## Algorithms Used in Maple

by:
A student of mine recently asked what algorithm Maple uses to calculate Eigenvalues. So, I tried diving into Maple Procedures. For example: >showstat(`Eigenvalues`); LinearAlgebra:-Eigenvalues := proc(A) .. [error catchers ommitted] .. 17 LinearAlgebra:-LA_Main:-Eigenvalues(`if` ... end proc How should I interpret that last line? Can I get Maple to show me what that procedure does? So far I've no luck cracking it. Also, is this the best/easiest way of going about learning what types of algorithms Maple uses. I understand that some (/many/all) of them may be proprietary and the persons at Waterloo may not want the general public knowing them, but even an answer as simple as "Accelerated Newton-Jacobi algorithm" would be good.

## local extremity command

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Hi, I have plotted the following chart using maple 10 on windows xp > plot(((x^2)+x-4)/(x-2),x=-4..6,y=-2..10); X being -4, 2 Which command needs to be executed to find the local extremity? Thanks in advance for any help… Robert

## erroneous copy behavior?

by:
Another hour, another possible problem. Consider the following Maple statements:

> f := table([index=m]);
f := table([index = m])
> g := copy(eval(f));
g := table([index = m])
> g[index] := one;
g[index] := one
> h := g;
h := g
> f[index], h[index];
m, one
> g := copy(eval(h));
g := table([index = one])
> g[index] := two;
g[index] := two
> l := g;
l := g
> f[index], h[index], l[index];
m, two, two

So, after the first copy, the second table h has value one for index, while f still has value m for index. Yet, after the second copy, not only the third table l has value two for index, but also the second table h now has value two for index, while I have explicitly used copy to make a copy of h. Does this indicate a problem with the copy function?

## Maple 10 versus Maple 9.5 : Psi

by:
Hello,

a colleague just noticed the following (erroneous) behavior in Maple 10 :

> a := Psi(2, 2+2*I);
a := Psi(2, 2 + 2 I)
> printf("%+.6e\n", Re(a));
Error, (in fprintf) number expected for floating point format
> evalb(Im(a) <> 0);
false

The behavior is correct in Maple 9.5 :

> a := Psi(2, 2+2*I);
a := Psi(2, 2 + 2 I)
> printf("%+.6e\n", Re(a));
+3.902435e-02
> evalb(Im(a) <> 0);
true

-- Regards,

Franky.

## Intercepts - Sine curve and x-axis...

by:
Yet another question (after scouring the Maple documentation and coming up empty-handed): The following commands: with(student) intercept(y=sin(x), y=0) Result in this output: {y=0, x=0} How can I return the other intercepts with the x-axis? For instance, the first positive and first negative non-zero intercepts? (i.e. the "first" x-intercepts traveling left and right away from the y-axis?) Thanks as always, Bryan

## Square Root of a Number - only positive result?

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Quick question: in maple , sqrt(4) returns 2. Why not plus/minus 2, since -2 is also a valid square root of 4? Thanks! Bryan

## Maple and LabVIEW

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anyone has done significant development with these two?

## Invalid evaluation of derivative (more examples)

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Additionally to my previous post: First example returns (mathematically) wrong result,
```eval(diff(v(z), z), [v = (x->x*H), z = H])
2H
```
Equivalent works fine (just because multiplier "a" leads to implicit conversion of diff to D).
```eval(diff(v(a*z), z), [v = (x->x*H), z = H, a = 1])
H
```
And the most exiting example (I think, that result can't be predicted by Maple developers also ):)))
```eval(diff(v(x, y), x, y), {x = H, y = H})
(D[1,1](v))(H,H)+2 (D[1,2](v))(H,H)+(D[2,2](v))(H,H)
```
Functional analog works, of course, without any errors.

## Invalid evaluation of derivative (Maple 10)?

by: Maple 10

Create new document (or worksheet) with content below and execute it step by step: > restart; > Eval(diff(v(z),z),z=H)==eval(diff(v(z),z),z=H); Eval(diff(v(z),z),z=H)=diff(v(H),H) > v:=z->z*H; v:=z->z*H > value((1)); H=2H As you can see, result of eval, which in this case is equivalent to subs(z=H,diff(v(z),z)), at the right side of first equation leads to wrong final result :( This...

## Using Maple for Principle Component Analysis

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Where can I find Maple worksheets for viewing/download with regards to the following fields of application?:- 1) soft independent modelling of class analogy (SIMCA), regularized discriminant analysis (RDA) and discriminant analysis with shrunken covariances (DASCO) for multivariate classification, 2) principal component scores-based multivariate statistical process control (MSPC), 3) modelling of multiplicative terms in analysis of variance (ANOVA), 4) generalized rank annihilation method (GRAM) and iterative target transformation factor analysis (ITTFA) for curve resolution and optional second-order bilinear calibration, and

## Screenshot of strange maple behavior (fixed link)

by:
This is regarding an earlier thread about Maple's misleading output of exponentials. Here is a link with a screenshot of what I am talking about: Maple output It seems like no one else is experiencing this problem. Maybe it has something to do with the version of java or OS X I am running, which is OS 10.4.3, Java 1.5, and Maple 10.01.

## Easily Misinterpreted Output

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Try typing the following input in Maple 10.01 in 2D mode (on Mac OS X) input: (e) output: e when in fact what maple means is this: e The intended answer appears when you call simplify on the first result, but this seems dangerously easy to confuse, especially for inexperienced maple users, or if this was returned as the answer to a problem (like taking residues, where I discovered it) it could be easily overlooked -Matt

## Problem with Maple under Java 1.5 on OSX

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I'm running Maple 10.01 under Mac OS X ( 10.4.2), and when set my Java Preferences so that the J2SE 5.0 being used in the runtime environment, Maple will not open and gives the following error: Uncaught exception in main method: java.lang.NoClassDefFoundError: org/apache/crimson/parser/XMLReaderImpl Maple works fine for me when the runtime environment is set to use J2SE 1.4.2. -Matt

## Maple for undergraduate mathematics education:...

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I teach some mathematics subjects to students studying a computer science course. Most of these students dislike maths (I'm Australian, hence "maths" instead of "math"), and are doing it only because it's a core subject in their first year. I should also point out that many of my students have a very weak maths background, and so find the maths that I teach (which over a year covers logic and boolean algebra, some combinatorics, and linear algebra and calculus) very difficult and demanding, and often simply dull. I've been using Maple for about four or five years now; each week the students work through a sheet of Maple exercises (which are all marked) designed to enhance their learning. But here's the thing - the students actually don't like Maple! They would much rather spend that hour having a standard tutorial, working through pencil-and-paper problems, than in a computer lab with Maple. So I need to change my approach; to somehow make Maple more central, more enjoyable, and more "enhancing" than I've been doing up to now.

## Mathematics as Art

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I came across this cool site created by Justin Mullins of the New Scientist. The site contains artwork created by mathematical expressions. The creator describes it as Mathematical Photography, "In the same way that an ordinary photograph is a snapshot of an area of outstanding natural beauty, a mathematical photograph is a snapshot of mathematical beauty."
There are many examples to be seen on the site. And they will be shown at the UK gallery exhibition in London next February. Link (via Boing Boing)
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