## Ore_algebra or OreTools - which package to use for...

Hello everybody, I hope some of you have experience with multivariate Ore polynomials in Maple and will be able to answer the title question. So far I've needed only univariate Ore polynomials, used the OreTools package for them and have been very satisfied with it. However, now I've come across a problem that needs to employ multivariate ones - therefore I am forced to try the Ore_algebra package, which should make computations with multivariate Ore polynomials possible (as far as I know, OreTools cannot handle multivariate Ore polynomials - or am I wrong? I wish I was) And here comes my trouble! Not only that I am not able to solve my multivariate problem with Ore_algebra, I don't even know how to do simple calculations (which can be so easily performed with OreTools) using Ore_algebra.

## create a real function f of real variables r and z...

Hi everyone, I m a beginner with maple, so please, be patient with me! I m trying to use some complex algebra in maple. In particular, I want to define a function f(r,z) and I want to impose it to be REAL. So I thought, let's first impose the variables to be real(I'm using Maple 10, so I write everything as if I was in a document, ok?): assume(r,real) assume(z,real) after I have done this, I define the function, using the appropriate f(x,y) button in the toolbar: F:=f(r,z) and I impose it to be real: assume(F, real) but for some reason this does not work. Anyone knows why? The reason why I need to impose the function to be real is that F will be later multiplied by exp(Iz) to form a complex number.

## How do I generate a matrix given a formula involvi...

Here is a technique which I need to do over and over and over in Maple. I am currently writing a research paper for the International Journal of Mathematics and Mathematical Sciences. I need to get this example out as soon as possible. Suppose I want to create a matrix where the (i,j) entry is the polynomial x^i + (x+1)^j whatever the entry is.. it doesn't matter. Point is that the entry depends upon the row i and column j How can I create and fill such a matrix? My matrices a slightly more complicated, involving entries such as diff(x^i + (x+1)^j,x) where it is actually easier

Hello, I am just learning how to use Maple and only have Maple 9.5. I am attempting to read in a single column of data from a pre-made txt file into Maple but I am having difficulty. For some reason Maple states that it cannot find the file that I am pointing it to. This was what I wrote... >restart; >RD:=readdata("c:\temp\test.txt"); I tried using " instead of ' and it gave me an error message as well. Any ideas what the problem might be? Thanks.

## Hermitian / Unitary Matrices...

Two matrices U and H are related by U = exp(i*a*H), where I assume a is a real constant, and i denotes the square root of -1. (a): If H is Hermitian, show that U is unitary. (b): If U is unitary, show that H is Hermitian. (H is independent of a.) Any advice or hints greatly appreciated, v/r, This is from the title "Mathematical Methods for Physicists" by Arfken and Weber. 6th ed. (section 3.4)

## Seeking Optimization...

I've got two procedures set up that work, but I know there have to be better ways to accomplish the same goals. First, I've got a procedure that finds to how many digits two floats (a and b) agree. I had tried a few methods of examining the SFloatMantissa and SFloatExponent of the difference, but those methods would fail in unpredictable ways. My current method explodes the floats into lists and compares every entry in a for loop. The example below is basically the heart of my procedure (I do take into consideration things like the location of the decimal and trailing zeros):

## obtaining distrutions/densities...

I already was explained that with maple is difficult to obtain the CDF of CharacteristicFunction of Z= (y1)^(1/2)+log((40-y2)*(80+2*y2-3y1))? where y1 = min(s1+X1, s2+X2) y2 = min(s3+X1, s4+X2) and Xi is IID uniforme[-1,1]. But .. could someone help me with some bibliographical references to deal with my problem?. It would help me to understand better and if possible to modify my formulation. Thanks in advance! Jean (I am using maple 10 under windows).

## 2-D plot with context menu...

I am trying to produce a 2-D plot of the function (sin(x))^2 using the context menu in document mode but Maple returns this error: sin(x)^2 -> Error, invalid input: smartplot uses a 1st argument, f (of type {algebraic, algebraic = algebraic, {set({algebraic, algebraic = algebraic}), list({algebraic, algebraic = algebraic})}}), which is missing It does the same when I change the function. What's wrong? Thanks Stéphane