Maple Questions and Posts

These are Posts and Questions associated with the product, Maple

I am trying to solve this type of problem:

I thought I could double check my answers by creating a RandomVariable and calculating the probablity using the Probability function.

But from the RandomVariables documentation,  it seems only univariate random variables are supported.

Is there really no way to define a RandomVariable given a joint distribution?

so i have a little school laptop and maple on it works just fine. Then i have my all powerful gaming desktop with an AM RTX 3700x ,RTX 2070S, SSD and 32GB ram.

I have never seen maple run so slow on any pc as i have on my desktop. It is completely impossible to use maple. Just writing normal input like 123 takes forever. One thing i have noticed is evertime i do some sort of action, then the icons to the left slowly go from being colored to grey and back to colored before i can do a new action.

The two images below show an example here you can see it is about to go from being colored to being grey, when i try to mark stuff. I have tried to install the x64 and x86 version, i have tried giving it 4096 ram in the ini file and i have tried removing splash. Nothing works....

 

This is the last step of my calculation. I get  following system of equations:

s:={a__11 = -b__1^2 + 5/4, a__12 = -b__1*b__2 + 7/4, a__13 = -b__1*b__3 - 1/2, a__14 = -b__1*b__4 - 1/2, a__15 = -b__1*b__5 - 1/2, a__16 = -b__1*b__6 - 1/2, a__17 = -b__1*b__7 - 1/2, a__22 = -b__2^2 + 5/4, a__23 = -b__2*b__3 - 1/2, a__24 = -b__2*b__4 - 1/2, a__25 = -b__2*b__5 - 1/2, a__26 = -b__2*b__6 - 1/2, a__27 = -b__2*b__7 - 1/2, a__33 = -b__3^2 - 1, a__34 = -b__3*b__4 + 1, a__35 = -b__3*b__5, a__36 = -b__3*b__6, a__37 = -b__3*b__7 + 1, a__44 = -b__4^2 - 1, a__45 = -b__4*b__5 + 1, a__46 = -b__4*b__6, a__47 = -b__4*b__7, a__55 = -b__5^2 - 1, a__56 = -b__5*b__6 + 1, a__57 = -b__5*b__7, a__66 = -b__6^2 - 1, a__67 = -b__6*b__7 + 1, a__77 = -b__7^2 - 1, b__1 = b__1, b__2 = b__2, b__3 = b__3, b__4 = b__4, b__5 = b__5, b__6 = b__6, b__7 = b__7}

 

I want to solve this system of equations

solve(s,{a__11, a__12, a__13, a__14, a__15, a__16, a__17, a__22, a__23, a__24, a__25, a__26, a__27, a__33, a__34, a__35, a__36, a__37, a__44, a__45, a__46, a__47, a__55, a__56, a__57, a__66, a__67, a__77, b__1, b__2, b__3, b__4, b__5, b__6, b__7})

 

But I  didn't get any more valuable information 

Actually I'd like to  know if there is no  real solution.

If there is a real number solution,   one is enough for me.

Any help would be greatly appreciated

 

contour.mw

I'm having trouble executing the following contour plot.

I'm attaching my file. Kindly Help!

Hello there, 

Would you allow me to ask this question?

What would be a way to simplify the expression 'eq9_32a' below to the 'Desired' expression?

Intuitively, the numerator and denominator can be divided by 'sqrt(r^2 + 1)', but the 'Simplify' instruction did not do that. 
 

restart;

eq9_30 := T__e_n = 2*(s/s_hat) / ((1+r*s/s_hat)^2+(s/s_hat)^2);

T__e_n = 2*s/(s_hat*((1+r*s/s_hat)^2+s^2/s_hat^2))

(1)

eq9_31 := solve(diff(rhs(eq9_30), s)=0,s);

s_hat/(r^2+1)^(1/2), -s_hat/(r^2+1)^(1/2)

(2)

eq9_32a :=  T__e_np = simplify(subs(s=eq9_31[1] , rhs(eq9_30))) assuming r::real;

T__e_np = (r^2+1)^(1/2)/(r^2+(r^2+1)^(1/2)*r+1)

(3)

Desired := T__e_np = 1/(sqrt(r^2 + 1) + r);

T__e_np = 1/((r^2+1)^(1/2)+r)

(4)

 


Merry Christmas!

Download Q20201208.mw

Dear All,

We consider the polynomial 

P(x)=(x+1)(x+2)...(x+n)

Question The Coefficient of x2 in Pn.

Hi, 

A few times ago a trainee asked me this question
         "given a matrix formula, can Maple find the transpose of this formula?"

More precisely, let's say E, A, B and C are four (abstract) matrices (let's say symbols) with consistent dimensions such that E = A+B*C, can Maple "find" that ET = AT + CT * BT (where  ET represents the transpose of E)?

I come back to this problem regularly because the trainee was quite frustrated by my negative answer (note she had the same request form the inverse of a matrix formula).

The best I'm capable to do is given in the attached file (transposition only).
This seems to work correctly even if did not do intensive testing.

Do you have any ideas on how to implement the transposition and inversion computation rules in Maple?
For example, given 

E := A &* B^(-1))

Maple would return 

Transpose(E);
      (B^(-1))^T &* A^T 
# or better   E^(T) = (B^T)^(-1) &* A^T
# and 
Inverse(E);
   B &* A^(-1)


Thanks in advance for you involvement
 

restart:

Transpose := proc(e)
  local tr, t:

  tr := `#mo("т")`:

  define(
    t,
    t(`&*`(a::anything, b::anything)) = &*(b^tr, a^tr),
    t(a::anything+b::anything)=a^tr+b^tr,
    t(a^tr)=a,
    'linear', 'flat'
  ):
 
  t(expand(e));

  return eval(%, map(u -> (u^tr)^tr = u, indets(e, name)));
end proc

proc (e) local tr, t; tr := `#mo("т")`; define(t, t(`&*`(a::anything, b::anything)) = `&*`(b^tr, a^tr), t(a::anything+b::anything) = a^tr+b^tr, t(a^tr) = a, 'linear', 'flat'); t(expand(e)); return eval(%, map(proc (u) options operator, arrow; (u^tr)^tr = u end proc, indets(e, name))) end proc

(1)

Transpose(A+B)

B^`#mo("т")`+A^`#mo("т")`

(2)

Transpose(2*A + B &* C)

2*A^`#mo("т")`+`&*`(C^`#mo("т")`, B^`#mo("т")`)

(3)

Transpose((A + B) &* (A + B))

`&*`(A^`#mo("т")`, A^`#mo("т")`)+`&*`(B^`#mo("т")`, A^`#mo("т")`)+`&*`(A^`#mo("т")`, B^`#mo("т")`)+`&*`(B^`#mo("т")`, B^`#mo("т")`)

(4)

Transpose((A + B) &* Transpose(A + B) + Transpose(Transpose(A)) )

`&*`(B, A^`#mo("т")`)+`&*`(A, A^`#mo("т")`)+`&*`(B, B^`#mo("т")`)+`&*`(A, B^`#mo("т")`)+A^`#mo("т")`

(5)

 


 

Download transposition.mw

Hi and Welcome Everyone here.

It is my first post and I am happy to have Maple 2020 Personal Edition. It is great tool and I am still learning.

Durng first weeks I solved many things with help and forums but I can't solve this simple one below:

How to force maple to divide a sqrtof (4*n^2 + 5*n - 7) by n to have each expression divided separately and all still inside of sqrt?

sqrt(4*n^2 + 5*n - 7)/n to get:sqrt(4 + 5/n - 7/n^2) by collect or expand function or anything else. I was able to do it by rewriting combine(((4*n^2 + 5*n - 7)/n^2)^0.5, radical) in such form but it is not what I want to have since I need to rewriting it manually.

Can any "wizard of maple" help me to find an answer? Or at least give a hint in what direction to go, I will dig later myself.

Regards

Marcin

 

At the moment t=0, we place a body at 100 ° C in a room at 25°C; we designate by q(t) the temperature at the moment t. The differential equation is.q'(t)+k*(q(t)-25)=t, with k cooling coefficient equal to 2.
Determine the solution that checks the initial condition.
What is the body temperature after 30 minutes.
After how long the temperature drops to 50°C. Thank you for the help.

Hi, 

Using InertfForm, I found this strange result: 

e := (A+B)*(A+C);

ife  := InertForm:-Parse(convert(e, string));
InertForm:-Display(ife);

(A+B)*(A+C)

 

`%*`(`%+`(A, B), `%+`(A, C))

 

`%*`(`%+`(A, B), `%+`(A, C))

(1)

 

Download Precedence.mw

Why doesn't Display(..) return (A+B)*(A+C) ?

 

Can anyone assist with Heat Map plotting questions?

 

I am interested in specifically formating axis.  i.e., can an axis be labels such as RPM range text =  "0-100, 101-200, 201-300", etc.  for each bin and rotated vertical to fit.   I tried most of the plot options with no success including labeldirections=[x, y].

Also, can I invert the data so the 1,1 bin is lower left corner vs upper left? tried to reverse the indices and errored with "inverted index" without resolution.

 

Lastly, I noted that I couldn't stack a frame Text plot of same size by assigning a plot to a variable and using display to overlay them.   The heat map is always on top and transparency option doesn't let the text come through.   

 

Plt1 := HeatMap(Array3[2 .. 101, 2 .. 31], color = C_List, size = [750, 450], transparency = 0.5)

 

Thanks in advance,

Bill

 

 

 

I'm trying to solve the problem which is published in the research article. The paper is attached. 

This work done with the help of shooting technique in maple 18

1.Is it possible to solve in maple 17

2. How to obtain the triple soln

3. How to implement Shooting technique

Please anyone help me to get this 

 

restart:

with(plots):

eq1 := (1+K)*(diff(f(eta), `$`(eta, 3)))+f(eta)*(diff(f(eta), `$`(eta, 2)))+K*(diff(g(eta), eta))-2*(diff(f(eta), eta))^2-M*(diff(f(eta), eta)) = 0;

(1+K)*(diff(diff(diff(f(eta), eta), eta), eta))+f(eta)*(diff(diff(f(eta), eta), eta))+K*(diff(g(eta), eta))-2*(diff(f(eta), eta))^2-M*(diff(f(eta), eta)) = 0

(1)

eq2 := (1+(1/2)*K)*(diff(g(eta), `$`(eta, 2)))+f(eta)*(diff(g(eta), eta))-3*g(eta)*(diff(f(eta), eta))-2*K*g(eta)-K*(diff(f(eta), `$`(eta, 2))) = 0;

(1+(1/2)*K)*(diff(diff(g(eta), eta), eta))+f(eta)*(diff(g(eta), eta))-3*g(eta)*(diff(f(eta), eta))-2*K*g(eta)-K*(diff(diff(f(eta), eta), eta)) = 0

(2)

eq3 := (1+(4/3)*Rd)*(diff(theta(eta), `$`(eta, 2)))/Pr+f(eta)*(diff(theta(eta), eta))+Nb*(diff(chi(eta), eta))*(diff(theta(eta), eta))+Nt*(diff(theta(eta), eta))^2 = 0;

(1+(4/3)*Rd)*(diff(diff(theta(eta), eta), eta))/Pr+f(eta)*(diff(theta(eta), eta))+Nb*(diff(chi(eta), eta))*(diff(theta(eta), eta))+Nt*(diff(theta(eta), eta))^2 = 0

(3)

eq4 := diff(chi(eta), `$`(eta, 2))+Sc*f(eta)*(diff(chi(eta), eta))+Nt*(diff(theta(eta), `$`(eta, 2)))/Nb = 0;

diff(diff(chi(eta), eta), eta)+Sc*f(eta)*(diff(chi(eta), eta))+Nt*(diff(diff(theta(eta), eta), eta))/Nb = 0

(4)

bcs := f(0) = S, (D(f))(0) = -1, g(0) = -m*((D^2)(f))(0), (D(theta))(0) = -A*(1-theta(0)), chi(0) = 1+delta*(D(chi))(0), (D(f))(10) = 0, g(10) = 0, theta(10) = 0, chi(10) = 0;

f(0) = S, (D(f))(0) = -1, g(0) = -m*(D(f))(0)^2, (D(theta))(0) = -A*(1-theta(0)), chi(0) = 1+delta*(D(chi))(0), (D(f))(10) = 0, g(10) = 0, theta(10) = 0, chi(10) = 0

(5)

params := [K = .1, S = 2.1257, m = .5, Pr = 2, Nb = .3, Nt = .5, Sc = 2, Rd = .5, delta = .1, A = 5];

[K = .1, S = 2.1257, m = .5, Pr = 2, Nb = .3, Nt = .5, Sc = 2, Rd = .5, delta = .1, A = 5]

(6)

sol := dsolve(eval([eq1, eq2, eq3, eq4, bcs], params), numeric, output = listprocedure, maxmesh = 5000)

Error, (in dsolve/numeric/bvp/convertsys) too few boundary conditions: expected 10, got 9

 

``


 

Download Triple.mw

Dear Community,

I try to solve a simple flow problem between two fluid tanks. They are connected with a pipe and a pump. Simulation runs from 0s to 3000s. Fluid levels are H1(t), H2(t), and flow rate between the tanks is Q1(t). I operate the pump between 500s and 2000s, with a constant head, and after that I would like to shut down the system from 2000s to 2500s (i.e. for 500s Q1(t) should be 0, and consequently H1, H2 remain constant) and then reopen it again, so tanks can equilibrate. I've attached the worksheet (FlowProblem.mw).

I tried to achieve this in the event section of dsolve (indicated in red), but it seemingly did not work out. So my question is: how to correctly specify it in dsolve, so flow (Q1) remains 0. between 2000s and 2500s, and can flow again afterwards? Am I right to do it in dsolve, or is there any other way to do it?

Your kind help is appreciated in advance,

best regards

Andras

FlowProblem.mw

How do I retrieve data table from Numbers (apple) Worksheet to use in Maple Document (for fit analysis)? Information for Excel exists (not useful) pathway for me), but I could  not locate corresponding information for Numbers

I want to find fundamental matrix of the system: X(t).

Actually I need A=X(T) where T is 2*Pi.

So then I can find whether the solution is stable.

The problem is, I don't understand how to find X(t) in Maple. 

Tried to solve numerically with dsolve at t=T but the next step is not obvious.

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