## How to shade area between 3 functions and define a...

I tryed this, because i thought i might be abel to shade this new piecewise function later on, but i dont know how to tell maple that there is 2 y-axes values in the interval from (2;3):

so it failed.

pleace help regards Niklas.

## how to create a matrices by eigenvalues...

Generate 8 random 3 by 3 matrices using the RandomMatrix command from the  LinearAlgebra package. As each matrix is generated use Eigenvalues to compute its eigenvalues. Then take the product of the eigenvalues, and check that for each matrix, this product is equal to the determinant of the matrix.

## Bug in Maple solve?...

When I use Maple solve on functions that involves exp, ln to decide the maxima, minima points by solving derivative equals zero, it only returns the first point, not the second point.

Which by definition it shall return two points, one at 2.030837315, the other around 6.7.

See the Maple code and exported PDF attached.

Maple_Solve_MinMaxma.mw

Maple_Solve_MinMaxma.pdf

## Problem with Paraboloid...

How can I plot a paraboloid?

## Conversion of this mathematica expression to Maple...

I am not unfamiliar with the Wolfram syntax but also not very good with it, and there is a particular element in a Mathematica code I have been given which I do not entirely understand how to efficiently write in Maple. The basic idea is to read in a list of expressions from an external file (LIST) and process the non zero elements and assign them to a function (COEF) which can be called later on. Here is the Mathematica exert:

```k = 0;
i = 0;
a = b = \[Theta];
Do[k = k + 1; KK = LIST[[k]];
If[KK =!= 0, i = i + 1; ff = Factor[KK];
COEF[x,y, z, l_, m_, n_] = ff], {z, -2,
2}, {y, -2, 2}, {x, -2, 2}];

```

The LIST has the following form and only contains l, m and n and another factor E which is left undefined for now. It does not contain x, y or z. The LIST can contain any number of terms depending on the problem. Here is an example:

`LIST={0, 0, 0, 0, 0, 0, 0, a^2 b m (-1 + n) n (a^2 + b^2 - 2 E), ... ,0,0, a^3 n(l+1+m) ... }`

So the Do loop cycles through the LIST and extracts out the non zero terms. What I am unsure about is how it is looping over x,y and z when they do not appear in the LIST at all. I assume it is attaching a x,y,z combination to each COEF and they can be called like this:

```COEF[0,1,1,0,2,3]
```

For the instance of when x=0, y=1, z=1, l=0, m=2 n=3. Is this correct? What would be the best way to replicate this in Maple?

- Yeti

## How to color a copy of a Graph without altering th...

Hi,

This question concerns the package GraphTheory
( Maple 2015 on a Windows 7 PC )

Let G1 be some graph and V a list of vertices in G1
The default colors DrawGraph uses for the vertices is yellow

I define the graph G2 this way :
G2 := copy(G1):
HighlightVertex(G2, V, red);
DrawGraph(G2);
Obviously the result is a graph where vertices in V are red while the remaining ones are still yellow

Question 1 :  Why does the command DrawGraph(G1) returns exactly the same picture ?
I have thought that defining G2 as a copy of G1 would have preserved the default colouring of the vertices.
Note that the same undesired (at least for me) thing occurs with the  HighlightEdges command.

Question 2 : Is it possible to retrieve the original colouring of G1 without using HighlightVertex(G1, V, yellow)  ?

## Finding all solutions to 2 simultaneous trigonomet...

Hey there folks - I have the following headcracker...

I have 2 equations:

cos(a t) = cos(b t + c)
&
sin(a t) = sin(b t + c)

Where a, b and c are known constants, and t is a variable.

I would like to find a way to solve these 2 equations simultaneously, i.e. find the t values that solve both equations at the same time. Of course, there will be an infinite number of solutions, so I also need a way to define an interval that t needs to be restricted to, e.g. t = 0..20 * Pi .

The best I've managed is:

... but I can't seem to make this work for solving the 2 trig. equations simultaneously

nor can I figure out the syntax for getting all solutions compiled as a list, e.g.

- which would be enormously helpful for further calculations.

Can anyone give some help on this?

Regards,  Matthew

## About numerical solution of DEs...

Hello friends!

I have one question, whenever I solved system of ODEs using numerical solution (bilton command i.e., dsolve(dsys1, numeric, output = listprocedure, range = 0 .. 1)), its accutacy always like 10 or 12 digits not above at all. I want to how i improve the accuracy. I am waiting your postive answer.

## how to solve fourth ordered Initial Value Problem ...

restart;

Digits := 18;
with(LinearAlgebra);
f := proc (n) 3*sin(x[n]) end proc;

g := proc (n) 3*cos(x[n])

end proc;

#problem call.
for n from 0 to 0 do

e1 := expand(-y[n+3/2]+y[n]-3*y[n+1/2]+3*y[n+1]+1/11612160*(5856*h^4*g(n+1/2)-19968*h^4*g(n+3/2)+2343*h^4*g(n)-76356*h^4*g(n+1)-7058*h^4*g(n+2)+608864*h^3*f(n+1/2)+104864*h^3*f(n+3/2)+28489*h^3*f(n)+702864*h^3*f(n+1)+6439*h^3*f(n+2)));

e2 := expand(-y[n+2]+3*y[n]-8*y[n+1/2]+6*y[n+1]+1/5806080*(18768*h^4*g(n+1/2)-32880*h^4*g(n+3/2)+3867*h^4*g(n)-76356*h^4*g(n+1)-2229*h^4*g(n+2)+965728*h^3*f(n+1/2)+461728*h^3*f(n+3/2)+45953*h^3*f(n)+1405728*h^3*f(n+1)+23903*h^3*f(n+2)));

e3 := expand(-z[n]+(1/383201280*(-4207440*h^4*g(n+1/2)-930192*h^4*g(n+3/2)+371973*h^4*g(n)-3631932*h^4*g(n+1)-41259*h^4*g(n+2)+16136096*h^3*f(n+1/2)+3866720*h^3*f(n+3/2)+5752543*h^3*f(n)+5810400*h^3*f(n+1)+367681*h^3*f(n+2))+4*y[n+1/2]-3*y[n]+y[n+1])/h);

e4 := expand(-z[n+1/2]+(1/191600640*(376320*h^4*g(n+1/2)+118896*h^4*g(n+3/2)-29469*h^4*g(n)+532764*h^4*g(n+1)+5079*h^4*g(n+2)-5812112*h^3*f(n+1/2)-508016*h^3*f(n+3/2)-381553*h^3*f(n)-1236168*h^3*f(n+1)-45511*h^3*f(n+2))-y[n]+y[n+1])/h);

e5 := expand(-z[n+1]+(1/383201280*(-31920*h^4*g(n+1/2)-433776*h^4*g(n+3/2)+71547*h^4*g(n)-2519748*h^4*g(n+1)-17493*h^4*g(n+2)+18565216*h^3*f(n+1/2)+1933216*h^3*f(n+3/2)+885665*h^3*f(n)+10391328*h^3*f(n+1)+158015*h^3*f(n+2))-5*y[n+1/2]+y[n]+3*y[n+1])/h);

e6 := expand(-z[n+3/2]+(1/95800320*(250224*h^4*g(n+1/2)-730680*h^4*g(n+3/2)+61266*h^4*g(n)-1526256*h^4*g(n+1)-22044*h^4*g(n+2)+15680504*h^3*f(n+1/2)+4712456*h^3*f(n+3/2)+735469*h^3*f(n)+22576428*h^3*f(n+1)+203623*h^3*f(n+2))-8*y[n+1/2]+3*y[n]+5*y[n+1])/h);

e7 := expand(-z[n+2]+(1/383201280*(3873264*h^4*g(n+1/2)+332976*h^4*g(n+3/2)+497649*h^4*g(n)-1407564*h^4*g(n+1)-720255*h^4*g(n+2)+114710816*h^3*f(n+1/2)+93716192*h^3*f(n+3/2)+5705827*h^3*f(n)+191366496*h^3*f(n+1)+9635389*h^3*f(n+2))-12*y[n+1/2]+5*y[n]+7*y[n+1])/h);

e8 := expand(-p[n]+(1/191600640*(13423440*h^4*g(n+1/2)+3068304*h^4*g(n+3/2)-1621317*h^4*g(n)+11615292*h^4*g(n+1)+137451*h^4*g(n+2)-32503712*h^3*f(n+1/2)-12664928*h^3*f(n+3/2)-32539039*h^3*f(n)-16869600*h^3*f(n+1)-1223041*h^3*f(n+2))-8*y[n+1/2]+4*y[n]+4*y[n+1])/h^2);

e9 := expand(-p[n+1/2]+(1/191600640*(-3053856*h^4*g(n+1/2)-213216*h^4*g(n+3/2)+98049*h^4*g(n)-509436*h^4*g(n+1)-10191*h^4*g(n+2)-1045120*h^3*f(n+1/2)+831104*h^3*f(n+3/2)+1331083*h^3*f(n)-1207008*h^3*f(n+1)+89941*h^3*f(n+2))-8*y[n+1/2]+4*y[n]+4*y[n+1])/h^2);

e10 := expand(-p[n+1]+(1/63866880*(194160*h^4*g(n+1/2)-373968*h^4*g(n+3/2)+52329*h^4*g(n)-2514924*h^4*g(n+1)-14727*h^4*g(n+2)+14006304*h^3*f(n+1/2)+1695712*h^3*f(n+3/2)+634955*h^3*f(n)+15463008*h^3*f(n+1)+133461*h^3*f(n+2))-8*y[n+1/2]+4*y[n]+4*y[n+1])/h^2);

e11 := expand(-p[n+3/2]+(1/191600640*(1491168*h^4*g(n+1/2)-4758240*h^4*g(n+3/2)+190977*h^4*g(n)-509436*h^4*g(n+1)-103119*h^4*g(n+2)+46274944*h^3*f(n+1/2)+48151168*h^3*f(n+3/2)+2215307*h^3*f(n)+93985056*h^3*f(n+1)+974165*h^3*f(n+2))-8*y[n+1/2]+4*y[n]+4*y[n+1])/h^2);

e12 := expand(-p[n+2]+(1/191600640*(4772688*h^4*g(n+1/2)+11719056*h^4*g(n+3/2)+338619*h^4*g(n)+11615292*h^4*g(n+1)-1822485*h^4*g(n+2)+59770976*h^3*f(n+1/2)+79609760*h^3*f(n+3/2)+3528289*h^3*f(n)+109647648*h^3*f(n+1)+34844287*h^3*f(n+2))-8*y[n+1/2]+4*y[n]+4*y[n+1])/h^2) end do;
M := {e || (1 .. 12)};

y_init := 1;

z_init := 0;

p_init := -2;

x_init := 0; A := 0; B := 1; N := 40;

h := evalf((B-A)/N); count := 1;

X := y[k], y[k+1/2], y[k+1], y[k+3/2], z[k], z[k+1/2], z[k+1], z[k+3/2], p[k], p[k+1/2], p[k+1], p[k+3/2];

step := seq(eval(x, x = n*h), n = 1 .. N);

y_exact := ([seq])(eval(3*cos(x)+(1/2)*x^2-2, x = n*h), n = 1 .. N);

z_exact := ([seq])(eval((1/3*(3*x^2+6*x+3))/(x^3+3*x^2+3*x+1), x = n*h), n = 1 .. N);

p_exact := ([seq])(eval((1/3*(6*x+6))/(x^3+3*x^2+3*x+1)-(1/3)*(3*x^2+6*x+3)^2/(x^3+3*x^2+3*x+1)^2, x = n*h), n = 1 .. N);
vars := seq(X, k = 1);
printf("\n%4s%13s%15s%15s\n", "@", "y_Num", "y_Exact", "y_Error");

for q to N do

for ix to 4 do

x[ix] := h*ix+x_init end do;

result := eval(`<,>`(vars), fsolve(eval(M, [x[0] = x_init, x[1/2] = x_init, x[3/2] = x_init, y[0] = y_init, y[1/2] = y_init, y[3/2] = y_init, z[0] = z_init, z[1/2] = z_init, z[3/2] = z_init, p[0] = p_init, p[1/2] = p_init, p[3/2] = p_init]), {vars}));

for k to 4 do

printf("%5.2f %14.15f", step[count], result[k]);

printf("%20.15f %10.18G \n", y_exact[count], abs(result[k]-y_exact[count]));

count := count+1;

P := [result[k]]

end do;

x_init := x[ix-1];

y_init := result[4];

z_init := result[8];

p_init := result[12]

end do;

please that is the code i write to solve the problem after using the matrix form to generate the value but is given me error of the form

@        y_Num        y_Exact        y_Error
Error, invalid input: eval received fsolve({-6398.00004614630940+6400.00000000000000*y[1], -6397.99992849910140+6400.00000000000000*y[1], -6397.99909739580050+6400.00000000000000*y[1], -199.999989717789185+200.000000000000000*y[1], -40.0000000791700798+40.0000000000000000*y[1], -2.99999993737911015+3*y[1], 39.999999768462113+40.0000000000000000*y[1], -p[1]-6399.99961623646730+6400.00000000000000*y[1], -p[2]-6399.99798489466010+6400.00000000000000*y[1], -y[2]-4.99999972458202552+6*y[1], -z[1]-159.999999048856193+120.000000000000000*y[1], -z[2]-279.999973921987948+280.000000000000000*y[1]}, {p[1], p[2], p[3/2], p[5/2], y[1], y[2], y[3/2], y[5/...

## How to avoid the "no solution found" warning when ...

Morning all,

I repeatedly solve (command solve) a collection of systems of inequalies. Some of them can have no solution, but I am able to check if a solution has been found or not, and then take some decision about the system in question.

I have placed a few print commands at different critical locations within the loop where those systems are constructed and possibly solved.
Every time solve fails finding a solution it returns me a "no solution found" warning.
In order to keep my printings readable, could it be possible to avoid those warnings ?
Is there some "try & catch" like mechanism to manage warnings ?

## Statistics Social - Cronbach - Pearson

Maple 2015

Application that allows us to measure the reliability of a group of data through a row and columns called cronbach alpha at the same time to measure the correlation of items through the pearson correlation of even and odd items. It can run on maple 18 to maple 2017. This will be useful when we are developing a thesis in the statistical part.

In Spanish

StatisticsSocialCronbachPearson.zip

Lenin Araujo Castillo

## Find equation of line which has minimum distance f...

I've got some points:

I have to find the (equation of) line which has minimum distance from these points but the distance formula that I have to use is:

I think we should settle with a for loop.

## Warning, solutions may have been lost ...

I need some help. I'm trying to solve this system of equations, but maple says the solutions may have been lost. Here are the equations:

phi := alpha+theta;
sigma := b*c/(2*pi*r);
f := 2*arccos(exp(-(1/2)*b*(1-r/R)*R/(r*sin(phi))))/pi;
d := 4*f*sin(phi)*(cos(phi)-lambda*sin(phi))/(sigma*(sin(phi)+lambda*cos(phi)));
e := .1152*alpha+.6634;
x := solve(d = e, alpha)

I am trying to solve for alpha by setting d = e. Any help  would be greatly appreciated.

## Calculate Error of parameter in a fit...

Hi all,

I tried to fit my data (x,y) with a model by using Minimize the Chisquare. By example the model is y=a*x+b, Chisquare is (y-yexp)^2. And I performed a function Minimize(Chisquare) to have a and b.

I need to extract the error of parameter like a±aerror, and b±berror.

Best regards,

## Why is the plot not continuous ? ...

Hi everybody,

I have a continuous function f of a single variable (all the details can be found in the attached file) and I want to build a more regular approximation of it (let's say F). The construction process ensures that F is C-infinite.

When I plot f and F (command "plot"), for visual comparisons, the F curve presents "holes", that is intervals where there is no plot.
However, the value of F(x) for any x in those void ranges is a real just as F(y) is for any y in a plotted interval.

Note that this phenomenon does not appear  when I use PLOT(CURVES(...)) for F (attached file)

I guess I probably use "plot" in a wrong way, or maybe some option I don't know
could prevent it to happen ?

Could you please have a look to the attached file ?
I look forward for your response.

LacunaryPlot.mw

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