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MaplePrimes Questions

How do you solve an equation for two unknowns coup...

Asked by: GFY 65
ode syntax dsolve
September 27 2024
0  5

How to use maple to compute the solution of two coupling equations that both have higher order derivatives? I used dsolve and couldn't solve it.

question928.mw

Approximate solution for exponential equation...

Asked by: MichaelVio 40
exponential regression plotting
September 27 2024
0  10

I must approximate the coefficients a, b, c, and d in an exponential equation. Is it possible to plot?

Please help!

Ea := 0.00762014687*t + a*t^2 + b*t^3 + c*t^4 + d*t^5;
E1 := diff(Ea, t);
E2 := subs(t = 435, Ea);
E3 := subs(t = 528, Ea);
E4 := subs(t = 33168, Ea);

E1 = 5.012764943*10^(-24)*Ea/(exp(Ea/(4.100527530*10^(-21))) - 1)

Aph1.mw

Error when executed as MLA file...

Asked by: goebeld 65
procedure
September 26 2024
0  4

the programs calculates the gcd of 2x2 matrices using procedures. I created a MLA file and loadad this in another work sheet. To my surprise I received an error altghough the original version runs fine.

240926_gcd.mw

cancelling common terms betweeen numerator and den...

Asked by: jrive 210
simplification
September 26 2024
3  19

given :

Zin := ((Rsp + (omega*L2 - omega02^2*L2/omega)*I)*(Rpp + (omega*L1 - omega01^2*L1/omega)*I) + 0.01*omega^2*L1*L2)/(Rsp + (omega*L2 - omega02^2*L2/omega)*I)

how do I get Maple to cancel out the common term, and simplify this equation into:

Zin := Rpp + (omega*L1 - omega01^2*L1/omega)*I + (0.01*omega^2*L1*L2)/(Rsp + 
(omega*L2 - omega02^2*L2/omega)*I)

Why doesn't Maple do this automatically with something like simplify or some other command?

Thank you!

How to find KKT conditions using maple for maximiz...

Asked by: Andiguys 65
optimization homework
September 26 2024
0  2

How to find KKT conditions using maple for maximization function with constraint?

Decision variable are k1 and k2.

Attaching sheet:Q_KKT.mw

How to test if all elements of a list or a set are...

Asked by: jasser 95
September 26 2024
0  1

Hi

I want to count in a list L with many sublists the number of sublists, that contain m elements and only primes. How can I do that?

Example:

L:=[[2,3,5,7],[7,13,29],[2,3,4],[5,31,53]], m=3

The result should be 2, because only [7,13,29] and [5,31,53] satiesfy both criteria.

Thank you for an answer!

ODESteps gives improper op or subscript selector...

Asked by: nm 11353
ode step-by-step differential-equations
September 26 2024
2  2

Why Maple gives

           improper op or subscript selector

On this ode? I was not expecting to see steps for this, but was just trying to see what it will show.

> 

restart;
> 

interface(version);

`Standard Worksheet Interface, Maple 2024.1, Windows 10, June 25 2024 Build ID 1835466`

> 

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1810 and is the same as the version installed in this computer, created 2024, September 18, 18:16 hours Pacific Time.`

> 

libname;

"C:\Users\Owner\maple\toolbox\2024\Physics Updates\lib", "C:\Program Files\Maple 2024\lib"

> 

restart;
> 

ode:=sin(x)*diff(y(x),x$2)+cos(x)*diff(y(x),x)+(sin(x)-cos(x))*y(x)=0;

sin(x)*(diff(diff(y(x), x), x))+cos(x)*(diff(y(x), x))+(sin(x)-cos(x))*y(x) = 0

> 

dsolve(ode);

y(x) = c__1*(tan((1/2)*x)+I)^(1/2+(1/2)*(5-4*I)^(1/2))*(tan((1/2)*x)-I)^((1/2)*(5+4*I+(5+4*I)^(1/2))/(5+4*I)^(1/2))*HeunG(2, 2*(((3/4)*(5-4*I)^(1/2)+7/4-I)*(5+4*I)^(1/2)+5/4+I+(5/4+I)*(5-4*I)^(1/2))/(5+4*I)^(1/2), 1+(1/2)*(10+2*41^(1/2))^(1/2), (1/2)*((5+4*I)^(1/2)*(5-4*I)^(1/2)+5+4*I+2*(5+4*I)^(1/2))/(5+4*I)^(1/2), 1+(5-4*I)^(1/2), 1, 1-I*tan((1/2)*x))+c__2*(tan((1/2)*x)+I)^(1/2-(1/2)*(5-4*I)^(1/2))*(tan((1/2)*x)-I)^((1/2)*(5+4*I+(5+4*I)^(1/2))/(5+4*I)^(1/2))*HeunG(2, -2*(((3/4)*(5-4*I)^(1/2)+(-7/4+I))*(5+4*I)^(1/2)+(-5/4-I)+(5/4+I)*(5-4*I)^(1/2))/(5+4*I)^(1/2), -(1/2)*(5-4*I)^(1/2)+1+(1/2)*(5+4*I)^(1/2), (1/2)*(-(5+4*I)^(1/2)*(5-4*I)^(1/2)+5+4*I+2*(5+4*I)^(1/2))/(5+4*I)^(1/2), 1-(5-4*I)^(1/2), 1, 1-I*tan((1/2)*x))

> 

Student:-ODEs:-ODESteps(ode)

Error, (in Student:-ODEs:-OdeSolveOrder2) improper op or subscript selector

> 

 


 

Download internal_error_ODEsteps_sept_26_2024.mw

How to reverse the operation of function map in a ...

Asked by: Aixleft math 120
reverse incomplete-question
September 26 2024
0  3

Hi I wanna move the expressions except a^2 in the first term of p1 to after a^2 in the last term, and move the expressions except a^2+b^2 in the second term to after a^2+b^2 in the second-to-last term, etc., and achieve the reverse effect on p1 through  operation.

Maple code is as below (I add more letters in maple code compared to the above image)

> 

with(ListTools)
> 

p := map[scan = `+`](proc (x) options operator, arrow; x^3 end proc, [a, b, c, d, e, f, g, h, i, j, k])

[a^3, a^3+b^3, a^3+b^3+c^3, a^3+b^3+c^3+d^3, a^3+b^3+c^3+d^3+e^3, a^3+b^3+c^3+d^3+e^3+f^3, a^3+b^3+c^3+d^3+e^3+f^3+g^3, a^3+b^3+c^3+d^3+e^3+f^3+g^3+h^3, a^3+b^3+c^3+d^3+e^3+f^3+g^3+h^3+i^3, a^3+b^3+c^3+d^3+e^3+f^3+g^3+h^3+i^3+j^3, a^3+b^3+c^3+d^3+e^3+f^3+g^3+h^3+i^3+j^3+k^3]

 (1)
> 

p1 := Reverse(p)

[a^3+b^3+c^3+d^3+e^3+f^3+g^3+h^3+i^3+j^3+k^3, a^3+b^3+c^3+d^3+e^3+f^3+g^3+h^3+i^3+j^3, a^3+b^3+c^3+d^3+e^3+f^3+g^3+h^3+i^3, a^3+b^3+c^3+d^3+e^3+f^3+g^3+h^3, a^3+b^3+c^3+d^3+e^3+f^3+g^3, a^3+b^3+c^3+d^3+e^3+f^3, a^3+b^3+c^3+d^3+e^3, a^3+b^3+c^3+d^3, a^3+b^3+c^3, a^3+b^3, a^3]

 (2)
> 

nops(p1)

11

 (3)
 

``

Download The_inverse_operation_of_map_on_the_elements_in_list.mw

How to collect coefficients?...

Asked by: mz6687 40
coefficients incomplete-question
September 26 2024
0  1

How to collect coefficients of eta^j, j=0,1 from (7)?

> 

restart
> 

with(LinearAlgebra)
> 

with(plots)
> 

with(Physics)
> 

interface(showassumed = 0)
> 

Setup(mathematicalnotation = true)

[mathematicalnotation = true]

 (1)
> 

quantumOperators := {H, Id, Mqu, Mqu1, Theta, X, X1}

{H, Id, Mqu, Mqu1, Theta, X, X1}

 (2)
> 

Setup(quantumoperators = quantumOperators)

[quantumoperators = {H, Id, Mqu, Mqu1, Theta, X, X1}]

 (3)
> 

assume(x::real); assume(t::real)
> 

alias(q = q(x, t), qb = qb(x, t), r = r(x, t), rb = rb(x, t), psi = psi(x, t), phi = phi(x, t), g = g(x, t), gb = gb(x, t), H = H(x, t), X = X(x, t), X1 = X1(x, t), Theta = Theta(x, t), eta = eta(t), Mqu = Mqu(x, t))

q, qb, r, rb, psi, phi, g, gb, H, X, X1, Theta, eta, Mqu

 (4)
> 

``
> 

NULL
> 

D1 := (Id*eta-H).X

eta*Physics:-`*`(Id, X)-Physics:-`*`(H, X)

 (5)
> 

D2 := diff(D1, x); D3 := subs({diff(X, x) = Mqu}, D2)

eta*Physics:-`*`(Id, diff(X, x))-Physics:-`*`(diff(H, x), X)-Physics:-`*`(H, diff(X, x))

  

eta*Physics:-`*`(Id, Mqu)-Physics:-`*`(diff(H, x), X)-Physics:-`*`(H, Mqu)

 (6)
> 

D3+D1 = D1*Mqu1

eta*Physics:-`*`(Id, Mqu)-Physics:-`*`(diff(H, x), X)-Physics:-`*`(H, Mqu)+eta*Physics:-`*`(Id, X)-Physics:-`*`(H, X) = Physics:-`*`(eta*Physics:-`*`(Id, X)-Physics:-`*`(H, X), Mqu1)

 (7)
> 

collect(coeff, eta, 1)

1

 (8)
> 

collect(coeff, eta, 0)

0

 (9)
 

NULL

Download coefff.mw

How to display radical roots?...

Asked by: maltz 5
solve
September 25 2024
1  4

Hello,

I am a completely new user; please forgive me for this newbie quesiton:

When trying to solve for the intersection between a parabola and a line (or a similar system), if the solutions involve integers, Maple display the solutions well. However, when the solutions involve square roots, the solution is much less "neat". Please see the picture below.

I wonder if there is some setting I can flip so that Maple outpus solutions with radicals? Thank you.

Daniel

Differences in Domain Results Between solve(0 < x ...

Asked by: Paras31 245
solve inequality
September 25 2024
2  2

I recently encountered an interesting issue when solving for the domain of a function in Maple using two different approaches, and I am curious about the differences in results between the following commands:

  1. domain := solve(0 < x and x <> 2, x);
  2. domain := solve({0 < x, x <> 2}, x);

I wonder if anyone could explain why Maple might treat these two syntaxes differently.

> 

restart
> 

``
> 

h := proc (x) options operator, arrow; ln(x)/(x-2) end proc

proc (x) options operator, arrow; ln(x)/(x-2) end proc

 (1)
> 

domain_ln := solve(x > 0, x)

RealRange(Open(0), infinity)

 (2)
> 

denom_undefined := solve(x-2 = 0, x)

2

 (3)
> 

domain := solve(`and`(x > 0, x <> 2), x)

RealRange(Open(0), infinity)

 (4)
> 

solve({x > 0, x <> 2}, x)

{2 < x}, {0 < x, x < 2}

 (5)
> 

``
> 

plot(h(x), x = 0 .. 10, discont = true, color = blue)

 
> 

``


 

Download domain.mw

fsolve within loop returns unevaluated...

Asked by: smart2718 0
September 25 2024
1  5

I am new to Maple will appreciate any advice.

I am trying to write a procedure to solve a cubic equation using fsolve, print the root at each stage, and store results in a table for later use.  

I have restricted the range of fsolve, but I know from other sources that there is a solution within this range.

The instructions work if entered manually line by line, but not as a procedure.

The code is copied below.  Thanks for any suggestions.

Stephen Martin

Reg_IV := proc (beta, n) local alpha, b, c, d, k, `&alpha;L`, 

   `&alpha;R`, delta, eqn, x; `&alpha;L` := 3+beta-6*beta^(1/2);\

   `&alpha;R` := 1-beta; delta := (`&alpha;R`-`&alpha;L`)/n; 

   print(`&beta; = `, evalf(beta, 5), `n = `, evalf(n, 5)); 

   print(`&alpha;L = `, evalf(`&alpha;L`, 5), ` &alpha;R = `, 

   evalf(`&alpha;R`, 5), `&delta; = `, evalf(delta, 5)); 

   print(``); for k from 0 to n+1 do alpha := `&alpha;L`+k*delta\

  ; b := -5+alpha-3*beta; c := 8-4*alpha-6*beta+2*beta^2-2*alpha\

  *beta; d := -(4*beta+4)*(1-alpha-beta); eqn := proc (b, c, d, 

   x) options operator, arrow; {x^3+b*x^2+c*x+d} end proc; x[k] 

   := fsolve(eqn, 0 .. 2); print(evalf(x[k], 5)) end do; 

   print(``); print(evalf(x, 5)) end proc


Reg_IV(0.2, 4);
                    &beta; = , 0.2, n = , 4.

 &alpha;L = , 0.51672,  &alpha;R = , 0.8, &delta; = , 0.070820


                      fsolve(eqn, 0 .. 2)

                      fsolve(eqn, 0 .. 2)

                      fsolve(eqn, 0 .. 2)

                      fsolve(eqn, 0 .. 2)

                      fsolve(eqn, 0 .. 2)

                      fsolve(eqn, 0 .. 2)


   TABLE([0 = fsolve(eqn, 0 .. 2), 1 = fsolve(eqn, 0 .. 2), 

     2 = fsolve(eqn, 0 .. 2), 3 = fsolve(eqn, 0 .. 2), 

     4 = fsolve(eqn, 0 .. 2), 5 = fsolve(eqn, 0 .. 2)])


 

animation of circle with its radius as parameter ...

Asked by: P M Dearing 15
plotting animate incomplete-question
September 25 2024
2  2

Using the parametric representation of a circle in 2 dimensions:  c + r*cos(t)*v + r*sin(t)*u, t = 0..2*Pi,  where c is the center, r is the radius, v and u are orthogonal unit vectors, I want to animate the circle for r = r1..r2.

Example:

animate(plot, [c+r*cos(t)+r*sin(t),t=0..6.3],r=5..10);

I don't understand why this doesn't work!!  

Thank you

How to find the Divisors of n smaller than m?...

Asked by: jasser 95
divisors
September 25 2024
0  4

Hi

I am looking for a more efficient way to find all Divisors of n that are smaller than m as

Divisors(n) intersect {seq(i),i=1..m}

For example: For n=24 and m=7 it should result {1.2.3.4.6}.

Thanks for your help!

How do I get cyclic multiplication T_1*P_1*T_2*P_2...

Asked by: felixiao 15
September 25 2024
0  13

mm.mw    I want to obtain T_1*P_1*T_2*P_2*T_3*P_3. What should I do?

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