0^0 gives error ,0^0 is undefined, why  maple gives this result?

The uploaded worksheet animates a cam formed of two Archimedean spirals as the cam rotates, creating vertical motion in a circular cam follower.

DirectSearch is used to locate the centre of the follower, however I experience two problems with this use.

First: DirectSearch places the follower centre sometimes above and sometimes below the cam surface, seemingly at random.

Second: seemingly at random, DirectSearch produces completely wrong values for the follower centre unless its SolveEquations command is executed with the initialpoint values stated in the worksheet. I arrived at these by extensive trial and error.

Why does the first problem occur and is there a way to code SolveEquations to avoid it?

Is there a writeup anywhere which can guide me to correct initialpoint values for a particular SolveEquations attempt?

Archimedian_spiral_cam_follower.mw

Hi Mapleprimes,

I have tried to search solutions online without luck. My problem is this. Suppose I have three equations:

f(x,y,z)

g(x,y,z)

h(x,y,z)

I would solve using solve({f,g,h},{x,y,z}) which would give me solutions x*, y* and z*. I need to assign the solutions to use them in subsequent computations. I would like to impose non-negativity constraints, however. Hence, the solution of x is max(x*,0). Obviously if a non-negativity constraint binds, this affects the solutions of y* and z*. I would like to assign the solutions taking this into account. How would you propose I do this? Bear in mind that the solution of x* might be a-b where the relative magnitudes of paramenters a and b are not given. Further down in my code, I would like to assign values to parameters and then let Maple give me the solutions with the non-negativity constraints. I hope I am making sense.

Thanks very much in advance.

Best,

Christian

Say I have an expression

ex:=sqrt(x)/2h

what do I tell maple to pull the 2h into the sqrt

sqrt(x/4h^2)

Hello everybody,

I'm a newbie in Maple, but as far as I read so far this does not seem to be a trivial question.

I have a very large symbolic expression in Maple, where several terms in the form

appear, with  i = 1, ... , 5 and j = 1, ..., 5. This means that there will appear , , , ..., . For each possible combination (i,j) of powers, I would like to have a separate variable whose name depends on those powers, e.g., m_ij. 
 

Is there a way to do that in a single-line definition, without explicitly define 25 different variables?

If this is not possible, assuming I define all 25 variables I need in advance, would it be possible  substitute them in my large expression, wherever they occur? E.g., assuming to have the following expressions

I would like to get the following

Thank you in advance for your replies!

Hellow sir how to plot stream lines for different values of alpha =6,7,8,9.

 I am attaching the sample graph and codes.
How to get the output like that only.

Thanks in advaned

eq1:= alpha*diff(f(eta),eta$3)+f(eta)*diff(f(eta),eta$2)-diff(f(eta),eta)^2+1:
eq2:= diff(h(eta),eta$2)+f(eta)*alpha*diff(h(eta),eta)-diff(f(eta),eta)*h(eta):
eq3:= diff(H(eta),eta) = h(eta):
bc:= f(0)=0, D(f)(0)=0, D(f)(6)=1, h(0)=0, D(h)(6)=1, H(0)=0:
A1:= dsolve(
     {eq||(1..3), bc}, 
     numeric, method= bvp[midrich], abserr = 1e-10, output= operator
):

psi:= unapply(eval(x*f(eta)+H(eta), A1), (x,eta)):
plots:-contourplot((psi(x,eta), x= 0..6, eta= 0..6),alpha=6);

I've asked Maple to solve an equation, and the result is difficult to read because it is separating single variables into multiple multiplicative instances of that variable raised to different powers. Is there a way to tell Maple to combine all instances of a variable into one instance raised to the appropriate power?

I've already tried simplify.

For example:

pceq := (2/3)*Pi*G*rho^2*R^2:
pnonreleq := (1/5)*(3*Pi^2)^(2/3)*hbar^2*n^(5/3)/m:
rhocomposition := rho = m/((4/3)*Pi*R^3), n = Z*rho/(A*m_p):
obj := subs(rhocomposition, rhocomposition, pceq = pnonreleq):
req := R = simplify(solve(obj, R)[1]);

The above code produces 

In the first place, I can't see why Maple would show what should be (Z/A)^(5/3) as z^3 / (A * [A*Z^2]^(2/3)), but I'd like to somehow tell it to not break up the variables like this.

Is this possible? Thanks for the help.

Based on information I learned here last week, I tried the following.  Summary: I enter three functions f,g,h. f Is a function of x and t, g is a function of y and t, h of z and t.  I want to plot a 3D curve. I know an intial value.  The curve looks good but quite very early saying "cannot evaluate the solution further right of 3.4774922, probably a singularity."  HELP!

f := 4.61376*x+1.320192000*cos(t)^2*x-.320192000*sin(t)*cos(t)^2*x+4.304656800*cos(t)^2*x^2+17.21862720*cos(t)*x^2+12.9477168*sin(t)^2*x^2-25.8954336*sin(t)*x^2+7.147008*sin(t)^3*x-21.441024*sin(t)^2*x+9.68025600*sin(t)*x+3.181248*sin(t)*x^3-1.3251456*sin(t)*cos(t)^2+2.6502912*sin(t)^2*cos(t)+0.6625728*sin(t)^2*cos(t)^2+5.2807680*cos(t)*x-5.3005824*sin(t)*cos(t)+0.9443529*x^4-3.181248*x^3+147.0230064*cos(t)^2+67.10736960*sin(t)^2+23.693094*x^2+6.8757264*cos(t)^4-61.58338560*sin(t)^3-11.047968*sin(t)+15.3958464*sin(t)^4+148.045536*cos(t)+55.0058112*cos(t)^3-5.2807680*sin(t)*cos(t)*x+38.16801;

g := 0.9443529*y^4-42.29607960*y^2-3.437942400*y^3-1.3314096*sin(t)^2*y^2+2.662819200*sin(t)*y^2-17.5101696*sin(t)^3*y+52.530508800*sin(t)^2*y+25.45344*cos(t)^2*y+3.437942400*sin(t)*y^3-11.85948*cos(t)^2*y^2-47.43792*cos(t)*y^2-138.4682688*sin(t)*y+101.81376*cos(t)*y-101.81376*sin(t)*cos(t)*y-25.45344*sin(t)*cos(t)^2*y+632.4697764-91.635840*sin(t)*cos(t)^2+183.27168*sin(t)^2*cos(t)+45.8179200*sin(t)^2*cos(t)^2-366.5433600*sin(t)*cos(t)+942.16392*cos(t)^2+247.7287584*sin(t)^2+39.20400*cos(t)^4-61.5833856*sin(t)^3-372.2907456*sin(t)+15.3958464*sin(t)^4+1259.59968*cos(t)+313.63200*cos(t)^3+103.4479296*y; 
h := z-2*sin(t)+2;
eqs := {f, g, h};
eqs2 := subs(x = x(t), y = y(t), z = z(t), eqs);
x0 := -0.896661124832438;
y0 := -1.7877356703982348;
z0 := -2;
ics := {x(Pi) = x0, y(Pi) = y0, z(Pi) = z0};
odes := diff~(eqs2, t);
res := dsolve(odes union ics), numeric);
plots:-odeplot(res, [x(t), y(t), z(t)], Pi .. 2*Pi); p1 := %;

A good graph is produced of maybe 10% of the answer.  Then:

Warning, cannot evaluate the solution further right of 3.4774922, probably a singularity

Dear Sirs, 

I am trying to construct for my students the situation in Maple how to calculate the maximum area of a right triangular garden, if the perimeter is 60 meters long, and the two known sides are x, y and the third side is z and is part of the garden which isn't covert by the perimenter fence. 

perimenter P = 60 -> x+y = 60 

Next using the Pythagoran theorem and solve. 

solve(x^2+z^2=y^2) and maple gives the solution z = sqrt(-x^2+y^2)

The area of the right triangle is T = 1/2*x*z 

where y can be found solve(x+y=60,y) - > y = 60-x

I insert this into the formula for my area formula. 

T(x) = 1/2*x*(sqrt(-x^2+(60-x)^2)

I solve(T'(x)=0) and get x = 20. 

However if I wanna show the that they can insert x = 20 into T(x), then the following happens. 
T(20) = 1/2*20*(sqrt(-x^2+(60-x)^2)

meaning Maple only inserts 20 the first x and not the second or third x. Any idea why this happens?  Does Maple think that the second and third x are functions? 

Best Regards

Fred 

I have a numerical solution for an ODE. (You can find the attached code: numerical_solution.mw)

What are the simple methods in order to create a table as follows in Latex by using these datas which we derived in Maple?

Hi, i will post the executed code so you can see what i am saying, essentially i want to know what i am doing wrong here to have simplify not work as a command line function but  it does when i right click the output and select it and the equation label of that output is inserted as the oprand.

I feel like maple is not wanting to be entirely forthcoming with me today or something, but in a more deeper contemplation, i see that refering to the maple interface as if it is a sentient entity is a true indication that i need a social life.

But as you will see, the same failure occurs for the ListTools partial sums feature when implemented in commandline code, but works perfectly well when it is selected by right clicking on the output intended 

Download MAPLE_PLEASE_HELP_aGAIN.mw

Download MAPLE_PLEASE_HELP_aGAIN.mw

I can not integrate the following integral using maple 2016. Please guide me how to do it. I am a new user.

int(12.*x^3*c[2]+6.*x^2*c[1]+x^2*exp(x^3*c[2])*exp(x^2*c[1]), x = 0. .. 1.)

Letter_V_kaput.mwsLetter_V_working.mws

The two attached programs are such that the "kaput" version uses a procedure to draw the letter V, with the option of a flat top or pointed top.  The last parameter, s, takes on values "p" or "f" for pointed or flat respectively. - but I get error messages.  The Letter_V_working programdoes not use a proc, but works.  Where is the error?

  Thanks in advance for any help.

   .  .

Hi, I'm new to Maple and I'm trying to create a phaseportrait for the equation:

dy/dx = x²-y² 

when x = -3..3 and y = -3..3

If anyone can help me that would be great.

Thanks.

Above in the figure, the trapezoid method. How to fix the error?

And how to solve this interval using the method of rectangles?