## 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

## Why Maple does not solve this simple system of dif...

Hi,

Can somebody help me to find out why Maple can't completely solve this system of differential equations?

The answer to the previous command is

but I don't get the solution for u(x). This should be u(x)=-x+x^2/2.

## Plotting the movement of 4 planets...

Greetings,

currently im working on a project in which i basically have to calcuate and plot a little solar system, using newton mechanic. The work is done, but as it appears, the solution simply cannot be true. In the given example you can see that the planets move in more or less straight lines. I presume that the error is somewhere in the solution of the system of differential equations, but i can't see where it is.

I am grateful for every advice.

PlanetenSpacecurve.mw

## How to convert a system of differential equations ...

How to convert a system of differential equations to a matrix?

can infolevel show this matrix during the process?

## How to get custom function name?...

If not define a procedure

just pass day(hello(a,b), c)

as parameter how to get hello , this function name and day this function name

## Crypt and decrypt with Vigenère...

```I have to crypt and decrypt with vigenere.
```

(procedures need lists)

```"In a Caesar cipher, each letter of the alphabet is shifted along some number of places; for example, in a Caesar cipher of shift 3, A would become D, B would become E, Y would become B and so on. The Vigenère cipher consists of several Caesar ciphers in sequence with different shift values.

To encrypt, a table of alphabets can be used, termed a tabula recta, Vigenère square, or Vigenère table. It consists of the alphabet written out 26 times in different rows, each alphabet shifted cyclically to the left compared to the previous alphabet, corresponding to the 26 possible Caesar ciphers. At different points in the encryption process, the cipher uses a different alphabet from one of the rows. The alphabet used at each point depends on a repeating keyword.[citation needed]

For example, suppose that the plaintext to be encrypted is:

ATTACKATDAWN
The person sending the message chooses a keyword and repeats it until it matches the length of the plaintext, for example, the keyword "LEMON":

LEMON
Each row starts with a key letter. The remainder of the row holds the letters A to Z (in shifted order). Although there are 26 key rows shown, you will only use as many keys (different alphabets) as there are unique letters in the key string, here just 5 keys, {L, E, M, O, N}. For successive letters of the message, we are going to take successive letters of the key string, and encipher each message letter using its corresponding key row. Choose the next letter of the key, go along that row to find the column heading that matches the message character; the letter at the intersection of [key-row, msg-col] is the enciphered letter.

For example, the first letter of the plaintext, A, is paired with L, the first letter of the key. So use row L and column A of the Vigenère square, namely L. Similarly, for the second letter of the plaintext, the second letter of the key is used; the letter at row E and column T is X. The rest of the plaintext is enciphered in a similar fashion:

Plaintext:	ATTACKATDAWN
Key:	LEMON
Ciphertext:	LXFOPVEFRNHR
Decryption is performed by going to the row in the table corresponding to the key, finding the position of the ciphertext letter in this row, and then using the column's label as the plaintext. For example, in row L (from LEMON), the ciphertext L appears in column A, which is the first plaintext letter. Next we go to row E (from LEMON), locate the ciphertext X which is found in column T, thus T is the second plaintext letter."```

I think that it can be done with a for loop but I do not know where to start.