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## Problem with inconstant integration of probablity ...

SlitRecoil.mw

At line 46 I do some integrals of a probablity function obainted from complex amplitudes. The plot of the function is shown above. However, the integral suddlenly drops to almost nothing when I increase the limits from +/- 0.195 to +/-0.2. The transition actually occus at ~0.196 (not shown)

This makes no sense. It doesn't seem  from the plot that the step size could get so large as to miss the peak! However, I don't know how to change numerical integral step size to test that.

---Arthur (a.k.a. Traruh)

## Numerical solution of the boundary value problem f...

Hello. There is some system of differential equations with respect to the unknowns u1(x), u2(x), u3(x) with boundary conditions. Solved numerically using the dsolve command.
Is it possible to build a graph of a function of the form W=a*u1(x)+b*u2(x)+c*u3(x) based on this solution?

## Why my second curve is not plotted?...

Hi

I want to solve two equations (Eqmin and Eqmax) numerically  and plot curves of Mmin and Mmax versus "sigma" in one frame, But the  second curve (Mmax) is not plotted !  What should I do?
(We know that only real and positive roots are acceptable)
Eq.mw

## What does this error mean in pdsolve?...

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I am trying to solve these two coupled PDE and am getting this error. Does anyone know what this mean?

## Bug in analytic integration...

Hello everyone,

I'm not quite sure, if this is the correct place but i think i found a bug in the analytic integration tool in Maple.

Since i have the student edition and i didn't find a bug report form i will post it here:

restart:

R:=1:
delta:=1:

f:=R^4*delta*cos(theta)*sin(x)*sin(-x+theta)/(8*Pi*(R^2*cos(x)+sqrt(2*R^2*cos(x)+2*R^2+4*delta^2)*delta+R^2+2*delta^2));

intfAna:=int(f,x= -Pi + theta .. Pi+ theta);

intfNum:=Int(f,x= -Pi + theta .. Pi+ theta);
intNum:=evalf(Int(eval(intfNum),theta=0..2*Pi));
intAna:=evalf(int(eval(intfAna),theta=0..2*Pi));


the last two statements yield:

intNum := -0.07343950362
intAna := -0.7853981635

Thus the numerical integrated value differes from the analytical result.

Since I also tried to integrate this with scipy in python I'm pretty sure that the numerical result is correct  and the analytical one is not.

Is my deduction here correct?

I have Maple 2018 here on my private PC. But at work i have Maple 2021 and the difference is the same.

Interestingly the analytic result seems to be -cos(theta)^2/4. If we plot the analytical and numerical integrand, we get:

plot(intfNum,theta=0..2*Pi);
plot(intfAna,theta=0..2*Pi);


Thus both integrands seem to be cosines of theta but the analytical has the wrong factor.

## Maple to Latex - empty page pdf only...

When I export a very simple Maple 2018 (MaxOS) document to Latex, this tex file results:

%% Created by Maple 2018.2, Mac OS X

%% Source Worksheet: untitled 3

%% Generated: Sun Jul 03 16:34:49 CEST 2022

\documentclass{article}

\usepackage{maplestd2e}

\def\emptyline{\vspace{12pt}}

\begin{document}

\pagestyle{empty}

\DefineParaStyle{Maple Bullet Item}

\DefineParaStyle{Maple Warning}

\DefineParaStyle{Maple Dash Item}

\DefineParaStyle{Maple Error}

\DefineParaStyle{Maple Title}

\DefineParaStyle{Maple Text Output}

\DefineParaStyle{Maple Normal}

\DefineCharStyle{Maple 2D Output}

\DefineCharStyle{Maple 2D Input}

\DefineCharStyle{Maple Maple Input}

\DefineCharStyle{Maple 2D Math}

\begin{Maple Normal}{

\begin{Maple Normal}{

\mapleinline{inert}{2d}{restart; 1}{$\displaystyle$}

}\end{Maple Normal}

}\end{Maple Normal}

\begin{Maple Normal}{

\begin{Maple Normal}{

\mapleinline{inert}{2d}{a := b^2-sqrt(4); "_noterminate"}{$\displaystyle$}

}\end{Maple Normal}

}\end{Maple Normal}

\begin{maplegroup}

\begin{Maple Normal}{

\mapleinline{inert}{2d}{a := b^2-sqrt(4); "_noterminate"}{$\displaystyle$}

}\end{Maple Normal}

\mapleresult

\begin{maplelatex}

\mapleinline{inert}{2d}{a := b^2-2; "_noterminate"}{$\displaystyle$}

\end{maplelatex}

\end{maplegroup}

\begin{Maple Normal}{

\begin{Maple Normal}{

\mapleinline{inert}{2d}{a := b^2-sqrt(4); "_noterminate"}{$\displaystyle$}

}\end{Maple Normal}

}\end{Maple Normal}

\begin{maplegroup}

\begin{Maple Normal}{

\mapleinline{inert}{2d}{a := b^2-sqrt(4); "_noterminate"}{$\displaystyle$}

}\end{Maple Normal}

\mapleresult

\begin{maplelatex}

\mapleinline{inert}{2d}{a := b^2-2; "_noterminate"}{$\displaystyle$}

\end{maplelatex}

\end{maplegroup}

\begin{Maple Normal}{

\begin{Maple Normal}{

\mapleinline{inert}{2d}{}{$\displaystyle$}

}\end{Maple Normal}

}\end{Maple Normal}

\end{document}

However, when trying to process the tex file in both Overleaf and TexShop the pdf output is only an empty page. No error occurs, i.e. the maplestd2e.sty file is recognised by both Overleaf and TexShop.

What is going wrong here?

## How can I attach labels to LP solution matrices an...

Good day.

I am working on a network flow problem that uses a linear programming (simplex) technique.The flow is directed across 3 regions (a, b, and c) and there are 2 nodes within region a, 4 nodes in region b, and 5 nodes in region c.

I wish to determine the minimum cost from regions a to c and from regions b to c that satisfies the requirement of each of the 5 nodes in region c. The objective and constraints are constructed and Maple produces the minimum solution (see attached). While the output is useful when the number of nodes is small, I would like to extend this to a larger-scale case and so the output would need to be more user-friendly / graphic.

I have 2 questions -

1. Does anyone know a way to attach labels for each region and each node to these solution matrices?
For instance -  the first matrix, x, specifies a quantity of 2,000 that flows from node #1 in region a to node #2 in region b
2. Is it possible to produce a network graph showing the directed flow from each region and from node to node?

Thanks to all for reading this!

MaplePrimes_Network.mw

## How can I write a sum over even numbers, of a term...

Hello

I have the following summation to do,

d(l,m')=\sum_{N=-l'}^{l'}d(l',N,m')=d^{l'}_{00}(\dfrac{\pi}{2})d^{l'}_{0m'}(\dfrac{\pi}{2})f_{m'0}+\sum_{N=1}^{l'}((-1)^{l'}+1)d^{l'}_{0N}(\dfrac{\pi}{2})d^{l'}_{Nm'}(\dfrac{\pi}{2})f_{m'N}

where  d^{l'}_{0N} are the rotation matrix functions and  f_{m'N} is a piecewise function which takes a certain value at N=0, another value for N even and it takes 0 as a value for N odd.

The prblem is that I don't know how to write a summation for N even only so that in that case i can replace f_{m'N} by its expression for N even. The other way is to write f_{m'N} as a piecewise function but in that case, i don't know how to do it (I tried to use assuming N even ..) but got wrong answer.

Thank you for helping me solving my proble.

Best regards.

## How to plot this equation?...

where p, q, r, a are positive constants and phi(0) be a initial condition

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## I have a problem with the "Diff" command....

Hi !

Looks like there is a bug in the inert "Diff" command.

I have Maple 2018 on Windows 10 ,64 bits.

Does Maple consider Diff(f(x),x) to be equal to Diff(f(x),[x]) ?

It should be the same.

Maple displays  that it is equal but keeps in memory something else.

In the attached file, I give a very simple example.

I don't like to say this but my old version of Maple V Release V (1997) is more consistent i.e.

this version shows it's different and  keeps in memory that difference.

diff-problem.mw

I wonder if newer versions have this problem ?

Best regards !

## DirectSearch finds nonexisting roots...

DirectSearch finds nonexisting roots....     DirectSearch_finds_nonexisting_roots.mw

 >
 > restart
 > plot([cos(x), 0.001*x*x],x=-40..40,y=0..2)     ### test function plot
 > eq:= cos(x)= 0.001*x*x;     ###   float
 (1)
 > use RealDomain in solve(eq,x,explicit) end use   ## lacking some of the roots
 (2)
 > use RealDomain in solve(eq,x) end use
 (3)
 > fsolve(eq,x=-30)
 (4)
 > plot([cos(x), 0.001*x*x],x=-32..-31,y=0.9..1)
 > fsolve(eq,x=-32..-30);  fsolve(eq,x=-31.7..-31.4)
 (5)
 > with(DirectSearch)
 (6)
 > eq; SolveEquations(eq,AllSolutions):
 (7)
 > interface(rtablesize=90); SolveEquations(eq, AllSolutions)
 (8)

DirectSearch finds nonexisting roots!!!

Dr. Ali GÜZEL

 >

## How do i solve State Space system in Maple??...

Hii!!

I need your help in state space system.... kindly guide me how to solve State Space system in maplesoft.....i excecute the command but i didn't find the answer....can you plz help me?I have been trying for two weeks now but it is not working.Thank you!!