Hi Dears,

I know "randpoly" command of Maple and I need to generate some random polynomials with parametric coefficients. For this I used this command for input set {a,b,c,d,x,y,z,w} which {a,b,c,d} are parameters and {x,y,z,w} are variables. But, the generated polynomials were not interestting. For example, some polynomials such as $(a-b)xy+(c^2-a)x*y*z-a*b+(d-1)z^2w$ are interested for me. In fact, difference parametric coefficients is important. 

Could you please help me to generate them?

Sincerely yours 

I am interested in the 5 circle theorem of Miquel.  Search on the internet 'Miquel five circle theorem' for more details. I would like to prove this theorem using Maple, and also see if there is a generalisation to this for more than 5 circles.  I wish to find the points of intersection of the circles and am using the fsolve command:

fsolve({(x-x[i])^2+(y-y[i])^2-r[i]^2, (x-x[i-1])^2+(y-y[i-1])^2-r[i-1]^2}, {x, y});

I am using the curly braces for sets - as I can't seem to get it to work for [] lists.   The output gives something like {x=12.0005, y=4.65}.  I want to use these values to obtain straight line equations and verify that the lines formed by successive circles form a pentagram, with all vertices on the five circles.  I just want to get to the floating point values, without the x= part.  The type of the returned expressions is '=' - whatever that means!

    I'm also wondering if using the plottools and plots packages is sufficient - as opposed to the geometry pakage.

I'm interested in how many people have heard of this theorem.  Does it have any generalisations to 6, 7, ... circles?

Any help or comments gratefully received.

    David.   

Hellow dears!!!

Hope everyone is fine with everything. I want the animation of the numerical solution of ODE i,e., f4 for delta=[0,1.5]. Please see the attachment and fix my problem. I Shall be very thankful to you.

Graph.mw

Special request to  acer 13834, @Carl Love ,Preben Alsholm 10271

As part of the class I am teaching in biofluid mechanics, the students are learning about the Buckingham Pi theory for finding dimensionless groups (pi-groups).  The process involves the dimensions of parameters in terms of their basic units of measure: mass, M, length, L, and time, T.  Fore example, fluid density is M/L³ .  A typical step is to represent a product of parameters in terms of these measures raised to exponents.  Here is an example

(M/LT)^a(M/L³)^b(L²)^c

where the exponents a,b,c are to be determined. What command(s) will massage this form to look like

M^a+b  L^2c-3b-a T^-a  ?

Cheers

Greetings to all.

A basic Euler-MacLaurin Summation recently appeared at this Math.Stackexchange Link . Several users computed an asymptotic expansion for the sum given by sum(1/k^sigma, k=1..n) with sigma a parameter between zero and one. E.g. for sigma=1/3 we find

       2/3
    3 n                     1           1           7            13            247
    ------ + Zeta(1/3) + -------- - --------- + ---------- - ----------- + ------------
      2                     (1/3)       (4/3)         10/3          16/3           22/3
                         2 n        36 n        4860 n       26244 n       590490 n

Comparing this with Euler-Maclaurin Maple produces the following:

> eulermac(1/n^(1/3), n, 8);
       2/3
    3 n         1           1           7            13            247             1
    ------ - -------- - --------- + ---------- - ----------- + ------------ + O(-------)
      2         (1/3)       (4/3)         10/3          16/3           22/3      (28/3)
             2 n        36 n        4860 n       26244 n       590490 n         n

The sign on the second term is incorrect. I would be curious to know what is happening here. BTW Mathematica also yields a plus sign on this term, same as what was obtained at the link.

Thank you for any comments you may have.

Marko Riedel

Hi 

I need yours help to solve the given integral 
 

q,c,a and r are parameters.
Γ is a gamma function.

Download Karim.mw
 

I am trying to draw a tetrahedron and square based pyramid, having its triangular faces the same asthat of the tetrahedron.  While the geom3d package in Maple 7 has several polyhedra, a pyramid, or pentahedron(?) seem to be missing.  The closest is the octohedron - but this is two square pyramids "glued" together!   I'm totally bamboozled by the Polyhedron command with all its options.  Is it possible to somehow cut the octohedron in two, to get a pyramid?  Below is my Maple program, including at the end aplottools command to draw a separate ocotohedron.  

  Any help gratefully received.

     David

restart:
> #Puzzle Problem with tetrahedron and pyramid.  How many faces will
> #resultant polyhedron have when a triangular face of the pyramid is "glued" to  the tetrahedron.
> with(geom3d):
> 
> print(`A pyramid and tetrahedron are shown: the triangular faces of each being the same dimensions. The`);
> print(`triangular face of the pyramid is attached to a triangular face of the tetrahedron.`);
> 
> print(`How many faces does the resulting polyhedron have?`);
> print(`  a.) 5    b.) 6     c.) 7     d.) 8     e.) 9`);

> # octahedron, hexahedron, cube, icosahedron, dodecahedron - but pentahedron not supported in Maple 7 :-(
> RegularPolyhedron(d,[3,4],point(o,4,4,0),3):
> #dodecahedron(t,point(p,5,0,0),3):
> 
> tetrahedron(t,point(p,5,0,0),3):
> #draw([d(color=red),t(color=green)],cutout=7/8,lightmodel=light4,
> draw([d(color=red),t(color=green)],title=`Tetrahedron & pyramid`,orientation=[45,45]);
> with(plottools):
> f := octahedron([0,0,0],1):  #, octahedron([1,1,1],0.5):
> plots[display](f,style=patch);

Dear Team, I have used RKF45 to solve my ODE with Maple. now I am required to solve same ODE using RK4 for comparison of solution. Ps help me with an example. Pls find my Parameters, intial values and ODE below:

Download ODE_EQNS.mw

How can I solve this non-linear ODE exactly or approximately in some series solution?

Non_linear_ode.mw

I'm a new Maple user so there may be a better way to do this, but Maple is not handling units the way I would expect.

Here is an example document (inline graphical below, also here: Plots_With_Units.mw) showing the impedance of a parallel resistor, inductor, and capacitor.  The plot is correct and it shows kHz along the abscissa like I want.  In order to get this I used kHz in the range fr, which is fine, but I had to also use kHz in the basic definition functions for Zl and Zc.

Now in order to get correct results from any of the Z functions I must use them with a kHz argument for f.  If I want to use them where other unit multipliers are more appropriate they won't work right, and many times I don't know what the appropriate multiplier should be until I'm into the design.  Then I need to go back and change the multipliers in the functions.  Or maybe in a single design I'll want to show Hz and kHz for the same function.

This seems like confusing units and dimensions.  The dimensions of inductive impedance (Zl), for example, can be expressed as frequency times inductance.  Whether the frequency is in units of Hz, kHz, or uHz doesn't matter and should simply scale the results.  I should be able to specify functions in dimensions and use units elsewhere as I want for convenient plotting and result formatting.

Is there a better way to do this, or is it a limitation in Maple?  The overall goal is to define functions with units but be able to use them and to format plots in whatever other units I like.

Hi,

I am trying to solve a 2nd order ODE. But I get the Error:

Error, (in dsolve/numeric/bvp/convertsys) unable to convert to an explicit first-order system

I have uploaded the worksheet. Can anybody please help me?

I am teaching a course in biofluid mechanics and am looking to help the students get more use out of Maple. Often it is advantageous to scale a differential equation (and initial conditions) using dimensionless variables to reduce the number of free parameters in a problem. For example, the simple linear oscillator differential equation:

Eq(1)         m*d²x(t)/dt² + k*x(t)=0

where k and m are parameters.  If we define a dimensionless time, s=t/T, and a dimensionless position, X=x/L, where T and L are constants, , Eq(1) becomes

Eq(2)         (mL/T² ) *d²X(s)/ds² +  kL*X(s)=0

Then choosing T=sqrt(m/k) we arrive at

Eq(3)         d²X(s)/ds² +  X(s)=0

which has no parameters.  Can this sequence be done in Maple for a differential equation...i.e. change of variables?

Thanks

I recently moved to a new research institute and have to make a decision on either buy a licence for Maple or Mathematica. My needs are PDE hyperbolic system (e.g. shallow water, tsunami...) resolution and when possible export to standalone C/Fortran code based on package like MathPDE.

I know a little of Mathematica, but have a bunch of notebooks. I tried with the help of MapleSoft support to import them into Maple with no success so far.

So as I'm not tied to any of both, I have the impression that I would be more comfy with Mma but Maple is cheaper and seems more open. Is there any rationals for picking one over the other?

I have a difficult problem by NLPSolve & mnimize (optimization)

How do I solve the erroe"unexpected parameters" in Maple?

The code is uploade under the line.
Maple Worksheet - Error

Failed to load the worksheet /maplenet/convert/example1.mw .

Download example1.mw