Is there a way with Maple 18 to place a bracket as shown below to contain two DE's? I am not trying to solve them. Only for note-taking purposes. If there is can you please share how to do it?

How to solve the equation
2^(sin(x)^4-cos(x)^2)-2^(cos(x)^4-sin(x)^2) = cos(2*x)
symbolically? The solve command produces a weird answer. Evalfing all its values, one sees
0.7853981634, -0.7853981634, 2.356194490, -2.356194490,

1.570796327 - 1.031718534 I, -1.570796327 + 1.031718534 I,

1.570796327 + 1.031718534 I, -1.570796327 - 1.031718534 I,

0.7853981634, -0.7853981634, 2.356194490, -2.356194490,

1.570796327 - 1.031718534 I, -1.570796327 + 1.031718534 I,

1.570796327 + 1.031718534 I, -1.570796327 - 1.031718534 I

The identify command
interprets the real solutions on -Pi..Pi as -3*Pi/4, -Pi/4, Pi/4, 3*Pi/4
(for example,
identify(2.356194490);

3*Pi/4 ).
Is it possible to obtain these with Maple in a simpler way?

PS. Mathematica 10 does the job.

PPS. So does even Mathematica 7.

Hello people in mapleprimes,

I have a question of labels of equations.

For example, suppose that there is a following description in a worksheet.

>2*x+y=5;

  2*x+y=5   (1)

>3*x+y=6;

  3*x+y=6   (2)

>solve({(1),(2)},{x,y});

 {x=1,y=3}          (3)

subs((3),100+x+100*y)

    400   

And, when I moved (2) to the next to (1) with dragging, and then, clicked !!! to execute it, then the worksheet 

changes as follows, which is wrong as accompanying ??

>2*x+y=5;3*x+y=6;

  2*x+y=5

 3*x+y=6   (1)

>solve({(1),??},{x,y})

{x = x, y = -3*x+6}          (2)

>subs({(1),??},100*x+100*y)

-200*x+600

Do you know some good way for ?? not to appear in the above sitiation.

I will appreciate when you tell me some measures about this.

Best wishes.

taro

Hi 

I'm having a problem with the statements inside a for-loop somehow being read in a different way than outside the loop. 

I've defined some functions earlier, and then I need to perform an integration using these functions, while I change one variable a little for each loop of the for-loop. 

The problem is that IN the for-loop, I get the same value from my integration for all loops. But when I execute the exsact same code OUTSIDE of the loop, I get the correct values, which are changing whenever i change the one variable. 

Here is the loop:

for i from 0 to 42 do

rotorshift := evalf[6](2*((1/180)* i *Pi*((1/2)*Ø[gap]))/N[m]-1/2*(tau[p]-tau[s]));

PMmmf_func := x-> proc (x) if type(x-rotorshift, nonnegative) then if type(trunc((x-rotorshift)/tau[p]), odd) = true then -H[c]*l[m] else H[c]*l[m] end if else if type(trunc((x-rotorshift)/tau[p]), odd) = true then H[c]*l[m] else -H[c]*l[m] end if end if end proc

B[g] := proc (x) -> 1000*mu[0]*(PMmmf_func(x)+MMF_func(x))/d[eff, stator](x) end proc;

Flux(i+1) := (int(B[g](x), 0 .. tau[s])+int(B[g](x), 3*tau[s] .. 4*tau[s])+int(B[g](x), 6*tau[s] .. 7*tau[s])+int(B[g](x), 9*tau[s] .. 10*tau[s]))*10^(-3)*L[ro];

end do;

And for all the values in the "Flux" vector, I get the same value. But when I remove the loop, and change the value of i manually, I get the correct (changing) values of flux!! 

Any ideas why this may be? This is really dricing me nuts. I've spent the beter part of the day on this, and I just can't seem to find a workaround, much less a reason for this behaviour.

many thanks!

I have generated an 8x8 Jacobian, containing a few variables and several zeros as elements. I would like to translate this to LaTeX code. How can I first simplify what I have, to make it tractable?

Here is the Maple code:

eq_1 := Lambda-mu*S-(beta*(H+C+C1+C2)*S+tau*(T+C)*S)/(S+T+H+C+C1+C2+C1M+C2M);
eq_2 := (-beta*(H+C+C1+C2)*T+tau*(T+C)*S)/(S+T+H+C+C1+C2+C1M+C2M)-(mu+mu[T])*T;
eq_3 := (beta*(H+C+C1+C2)*S-tau*(T+C)*H)/(S+T+H+C+C1+C2+C1M+C2M)-(mu+mu[A])*H;
eq_4 := (beta*(H+C+C1+C2)*T+tau*(T+C)*H)/(S+T+H+C+C1+C2+C1M+C2M)-(mu+mu[T]+mu[A]+lambda[T])*C;
eq_5 := lambda[T]*C-(mu+mu[A]+rho[1]+eta[1])*C1;
eq_6 := rho[1]*C1-(mu+mu[A]+rho[2]+eta[2])*C2;
eq_7 := eta[1]*C1-(mu+rho[1]+gamma)*C1M;
eq_8 := eta[2]*C2+rho[1]*C1M-(mu+rho[2]+gamma*rho[1]/(rho[1]+rho[2]))*C2M;
J := VectorCalculus:-Jacobian([eq_1, eq_2, eq_3, eq_4, eq_5, eq_6, eq_7, eq_8], [S, T, H, C, C1, C2, C1M, C2M]);

JQDFE := eval(J, [S = Lambda/(beta-mu[A]), T = 0, H = Lambda*(beta/(mu+mu[A])-1)/(beta-mu[A]), C = 0, C1 = 0, C2 = 0, C1M = 0, C2M = 0]);

Thanks.

Hi,

I am trying to interpolate a set of arbitrary numbers including real ones like Pi and plot them using ArrayInterpolate. This does not work. Is there a simple way around this?

Thank you.

Hi,

I use the VectorCalculus package to calcutate derivative formula for geometric functions, and met difficulity simplifying the result expression.

For example, I define some vectors P, S, V like below:

P:=<Px, Py, Pz>, S:=<Sx, Sy, Sz>, V:=<Vx, Vy, Vz>

then define an intermediate variable Q:=P - S,

then define a function d:= sqrt(DotProduct(Q, Q)-(DotProuct(Q,V))^2)

by calculating the function's derivative w.r.t Px I got a very complex result expression:

dpx:=1/2 * (2Px - 2Sx - 2 ( (Px - Sx) Vx + (Py - Sy) Vy + (Pz - Sz)Vz )Vx ) / (sqrt( (Px-Sx)^2 + (Py-Sy)^2 + (Pz-Sz)^2 - .....)

Apparently this expression can be simplified by substituting its sub-expression with pre-defined variables like Q and d.

I know I can use subs, eval, and subsalg to do it manually:

subs(1/(sqrt( (Px-Sx)^2 + (Py-Sy)^2 + (Pz-Sz)^2 - .....) = 1/dv, dfdpx)

subs((Px - Sx) Vx + (Py - Sy) Vy + (Pz - Sz)Vz = dotproduct_q_v, dfdpx)

and I can get a simplified expression like this:

(qx-dotproduct_q_v*vx)/d

But it's like my brain does the simplification first, and Maple only does the text substitution for me.

Is there any way to do it automatically?

Thanks,

-Kai

Hi i 2 questions. all pertaining to solving a systems of equations mod 2

First if i have a large set of equations, 11^3 equations in 11 unknowns and i want maple to give me ALL solutions mod 2 how can i do that? Maples msolve is loosing solutions.

Second suppose i want all unique solutions that say 6 of the variables can have but dont care what the solution to the other variables are as long as it is a solution. 

mini example:

say x=1,y=1,z=1 is a solution as well as x=1,y=1,z=0, i just want to know about x=1,y=1.

I have produded a 3D plot where I have used the graphic's lighting->user GUI to set the light color, direction, and ambient lighting to my liking.

I would like to save the lighting parameters so that I can reproduce the identical lighting in other plots.  I see no way of reading off the lighting parameters from the GUI.  I tried to "lprint(myplot)" to see if it contains that information but apparently it doesn't.

So my question is: Is there a way to retrieve the lighting parameters from a 3D plot?

--

Rouben Rostamian

I experienced strange operation of "union" for sets of vectors.

Mt1:=Matrix(2, 4, [[ 0,1, 0, 0], [ 0,  0,  1, 1]]); Ms := Vector[column](4, [8,4,2,1]); St1 := {}:

St1:= `union`(St1, {Mt1 . Ms});

I am surprised, because each execution of union adds new and the same vector <4 | 3> to set St1:

But after copying any set in the clipboard and pasting the set St1 has only one instance of vector <4 | 3>:

What does it mean?

How to solve the system
{sqrt((x-1)^2+(y-5)^2)+(1/2)*abs(x+y) = 3*sqrt(2), sqrt(abs(x+2)) = 2-y}
over the reals symbolically? Of course, with Maple. Mathematica does the job.

I want to solve maximize of equation,but the maximize failed to solve it,who can help me.thanks.

Download maximize.mw

Does anyone know how to incorporate the tetrad with the directional derivative? I tried using the SumOverIndices, but get crazy results. I know Maple can find the answer easily because I have done the same thing by hand. What am I missing?

The directional derivative should take the form f,₁ = e_a^μ df/dx^μ . The answer is Y,₁ = dY/dζ – Ybar dY/du.  I obviously do not get this result.

Download Directional_Derivative.mw

Dear All,

I'm trying to solve the following in Maple.

minimize(int(0.1e-3+.5*t+0.2e-2*t^2-b*t-a, t = 0 .. 300), location = true)

But Maple told me that the answer is

Float(-infinity), {[{a = Float(infinity), b = Float(infinity)}, Float(-infinity)]}.

I really need to get a kind of numerical answer. Would it be possible? Please Help me!!