Maple Questions and Posts

These are Posts and Questions associated with the product, Maple

i want to do export  the table to latex there is command to do?

table.mw

In the screen shot below taken from a 3D animation I want to vastly shrink the area I have stippled with spots (it's actually white on the worksheet).  It's outside the cube defining the 3D animation and inside the square that defines the part of the worksheet used for an image.

in my iteration when i got answer the error is so big and the method is powerfull i don't know i did mistake or my exact function i have to change it, becuase error is so big , how i can make error be smaller i did any mistake ?
and how i can plot them together exact and approximate in one graph also 3D and 2D

Num-e1.mw

I am working with a symbolic expression in Maple that combines exponential terms. How can exponential terms be fully converted into hyperbolic functions? 

restart

with(Student[Precalculus])

interface(showassumed = 0)

assume(x::real); assume(t::real); assume(lambda1::complex); assume(lambda2::complex); assume(a::real); assume(A__c::real); assume(B1::real); assume(B2::real); assume(delta1::real); assume(delta2::real); assume(`ω__0`::real); assume(g::real); assume(l__0::real)

expr := A__c*exp(-(2*I)*(A__c^2*g*l__0^2-1/2)*`ω__0`*t)+(2*I)*exp(-I*(A__c^2*g*l__0^2-1/2)*`ω__0`*t)*(sqrt(delta1+I*delta2-sqrt(-A__c^2*g+(delta1+I*delta2)^2))*exp(-2*sqrt(-A__c^2*g+(delta1+I*delta2)^2)*(l__0^2*(I*delta1-delta2)*t*`ω__0`+(1/2)*x))-sqrt(delta1+I*delta2+sqrt(-A__c^2*g+(delta1+I*delta2)^2))*exp(sqrt(-A__c^2*g+(delta1+I*delta2)^2)*(x+(2*I)*`ω__0`*l__0^2*(delta1+I*delta2)*t)))*(sqrt(-delta1+I*delta2-sqrt(-A__c^2*g+(delta1-I*delta2)^2))*exp((2*(l__0^2*(I*delta1+delta2)*t*`ω__0`-(1/2)*x))*sqrt(-A__c^2*g+(delta1-I*delta2)^2))-sqrt(-delta1+I*delta2+sqrt(-A__c^2*g+(delta1-I*delta2)^2))*exp(-(2*(l__0^2*(I*delta1+delta2)*t*`ω__0`-(1/2)*x))*sqrt(-A__c^2*g+(delta1-I*delta2)^2)))*delta2/(exp(I*(A__c^2*g*l__0^2-1/2)*`ω__0`*t)*(((-sqrt(delta1+I*delta2-sqrt(-A__c^2*g+(delta1+I*delta2)^2))*sqrt(-delta1+I*delta2+sqrt(-A__c^2*g+(delta1-I*delta2)^2))-sqrt(delta1+I*delta2+sqrt(-A__c^2*g+(delta1+I*delta2)^2))*sqrt(-delta1+I*delta2-sqrt(-A__c^2*g+(delta1-I*delta2)^2)))*exp((2*(l__0^2*(I*delta1+delta2)*t*`ω__0`-(1/2)*x))*sqrt(-A__c^2*g+(delta1-I*delta2)^2))+exp(-(2*(l__0^2*(I*delta1+delta2)*t*`ω__0`-(1/2)*x))*sqrt(-A__c^2*g+(delta1-I*delta2)^2))*(sqrt(delta1+I*delta2-sqrt(-A__c^2*g+(delta1+I*delta2)^2))*sqrt(-delta1+I*delta2-sqrt(-A__c^2*g+(delta1-I*delta2)^2))+sqrt(-delta1+I*delta2+sqrt(-A__c^2*g+(delta1-I*delta2)^2))*sqrt(delta1+I*delta2+sqrt(-A__c^2*g+(delta1+I*delta2)^2))))*exp(-2*sqrt(-A__c^2*g+(delta1+I*delta2)^2)*(l__0^2*(I*delta1-delta2)*t*`ω__0`+(1/2)*x))+exp(sqrt(-A__c^2*g+(delta1+I*delta2)^2)*(x+(2*I)*`ω__0`*l__0^2*(delta1+I*delta2)*t))*((sqrt(delta1+I*delta2-sqrt(-A__c^2*g+(delta1+I*delta2)^2))*sqrt(-delta1+I*delta2-sqrt(-A__c^2*g+(delta1-I*delta2)^2))+sqrt(-delta1+I*delta2+sqrt(-A__c^2*g+(delta1-I*delta2)^2))*sqrt(delta1+I*delta2+sqrt(-A__c^2*g+(delta1+I*delta2)^2)))*exp((2*(l__0^2*(I*delta1+delta2)*t*`ω__0`-(1/2)*x))*sqrt(-A__c^2*g+(delta1-I*delta2)^2))-exp(-(2*(l__0^2*(I*delta1+delta2)*t*`ω__0`-(1/2)*x))*sqrt(-A__c^2*g+(delta1-I*delta2)^2))*(sqrt(delta1+I*delta2-sqrt(-A__c^2*g+(delta1+I*delta2)^2))*sqrt(-delta1+I*delta2+sqrt(-A__c^2*g+(delta1-I*delta2)^2))+sqrt(delta1+I*delta2+sqrt(-A__c^2*g+(delta1+I*delta2)^2))*sqrt(-delta1+I*delta2-sqrt(-A__c^2*g+(delta1-I*delta2)^2)))))*(-delta1+I*delta2)*(delta1+I*delta2))

A__c*exp(-(2*I)*(A__c^2*g*l__0^2-1/2)*omega__0*t)+(2*I)*exp(-I*(A__c^2*g*l__0^2-1/2)*omega__0*t)*((delta1+I*delta2-(-A__c^2*g+(delta1+I*delta2)^2)^(1/2))^(1/2)*exp(-2*(-A__c^2*g+(delta1+I*delta2)^2)^(1/2)*(l__0^2*(I*delta1-delta2)*t*omega__0+(1/2)*x))-(delta1+I*delta2+(-A__c^2*g+(delta1+I*delta2)^2)^(1/2))^(1/2)*exp((-A__c^2*g+(delta1+I*delta2)^2)^(1/2)*(x+(2*I)*omega__0*l__0^2*(delta1+I*delta2)*t)))*((-delta1+I*delta2-(-A__c^2*g+(delta1-I*delta2)^2)^(1/2))^(1/2)*exp(2*(l__0^2*(I*delta1+delta2)*t*omega__0-(1/2)*x)*(-A__c^2*g+(delta1-I*delta2)^2)^(1/2))-(-delta1+I*delta2+(-A__c^2*g+(delta1-I*delta2)^2)^(1/2))^(1/2)*exp(-2*(l__0^2*(I*delta1+delta2)*t*omega__0-(1/2)*x)*(-A__c^2*g+(delta1-I*delta2)^2)^(1/2)))*delta2/(exp(I*(A__c^2*g*l__0^2-1/2)*omega__0*t)*(((-(delta1+I*delta2-(-A__c^2*g+(delta1+I*delta2)^2)^(1/2))^(1/2)*(-delta1+I*delta2+(-A__c^2*g+(delta1-I*delta2)^2)^(1/2))^(1/2)-(delta1+I*delta2+(-A__c^2*g+(delta1+I*delta2)^2)^(1/2))^(1/2)*(-delta1+I*delta2-(-A__c^2*g+(delta1-I*delta2)^2)^(1/2))^(1/2))*exp(2*(l__0^2*(I*delta1+delta2)*t*omega__0-(1/2)*x)*(-A__c^2*g+(delta1-I*delta2)^2)^(1/2))+exp(-2*(l__0^2*(I*delta1+delta2)*t*omega__0-(1/2)*x)*(-A__c^2*g+(delta1-I*delta2)^2)^(1/2))*((delta1+I*delta2-(-A__c^2*g+(delta1+I*delta2)^2)^(1/2))^(1/2)*(-delta1+I*delta2-(-A__c^2*g+(delta1-I*delta2)^2)^(1/2))^(1/2)+(-delta1+I*delta2+(-A__c^2*g+(delta1-I*delta2)^2)^(1/2))^(1/2)*(delta1+I*delta2+(-A__c^2*g+(delta1+I*delta2)^2)^(1/2))^(1/2)))*exp(-2*(-A__c^2*g+(delta1+I*delta2)^2)^(1/2)*(l__0^2*(I*delta1-delta2)*t*omega__0+(1/2)*x))+exp((-A__c^2*g+(delta1+I*delta2)^2)^(1/2)*(x+(2*I)*omega__0*l__0^2*(delta1+I*delta2)*t))*(((delta1+I*delta2-(-A__c^2*g+(delta1+I*delta2)^2)^(1/2))^(1/2)*(-delta1+I*delta2-(-A__c^2*g+(delta1-I*delta2)^2)^(1/2))^(1/2)+(-delta1+I*delta2+(-A__c^2*g+(delta1-I*delta2)^2)^(1/2))^(1/2)*(delta1+I*delta2+(-A__c^2*g+(delta1+I*delta2)^2)^(1/2))^(1/2))*exp(2*(l__0^2*(I*delta1+delta2)*t*omega__0-(1/2)*x)*(-A__c^2*g+(delta1-I*delta2)^2)^(1/2))-exp(-2*(l__0^2*(I*delta1+delta2)*t*omega__0-(1/2)*x)*(-A__c^2*g+(delta1-I*delta2)^2)^(1/2))*((delta1+I*delta2-(-A__c^2*g+(delta1+I*delta2)^2)^(1/2))^(1/2)*(-delta1+I*delta2+(-A__c^2*g+(delta1-I*delta2)^2)^(1/2))^(1/2)+(delta1+I*delta2+(-A__c^2*g+(delta1+I*delta2)^2)^(1/2))^(1/2)*(-delta1+I*delta2-(-A__c^2*g+(delta1-I*delta2)^2)^(1/2))^(1/2))))*(-delta1+I*delta2)*(delta1+I*delta2))

(1)

NULL

Download simplify.mw

  1. Further simplify the expression under three physical scenarios, assuming delta__1 > 0:

    • Case (i): When A__c = 0

    • Case (ii): When delta__1 > g * A__c

    • Case (iii): When delta__1 < g * A__c

i got some issue regarding to solving numerical example, he got combine function of infinite term i don't know how when he give alpha a number ? and when didn't give number  to order of fractional laplace and stay alpha letter he got outcome i want apply laplace while is for general alpha betwen n-1<alpha<n when n is number of initial condition, i want to get same result as he did steps are not wrong but outcome have problem .

i have same problem in three example in one paper, is related to update maple to 2025, i saw talking about calculating inverse laplace at new version  any one  know how fix this?

Ex1.mw

EX2.mw

Ex3.mw

When I load LinearAlgebra and give the command

{Matrix([1])} union {Matrix([1])};

I receive a set with two elements, each equal to the matrix [1]. Why does this happen? How can I eliminate this duplicate element?

I get this ->

sum(i^2, i = 1 .. 5)

55``

(1)

 

But would like this ->

First impressions, I have mixed feelings - one being it's cool and new, the other feeling that it's a bit clunky.

In my opinion Maple is starting to look like the interface is being modelled after Microsoft Office, or like the ribbon toolbars of AutoCad or Inventor.  Maple's "uniqueness" is disappearing.  I rather liked the old interface. 

The toolbar icons are larger, taking up more space.

The toolbar layout is indeed simpler, but also less efficient maybe.  I mean there were more useful available icons at once before, more functional is the word I guess.  Now it might be a couple of clicks away to pull up your favorite icon(s).  The icons all look very nice, that's a plus but they could be smaller.  

Perhaps we could make a customized menu toolbar?  That is, allow users to put all the most useful icons we use or would like the most to be displayed?  This would help some of the strange organization of some of the icons and allow us to make our maple "sandbox" feel more at home. 

Where have all the tools options display / interface / Precision tabs all gone?  That is typsetting (extended or Maple standard) options
plot or font anti-aliasing (Enabled Disabled) options
plot dislpay (inline window) options
Precision (limit expression length to etc...)

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"],[,,[(&DifferentialD;)/(&DifferentialD;t) x(t)=2 x(t)+3 y(t),(&DifferentialD;)/(&DifferentialD;t) y(t)=2 x(t)+y(t)]],["&bullet;",,"Define vector"],[,,x(t)=[?]],["&bullet;",,"Convert system into a vector equation"],[,,(&DifferentialD;)/(&DifferentialD;t) x(t)=[?]*x(t)+[?]],["&bullet;",,"System to solve"],[,,(&DifferentialD;)/(&DifferentialD;t) x(t)=[?]*x(t)],["&bullet;",,"Define the coefficient matrix"],[,,A=[?]],["&bullet;",,"Rewrite the system as"],[,,(&DifferentialD;)/(&DifferentialD;t) x(t)=A*x(t)],["&bullet;",,"To solve the system, find the eigenvalues and eigenvectors of" A],["&bullet;",,"Eigenpairs of" A],[,,[[-1,[?]],[4,[?]]]],["&bullet;",,"Consider eigenpair"],[,,[-1,RTABLE(18446744074191517278,MATRIX([[-1], [1]]),Vector[column])]],["&bullet;",,"Solution to homogeneous system from eigenpair"],[,,(x)[1]=[]],["&bullet;",,"Consider eigenpair"],[,,[4,RTABLE(18446744074192645174,MATRIX([[3/2], [1]]),Vector[column])]],["&bullet;",,"Solution to homogeneous system from eigenpair"],[,,(x)[2]=[]],["&bullet;",,"General solution to the system of ODEs"],[,,x=`c__1` (x)[1]+`c__2` (x)[2]],["&bullet;",,"Substitute solutions into the general solution"],[,,x=[]+[]],["&bullet;",,"Substitute in vector of dependent variables"],[,,[?]=[?]],["&bullet;",,"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

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