complex plot of an expression in "r" and "theta"...

how can i plot this complex expression with polar plot and 3d complex plot? i want both 2d polar form and 3d plot of this.
thnx for the help

 > restart:with(plots,complexplot,implicitplot)
 (1)
 > f:=(r,theta)->I*sinh(theta-Pi/6)+cos(Pi/4)=r;
 (2)
 > complexplot(f(r,theta), r = 0 .. 1, theta = 0 .. 2*Pi, coords=polar);
 >

Relation between w and k...

I want to find the relation between w and k by putting Determinant(A) is equal to zero. Since the determinant is large (A is a matrix of size 6x6) and I am not able to find the simplified expression. How to do that?

determinant.mw

Big problems with parabolic groups in the "LieAlge...

Hi,

I use Maple version 2022.1 on macOS 10.14.6.

I have big problems with the parabolic groups in the "LieAlgebra" package.

First of all in the help for "Query > Parabolic", the link refers to the help page for the commands "CylinderU, CylinderV, CylinderD" which have nothing to do with it. Also, the command "Query(Alg, "Parabolic")" does not work.

Below is a list of commands that give an error for "Query".

```restart:with(LinearAlgebra):with(DifferentialGeometry):with(LieAlgebras):

L:=[
Matrix(5, 5, [[0, 0, 1, 1, 1], [0, 0, 0, 0, 0], [-1, 0, 0, 0, 0], [-1, 0, 0, 0, 0], [-1, 0, 0, 0, 0]]),
Matrix(5, 5, [[0, 1, 0, 1, 1], [-1, 0, 0, 0, 0], [0, 0, 0, 0, 0], [-1, 0, 0, 0, 0], [-1, 0, 0, 0, 0]]),
Matrix(5, 5, [[0, 1, 1, 0, 1], [-1, 0, 0, 0, 0], [-1, 0, 0, 0, 0], [0, 0, 0, 0, 0], [-1, 0, 0, 0, 0]]),
Matrix(5, 5, [[0, 1, 1, 1, 0], [-1, 0, 0, 0, 0], [-1, 0, 0, 0, 0], [-1, 0, 0, 0, 0], [0, 0, 0, 0, 0]]),
Matrix(5, 5, [[0, 0, 0, 0, 0], [0, 0, 0, 1, 1], [0, 0, 0, 0, 0], [0, -1, 0, 0, 0], [0, -1, 0, 0, 0]]),
Matrix(5, 5, [[0, 0, 0, 0, 0], [0, 0, 1, 0, 1], [0, -1, 0, 0, 0], [0, 0, 0, 0, 0], [0, -1, 0, 0, 0]]),
Matrix(5, 5, [[0, 0, 0, 0, 0], [0, 0, 1, 1, 0], [0, -1, 0, 0, 0], [0, -1, 0, 0, 0], [0, 0, 0, 0, 0]]),
Matrix(5, 5, [[0, 0, 0, 0, 0], [0, 0, -1, 0, 0], [0, 1, 0, 0, 1], [0, 0, 0, 0, 0], [0, 0, -1, 0, 0]]),
Matrix(5, 5, [[0, 0, 0, 0, 0], [0, 0, -1, 0, 0], [0, 1, 0, 1, 0], [0, 0, -1, 0, 0], [0, 0, 0, 0, 0]]),
Matrix(5, 5, [[0, 0, 0, 0, 0], [0, 0, 0, -1, 0], [0, 0, 0, -1, 0], [0, 1, 1, 0, 0], [0, 0, 0, 0, 0]]),
Matrix(5, 5, [[0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 1, 1], [0, 0, -1, 0, 0], [0, 0, -1, 0, 0]]),
Matrix(5, 5, [[0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, -1, 0], [0, 0, 1, 0, 1], [0, 0, 0, -1, 0]]),
Matrix(5, 5, [[0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, -1], [0, 0, 0, 0, -1], [0, 0, 1, 1, 0]]),
Matrix(5, 5, [[0, 0, 0, 0, 0], [0, 0, 0, -1, 0], [0, 0, 0, 0, 0], [0, 1, 0, 0, 1], [0, 0, 0, -1, 0]]),
Matrix(5, 5, [[0, 0, 0, 0, 0], [0, 0, 0, 0, -1], [0, 0, 0, 0, 0], [0, 0, 0, 0, -1], [0, 1, 0, 1, 0]]),
Matrix(5, 5, [[0, 0, 0, 0, 0], [0, 0, 0, 0, -1], [0, 0, 0, 0, -1], [0, 0, 0, 0, 0], [0, 1, 1, 0, 0]]),
Matrix(5, 5, [[0, 0, 0, 0, 0], [0, 0, -1/2*sqrt(2), -1/2*sqrt(2), -1/2*sqrt(2)], [0, 1/2*sqrt(2), 0, 0, 0], [0, 1/2*sqrt(2), 0, 0, 0], [0, 1/2*sqrt(2), 0, 0, 0]]),
Matrix(5, 5, [[0, 0, 0, 0, 0], [0, 0, 1/2*sqrt(6), 1/6*sqrt(6), 1/6*sqrt(6)], [0, -1/2*sqrt(6), 0, -1/3*sqrt(6), -1/3*sqrt(6)], [0, -1/6*sqrt(6), 1/3*sqrt(6), 0, 0], [0, -1/6*sqrt(6), 1/3*sqrt(6), 0, 0]]),
Matrix(5, 5, [[0, 0, 0, 0, 0], [0, 0, 0, 2/3*sqrt(3), 1/6*sqrt(3)], [0, 0, 0, 2/3*sqrt(3), 1/6*sqrt(3)], [0, -2/3*sqrt(3), -2/3*sqrt(3), 0, -1/2*sqrt(3)], [0, -1/6*sqrt(3), -1/6*sqrt(3), 1/2*sqrt(3), 0]]), Matrix(5, 5, [[0, 0, 0, 0, 0], [0, 0, 0, 0, 1/2*sqrt(5)], [0, 0, 0, 0, 1/2*sqrt(5)], [0, 0, 0, 0, 1/2*sqrt(5)], [0, -1/2*sqrt(5), -1/2*sqrt(5), -1/2*sqrt(5), 0]])];

DGsetup(LieP);
Query(Alg,"Parabolic");```

An graph theory a algorithm to be implemented...

Let G(V,E)  be a graph

Step 1 : Choose the subsets S of the V of size k and LABEL it with the say "1"

Step 2: LABEL all the neighbours of the vertices of S with "1"

Step 3: Now LABEL "1" all the UNLABELED neighbours of the previously LABELED veritices only if its neighbours are all LABELED already

Step 4: IF atleast one vertex is LABELED in step 3 then repeat step 3   ELSE  If all vertices are already LABELED with "1" goto step 5 ELSE if some of the VERTICES are still not LABELED we reject this set GOTO step 6

Step 5: append the the the set S into the list

Step 6: Remove all the perivious labels choose a new set of size k from S label its vertices with "1" and goto step 2  if all all sets of size k have already been choosen we end and print the list.

That is we a Function F(Graph::G,k)     the function which does the above so that it can be called with parameter when required for any graph G

I am going to try too but i am not that great at coding I have desinged the algorithm need help if possible kind help

I will also be trying

I apologize to distrub all in your busy schedule.

Your work will be surely acknowledged

First_sample_1.mw

https://www.mapleprimes.com/questions/234533-How-To-Relabel-Only-A-Subset-Of-Vertex-Of-G#comment287899

In code attached

I would like to

I have to on say L list.

And I have done steps at the top in that code

After the above code I have attached steps

"Find the vertices with the condition that if  all its neighbors are labeled as character (FIND(G)) then label those vertices  also as `character"`  then add those vertices also to  L1 list"  then Need to be do again and again on the same graph with new labels G

If no such vertex exits and NumberOfVertices(G) not equal to numelems(L1) then i have to break out of the loop.

or

if NumberOfVertices(G)=numelems(L1) then I print That list or store it some where

KInd help it will help me a lot and it will surely be acknowledged kind help.

The help will be surely acknowledged

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.

Given a graph G , vertex v enumerate all possible ...

Give a graph G enumerate all possible shortest paths from that vertex to all other vertices like

From vertex v1

P1={(1,2),(2,3)} shortest path from 1 to 3 is stored in P1

P2={(1,2)} shortest path from 1 to 2 of length 1

Put all possible path of length k  from a verex v in a list seperate

That is length 1 in a seperate from vertex v in a seperate list

Etc

Function with be F(Graph::G,v)

Function will return all those lists

Number of possible paths of length k in any arbitr...

```restart;
with(GraphTheory);
with(combinat, cartprod);
with(SpecialGraphs);
with(RandomGraphs);
```

Given any arbitary graph G how many possible paths of length k are possible

G := CartesianProduct(PathGraph(3), PathGraph(3));
s := AllPairsDistance(FLT)

How to find how may possible paths of length say 4 from vertex 1:1

" for example this CartesianProduct(Path(3),Path(3)) number of possible paths of length 2 are

```1:1 - 1:2 -2:2

1:1 -2:1-2:2

1:1-1:2 -1:3

1:1-2:1-3:1```

so a total of 2 length paths

next say how may possible paths of length say 3 from vertex 1:2

similar given a vertex and path length how many possible path of that length are possible from that vertex.

It is not restricted to this graph given any graph G in general , a vertex v and k a path length i should get total number of paths of that length in that graph G

That is function say   F(G::Graph,vertex,k) i should get output of the number of path of length k from that vertex v.

"Only a idea but I may be wrong

I had an idea taking a row of a vertex in the graph G in the shortest path matrix and finding the number of possible totals which can get  length k I may be wrong to or correct but I finding to implement this in code neatly too.

That is if (0,1,2,1,3,4,1,2)

The number of possible 2 this are

```0+2=2

0+2=2

1+1=2

1+1=2

1+1=2```

So a total of 5 , 2 length path with respect to that vertex moving from left to right

Again if number of 3 length paths

Moving left to right

```0+3=3

1+2=3

1+1+1=3

1+2=3

2+1=3

2+1=3

1+2=3

1+2=3```

Total 8 paths of length 3

Until maximum possible length path from that vertex with respect to that graph.

Their is a mistake in the above logic is if the length paths intersection in some edges the path length will decrease so need to be careful so it looks difficult for me.

But I may be wrong in logic need help."

I am trying too

Kind help

how to produce Inert integral( dx) in Maple? For...

I use Int to show some step before evaluating it to become normal int

I'd like to show the following when the integrand is one:

But Int(x) does not work, and Int(,x) gives syntax error. So only choice is to use Int(1,x) which does not look as nice as the above

Is there a trick to use? i.e. when the integrand is one, I want to display it as the first image and not as the second image. This is just to make the Latex look a little nicer only.

I tried few things, but nothing worked so far, as Int needs something there where I want the empty spot to be (There is actually 1 there ofcourse, but I do not want to show the 1).

May be we need a Latex settings for this?  Or interface setting?

Maple 2022.1

Bifurcation of SEIR...

Hi,

Please can someone help me with a sample code for bifurcation? You can use parameter values for the parameters. I'm using maple 18. Below is my model:

 > restart:
 > f__1 := Delta -(psi + mu)*S(t);
 (1)
 > f__2 := psi*S(t) -(delta + mu)*E(t);
 (2)
 > f__3 := Delta*E(t) -(gamma+gamma__1 + mu)*X(t);
 (3)
 > f__4 := gamma__1*X(t)-(eta + xi + mu)*H(t);
 (4)
 > f__5 := xi*H(t) - mu*R(t);
 (5)
 > f__6 := gamma*X(t)-eta*H(t) - d*D(t);
 (6)
 > f__7 := b*D(t) - b*B(t);
 (7)
 > f__8 := phi__p + sigma*X(t)+eta__1*H(t) +d__1*D(t)+ b__1*B(t) - alpha*P(t);
 (8)

How to solve system of equations explicitly...

Please I need your assistance. I want to solve for c__4, c__5, c__6, and c__8  from 4 systems of the equation: See my code below:

Since there 4 equations and 4 unknowns, is it possible to get the result explicitly without setting c__6=c__8 as maple did? The solution is at the end of the maple file.

 > ##
 > ###
 > ###
 > restart:
 > f__1 := Delta -(psi + mu)*S(t);
 (1)
 > f__2 := psi*S(t) -(delta + mu)*E(t);
 (2)
 > f__3 := Delta*E(t) -(gamma+gamma__1 + mu)*X(t);
 (3)
 > f__4 := gamma__1*X(t)-(eta + xi + mu)*H(t);
 (4)
 > f__5 := xi*H(t) - mu*R(t);
 (5)
 > f__6 := gamma*X(t)-eta*H(t) - d*D(t);
 (6)
 > f__7 := b*D(t) - b*B(t);
 (7)
 > f__8 := phi__p + sigma*X(t)+eta__1*H(t) +d__1*D(t)+ b__1*B(t) - alpha*P(t);
 (8)
 > S__1 := Delta/mu - a__1*E__1/mu: X__1:= delta*E__1/a__2: H__1 := delta*gamma__1*E__1/a__2*a__3: R__1 := delta*gamma__1*xi*E__1/a__2*a__3*mu: B__1 := 1/b*(gamma*delta/a__2 + delta*eta*gamma__1/a__2*a__3)*E__1: D__1 := 1/d*(gamma*delta/a__2 + delta*eta*gamma__1/a__2*a__3)*E__1: P__1 := (1/alpha)*(delta*sigma/a__2 + delta*eta*gamma__1/a__2*a__3 + (d__1/d - b__1/b)*(delta*gamma/a__2 + delta*eta*gamma__1/a__2*a__3))*E__1 + phi__p/alpha:
 > M__1 := c__1*f__1*(1-S__1/S(t));
 (9)
 > M__2 := c__2*f__2*(1-E__1/E(t));
 (10)
 > M__3 := c__3*f__3*(1-X__1/X(t));
 (11)
 > M__4 :=c__4*f__4*(1-H__1/H(t));
 (12)
 > M__5 := c__5*f__5*(1-R__1/R(t));
 (13)
 > M__6 := c__6*f__6*(1-D__1/D(t));
 (14)
 > M__7 := c__7*f__7*(1-B__1/B(t));
 (15)
 > M__8 := c__8*f__8*(1-P__1/P(t));
 (16)
 > restart:
 > u__1 := (psi+mu)*S__1;
 (17)
 > u__2 := psi*S__1;
 (18)
 > u__3 := delta*E__1;
 (19)
 > u__4 := gamma__1*X__1;
 (20)
 > u__5 := xi*H__1;
 (21)
 > u__6 := gamma*X__1 + eta*H__1;
 (22)
 > u__7 := b*D__1;
 (23)
 > u__8 := phi__p + sigma*X__1+eta__1*H__1 +d__1*D__1+ b__1*B__1;
 (24)
 > M__1 := c__1*(Delta-(psi+mu)*S(t))*(1-(Delta/mu-a__1*E__1/mu)/S(t));
 (25)
 > M__2 := c__2*(psi*S(t)-(delta+mu)*E(t))*(1-E__1/E(t));
 (26)
 > M__3 := c__3*(Delta*E(t)-(gamma+gamma__1+mu)*X(t))*(1-delta*E__1/(a__2*X(t)));
 (27)
 > M__4 := c__4*(gamma__1*X(t)-(eta+xi+mu)*H(t))*(1-delta*gamma__1*E__1*a__3/(a__2*H(t)));
 (28)
 > M__5 := c__5*(xi*H(t)-mu*R(t))*(1-delta*gamma__1*xi*E__1*a__3*mu/(a__2*R(t)));
 (29)
 > M__6 := c__6*(gamma*X(t)-eta*H(t)-d*D(t))*(1-(gamma*delta/a__2+delta*eta*gamma__1*a__3/a__2)*E__1/(d*D(t)));
 (30)
 > M__7 := c__7*(b*D(t)-b*B(t))*(1-(gamma*delta/a__2+delta*eta*gamma__1*a__3/a__2)*E__1/(b*B(t)));
 (31)
 > M__8 := c__8*(phi__p+sigma*X(t)+eta__1*H(t)+d__1*D(t)+b__1*B(t)-alpha*P(t))*(1-((delta*sigma/a__2+delta*eta*gamma__1*a__3/a__2+(d__1/d-b__1/b)*(gamma*delta/a__2+delta*eta*gamma__1*a__3/a__2))*E__1/alpha+phi__p/alpha)/P(t));
 (32)
 > J := M__1 + M__2 + M__3 + M__4 + M__5 + M__6 + M__7 + M__8;
 (33)
 > ##
 > L__1 := factor(expand(subs(Delta=u__1, M__1)));
 (34)
 > L__2 := expand(subs((delta+mu)*E(t)=u__2, M__2));
 (35)
 > L__3 := expand(subs((gamma+gamma__1+mu)*X(t)=u__3, M__3));
 (36)
 > L__4 := expand(subs((eta+xi+mu)*H(t)=u__4, M__4));
 (37)
 > L__5 := expand(subs(mu*R(t)=u__5, M__5));
 (38)
 > L__6 := expand(subs(d*D(t)=u__6, M__6));
 (39)
 > L__7 := expand(subs(b*B(t)=u__7, M__7));
 (40)
 > L__8 := expand(subs(alpha*P(t)=u__8, M__8));
 (41)
 > L := L__1 + L__2 + L__3 + L__4 + L__5 + L__6 + L__7 + L__8;
 (42)
 > ## Collecting the coefficients of X, H, D, B and E
 > k__1 := coeff(L,X(t));
 (43)
 > k__2 := coeff(L,H(t));
 (44)
 > k__3 := coeff(L, D(t));
 (45)
 > k__4 := coeff(L, B(t));
 (46)
 > k__5 := coeff(L, E(t));
 (47)
 > ##
 > ## L terms that not coeffiecient X, H, D, B and E
 > W__12 := coeff(L, X(t), 0):
 > W__1 := coeff(W__12, H(t), 0):
 > W__11 := coeff(W__1, D(t), 0):
 > W__12 := coeff(W__11, B(t), 0):
 > k__6 := coeff(W__12, E(t), 0);
 (48)
 > ## from k__5, c__3 = 0 and choose c__1 = c__2 and c__3 =c__7
 > c__3 := 0:  c__7:=0:
 > k__1;
 (49)
 > k__2;
 (50)
 > k__3;
 (51)
 > k__4;
 (52)
 > ## Also choose
 > sys := solve({k__1=0, k__2 =0, k__3=0, k__4=0}, [c__4,c__5, c__6, c__8]);
 (53)
 > #
 > #
 >

How can i see maple calculations?...

How can i see analytical maple calculations?

Why does simple differenciation using palettes and...

I recently got introduced to fractional calculus, I saw this image on the internet and went to verify the 3rd block of image i.e fractional differentiation on Maple 2022. But Maple returned answer which does not match the result claimed in the image i.e x. I want to know what I am missing here. But when used fracdiff() the answer matches.I also wanted to know how its done by using showSolution command but didn't get the answer. Can I get the steps? meme.mw

 >
 (1)
 >
 >
 (2)
 >
 (3)
 >
 >
 (4)
 >
 >

Non-Linear System, fsolve fails to find a solution...

Non-Linear.mw

Hi, I have here a interesting non-linear system.

If I attempt to solve it using some specific form of the non-linear equations (form X*Y=Z) of the system, Maple (Verison 18) finds a solution.

But, if I replace some of them by some other forms (like form Y=Z/X), fsolve fails.

I usually use the non-quotient form. But is there any way to guide or configure fsolve to reach a solution?
I set up some of the regular options: placing a seed close to the solution, indicating intervals of possible solutions; but none of that works if I do not set up the non-quotient form of the equations. In some cases, fsolve does not reach a solution at all, no matter the form of the equations.

In the file, the equations that are causing the isssue are the last 3, those who start with the variable f1,f2 and f3.
I ran the system twice with both cases: non-quotient form and quotient form.

Why does Maple give sometimes erroneous results wh...

Consider the following integral, shown below in this image.

>> Link to the Maple sheet: example.mw <<

Why does Maple provide erroneous results? Is there a bug in the software? I use Maple 2021.

What is the reason for unable to compute steps of ...

I am curious to know steps of integration for e^(t^3)*(cos(t))^3 as Maple found the answer correctly. So I wanted to know how it got to that solution. I applied the commands shown in document but unable to get steps. I want to know the reason for this and is it possible to get it work.

 >
 >
 >
 (1)
 >
 >
 (2)
 >
 (3)
 > with(Student:-Calculus1):
 >
 >
 >