If we have two univariate polynomials $f(x)$ and $g(x)$ such that

$gcd(f(x),g(x))=1$

then we know there exist two other polynomials $a(x)$ and $b(x)$ such that $a(x)f(x)+b(x)g(x)=1$. For example, if $f(x)=x^3−1$ and $g(x)=x^2+2$, then we can set

$a(x)=\frac{2x−1}{9}$, $b(x)=\frac{−2x^2+x+4}{9}$

Here the polynomials $a(x)$ and $b(x)$ are known as Bezout polynomials and they can be found using the extended Euclidean algorithm, which I know how to do using pen and paper, but not in Maple.

So my question is: in Maple, is there a way, given $f(x)$ and $g(x)$, to solve for $a(x)$ and $b(x)$?

Another training example (number 2 and last) for finding all solutions to a system of equations:

f1 := x3^2-0.1*x1^4-0.05*x2^4+1;
f2 := x1^3+x2^3+0.05*x3^3-1; 
f3 := -2*cos(3*x1)+2*cos(3*x2)-2*cos(3*x3)+1;

In my version, there are 116 solutions.
Is it so?

What kind of solution is it (see (3))? Why is there no solution when I put the initial condition v(0)=C1? Secondly, eq. (2) can be reduced to a first-order differential equation?

Download CD_ode.mw

I have been making animated 3d plots recently; the last time was perhaps three years ago, and I had some problems then.  If I recall correctly, I couldn't make an animated 3d plot that was plotted in non-Cartesian coordinates.

I am very happy to report that this works very smoothly now in Maple 2022, and it's pretty fast, too.  I have a fairly complex function to plot, involving piecewise polynomials on a tensor product grid in the xi and eta variables (actually, I let plot3d pick out the grid; it seems happier to do so) and then plot them on an elliptical base, in coordinates x = d*cosh(xi)*cos(eta) and y=d*sinh(xi)*sin(eta)  (d is just a numerical constant, giving the location of the foci at (d,0) and (-d,0)), for 0 <= xi <= xi[0] (the outer elliptical boundary) and 0 <= eta <= 2Pi.  The straightforward command works, and building a sequence of plots and using plots[display] works.  I put option remember into my procedure w(xi,eta) and because the sample points are consistent for the time-dependent function exp(I*omega*t)*w(xi,eta) the xi-eta grid needs only to be done once and then one can compute (basically) as many frames as one wants in rapid succession.

Works great.  Thanks, folks!

for k to nplots do
    t := evalf(2*Pi*(k - 1)/nplots);
    plts[k] := plot3d([(xi, eta) -> focus*cosh(xi)*cos(eta), (xi, eta) -> focus*sinh(xi)*sin(eta), (xi, eta) -> Re(exp(omega*t*I)*w(xi, eta))], 0 .. xi[0], 0 .. 2*Pi, colour = ((xi, eta) -> Re(exp(omega*t*I)*w(xi, eta))), style = surfacecontour, lightmodel = "none");
end do;
plots[display](seq(plts[k], k = 1 .. nplots), insequence = true);
 

File:

PCA.mw

I am a student in the middle of a projekt, where math is an essential part of the task. I have done a lot of work in a maple document, but this document suddenly became corrupted. I've tried restarting and loading backups and f ollowed Can I repair a corrupted Maple document/worksheet file? (maplesoft.com) but the solutions didn't work on my document.

Also tried the DeleteBadCharacters() proccess, but i get the error "Error, (in XMLTools:-ParseString) Element type "Equation" must be followed by either attribute specifications, ">" or "/>"."

Is there a way to fix this issue, and prevent the same issue occuring in the future? 

Thanks in advance!

PROBLEM-IP.mw

Download PROBLEM-IP.mw

Hi !

I want to create a notation for a function, let's say :

f:=(x,y,z)->something

such that when I ask for

f(x,y,z) 

Maple returns

f^x,y(z) or anyother "nicer view" of that expression.

This is (I think) a similar action of replacing BesselJ(n,x) by J_n(x).

Many thanks for your answers !

Kevin

This is a follow-up to a previous question I asked that was answered with code that used "%.". From the documentation I can see that % is a nullary operator that gives us the value of "the last expression", which I think means the last result of an evaluated expression.

In my previous question, I wanted to be able to display for example, a constant times a matrix, without the product being evaluated.

For example, given A:=<1,2;3,4>:, we need to use Maple Input, and then we can write c__1.A and the output will be an expression that has c__1 then the dot product symbol and then the matrix A written out.

My question is simply: what exactly is "%."?

Hi all, 

I am working with the physics package and I want to know if there is a difference between Physics:-CompactDisplay and PDEtools:-declare ?

As well as the difference between Physics:-Simplify and simplify.

For both cases, can they be used as the same ? Are they incompatible in some case?

Thanks !

Kevin

I would like to display an expression that is a matrix, the dot operator, and another matrix. That is, I want to display a multiplication of matrices, without the multiplication being evaluated.

Something like

<1,2;3,4> '.' <6,7,8,9>

Is this possible?

Here is some context around why I want to do this. Perhaps the main reason I use Maple is for the symbolic math capabilities using 2d math input. I want to create worksheets that look like what I would write on paper. 

For example, let's say I have a matrix that is defined by <I, F;0,0>, where each of elements is actually another matrix. I want to multiply this matrix by its transpose, which would be something like <I, 0^T; F^T, 0^T>.

I would like to display <I, 0^T; F^T, 0^T> .  <I, F;0,0>.

Hello guys
I created a document recently and, the next day, when I tried to open it, I received the following message:

        Recover corrupted file and save as

Does anyone know how to recover a corrupted file?
Regards,
Oliveira

Dear all

I would like to expand x^m using JacobiP  ( jacobi polynomials), with the two parameter alpha  and alpha +2, I have a result in my book using alpha and alpha+1 but i would like to get a similar result using alpha and alpha+2 

Inverse_formula_jacobi_polynomials.mw

Thank you 

I have a system of ODE's which are solved numerically (with rkf45) to get function values over time. And i have datapoints for these functions, and would like to compare and calculate the error/deviation between model and data. I can't find a command / mechanism that does this.

Is it possible?

I know maple help has exercies where you can learn from. I was, however, wondering if there is a standard place where people upload their specialized worksheets and maple documents they have used for research once they make it public.

Suppose I have a excel file with say 20 columns of data with equal number of rows of data. All numeric data

How to read each column data to a seperate variable

Or 

The entire data into a matrix