## Implicit differentiation (finding extreme values)...

Hello, I have a problem with this implicit equation: > eq:=(x^2+4*y)^2+(x+y^2)^2=65 I can find the tangent line for a point on the curve, e.g. (-2,1). This is the slope on the point. > a:=subs(y=1,x=-2,implicitdiff(eq,y,x)); It will give this tangent line. > tanline:=a*(x+2)+1; Here's a plot: But now I want to find the locations of its extreme values. That's where I got stuck. The tangent line must be horizontal so dy/dx = 0. So I have to the implicit equation for the condition dy/dx=0. For explicit functions it's not that hard, e.g.:

## Solve equations system...

> p:=x->log[b](x); p := x -> log[b](x) > o:=x->b^x; x o := x -> b > fsolve( p(x) = o(x) , {x,b} ); Error, (in fsolve) number of equations, 1, does not match number of variables, 2 I need to find the location (x,y) where they touch each other, thanks for the help.

## Getting numerical results when using symbols?...

What do I have to change in the settings to get numerical results from simple expressions using symbols? In other words, when I enter something like 2 x pi or e, I want the numerical answer, or rather something that reads 6.28... As it is, it just returns 2 x pi again.

Maple

Inspired by my own post The art of linking, I here bring an expanded version (I hope that it does not appear too self-centred to do so): You can link to other parts of MaplePrimes, or to external webpages, using the HTML tag `a` with its associated attribute `href`. This tag and its attribute you may enter by pressing the link-image  (please disregard the black background), which is located above the area where you enter your text, the result being `<a href="http://">` The part between the two "'s is where the address of your link, the socalled URL (Uniform Resource Locator) must be inserted. Below, four typical link situations are treated:

• Linking to a thread: Taking as an example the thread in which the above post appears, you could write (for long URL's, as this one, use copy-paste to avoid typos) `<a href="http://www.mapleprimes.com/forum/why-does-evalb-evalf-10-0-evalf-10-0-float-1-0-30-false">The other thread</a>` which would appear on the screen as The other thread.
• Linking to a specific post: Each post in MaplePrimes has its own unique ID. It can be found by placing the mouse over the link `email this comment` of the post to which you want to link, and then reading of a five-digit number at the end of the line at the lower left of your screen (in Microsoft Internet Explorer). A link to that post is then created by appending to the URL of the thread itself the following code: `#comment-.....`, where for `.....` the five-digit ID has to be inserted. It was William Spaetzel who originally told me this. Taking as an example the above post, which has the unique ID `11566`, you could write `<a href="http://www.mapleprimes.com/forum/why-does-evalb-evalf-10-0-evalf-10-0-float-1-0-30-false#comment-11566">The other post</a>` which would appear on the screen as The other post.
• Linking to or showing a picture: First of all you have to upload your picture using `my files` under `Navigation`. Having done so you can copy-paste the text in the column `Download Link Code`. This text contains both the HTML `a` and `image` tags. You can then choose to keep the full text, thereby having a clickable image (a link to the image), or you can manually strip away all `a` tags (remember the ends also) thereby having a non-clickable picture, as I have above.
• Linking to an external web page: Taking Maplesoft as an example, you could write `<a href="http://www.maplesoft.com/">Maplesoft</a>` which would appear on the screen as Maplesoft. The part `target='_new'` has been automatically inserted by the MaplePrimes system (click on `Input format`, which is located below the input text area, to see the various input formats), and so it need/should not be entered manually.

## Maple V (1996) vs. Maple 11 (2007) .ps exporting...

I am exporting 3d shapes generated by plot3d/surf3d to postscript, here is a comparison between my 11-year old copy of Maple from when I was a Freshman (left), and my current version(right): torus :( I've pretty much given up fiddling with the settings in Maple 11 to improve the quality; at this point, I'm wondering if anyone has any idea how to modify the .ps file itself to get rid of the thin diagonal lines that go through every quad in the (right) version. If it's simple enough, I could write a perl script to post-process my plots...

## Matrix-generation...

Hiya! I'm at a loss for how to properly generate a set of n x n-matrices of the form [-1]; [[0,-1], [-1,0]]; [[0,0,-1], [0, -1, 0], [-1, 0, 0]] ... and so on, for n from 1 to an arbitrary value. I've had a good look at the constructer options for Matrix() but failed to spot the proper solution. I'd like to do so in a loop or seq, so I can perform the needed operations on them, without having to keep a lot of arbitrary variables. Any good hints or tips?

## Plotting the solutionpoint from an optimization....

Hi guys. How do I plot the solutionpoint from an optimization as a function of a parameter in an effective way? The problem I'm struggeling with is the following. I'm interested in the optimal E of V := (E,a) -> int(-1/2*E*(-r+E)/r*((1/2*r)^(-1+a)*(1-1/2*r)^(-1+a)/Beta(a,a)),r = E .. 2); for any given a, given 0<>

## Using SingularValues in a Procedure...

I am trying to write a procedure that uses LinearAlgebra[SingularValues]. For some reason, the line U,S,Vt := LinearAlgebra[SingularValues](covariance, output=['U','S','Vt']); causes the procedure to give the error message: Error, (in LinearAlgebra:-LA_Main:-SingularValues) invalid output (U) specified However, outside the procedure the same line works perfectly. Any help will be much appreciated!

## Java...

Hi, I was wondering if there is a way to use Document Components or Maplet Elements from Java? Is there a file that has the library for these components? I use the Netbeans environment, has anyone set up that environment to use Maple libraries? Thanks, Art

## Boundary conditions with PDE systems...

I have the initial and boundary conditions: cond := ro(x, 0) = 0, v(x, 0) = 0, {ro(0, t) = 10, ro(40, t) = 20}, {v(0, t) = 10, v(40, t) = 20}; The PDE system is: sys2 := {diff(ro(x, t), t)+diff(ro(x, t)*v(x, t), x) = 0, diff(v(x, t), t)+v(x, t)*(diff(v(x, t), x))+3*ro(x, t)*(diff(ro(x, t), x)) = 0}; I use: sol1 := pdsolve(sys2, {cond}, numeric, time = t, range = 0 .. 40); values := sol1:-value(); ... When I try to see the values I receive the following error: values(40, 20); Error, (in solnproc) unable to compute solution for t>0.: column vector dimension less than length of sparse data

## Second derivative...

I am trying to calculate the second derivative of a taylor expansion. Could anyone tell me how to enter this command? Thanks Rachel

## Maple into Java?...

Can someone point me in the direction to integrate a maple file into a java program? I made a maple file that has a variable and will output a final graph after long calculations.. What I want is a nice java app where the user can simply type in the variable they want, and a graph is displayed in a window? Just a general kick in the butt to the direction for documentation about such a process would be great! Thanks!

## Impenetrable Physics Environment?

Maple
Inspired by the post Re: the physics package I decided to have a closer look at the function `FeynmanDiagrams`. As the Lagrangian I thought I might as well take the QED Lagrangian for a massless spinor field `Q[i](X)` coupled to an external electromagnetic field `A[mu](X)`:
```restart:
with(Physics):
L_QED :=
+Dagger(Q[i](X)) * Dgamma[4] * Dgamma[mu][i,j] * I * diff(Q[j](X),X[mu])
+Dagger(Q[i](X)) * Dgamma[4] * Dgamma[mu][i,j] * e * A[mu](X) * (Q[j](X));
```