## Finding roots of a complex trigonometric expressio...

I have the following trigonometric expression:

`detA:= -(-((-16*cosh(beta*`&ell;`*xi[2])*sinh(beta*`&ell;`)+16*sinh(beta*`&ell;`*xi[2])*cosh(beta*`&ell;`))*sinh(beta*xi[1]*`&ell;`)+(-16*sin(beta*`&ell;`*xi[2])*cos(beta*`&ell;`)+16*cos(beta*`&ell;`*xi[2])*sin(beta*`&ell;`))*sin(beta*xi[1]*`&ell;`)-(16*(-sin(beta*`&ell;`*xi[2])*sin(beta*`&ell;`)+cosh(beta*`&ell;`*xi[2])*cosh(beta*`&ell;`)-sinh(beta*`&ell;`*xi[2])*sinh(beta*`&ell;`)-cos(beta*`&ell;`*xi[2])*cos(beta*`&ell;`)))*(cos(beta*xi[1]*`&ell;`)-cosh(beta*xi[1]*`&ell;`)))*sin(beta*`&ell;`*xi[2])+16*cos(beta*`&ell;`*xi[2])*((sin(beta*`&ell;`*xi[2])*sin(beta*`&ell;`)-cosh(beta*`&ell;`*xi[2])*cosh(beta*`&ell;`)+sinh(beta*`&ell;`*xi[2])*sinh(beta*`&ell;`)+cos(beta*`&ell;`*xi[2])*cos(beta*`&ell;`))*sin(beta*xi[1]*`&ell;`)+(sin(beta*`&ell;`*xi[2])*cos(beta*`&ell;`)-cos(beta*`&ell;`*xi[2])*sin(beta*`&ell;`))*(cos(beta*xi[1]*`&ell;`)-cosh(beta*xi[1]*`&ell;`))))*sinh(beta*`&ell;`*xi[2])+16*cosh(beta*`&ell;`*xi[2])*((sin(beta*`&ell;`*xi[2])*sin(beta*`&ell;`)-cosh(beta*`&ell;`*xi[2])*cosh(beta*`&ell;`)+sinh(beta*`&ell;`*xi[2])*sinh(beta*`&ell;`)+cos(beta*`&ell;`*xi[2])*cos(beta*`&ell;`))*sinh(beta*xi[1]*`&ell;`)+(sinh(beta*`&ell;`*xi[2])*cosh(beta*`&ell;`)-cosh(beta*`&ell;`*xi[2])*sinh(beta*`&ell;`))*(cos(beta*xi[1]*`&ell;`)-cosh(beta*xi[1]*`&ell;`)))*sin(beta*`&ell;`*xi[2])-(16*(cos(beta*`&ell;`*xi[2])*cosh(beta*`&ell;`*xi[2])-1))*((sin(beta*`&ell;`*xi[2])*cos(beta*`&ell;`)-cos(beta*`&ell;`*xi[2])*sin(beta*`&ell;`))*sinh(beta*xi[1]*`&ell;`)+sin(beta*xi[1]*`&ell;`)*(sinh(beta*`&ell;`*xi[2])*cosh(beta*`&ell;`)-cosh(beta*`&ell;`*xi[2])*sinh(beta*`&ell;`)))`

where:

```xi1_val:= 0.05:
xi2_val:= 0.10:
ell_val:= 12:

```

I want to determine the roots "beta[1]..beta[N]" of this expression. For this, I have tried:

```evalf(subs([xi[1] = xi1_val, xi[2] = xi2_val, `&ell;` = ell_val], detA)):
sol_beta:= Student[Calculus1][Roots](%, 1e-5..15);
```

which yields:

`sol_beta:= [10.4719755]`

However, I'm pretty sure there is another root before this, as we can see by the plot of the function:

```plot(subs([xi[1] = xi1_val, xi[2] = xi2_val, `&ell;` = ell_val], detA), beta = 5.2..5.3,
axes = boxed,
gridlines = true,
labels = [typeset(beta), typeset(`det A`)],
size = [0.5,0.5]
);```

it is clear that there is a root about beta = 5.2359, which is not captured by "Roots" function.

Can someone help me build an algorythm that will get all roots wihtin a given interval? Particularly, I need it to be an efficient routine, because I will later vary parameters "xi[1]" and "xi[2]" and make a surface with the solutions. So I will run it several times.

## Defining a Matrix ...

```restart:
k:=1:
M:=3:
U:=Matrix( (2^(k))*M,(2^(k))*M,symbol=u);
```

I defined a matrix U.

How to define all elements of the Matrix U is greater than 1? ( U consists of symbolic elements like u[1,1],u[1,2], etc. and all of them is greater than 1 )

## I get the error message: 'There were problems furi...

I get the error message: 'There were problems furin the loading process. Your worksheet may be incomplete.'

The file appears empty. Please, can I get a help to recover the file.

Calculation1.mw

## How to solve the unreasonable output form of pdf ...

I got a list containing all non isomorphic connected graphs with 6 vertices. Total number of the list members is 112 , and they are not too many . So I want to draw them all . It is good for Maple worksheet .

In order to save it and print it out on paper, I import it as pdf form . But the problem is that every page in pdf only contains 8 graphs . It wastes wasted too many spaces. It is unreasonable . I want to draw 20-30 graphs in one page of pdf. What is the solution to my problems? Thanks in advance. This problem has puzzled me for a long time.

```with(GraphTheory):
s1:=[NonIsomorphicGraphs(6,restrictto = connected,output=graphs,outputform=graph)]:
DrawGraph~(s1);```

## system of ODEs: stabilizing feedback...

Hi all;

I need to compute the stabilizing feedback for the system of nonlinear ODEs

stabilizing_Feedback.mw

## How can I obtain explicit solution for this equati...

I tried to solve the following equation to find an explicit expression for x in terms of n. But the answer is a long relation in terms of RootOf and _Z.

(1/4)*((-x^2+1)*(-4*Pi*(x^2-1)+n*(x^4-2*x^2+5))*cosh(n*x)*sinh(Pi*x)+sinh(n*x)*((-x^2+1)*(-4*n*(x^2-1)+Pi*(x^4-2*x^2+5))*cosh(Pi*x)-2*x*(x^4-2*x^2-3)*sinh(Pi*x)))/(x^2-1)^2=0

Any comment is welcomed.

## Plotting Graph for multi variables...

F(0) := a; F(1) := b; F(2) := c; F(3) := d

for k from 0 to 1 do F(k+4) := -(N[1]*G(k)+Re*(sum(F(k-m)*(m+1)*(m+2)*(m+3)*F(m+3), m = 0 .. k))-Re*(sum((k-m+1)*F(k-m+1)*(m+1)*(m+2)*F(m+2), m = 0 .. k)))/((1+N[1])*(k+1)*(k+2)*(k+3)*(k+4)) end do

How to plot a graph for this equation with different values of N_1 and Re number

## Animation with multi variables...

f(x):=1+B*x-(1/12)*B*x^3+0.1666666667e-4*B^3*x^3-4.166666667*10^(-8)*B^4*x^4+(1/160)*B*x^5+8.333333333*10^(-11)*B^5*x^5-0.5000000000e-2*B^2*x^2+0.1666666667e-4*B*x^3*C^2-4.166666667*10^(-8)*B*x^4*C^3+8.333333333*10^(-11)*B*x^5*C^4-0.5000000000e-2*B*C*x^2+0.3333333333e-4*B^2*x^3*C-1.250000000*10^(-7)*B^3*x^4*C-1.250000000*10^(-7)*B^2*x^4*C^2+3.333333333*10^(-10)*B^4*x^5*C+5.000000000*10^(-10)*B^3*x^5*C^2+3.333333333*10^(-10)*B^2*x^5*C^3+0.7291666667e-3*B*x^4*C-0.3333333333e-5*B*x^5*C^2+0.6250000000e-3*B^2*x^4-0.2083333333e-5*B^3*x^5-0.5416666667e-5*B^2*x^5*C;

How to plot f(x) with B and C are animation variables wih range -5 to 5?

## How to plot selected point from a set of points...

Dear Users!

Hoped everyone fine here. I have three main questions regarding the maple code given bellow:

restart; with(LinearAlgebra); with(plots);

alpha := 1; beta := 1; theta := 1/2;

UU := sinh(x)*sinh(y)*sinh(z)*exp(-1.*t);

NN := 3; L := 0; R := 1; T := 1; N := NN; Mx := NN; My := NN; Mz := NN; `&Delta;x` := (R-L)/Mx; `&Delta;y` := (R-L)/My; `&Delta;z` := (R-L)/Mz; `&Delta;t` := (R-L)/N;

kappa[1] := 1; kappa[2] := 2/x^2; kappa[3] := 1/x^2; kappa[X] := x^2+y^2+z^2+1; kappa[Y] := x^2+y^2+z^2+1; kappa[Z] := x^2+y^2+z^2+1; kappa[4] := 0; NL := 3;

ics := [seq(seq(seq([u[i, j, k, 0] = eval(UU, [x = i*`&Delta;x`, y = j*`&Delta;y`, z = k*`&Delta;z`, t = 0]), u[i, j, k, -1] = eval(u[i, j, k, 1]-2*`&Delta;t`*(eval(diff(UU, t), t = 0)), [x = i*`&Delta;x`, y = j*`&Delta;y`, z = k*`&Delta;z`, t = 0])][], i = 0 .. Mx), j = 0 .. My), k = 0 .. Mz)];

bcs := [seq(seq(seq([u[0, j, k, n] = eval(UU, [x = 0, y = j*`&Delta;y`, z = k*`&Delta;z`, t = n*`&Delta;t`]), u[Mx, j, k, n] = eval(UU, [x = L, y = j*`&Delta;y`, z = k*`&Delta;z`, t = n*`&Delta;t`])][], j = 0 .. My), k = 0 .. Mz), n = 1 .. N), seq(seq(seq([u[i, 0, k, n] = eval(UU, [x = i*`&Delta;x`, y = 0, z = k*`&Delta;z`, t = n*`&Delta;t`]), u[i, My, k, n] = eval(UU, [x = i*`&Delta;x`, y = L, z = k*`&Delta;z`, t = n*`&Delta;t`])][], i = 1 .. Mx-1), k = 0 .. Mz), n = 1 .. N), seq(seq(seq([u[i, j, 0, n] = eval(UU, [x = i*`&Delta;x`, y = j*`&Delta;y`, z = 0, t = n*`&Delta;t`]), u[i, j, Mz, n] = eval(UU, [x = i*`&Delta;x`, y = j*`&Delta;y`, z = L, t = n*`&Delta;t`])][], i = 1 .. Mx-1), j = 1 .. My-1), n = 1 .. N)];
Sol := {u[1, 1, 1, 1] = 0.2366497936e-1, u[1, 1, 1, 2] = 0.7589975856e-2, u[1, 1, 1, 3] = 0.6029906475e-3, u[1, 1, 2, 1] = 0.3778786317e-1, u[1, 1, 2, 2] = 0.7126415819e-2, u[1, 1, 2, 3] = -0.1197885714e-2, u[1, 2, 1, 1] = 0.3778786315e-1, u[1, 2, 1, 2] = 0.7126415820e-2, u[1, 2, 1, 3] = -0.1197885718e-2, u[1, 2, 2, 1] = 0.6038763054e-1, u[1, 2, 2, 2] = 0.4264591907e-2, u[1, 2, 2, 3] = -0.3509477851e-2, u[2, 1, 1, 1] = 0.3171958616e-1, u[2, 1, 1, 2] = -0.1327161715e-1, u[2, 1, 1, 3] = -0.4628647419e-2, u[2, 1, 2, 1] = 0.4979852397e-1, u[2, 1, 2, 2] = -0.3060811899e-1, u[2, 1, 2, 3] = -0.344914876e-4, u[2, 2, 1, 1] = 0.4979852397e-1, u[2, 2, 1, 2] = -0.3060811898e-1, u[2, 2, 1, 3] = -0.3449150010e-4, u[2, 2, 2, 1] = 0.7882396741e-1, u[2, 2, 2, 2] = -0.6192340018e-1, u[2, 2, 2, 3] = 0.1156615222e-1}

Using set of points given in ics, bcs and Sol

1. I want to contruct a vector at any time level (by fixing fourth suffix like u[i,j,k,n]) for i = 0..Mx,j=0..My,k=0..Mz and then find its L2 and L[infinity] norms.

2. Next I want contruct a vector by fixing two suffixes like u[i,j,k,n]) for i = 0..Mx,j=0..My and plot a surface in 3D

3. Finally I want to construct a vector by fixing three suffixes like u[i,j,k,n]) for i = 0..Mx, and plot a curve in 2D.

I'm waiting for your positive respone. I shall be very thankfull to you in advance.

Special request to:
@acer @Carl Love @Kitonum @Preben Alsholm

## How to save modules as package...

Hello

I have a couple of functions wrapped into a module and want to make them available as a package.  The two modules have been saved as a mpl file.   I read and tried to follow the instructions on the online help (11. Writing packages) but even copying line by line of commands there, they simply did not work at all.

Problems:

1) After following the instructions on how to add a home dir into libname and saved it .mapleinit (I guess) I issued the commands

`restart; libname;`

my lib path is not there anymore.

.mapleinit shows

libname := "mylibdir", libname:

libname:="/Users/eduardo/maple/toolbox/personal/lib", libname:

2) After issuing savelib, I did

`LibraryTools:-ShowContents(libname[1]);`

that returns [];

Could you send me a set of commands showing how to do it, please?

Many thanks

Ed

PS.  My next step is to write help files for each one of the functions.

## artificial ECG signal...

j:=500:tp:=0.07*j:Ap:=0.25:Aq:=0.3:tq:=0.03*j:tr1:=0.05*j:Ar:=2:As:=0.4:tr2:=0.04*j:ts:=0.04*j:tt:=0.17*j:At:=0.4:
u1:=0:
u2:=(Ap/2)*(sin((2*Pi*t/tp)+(3*Pi/2))+1);
u3:=0:
u4:=-(Aq/tq)*t:
u5:=(((Ar+ Aq)/tr1)*t)-Aq:
u6:=-(((Ar+ As)/tr2)*t)+Ar:
u7:=((As/ts)*t)- As:
u8:=0:
u9:=(At/2)*(sin((2*Pi*t/tt)+(3*Pi/2))+1):
u10:=0:
u2 := -0.1250000000 cos(0.1795195802 t) + 0.1250000000

r1:=plot([u1],t=1..0.1*j):
r2:=plot([u2],t=1..tp):
r3:=plot([u3],t=1..0.08*j):
r4:=plot([u4],t=1..tq):
r5:=plot([u5],t=1..tr1):
r6:=plot([u6],t=1..tr2):
r7:=plot([u7],t=1..ts):
r8:=plot([u8],t=1..0.1*j):
r9:=plot([u9],t=1..tt):
r10:=plot([u10],t=1..0.08*j):
with(plots):
display(r1,r2,r3,r4,r5,r6,r7,r8,r9,r10,view=[0..100,-1..3],axes=boxed);

the same above code works in matlab

in maple it isnot

Hi!

It seem like im not the only one with this problem, but i have a corrupted maple file containing much of my work throughout the semester, and now i cant open it, giving me the error message: "There were problems during the loading process. Your worksheet may be incomplete." It seems like im not the only one with this problem.. So im hoping that there is someone out there who can recover the document, or atleast parts of it. If so i would be very gratefull..

Maple Worksheet - Error

Failed to load the worksheet /maplenet/convert/Opgaver_paÌ_klassen_(1).mw .

## How to test whether all member in a list are all ...

`L1:=[1,2,5,6,9]:`

`L2:=[0,-2,5,6,9]:`

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