## Will Maple also be used in chatGPT (AI) ?...

For Mathematica  math software app,there is a plugin to use in chatGPT pro ( paid subscription ) and maybe this can be done for Maple too ?

Haven't used the plugin for Mathematica yet, am curious about it.
Let me have the AI look at the Riemann Hypothesis :)
Have a few books on it, but can't get through that math with all those special functions.

## any way to get two equations solved...

i have two euations including integration which has two unkwnon x1 and x2.
how can i get these equations solved, thanks for the help.

 > restart:
 > with(DirectSearch)
 (1)
 > with(LinearAlgebra):
 > with(Student:-Calculus1):
 > with(Student:-NumericalAnalysis):
 > A:=convert(taylor(exp(Q),Q,6),polynom);
 (2)
 > Q:=a[11]*(E[r])^2+a[22]*(E[theta])^2+2*a[12]*E[r]*E[theta];
 (3)
 > psi:=0.5*c*(exp(Q)-1);
 (4)
 > F:=Matrix(3,3,[[lambda[r],0,0],[0,lambda[theta],0],[0,0,lambda[z]]]);
 (5)
 > sigma[r]:=-p+diff(psi,E[r])*F[1,1]^2;
 (6)
 > sigma[theta]:=-p+diff(psi,E[theta])*F[2,2]^2;
 (7)
 > sigma[z]:=-p+diff(psi,E[z])*F[3,3]^2;
 (8)
 > p1:=diff(psi,E[r])*F[1,1]^2;#Pressure is constituted form 3 parts, one part is p1, other part is p2 and a constant p0
 (9)
 > E[r]:=0.5*(lambda[r]^2-1);
 (10)
 > E[theta]:=0.5*(lambda[theta]^2-1);
 (11)
 > E[z]:=0.5*(lambda[z]^2-1);
 (12)
 > lambda[r]:=x2*sqrt((r^2-x1)/x2)/r;
 (13)
 > lambda[theta]:=r/sqrt((r^2-x1)/x2);
 (14)
 > lambda[z]:=1/x2;
 (15)
 > sigma[r];
 (16)
 > sigma[theta]:
 > sigma[z]:
 > #p2:=int((sigma[r]-sigma[theta])/r,r):%Pressure is constituted form 2 parts, one part is p1, other part is p2 and and a constant p0
 > Digits:=10:
 > c:=790000:
 > a[11]:=0.539:
 > a[22]:=0.368:
 > a[12]:=0.653:
 > p_in:=10000:
 > p_out:=0:
 > r_in:=5.4e-3:
 > r_out:=6.1e-3:
 > F_a:=0.381846:
 > p21:=(c/2)*(((r^2-x1)/r^3)-(x2*r/(r^2-x1)))*exp(Q);
 (17)
 > p22:=(c/2)*Int(exp(Q)*(3*x2*r^6-r^6+5*x1*r^4-x1*x2*r^4-7*x1^2*r^2+3*x1^3)/(r^4*(r^2-x1)^2),r=r_in..r_out);#This is the part that should be maintained as an integral until the final solution
 (18)
 > p2:=p21-p22;#p2 is computed using the integration by part method
 (19)
 >
 > p0:=(p_out+eval(p2,r=r_out));#p0 is the constant which is defined form the boundary conditions either p_out=subs(r=r_out,sigma[r]) or p_in=subs(r=r_in,sigma[r])
 (20)
 >
 > p:=p1+p2+p0;#p is the total pressure
 (21)
 > #p:=H+H00;
 > eq1:=Int((sigma[r]-sigma[theta])/r,r=r_in..r_out);
 (22)
 > eq2:=Int(2*Pi*sigma[z]*r,r=r_in..r_out);
 (23)
 > eq1=evalf(p_out-p_in)
 (24)
 > eq2=F_a
 (25)
 > fsolve({eq1=evalf(p_out-p_in),eq2=F_a},{x1,x2});
 (26)
 > SolveEquations([eq1=evalf(p_out-p_in),eq2=F_a]);
 >
 >
 >

fsolve_problem.mw

## How is Maple able to arrive at an exact solution t...

For this integro-differential equation,

Equation:= int[y'(x)* (x^2)/[(x^2)-1],x)  =  (int[sqrt(y(x)])^(-2/3)

Maple is able to obtain an exact intrinsic solution

from which an exact solution can be extracted, namely,

ExtrinsicSolution:= y(x) = sqrt(3)*(-8*_C1*x^(8/3) + 12*x^2 - 3)^(3/4)

Even more, specifically, 'odeadvisor' suggests converting the

equation in question to the form

ode:= y = G(x,diff(y(x),x));

However, I cannot reconcile how this can be applied to an equation which

contains two integrals. (Regretably, I am not able to directly, attach my

Maple worksheet directly on to this sheet). The situation is that after

applying 'dsolve' to the above 'Equation', Maple comes back with an

intrinsic solution which can was used to obtain the 'ExtrinsicSolution' in

the above.  So it is the missing steps between applyingthe dsolve command

to Equation and the intrinsic solution which MS provides which, in turn, leads

to the 'Extrinsic Solution' above. I would greatly, appreciate if anyone can

fill in the missing steps.

## Conversion of barycentric coordinates into cartesi...

How to convert barycentric coordinates to cartesian ? Thank you

## Expression manipulation...

Is there a way to manipulate an equation so that it is in the form of (Expression of Primary Variables)*(Expression of Secondary Variables)
In the example below from Video 1: Fast Analytical Techniques for Electrical and Electronic Circuits (youtube.com), the primary variables are R1 and R2

PS. When I type ctrl-v to insert an image, I always get 2 copies.

## Proportional symbol ...

I got the proportional symbol to work once, typing "proportional" + CRTL + Space.  Went for wlak came back and could not get it to work at all.

Does it actually work or am I imagining things?

## Using pdsolve to find a potential function, with c...

Greetings All,

This is an application for control theory, specifially using Maple to solve control problems in the area of Interconnection and Damping Assignment Passivity Based Control (IDA-PBC).

- Assuming two variables (iL and Vo), there is a potential function that I am trying to solve for called "Ha".  I have two equations here, and I want to solve for Ha using the pdsolve() command:

eq1 := diff(Ha(iL, Vo), iL) = rhs(result[1]);
eq2 := diff(Ha(iL, Vo), Vo) = rhs(result[2]);
pdsolve( {eq1, eq2  } );

Once I do this, Maple gives me an expression for Ha that has arbitrary functions in it (I understand where these are coming from).  So far, so good.

--> In order to get help solving for these arbitrary functions, I also want to tell Maple some constraints.  For example:

"the Hessian matrix of Ha must be positive definite"

Is there a way to do this?

## How to obtain the Smith normal form of an integer ...

Certainly a standard question.

I have an integer n*n matrix A (the entries are explicitly integers; there is no variable -type x- in the matrix). I want the Smith normal form of A, that is A=UDV where U,V are integer matrices with determinant +-1 and D is a diagonal matrix with -eventually- some zero and positive integers d_i s.t. d_i divides d_{i+1}.

"SmithForm()" doesn't work directly (I get rational -non integer- matrices). Maybe it is necessary to declare the matrix A as 'Matrix(integer)' ...

## macOS Sonoma workaround...

Has anybody been able to get Maple working on macOS Sonoma 14.4. I know it's not supported yet, but I thought there might be someone who has solved the issue with the app crashing immediately after startup.

## How to ensure that the nip is within the arc of co...

How can a variable roller ensure that the nip is within the arc of contact between the web and the roller? Every time I run the simulation, it keeps failing.

## I cannot solve this problem of drawing...

point(A, xA, yA);
point(B, xB, yB);
point(C, xC, yC):
L3 := linestyle = 3
triangle(Tr, [A, B, C])
line(AP, [A, P]);
line(BP, [B, P]);
line(CP, [C, P]);
dr := draw([Tr(t3), AP(cbl, L3), BP(cbl, L3), CP(cbl, L3)]),
textplot([[coordinates(A)[], "A"], [coordinates(B)[], "B"], [coordinates(C)[], "C"]], align = {above, right});
display({dr, ellip}, scaling = constrained, axes = none, view = [-1 .. 14, -1 .. 11]);
Why doesn’t Maple show me the expected effect ? Thank you.

## How do I solve system of differential equations i...

How do  I solve system of differential equations in finite difference method or finite element method?

eq1 := (diff(f(x), x, x, x))*(a*beta*f(x)^2-1)+(diff(f(x), x))^2-2*a*beta*f(x)*(diff(f(x), x))*(diff(f(x), x, x))+(diff(f(x), x))*(M+k[1])-(diff(f(x), x, x))*f(x)-(alpha*theta(x)+delta*phi(x))/rho = 0;

eq2 := -(diff(theta(x), x, x))*K[SB]*(Df-(Rd+k[hnf]/k[bf])/Pr)+N[t]*K[SB]*(diff(theta(x), x))^2-N[b]*(diff(theta(x), x))*(diff(phi(x), x))-(diff(f(x), x))*(diff(theta(x), x))-lambda*theta(x)-mu*Ec*(M*(diff(f(x), x))^2+(diff(f(x), x, x))^2) = 0;

eq3 := diff(phi(x), x, x)+Le*Sr*(diff(theta(x), x, x))+Le*f(x)*(diff(phi(x), x)) = 0;

ics := f(0) = 0, (D(f))(0) = 0, theta(0) = 1, phi(0) = 1;

bcs := (D(f))(100) = 0, theta(100) = 0, phi(100) = 0;

Parameters1 := rho = 2063.905, k[hnf] = .29942, k[bf] = .2520, mu = .38694, a = .1, beta = 5, k[1] = 2.0, M = 10, alpha = 20, delta = 20, K[SB] = .5, Df = 3, Pr = 1.2, Rd = 5, N[t] = 1.2, N[b] = 1.0, lambda = 1.5, Ec = 5, Le = .1, Sr = .1;

## sir model Error code ...

dS := -beta*S*Q;
dQ := Q*S*beta - Q*alpha;
dR := alpha*Q;
beta := 0.2;
alpha := 0.1;
S0 := 0.8;
Q0 := 0.2;
R0 := 0;
RungeKutta := proc(f::list, y0::list, t0::float, tf::float, h::float) local n, t, y, k1, k2, k3, k4, i; n := 1 + floor((tf - t0)/h); t := Vector(n, fill = 0); y := Matrix(n, length(y0), fill = 0); t[1] := t0; y[1] := Vector(y0); for i to n - 1 do k1 := Vector(map(f, t[i], y[i])); k2 := Vector(map(f, t[i] + 1/2*h, y[i] + 1/2*h*k1)); k3 := Vector(map(f, t[i] + 1/2*h, y[i] + 1/2*h*k2)); k4 := Vector(map(f, t[i] + h, y[i] + h*k3)); y[i + 1] := y[i] + 1/6*h*(k1 + 2*k2 + 2*k3 + k4); t[i + 1] := t[i] + h; end do; [t, y]; end proc;
f = [dS, dQ, dR];
t0 := 0;
tf := 50;
h := 0.1;
result := RungeKutta(f, [S0, Q0, R0], t0, tf, h);
t_values := result[1];
S_values := result[2][() .. (), 1];
Q_values := result[2][() .. (), 2];
R_values := result[2][() .. (), 3];
plots:-display(plot(t_values, S_values, color = "blue", legend = "Susceptible"), plot(t_values, Q_values, color = "red", legend = "Infected"), plot(t_values, R_values, color = "green", legend = "Recovered"), legend = ["Susceptible", "Infected", "Recovered"], title = "Simulation of Infectious Disease Model", xlabel = "Time", ylabel = "Population", view = [0 .. tf, 0 .. 1]);
Warning, (in RungeKutta) `i` is implicitly declared local
dS := -0.2 S Q

dQ := 0.2 S Q - 0.1 Q

dR := 0.1 Q

beta := 0.2

alpha := 0.1

S0 := 0.8

Q0 := 0.2

R0 := 0

RungeKutta := proc (f::list, y0::list, t0::float, tf::float,

h::float) local n, t, y, k1, k2, k3, k4, i; n := 1+floor((tf-\

t0)/h); t := Vector(n, fill = 0); y := Matrix(n, length(y0),

fill = 0); t[1] := t0; y[1] := Vector(y0); for i to n-1 do

k1 := Vector(map(f, t[i], y[i])); k2 := Vector(map(f,

t[i]+(1/2)*h, y[i]+(1/2)*h*k1)); k3 := Vector(map(f,

t[i]+(1/2)*h, y[i]+(1/2)*h*k2)); k4 := Vector(map(f, t[i]+h,

y[i]+h*k3)); y[i+1] := y[i]+(1/6)*h*(k1+2*k2+2*k3+k4);

t[i+1] := t[i]+h end do; [t, y] end proc

[-0.2 S Q, 0.2 S Q - 0.1 Q, 0.1 Q] = [-0.2 S Q, 0.2 S Q - 0.1 Q,

0.1 Q]

t0 := 0

tf := 50

h := 0.1

Error, invalid input: RungeKutta expects its 3rd argument, t0, to be of type float, but received 0
t_values := result[1]

S_values := result[2][() .. (), 1]

Q_values := result[2][() .. (), 2]

R_values := result[2][() .. (), 3]

Warning, expecting only range variable result[2][(NULL) .. (NULL),1] in expression result[1] to be plotted but found name result[1]
Warning, expecting only range variable result[2][(NULL) .. (NULL),2] in expression result[1] to be plotted but found name result[1]
Warning, expecting only range variable result[2][(NULL) .. (NULL),3] in expression result[1] to be plotted but found name result[1]
Error, (in plots:-display) unexpected options: [xlabel = "Time", ylabel = "Population"]

## Center Align Math...

I want to center align all the math in my document. I have not been able to find a shortcut key for alignment, and I cannot find a default setting for alignment anywhere. I don't want to mouse click every single time.

## Automate Lie Algebra Computaitons...

Howdy,

I am trying to do explicit Lie algebra computations, and I am not sure the best way to automate these.

Suppose I have a Lie algebra with basis e1 through e8, and I have some linear functions:

f(e1,e2) = c1e1+c2e2+...+c8e8

Now suppose I want to compute something like

[e5, f] - f([e5,e1],e2) + f([e5,e2],e1), or more generally x.f with the typical module structure.

I can do this line by line - say [e5,e1] = -e1 and [e5,e2] = 0, then I can ask Maple for LieBracket(e5,f)+f(e1,e2)-0. However, I'd like to make an operator that does this for me. Can anyone please point me in the right direction?

Thanks!

 First 9 10 11 12 13 14 15 Last Page 11 of 340
﻿