Maple Questions and Posts

These are Posts and Questions associated with the product, Maple

hi all,

m := 1+(-21+.7*I)*sqrt((2.3*6.494)*10^13-x^2)/(2.3*sqrt(((-21+.7*I)*6.494)*10^13-x^2))

fsolve(m = 0, x, {x = 10^7+26500*I .. 2*10^7+26600*I}, complex)

 

the above characteristic equation m=0 will give complex roots if we solve it. but fsolve is not able to solve this equation evenif i provided the range.through some light for my problem.

thanks

Hi,

 

is there any analogous command to whos in Matlab to list the memory usage of specific variables in workspace?

Thanks!

Bye

Tom

Having read the above I decided to try it on a substitution problem I had last year on a set of equations. Work sheet containe an example. I successifuly applied algsubs to the problem. It can be slow and their is no easy way I see to know when the substitution is complete. so what I did go round the loop 2, 3, 4, 5 times. Crude!

Decided to try "side relations" with simplify here but it comes out with a totally different answer (not correct).

Could somebody explain why?

Dear Maple users,

Is there a way to describe derivatives treated as binary operators in infix notation, in which the derivatives is applied either to the left or right operands. This is useful, for example, when defining generalizations of the Poisson bracket. For a pair of functions f and g, the left and right derivatives are respectively defined as

Hi,

I have an expression which contains terms like cos(3*x)*cos(x) + sin(3*x)*sin(x). In this expression, I replace the prevous terms by using applyrule as:

applyrule([cos(3*x)*cos(x)=1/2*(cos(2*x)+cos(4*x)), sin(3*x)*sin(x)=1/2(cos(2*x)-cos(4*x))],expr);

 

Is there a way to generalize this so that I may replace all forms of sin(n*x)*sin(m*x) = 1/2(cos((n-m)*x)-cos((n+m)*x))?

 

Thanks for your help.

I want to write the equation of the plane passing through the three points A, B, C has the form ax + by + cz + d = 0 where a, b, c, d are integer numbers, a >0 if a <> 0; b>0 if a = 0 and b<>0,...and igcd(a, b, c) = 1.

If the coordinates of the vertices A, B, C are all integers, for example A(2,2,2), B(1,2, -1), C(1,-1,-4), I tried,

with(geom3d):

point(A,2,2,2):

point(B,1,2, -1):

How to color only certain bounded/intersection area of a graph in Maple?

Solve the equation : 58.54*x^2+19620*x^(1.85)-11485.54=0

how to graph this two paraboloids into one graph in Maple? z=x^2+y^2 and z=2-x^2-y^2  I try to use Display, Display3d commend, and it doesn't work.

>with(plots)

>f:=(x,y,z)->z=x^2+y^2;

>implicitplot3d(f(x,y,z),x=-5..5,y=-5..5,z=-5..5);

>f:=(x,y,z)->z=2-x^2-y^2;

>impliticitplot3d(f(x,y,z),x=-5..5,y=-5..5,z=-5..5);

 

and if I want to combine the two graph into one, what should I do next?

Find the function f:\mathbb{R}\to\mathbb{R} satisfying the following conditions:

f(-6)=2400,f(-4)=432,f(-3)=120,f(-2...

Problem_116_Solutio.htm

Hi, would like to know if maple commands can replicate/automate this solution.

rsolve({a(n)=9/19*a(n+1)+10/19*a(n-1),a(0)=0},a)

=-9a(1)+9a(1)(10/9)^n

.......?

The following (downsized) images of Lyapunov fractals were each generated in a few seconds, in Maple 16.

 

I may make an interface for this with embedded components, or submit it in some form on the Application Center. But I thought that I'd share this version here first.

I'm just re-using the techniques in the code behind an earlier Post on Mandelbrot and Julia fractals. But I've only used one simple coloring scheme here, so far. I'll probably try the so-called burning ship escape-time fractal next.

 

 

 

 

Here below is the contents of the worksheet attached at the end of this Post.

 

 

The procedures are defined in the Startup code region of this worksheet.

 

It should run in Maple 15 and 16, but may not work in earlier versions since it relies on a properly functioning Threads:-Task.

 

The procedure `Lyapunov` can be called as

 

          Lyapunov(W, xa, xb, ya, yb, xresolution)

          Lyapunov(W, xa, xb, ya, yb, xresolution, numterms=N)

 

where those parameters are,

 

 - W, a Vector or list whose entries should be only 0 or 1

 - xa, the leftmost x-point (a float, usually greater than 2.0)

 - xb, the rightmost x-point (a float, usually less than or equal to 4.0)

 - ya, the lowest y-point (a float, usually greater than 2.0)

 - yb, the highest y-point (a float, usually less than or equal to 4.0)

 - xresolution, the width in pixels of the returned image (Array)

 - numterms=N, (optional) where positive integer N is the number of terms added for the approx. Lyapunov exponent

 

 

The speed of calculation depends on whether the Compiler  is functional and how many cores are detected. On a 4-core Intel i7 under Windows 7 the first example below had approximately the following performce in 64bit Maple 16.

 

 

Compiled

evalhf

serial (1 core)

20 seconds

240 seconds

parallel (4 cores)

5 seconds

60 seconds

 

 

 

with(ImageTools):


W:=[0,0,1,0,1]:
res1:=CodeTools:-Usage( Lyapunov(W, 2.01, 4.0, 2.01, 4.0, 500) ):

memory used=46.36MiB, alloc change=65.73MiB, cpu time=33.87s, real time=5.17s


View(res1);


W:=[1,1,1,1,1,1,0,0,0,0,0,0]:
res2:=CodeTools:-Usage( Lyapunov(W, 2.5, 3.4, 3.4, 4.0, 500) ):

memory used=30.94MiB, alloc change=0 bytes, cpu time=21.32s, real time=3.54s


View(res2);


W:=[1,0,1,0,1,1,0,1]:
res3:=CodeTools:-Usage( Lyapunov(W, 2.1, 3.7, 3.1, 4.0, 500) ):

memory used=26.18MiB, alloc change=15.09MiB, cpu time=18.44s, real time=2.95s


View(res3);


W:=[0,1]:
res4:=CodeTools:-Usage( Lyapunov(W, 2.01, 4.0, 2.01, 4.0, 500) ):

memory used=46.25MiB, alloc change=15.09MiB, cpu time=33.52s, real time=5.18s


View(res4);

 

 

Download lyapfractpost.mw

Hi, 

     I'm using fsolve in a loop, as an example can we find the first 10 roots of sin(x) and store then in an array.

 restart;

x:=array(0..10):

x[0]:=0:

for i from 1 to 10 do

x[i]:= fsolve(sin(y)=0, y=x[i-1]..10 , avoid={y=x[i-1]});

end do;
 
Firstly this solve only 0,2*Pi, 3*Pi...Why does it skip Pi? also can I change the range to x[i-1]..infinity? 

Hello Everyone,

I got a question about the inverse laplace transform of the classic second order system:

Step_Respon=1/(s*((s^2/omega_n^2)+2*zeta*s/omega_n+1))

zeta < 1

if I take the inverse laplace transform, it will give me root of (zeta^2-1) term, how can I force maple to consider the range of zeta before doing inverse laplace transform?

the follow is a code that I've started.  This code is from working template that I created previously. that works and iterates as expected, but this equations with these parameters gives me the pintf error in bold at the bottom. 
Can you please help with the error at the bottom of code that is in bold????
 
> restart;
> Digits := 14;
14
> f := proc (x) options operator, arrow; 3-x-x*exp(r*(1-x...
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