maxcharheight.mw

The above worksheet contains some computations I needed for a paper I am writing for the next issue of Maple Transactions.  The computations are within reach of hand computation (which is why I know the right answers).  I wanted Maple to be able to do them, however.

I couldn't make Maple do anything but verify that I was right (this is useful, I will admit).  But can anyone find any artful ways to simplify or solve any of those steps?  I suspect that this is quite hard in general, but with these things involving phi = (1+sqrt(5))/2 it's likely that others would find some "art" useful.  By the way, phi is not built-in to Maple, as far as I know.  Any more votes for including it?

There is an undocumented feature reported here that is useful: asympt works with "leadterm" and this turns out to be necessary.  I forget how I found out that leadterm works with asympt.  It's not in ?asympt, though I think that it should be.

-r

This worksheet creates geodesics in the Poincare disk by transformation of a series of circles of diminishing radii in the complex plane.

The intersections of the geodesics are meant to create the first few pentagonal uniform tilings in the Poincare disk.

I do not know the mathematically correct way to create such a display, so the radii of the circles are only a trial and error approximation.

What Maple code will provide the radii of the complex circles which produce an accurate uniform pentagonal tiling?

Is there a better overall strategy for producing uniform tilings of the Poincare disk? 

HyperbolicTiling.mw

Hi

I have been trying to create a hyperlink to a bookmark in a maple document. I left the Target field blank, and entered the 

book mark in the book mark field. But I keep getting the error: " target cannot be blanK" Can anyone help ?

Rivan

For this assignment ... I have to basically find the right 'road' and 'wheel' and then animate my findings. 

Problem is I am having a hard time understanding my professor's derivations of equations to find these roads and wheels. 

Here is the PDF for the assignment : square_wheel.pdf

All help is appreciated.

Thanks. 

When I use Solve for a PDE with the option singsol=all, is Maple guaranteeing that I am getting all the solutions, and in partidcular , is it returning the *general* solution(s)? 

I have the following equations which I want to plot the curves of them by maple's:

1. |x+2|+|y|=3

2. |y|-|x|=2.

How to implement this task in maple?

thanks!

Hi

How to insert captions fig.1,fig.2,fig.3,fig.4 in the Tabulate command ( variable G) without taking into account the random order of the graphs

Thanks

TEST_-_Copie.mw

Dear all
Dear all, is  there any Maple code available to solve the heat  two dimensional heat equations using Rk4. The second derivative will be replaced using Finite difference, so that we get a linear system of odes.  
Thank you for any help 

Hello,

I realize that I can use solve to isolate a specific expression. However, often I have a complicated equation and I want to move 2 or more variables to one side, not knowing a-priori what the expression is going to look like. Is there a way to do this? It almost seems like I have to do work by hand to figure out what expression to pass to solve in this case.

It could be that I'm following the wrong workflow, but I often want to do this, move variables to one side as best as I can, and then look at what expression I endup with to make other decisions about how to solve the problem(computationally, etc).

Thanks.

One of our users asks how they can find the Re ( sqrt(a+I*b)) where a, b are real.

They had tried entering the latter as "assume", without any luck. 

We told them that it may not be very intuitive, but such expressions can be evaluated by wrapping into evalc which implicitly assumes that free parameters are real-valued:

evalc(Re(sqrt(a+I*b)));

Hello. I don't have much experience using Maple. Sorry if this question is really specific. I am trying to solve a system of six equations, with six variables. This is what i type into maple:

solve({0 = a_2*cos(7.5*b_2) + a_2, 250 = Pi*int((a_2*cos(b_2*x) + a_2)^2, x = 0 .. 7.5), 750 = Pi*int((a_1*x^2 + b_1*x + sqrt(d_1*x) + 7.5)^2 - (a_2*cos(b_2*x) + a_2)^2, x = 0 .. x_2), 2.5 = a_1*20^2 + 20*b_1 + sqrt(20*d_1) + 7.5, 2*a_1*x_2 + b_1 + sqrt(d_1)/(2*sqrt(x_2)) = 0, (2*a_1)*20 + b_1 + sqrt(d_1)/(2*sqrt(20)) = 0, x_2 <> 20}, {a_1, a_2, b_1, b_2, d_1, x_2})

When i try to solve i get the output "Warning, solutions may have been lost." When i try to remove the equeation that says that x_2 can't be equal to 20, i get some answers, but i want to know if there are any where x_2 is not 20. (I know that it also can be one other number, because of the type of function). Does the output i get mean that there simply aren't any answers where thos conditions are true, or that there might be some, that Maple can't figure out? If so, what could i do to figure it out? 

Thank you!

I am trying to get Maple 2021 to printout the intervals on which a differentiable function increases/decrease in a Maple document as part of a procedure. 

The function: 

A := x^2 + 400/x

the attempt. 

solve(evalf(diff(A, x) < 0))

which gives the result: RealRange(-infinity, Open(0.)), RealRange(Open(0.), Open(5.848035476))
There is no extreme point at x = 0 for A? So how do I get Maple to do an output which makes sense?  

I've been trying to implement numeric integration by using different methods of Int, for example _d01ajc, but when I use it, the following error comes up:

W := -16*(x - 1/2)*x*(t + 2*w)*(ln((m^2 + w*x*(-1 + x))/m^2)*ln(-1/(w*(t + w)*x^2 - w*(t + w)*x + m^2*t)) + ln(-x*w^2*(-1 + x))*ln((x^2 - x)*w + m^2) + ln(1/m^2)*ln((t + w)*(-1 + x)) + ln(-1/(x*w))*ln(m^2) + dilog(x*w^2*(-1 + x)/(w*(t + w)*x^2 - w*(t + w)*x + m^2*t)) - dilog(x*w*(-1 + x)*(t + w)/(w*(t + w)*x^2 - w*(t + w)*x + m^2*t)))/t^3 + 8*(x - 1/2)*((t + w)*x - t/2)*(-t*(w*x^2 + m^2 - w*x)*(t + w)*ln((x^2 - x)*w + m^2) + w*(x*w*(-1 + x)*(t + w)*ln((t + w)/w) + m^2*t*ln(m^2)))*(2*w*x + t)/(w*(t + w)*(w*(t + w)*x^2 - w*(t + w)*x + m^2*t)*t^3*x) + (16*x^2 - 8*x)/(t*w*(-1 + x)) + (2*t*x + 2*w*x - t - 2*w)*(2*w*x + t - 2*w)*(1 - 2*x)*ln((t*x + (-1 + x)*w)/((-1 + x)*w))/(((-1 + x)^2*w^2 + w*t*x*(-1 + x) + m^2*t)*t^2) + (-1 + 2*x)*(2*m^2 + w*x - w)*(2*w*x^2 + 2*m^2 - 3*w*x + w)*ln(m^2/(m^2 + w*x*(-1 + x)))/(w^2*(-1 + x)^2*((-1 + x)^2*w^2 + w*t*x*(-1 + x) + m^2*t)) + (-1 + 2*x)*(2*m^2 + w*x - w)*(2*w*x^2 + 2*m^2 - 3*w*x + w)*ln(m^2/(m^2 + w*x*(-1 + x)))/(w^2*(-1 + x)^2*(w*(t + w)*x^2 - w*(t + w)*x + m^2*t)) + (2*w*x + t)*((t + w)*x - t/2)*(x - 1/2)*ln(w^4/(t + w)^4)/(t^2*(w*(t + w)*x^2 - w*(t + w)*x + m^2*t)) - 8*(x - 1/2)*((-2 + 2*x)*w + t)*((-1 + x)*w + (x - 1/2)*t)*((t*x + (-1 + x)*w)*w^2*(-1 + x)^2*ln((t*x + (-1 + x)*w)/((-1 + x)*w)) + (-(t*x + (-1 + x)*w)*((x^2 - x)*w + m^2)*ln((x^2 - x)*w + m^2) + ln(m^2)*m^2*w*(-1 + x))*t)/((t*x + (-1 + x)*w)*w*(-1 + x)*t^3*((-1 + x)^2*w^2 + w*t*x*(-1 + x) + m^2*t)) + 16*(x - 1/2)*(ln(1/m^2)*ln((t*x + (-1 + x)*w)*(-1 + x)*w/((-1 + x)^2*w^2 + w*t*x*(-1 + x) + m^2*t)) + ln((x^2 - x)*w + m^2)*ln(1/((-1 + x)^2*w^2 + w*t*x*(-1 + x) + m^2*t)) + ln((-1 + x)^2*w^2)*ln((x^2 - x)*w + m^2) - dilog((t*x + (-1 + x)*w)*(-1 + x)*w/((-1 + x)^2*w^2 + w*t*x*(-1 + x) + m^2*t)) + dilog((-1 + x)^2*w^2/((-1 + x)^2*w^2 + w*t*x*(-1 + x) + m^2*t)))*(t*x + 2*(-1 + x)*w)/t^3

f3 := (mm, ss, tt, ww) -> Int(eval(W, [s = ss, t = tt, w = ww, m = mm]), x = 0 .. 1, _d01ajc)

A3 := evalf(f3(1, 3, -2, -1))

Error, (in evalf/int) number expected for float[8] parameter, got 0.+0.*I

What's wrong?

How is the matrix of the affinity of base the plan of equation x+2*y-z=1, of direction u <1,0,-1>and of ratio 2 determined? Thank you.

Download complex_numbers.mw