Maple Questions and Posts

These are Posts and Questions associated with the product, Maple

What is the installation time for Maple 2025?

I looked up the installation times for Matlab and Mathematica.  The AI assistant in google says Matlab takes several minutes to an hour, for Mathematica 20 minutes to an hour, for Maple it said around 15 minutes -  Is that about right? 

in thus example all of them are write in shape of matrix but all of them are linear differential equation which have critical point zero ,i want to plot thus example and decided the kind of critical point by eagenvalue and by eagenvector i can find the trajectory how i can plot by matrix of each example and show that that critical point is which type as mention in picture?

system-phase-examples.mw

in my iteration is appear Error, (in assuming) when calling 'evala/preproc4'. Received: 'floats not handled' which i know is  becuase assuming but how fix it?

and how i can get that table ?

error-problem.mw

my iteration u[i] in last step not working as i want where is the issue?

b1.mw

i want plot like that but i can't  and there is anyway for finding the equalibriom point of system? 

restart

with(PDEtools)

with(LinearAlgebra)

with(DEtools)

with(DynamicSystems)

sys := {diff(x(t), t) = 2*x(t)+3*y(t), diff(y(t), t) = 2*x(t)+y(t)}

{diff(x(t), t) = 2*x(t)+3*y(t), diff(y(t), t) = 2*x(t)+y(t)}

(1)

fns := {x(t), y(t)}

{x(t), y(t)}

(2)

sol := dsolve(sys, fns)

{x(t) = c__1*exp(4*t)+c__2*exp(-t), y(t) = (2/3)*c__1*exp(4*t)-c__2*exp(-t)}

(3)

ode := [diff(x(t), t) = 2*x(t)+3*y(t), diff(y(t), t) = 2*x(t)+y(t)]; S := dsolve(ode)

[diff(x(t), t) = 2*x(t)+3*y(t), diff(y(t), t) = 2*x(t)+y(t)]

 

{x(t) = c__1*exp(4*t)+c__2*exp(-t), y(t) = (2/3)*c__1*exp(4*t)-c__2*exp(-t)}

(4)

Student:-ODEs:-ODESteps(ode, {x(t), y(t)})

"[[,,"Let's solve"],[,,[(ⅆ)/(ⅆt) x(t)=2 x(t)+3 y(t),(ⅆ)/(ⅆt) y(t)=2 x(t)+y(t)]],["•",,"Define vector"],[,,x(t)=[?]],["•",,"Convert system into a vector equation"],[,,(ⅆ)/(ⅆt) x(t)=[?]*x(t)+[?]],["•",,"System to solve"],[,,(ⅆ)/(ⅆt) x(t)=[?]*x(t)],["•",,"Define the coefficient matrix"],[,,A=[?]],["•",,"Rewrite the system as"],[,,(ⅆ)/(ⅆt) x(t)=A*x(t)],["•",,"To solve the system, find the eigenvalues and eigenvectors of" A],["•",,"Eigenpairs of" A],[,,[[-1,[?]],[4,[?]]]],["•",,"Consider eigenpair"],[,,[-1,RTABLE(18446744074191517278,MATRIX([[-1], [1]]),Vector[column])]],["•",,"Solution to homogeneous system from eigenpair"],[,,(x)[1]=[]],["•",,"Consider eigenpair"],[,,[4,RTABLE(18446744074192645174,MATRIX([[3/2], [1]]),Vector[column])]],["•",,"Solution to homogeneous system from eigenpair"],[,,(x)[2]=[]],["•",,"General solution to the system of ODEs"],[,,x=`c__1` (x)[1]+`c__2` (x)[2]],["•",,"Substitute solutions into the general solution"],[,,x=[]+[]],["•",,"Substitute in vector of dependent variables"],[,,[?]=[?]],["•",,"Solution to the system of ODEs"],[,,{x(t)=-`c__1` (e)^(-t)+(3 `c__2` (e)^(4 t))/2,y(t)=`c__1` (e)^(-t)+`c__2` (e)^(4 t)}]]"

(5)
 

NULL

Download Plot-1.mw

Dear All, I hope this message finds you well. I am currently facing some issues and would appreciate your support or guidance in resolving them. Nusselt_RSM_Model.mw

 

restart;

with(Statistics): with(LinearAlgebra): with(plots):

local A, B, C, D;

Digits := 10:

 

# Step 1: Define the variables

vars := [A, B, C, D];

 

# Step 2: Generate Central Composite Design (CCD) coded matrix

coded := Matrix([

    [ 1,  1,  1,  1],

    [ 1,  1,  1, -1],

    [ 1,  1, -1,  1],

    [ 1,  1, -1, -1],

    [ 1, -1,  1,  1],

    [ 1, -1,  1, -1],

    [ 1, -1, -1,  1],

    [ 1, -1, -1, -1],

    [-1,  1,  1,  1],

    [-1,  1,  1, -1],

    [-1,  1, -1,  1],

    [-1,  1, -1, -1],

    [-1, -1,  1,  1],

    [-1, -1,  1, -1],

    [-1, -1, -1,  1],

    [-1, -1, -1, -1],

    [ 0,  0,  0,  0],

    [ 0,  0,  0,  0],

    [ 0,  0,  0,  0],

    [ 0,  0,  0,  0]

]):

 

# Step 3: Define uncoded variable ranges

rangeA := [0.1, 0.5]:

rangeB := [0.1, 0.5]:

rangeC := [0.1, 0.5]:

rangeD := [0.1, 0.5]:

 

decode := (val, r) -> r[1] + (val + 1)*(r[2] - r[1])/2:

 

# Step 4: Create actual values matrix

actual := Matrix(20, 4):

for i from 1 to 20 do

    for j from 1 to 4 do

        r := eval(cat("range", vars[j])):

        actual[i, j] := evalf(decode(coded[i, j], r));

    end do;

end do:

 

# Step 5: Define model coefficients (for simulation purposes)

beta := [1.5, 0.8, 0.6, 0.5, 0.3,  # Linear terms

         0.1, 0.2, 0.15, 0.18,  # Square terms

         0.05, 0.04, 0.03, 0.02, 0.01, 0.025]; # Interaction terms

 

# Step 6: Simulate Response (Nusselt number)

Nu := Vector(20):

for i from 1 to 20 do

    A := actual[i,1]; B := actual[i,2]; C := actual[i,3]; D := actual[i,4];

    Nu[i] := evalf(

        beta[1] + beta[2]*A + beta[3]*B + beta[4]*C + beta[5]*D +

        beta[6]*A^2 + beta[7]*B^2 + beta[8]*C^2 + beta[9]*D^2 +

        beta[10]*A*B + beta[11]*A*C + beta[12]*A*D +

        beta[13]*B*C + beta[14]*B*D + beta[15]*C*D

    );

end do:

 

# Step 7: Create data frame for ANOVA

X := Matrix(actual):

Y := convert(Nu, list):

 

# Step 8: Fit quadratic model

model := Fit(

    A + B + C + D + A^2 + B^2 + C^2 + D^2 + A*B + A*C + A*D + B*C + B*D + C*D,

    X,

    Y,

    vars

):

 

# Step 9: ANOVA table

anovaTable := ANOVA(model, significancelevel=0.05):

 

# Step 10: Display results with 8 decimal places

printf("RSM Model for Nu (Nusselt number):\n");

print(evalf[8](model));

printf("\nANOVA Table:\n");

print(anovaTable);

 

# Optional: Plotting

pointplot([seq([i, Nu[i]], i = 1..20)], style=point, symbol=circle,

          color=red, title="Nusselt Number vs Run Index",

          labels=["Run", "Nusselt Number"]);

[A, B, C, D]

 

[1.5, .8, .6, .5, .3, .1, .2, .15, .18, 0.5e-1, 0.4e-1, 0.3e-1, 0.2e-1, 0.1e-1, 0.25e-1]

 

Error, (in Statistics:-Fit) invalid input: Fit expects its 4th argument, v, to be of type {name, list(name)}, but received [1.5+2.2*"a"+.805*"a"^2, 1.5+1.9*"a"+.3*"r"+.56*"a"^2+.18*"r"^2+0.65e-1*"a"*"r", 1.5+1.7*"a"+.5*"r"+.57*"a"^2+.15*"r"^2+0.85e-1*"a"*"r", 1.5+1.4*"a"+.8*"r"+.35*"a"^2+.355*"r"^2+.10*"a"*"r", 1.5+1.6*"a"+.6*"r"+.525*"a"^2+.2*"r"^2+0.8e-1*"a"*"r", 1.5+1.3*"a"+.9*"r"+.29*"a"^2+.39*"r"^2+.125*"a"*"r", 1.5+1.1*"a"+1.1*"r"+.31*"a"^2+.37*"r"^2+.125*"a"*"r", 1.5+.8*"a"+1.4*"r"+.1*"a"^2+.585*"r"^2+.12*"a"*"r", 1.5+.8*"r"+1.4*"a"+.1*"r"^2+.585*"a"^2+.12*"a"*"r", 1.5+1.1*"r"+1.1*"a"+.31*"r"^2+.37*"a"^2+.125*"a"*"r", 1.5+1.3*"r"+.9*"...

 

RSM Model for Nu (Nusselt number):

 

model

 


ANOVA Table:

 

ANOVA(model, significancelevel = 0.5e-1)

 

Error, (in plots:-pointplot) incorrect specification of points data

 
 

``

Download Nusselt_RSM_Model.mw

Hi,

I’m not very familiar with how to handle complex numbers in Maple, but I’d like to solve a final exam exercise (June 2025) on complex numbers in this environment. I’ve already solved it using pen and paper. My goal is also to illustrate the different results graphically, for pedagogical purposes, so I’d like some guidance to translate my pen-and-paper solution.

Bac_25_SM_Complexes.mw

Epreuve_Bac_SM_2025_Ss1_Sol-Exo-02.pdf

I need to use a procedure where one of the parameters is a function. Conceptually, this seems straightforward, but I’m encountering unexpected behavior. Here’s a minimal example of my approach:

f1:=proc(t::numeric, fn::function)::numeric;
return fn(t+1)+1
end proc;

However, none of the following calls return the correct result:

f1(2, sin);
f1(2, sin());
f1(2, sin(x));
f1(2, u-> u^2);

Any guidance would be greatly appreciated!

we have a lot term which we add thus term we can get something near to our solution but i don't know how it is work , did any one did pade approximate of series solution?

restart

with(inttrans)

with(PDEtools)

with(DEtools)

with(Physics)

declare(u(x, t), quiet); declare(v(x, t), quiet); declare(U(x, t), quiet)

undeclare(prime)

approx_sol := -8*x + 3 - 208/3*x^3 + 24*x^2 + 2279/15*x^5 + 200*x^4 + 443/63*x^7 + 676/15*x^6 + 62/2835*x^9 + 62/105*x^8

-8*x+3-(208/3)*x^3+24*x^2+(2279/15)*x^5+200*x^4+(443/63)*x^7+(676/15)*x^6+(62/2835)*x^9+(62/105)*x^8

(1)
 

NULL

Download pade-approximate.mw


Hi
I want to plot M versus R=kappa for the mentioned parameters. (I know M must be a real and positive number)
But I couldn't. May someone please review and fix my uploaded file?

m1.mw

It is very strange, but I cannot find in v. 2025 shortcut or a button for stoping current evaluation.

I had no problem with this in previous version, but now the absence of immediate stoping make troubles for me,

Find the circle of maximum radius that is tangent to both curves. 
There are no other conditions or restrictions.
Equations of curves

 (x1-1/2)^4+x1*x2+2*x2^2-1=0; 
 (x1-sin(x1))^2+(x2-sin(x2))^2-1=0;

 

The link below goes to the Proceedings of the Maple 2024 Conference, which includes several articles that will be of interest to the readers of Maple Primes.

There may be one more paper coming in to the proceedings later as per policy; since most things are ready, away we go!

Proceedings of the Maple 2024 Conferenc

(1) The gray line above the working area is redundant.

(2) Line Style, Color, and the "Delete" key function to delete object are not working properly.

(3) IdentifySequence([1,3,5,7,9]) without the second argument does not work.

(4) IdentifySequence should first identify simple patterns (Arithmetic Progression, Geometric Progression, Arithmetic-Geometric Progression, Harmonic Progression) before attempting to find a more complex formula for the nth term of the sequence.

(5) It would be beneficial if IdentifySequence recognized sequences involving rational, irrational and symbolic numbers.

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