## Unable To Type In Maple, No Cursor...

I am currently unable to type in maple 2021, there is no cursor, nothing shows up when I type etc. I am also unable to save files. I went into document mode, nothing. Some of the dialogs don't show up. Where does maple save documents and how do I change that setting? That might be my problem. Furthermore, there are no tabs visable, like I can't access any documents I open.

## Differentiate three regions with implicitplot and/...

Dear Maple Expeets, In the attached Maple file, I have three procedures that are run smoothly. I am trying to compare outputs from each procedure to see which one if larger than the others. For changes on two parameters (alpha and delta), I used implicitplot and inequal commands to identify each region by a specific color. But the outcome is not reasonable. Would you please help with this? Thanks in advance!

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the final plot does not look reasonable. Would you please guide me?

## Two dimensional simple random walk to factorize...

by: Maple 2021

aRandStep2D := proc(X0, Y0, dx, dy)
local X, Y, P, R;
P := Array(1 .. 2);
R := rand(1 .. 8)();
if R = 1 then X := X0 - dx; Y := Y0 + dy; end if;
if R = 2 then X := X0; Y := Y0 + dy; end if;
if R = 3 then X := X0 + dx; Y := Y0 + dy; end if;
if R = 4 then X := X0 - dx; Y := Y0; end if;
if R = 5 then X := X0 + dx; Y := Y0; end if;
if R = 6 then X := X0 - dx; Y := Y0 - dy; end if;
if R = 7 then X := X0; Y := Y0 - dy; end if;
if R = 8 then X := X0 + dx; Y := Y0 - dy; end if;
P[1] := X; P[2] := Y;
return P;
end proc

SetStart := proc(b)
local alpha, R, P;
P := Array(1 .. 2);
alpha := rand(1 .. b)();
P[1] := alpha*b;
P[2] := alpha*b;
return P;
end proc

RandomFactTpq := proc(N, pb, dx, dy)
local alpha, X, Y, f, P, counter, B, n, T;
P := Array(1 .. 2);
counter := 0; f := 1;
B := floor(evalf(sqrt(N))); #Set maximal searching steps
T := floor(evalf(sqrt(N))); #For SetStart's use
P := SetStart(T);
X := P[1]; Y := P[2];
while f = 1 and counter < B do  #loop
n := pb - X - Y;
f := gcd(N, n);
if f > 1then break; end if;
P := aRandStep2D(X, Y, dx, dy); #A random move
X := P[1]; Y := P[2];
if X < 1 or Y < 1 or N - pb - 1 < X or X <= Y then
P := SetStart(T);       # Restart when out of borders
X := P[1]; Y := P[2];
end if;
counter := counter + 1;    #Counting the searched steps
end do;
if  f>1  then print(Find at point (X, Y), found divisor = f, searching steps = counter);
else print(This*time*finds*no*result, test*again!); end if;
end proc

## Numerical solution, Produce a graph with various v...

How can I produce a graph with various values for parameters? I also attached a sample of my Maple code.

`restart`

```with(plots); with(plottools); with(DEtools);```

`eqn1 := diff(V(t), t) = pi*p - (alpha + mu)*V(t), V(0) = ic1`

`eqn2 := diff(S(t), t) = alpha*V(t) + (1 - p)*pi - beta*S(t)*In(t)/N - mu*S(t), S(0) = ic2`

`eqn3 := diff(In(t), t) = beta*S(t)*In(t)/N - (mu + delta + gamma)*In(t), In(0) = ic3`

`eqn4 := diff(R(t), t) = gamma*In(t) - mu*R(t), R(0) = ic4`

```pi := 487845; p := 0.948; alpha := 0.054; beta := 0.955; mu := 0.005; delta := 0.03; localgamma := 0.935; ic1 := 484465; ic2 := 31999760; ic3 := 26305; ics4 := 12470; dsol := dsolve([eqn1, eqn2, eqn3, eqn4], numeric);```

`odeplot(dsol, [[t, V(t), color = plum], [t, S(t), color = blue], [t, In(t), color = cyan], [t, R(t), color = green]], t = 0 .. 1000, view = [0 .. 1000, 0 .. 300000000], thickness = 3)`

Let's say I want to produce a graph for eqn1 with various values of parameter p: p = 0.2, p = 0.5, p = 0.7, p = 0.8. How should I produce it?

## Plot the value of determinant vs omega...

I have created a several matrices for my analysis. I want to plot the determinant value of matrix vs the omega. The matrix that should be plotted is named as FINAL. I am not able to do that due to large value of matrix determinant. How to simplify the matrix and get  plot.

 (1)

## How to correctly perform numerical solutions for p...

Can someone kind help me? I encountered two issues when using the pdsolve function in Maple to obtain numerical solutions for partial differential equations. The first issue pertains to setting up the initial/boundary conditions correctly, and the second issue relates to configuring the plotting options. I'm wondering how to modify them in order to run the code correctly and generate the desired plots.

## How to find the solutions matrix(array) of ode ...

How to find Z(t) matrix(array) =[ [z[1,0](t),z[1,1](t)],[z[2,0](t),z[2,1](t)]]

 > restart;
 > with(IntegrationTools):with(Physics):
 >
 >
 >
 > h1 := (m,n)->(n+1/2)*KroneckerDelta[n,m];
 (1)
 > h2 := (mu,nu,m2,l)->-(nu*Pi/l)^2/(2*m2)*KroneckerDelta[mu,nu];
 (2)
 > v1 := (m,n,m1)->sqrt(min(n,m)!/max(n,m)!)*(2*m1)^(-abs(n-m)/2)*exp(-1/(4*m1))*LaguerreL(min(n,m),abs(n-m),-1/(2*m1));
 (3)
 > v2 := (mu,nu,l)->4*Pi^2*l*mu*nu*(exp(l/2)-(-1)^(mu+nu)*exp(-l/2))/((Pi*(mu+nu))^2+l^2)/((Pi*(mu-nu))^2+l^2);
 (4)
 > h:=(m,n,mu,nu,m1,m2,l)->evalf(h1(m,n)+h2(mu,nu,m2,l)+v1(m,n,m1)+v2(mu,nu,l));
 (5)
 > m1:=1:m2:=1:l:=1:
 > H:= (m,n,mu,nu)->h(m,n,mu,nu,m1,m2,l);
 (6)
 > H(1,1,0,0);
 (7)
 > eq1:= diff(z(m,nu,t),t)=-I*Sum(Sum(H(m,n,mu,nu)*z(n,mu,t),n=1..N),mu=0..M);
 (8)
 >
 > zint := Array([[1,0],[0,1]]);
 (9)
 > Z:= Array(1..2,1..2);  for i from 1to 2 do     for j from 1 to 2 do         Z[i,j]:= dsolve({eq1,zint[i,j]},numeric,output=listprocedure);     end do; end do;
 >
 >

## better way to write the code for the integration o...

how to write the code for integration of the orthogonal cosine function with nu=mu or with nu<>mu

 > restart;

 > phi:= (mu,Q2)->sqrt(2/l)*sin(mu*Pi*(Q2+l/2)/l);    # E:=mu->(Pi*mu/sqrt(2)/l)^2, mu=1,2...
 (1)
 > fh1:=simplify((-1/2/m2*Int(diff(phi(mu,Q2),Q2)*diff(phi(nu,Q2),Q2),Q2=-l/2..l/2)))
 (2)
 > convert(fh1,int) assuming(mu,integer,nu,integer);
 (3)
 > fh1_subs := simplify(subs(nu = mu, fh1));
 (4)
 > convert(fh1_substituted,int)assuming (mu,integer,nu,integer);
 (5)
 >

## Correct usage of command ConvertIn from Galois Fie...

Hi all,

I would like to use the command ConvertIn() from the Galois Field package to convert polynomials to field elements.

This is what I've done:

G:=GF(2,4)
G := &Fopf;[16]

b:=G:-random()
b := T mod 2

s:=G:-ConvertIn(T)
Error, (in ConvertIn) only integer polynomials in T can be converted

Why is this error showing up?? My argument of the command ConvertIn IS an integer polynomial in T.

How can I avoid this error?

BR David

## problem with draw...

restart;
with(geometry):
with(plots):
_EnvHorizontalName = 'x':  _EnvVerticalName = 'y':
point(A, -1, 9):
point(B, -5, 0):
point(C, 6, 0):
triangle(ABC,[A,B,C]):
midpoint(M1,A,C): midpoint(M2,B,C):midpoint(M3,A,B):
rotation(J, C, Pi/2, 'counterclockwise', M1):triangle(AJC,[A,J,C]):
rotation(Ii, C, Pi/2, 'counterclockwise', M2):triangle(BIC,[B,Ii,C]):
rotation(K, A, Pi/2, 'counterclockwise', M3):triangle(AKB,[A,K,B]):
midpoint(O1,K,J): coordinates(O1):
midpoint(O2,A,Ii): coordinates(O2):
poly:=[coordinates(A),coordinates(J),coordinates(Ii),coordinates(K)]:

display(draw([A(color = black, symbol = solidcircle, symbolsize = 12),
B(color = black, symbol = solidcircle, symbolsize = 12),
C(color = black, symbol = solidcircle, symbolsize = 12),
J(color = black, symbol = solidcircle, symbolsize = 12),
polygonplot(poly,color = "DarkGreen", transparency = 0.5),
ABC(color = red ),
BIC(color = green),
AKB(color = grey),
AJC(color =blue)]),
textplot([[coordinates(A)[], "A"],[coordinates(J)[], "J"],[coordinates(Ii)[], "I"],
[coordinates(B)[], "B"], [coordinates(K)[], "K"],
[coordinates(C)[], "C"]],
align = [above, right]),  axes = none);
Error, (in geometry:-draw) the option must be of type equation or name. I don't see how to correct this error/

## How to solve large sparse systems of linear equati...

I have some large systems of linear equations.  The solutions are probability generating functions.  I can get solutions in a few minutes for systems of up to n= 200 eqns or so, but Maple just cycles indefinitely if I try to solve much larger systems.  I really only need to perform Gaussian Elimination, as I only need to solve for one of the n solutions.  The matrices are sparse, there are only 3 non-zero entries per row.  I tried to get help from the manuals but I get the impression that sparse solutions are only available for numeric computations.   Doesn't Maple allow for sparse symbolic solutions?  If so, how to do it?

## Boring notation...

Does anyone know how to remove this boring notation? I would like to know why Maple does not give me "± 2x". Thanks in advance.

## Any way to speed up computation in Physics package...

I am trying to define a Tensor expression in the physics package but it seems to be taking eons to do so, it has been running for quite some time but still no result to the point where I halt the computation.

Does anyone have any ideas on how I could accelerate the process?

I have attached the file I am working with.

Define.mw