Hello

Let P(x)=ax^2n+bx^(2n-1)+....+h. Then, How can I find Q(x) and R(x) polynomials as P(x)=Q(x)^2-R(x)?

I am trying to calculate a symbolic complex sequence given in the below picture: 

I have written the following code; however, it is not efficient at all and it takes a very long time to calculate even the first elements of the sequences. Can anyone please help me fix that or suggest an efficient way of doing such calculation in complex domain? Any help is appreciated. Thanks

##########################################################

d(0):=1+1I;

M(0):=1-2I;

for k from 0 to 3 do u(k):=-d(k)/M(k);p(k+1):=M__s*u(k)+d__s;d(k+1):=d(k)+gamma*p(k+1)/(nu+abs(u(k))^2);M(k+1):=M(k)+gamma*p(k+1)*conjugate(u(k))/(nu+abs(u(k))^2);od;

Hello, I have attached an image that shows an example of what i want to do, but wanted to see if there was already conventional notation and a package that exists in maple. 

In general, i want to customize binary operations and assign index values, in the example here those index values are the modulo for the equivalence classes for which the binary operator may have elements of as operands, but in another example would be to say assign in to  "~"  in reference to it being the equivalence relation for a congruence class modulo that index.

Thanks in advance, 

Adam.

The  partition function is geven as'

Zvib(Beta)"=integrate(exp^Beta*alpha^2*h^2/4*units*m *(B-2A)+Beta*alpha^2*h^2*B^/8*units*m*(n+c)^2+Beta*alpha^2*h^2*rho^2*drho,rho=(c+n) from to lambda+c

Why can't MAple give me two solutions of

-2*sqrt(-K[1]^2+1)*K[1]+4*K[1]^2-Pi-2*arctan(sqrt(-K[1]^2+1)/K[1])=0

I only get -2*10^-13. There should be one K[1]=0.983 about

Hi there,

I have a function X that I am trying to plot a phase portrait for against it's derivative dX/dt. I currently have the code:

plot([X,diff(X,t),t=0..10],numpoints=1000) 

which sketches a graph but does not give any arrows to indicate direction.

Could anybody help?

Many thanks

Hi I found a subpackage in the help pages with functions and concepts in mathematics that i have had a very keen interest in for quite a number of years now, and so to find an area of specialization that also has a modern day application is of course a beautiful day for any mathematics enthusiast , and especially so in that the help page provides a very basic example of such an application.

My only problem is that i start laughing when i think of the name that has been given to the algorithm that produces the encryption key. 

Must i refer to the name "BlumBlumShub" in referencing it's creator in any essays or personal writings, or can i shorten this to BBS with the consent of Maple? 

Lett_K_etc_Coloring.mws

In the attached program the letters K, M, H are drawn.  These are examples of concave polygons.  (The fact that they happen to be letters is immaterial here.)  I'm interested in the coloring in process.  I experimented with simple shapes, like the letters I and L, which have a small number of points - and the letter I is convex.  These polygons colored in without a hitch.  It seems a general rule is:

    Color the first half dozen points given, then head home towards the first point - then return to the next point.  Does it color in by separating the polygon into pentagons, or hexagons?  

   I'm aware of how to draw & color shapes by splitting them into a smaller number of polygons, so please don't waste time improving my code.   I'dd appreciate my hunch being verified, or a reference to more information.  TIA

Hi

Why Maple can't  calculate following definite double integral:

Error, (in simpl/Re) too many levels of recursion

The approximated midpoint intgration gives the value -0.4552861717e-1

The Legendre root nodes with Christoffle weights gives the value -0.4552311444e-1

Thanks

I have the following two questions/issues:

1.) It seems to me that in the Tetrads package, some tetrad is automatically calculated in terms of the metric. Is there any way to reverse the roles, i.e., to have the vierbein determine the metric?, as is anyway a more natural setup, I think. The point is that I would like to work with an arbitrary, non-fixed vierbein, and from it having the metric, Christoffel symbols, etc., calculated 'on the fly', and then ultimatively construct the socalled minimal spin connection from these quantities.

2.) Consider the following expressions:

Simplify(e_[a,mu ]*Christoffel[~mu,nu,rho]);
Simplify(e_[a,nu ]*Christoffel[mu,~nu,rho]);
Simplify(e_[a,rho]*Christoffel[mu,nu,~rho]);

As the Christoffel symbols do not transform as tensors, I find this notation unfortunate, as one cannot simply move the vierbein through a (partial) derivative. Conversion between world indices and Lorentz indices should, I think, only be performed for world indices of tensorial type.

if there a series of matrix,

current matrix and previous matrix has same value , then defined as pattern

and

then define x and y are the position of pattern , if Matrix([[777,x,x],[77,7,7],[2,y,y]]

then code auto exchange x and y become Matrix([[777,y,y],[77,7,7],[2,x,x]]

but this recognization need to observe manually, 

can this be automated for any kind of pattern , such as exchange or other operations of pattern?

can neural network or deep learning in maple code recognize the operations such as exchange part of row or flip or symmetric about axis or other need imaginable operations ?

Is there something wrong with dsolve?

ode := diff(y(x), x) = sqrt(2*32.2*y(x)):
ics := y(0) = 0:
dsolve({ics, ode});

maple output:   y(x) = 0

The answer should be

y(x) = 16.1 x^2

Wolfram got it

I tried using restart, with(DEtools), still no luck. Though I don't think its necessary to call with(DEtools) for this simple equation.

To make the problem simpler, use dsolve on  dy/dx = √y , y(0)=0.

ode := diff(y(x), x) = sqrt(y(x)):
ics := y(0) = 0:
dsolve({ics, ode});

maple returns  y(x) = 0, which is incorrect.  Should be y(x) = x^2/4

I uploaded the worksheet just in case 'its just me'.

diffeqseperable.mw

how can plot a graph of V(r) against E0,B0 and EO*B0;

given that V(r)=V0/b(a-exp**-eta*r/1-exp**-eta*r)-V1exp^-eta*r/(1-exp^-eta*r)+V2exp^-2eta*r/(1-exp^-eta*r)^2;

E0=q*rho(electron)*velocity(vs)/mu;

B0=h/2^2*omega^2/16

The problem and the error in the attached worksheet. 

https://www.maplesoft.com/support/help/errors/view.aspx?path=Error,%20(in%20DocumentTools:-GetProperty)%20input%20is%20ambiguous

Download MAPLE_PLEASE_HELP.mw

Hi there,

I have a function defined as:

U:=-[0.25*exp(1/2*epsilon*t)*(1/v^2-1+exp(epsilon*t))^(-0.5)]*sin(4*t)

which I am trying to plot on a 2D graph of axes (t,u(t)).

In the specific case I have epsilon=1/10 and v=2

When I try plot(U), maple returns the error message:

Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct

Could anybody help me out please?

Many thanks