suppose to suppress but it isn't.

## How to stop maple from locking up and crashing and...

One problem I come across far to often is that if maple get's bogged down in a computation or I screwed something up I can't always stop it. Sometimes the red ! is greyed out and I have to kill the mserver. When I do this I get the error that I need to save but save doenst' work and I can't do anything because the the kernel was killed. Maple doesn't seem to be able to properly recover... even though it does it most of the time when I click on the red !.

Is there any way around this?

## Override function for new behavior...

I get tired of having to resize my plots constantly so I can get a nicer view.

setPlotSize:=proc(P,sz::[posint,posint])
op(0,P)(remove(type,[op(P)],'specfunc(ROOT)')[],
ROOT(BOUNDS_X(0),BOUNDS_Y(0),
BOUNDS_WIDTH(sz[1]),BOUNDS_HEIGHT(sz[2])));
end proc:

This let's one set the size(mine is usually 1200x500) but I have to stick it in every plot.

Is there a way to override the plot functions to automatically do this for every plot or create a simple short option to scale it to the window size or some specific size?

I could probably make a simple function like RPF()

that I can wrap every plot but I'd like to avoid that step and just apply it to all plots by default(since 99% of the time I have to scale them.

## Is "MultiSet" reliable?...

Something really weird is going on when I build a MultiSet in two different ways, using the "+" operation.  The two constructions give the same MultiSet (since U=V), but in some mysterious way they are not really equal (since X=Y is false).  Does anyone know how to avoid this?  Should the "+" operator be avoided altogether?

There is more:  I tried saving the values of X and Y using the command:  save X, Y, "anomaly.m"

I got the error message:  "Error, could not open anomaly.m for reading".

Thanks!

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## change variable in equation...

Hi everyone:

How can I re-write the EQ with transformation       s=1+2*((tau-t)/T0)    ?

EQ:=int(f1(t-tau)*(Sum(y[k]*F[k](tau), k = 0 .. M)), tau = t-T0 .. t)

tnx...

## How can I have a pretty display of a piecewise exp...

Hi,

How can I force the command InsertContent(Worksheet(Group(Input( T )))) to display the variable eq as it appears in label (2) ?

(a screen capture of the output of InsertContent(Worksheet(Group(Input( T )))) is given after the Maple code)

 > restart:
 > interface(version)
 (1)
 > with(DocumentTools):
 > with(DocumentTools[Layout]):
 > eq := piecewise(t < 1, sin(t), cos(t)); C := Cell( Textfield(style=TwoDimOutput,Equation(eq)) ): T := Table(Column(), widthmode=percentage, width=40, Row(C)): InsertContent(Worksheet(Group(Input( T )))):
 (2)
 >

## GKLS - Optimization test functions generator...

Hi!

There is a (relatively) known software code (written in C), called ." GKLS-generator" or "GKLS" to generate, according to certain user paramenters, optimization test functions. The code is available for free at the web

http://wwwinfo.deis.unical.it/%7Eyaro/GKLS.html

I would like to write this code in Maple. In the attached zip there is a PDF explaining how to build these functions. For now, I tried the follwoing Maple code GKLS_v4.mw

I think I'm doing something wrong, since the drawing generated by the attached Maple does not look much like the PDF in the attached zip (Fig. 1 of page 8).

Please, Can you help me with this?

## Typesetting vector names with up arrows in plots

by: Maple 2018

I was trying to display a Physics[Vectors] vector name in a 3dplot with an up arrow
on it. I found that this old 2008 trick still works in MAPLE 2018.

 > restart;
 > with(plots): with(Physics[Vectors]):
 > # Using MAPLE 2018.2
 > a:=arrow([-1,1,1],view=[-1.5..1.5,-1.5..1.5,-1.5..1.5]):
 > v_; t:= textplot3d([-1.1,1.1,1,v_]): display(a,t);
 > # I found this on an old 2008 post t:= textplot3d([-1.1,1.1,1,typeset(#mover(mi( || v ||  ),mo("→")))]): display(a,t);

## Maple not simplifies equation completly...

Hello

I have problem with Maple that is not simplifying equation completly:

My simplified equation:

Its sum of  for example 20 elements and only n is increasing so why maple will not move a,b,c,d ahead parenthesis ?

## Application of MapleSim in Science and Engineering...

Application of MapleSim in Science and Engineering: a simulationbased approach

In this research work I show the methods of embedded components together with modeling and simulation carried out with Maple and MapleSim for the main areas of science and engineering (mathematics, physics, civil, mechanical etc); These two latest scientific softwares belonging to the company Maplesoft. Designed to be generated and used by teachers of education, as well as by university teachers and engineers; the results are highly optimal since the times saved in calculations are invested in analyzes and interpretations; among other benefits; in this way we can use our applications in the cloud since web technology supports Maple code with procedural and component syntax.

FAST_UNT_2020.pdf

Lenin AC

## Collocating a vector...

Hi User!

Hope you would be fine with everything. I have a vector "POL" of M dimension obatined for the following expression

restart; with(LinearAlgebra); nu := 1; M := 3;
for k while k <= M do
Poly[k] := simplify(sum(x^i*GAMMA(nu+1)/(factorial(i)*GAMMA(2*nu)), i = 0 .. k-1))
end do;
POL := <,>`(seq(Poly[k], k = 1 .. M))

and I want to construct a matrix of M by M by collocating it on the points x=i/(M-1) for i=0,1,2,...,M-1 like the following way,

For M=3 I need

Matrix(3, 3, {(1, 1) = Poly[1](0), (1, 2) = Poly[1](1/2), (1, 3) = Poly[1](1), (2, 1) = Poly[2](0), (2, 2) = Poly[2](1/2), (2, 3) = Poly[2](1), (3, 1) = Poly[3](0), (3, 2) = Poly[3](1/2), (3, 3) = Poly[3](1)});

For M=4 I need

Matrix(4, 4, {(1, 1) = Poly[1](0), (1, 2) = Poly[1](1/3), (1, 3) = Poly[1](2/3), (1, 4) = Poly[1](1), (2, 1) = Poly[2](0), (2, 2) = Poly[2](1/3), (2, 3) = Poly[2](2/3), (2, 4) = Poly[2](1), (3, 1) = Poly[3](0), (3, 2) = Poly[3](1/3), (3, 3) = Poly[3](2/3), (3, 4) = Poly[3](1), (4, 1) = Poly[4](0), (4, 2) = Poly[4](1/3), (4, 3) = Poly[4](2/3), (4, 4) = Poly[4](1)})

and general form is like this

[[[Poly[1](0/(M-1)),Poly[1](1/(M-1)),Poly[1]((2)/(M-2)),...,Poly[1]((M-1)/(M-1))],[Poly[2](0/(M-1)),Poly[2]((1)/(M-1)),Poly[2]((2)/(M-1)),...,Poly[2]((M-1)/(M-1))],[Poly[3]((0)/(M-1)),Poly[3]((1)/(M-1)),Poly[3]((2)/(M-1)),...,Poly[3]((M-1)/(M-1))],[...,...,...,...,...],[Poly[M]((0)/(M-1)),Poly[M]((1)/(M-1)),Poly[M]((2)/(M-1)),...,Poly[M]((M-1)/(M-1))]]];

Another problem is I want to define a vector of M dimension using a function f(x)=sin(x) and two points a=1, b=2 like the following way,

Vec:=[[[a],[f((1)/(M-1))],[f((2)/(M-1))],[f((3)/(M-1))],[...],[f((M-1)/(M-1))],[b]]]