MaplePrimes Announcement

With Maple Flow, we’re regularly rolling out exciting updates. Each offers new features, as well as resolving many user-reported issues.

Flow 2024.2 lives up to that track record. Two major new features - drop-down menus and phasors - make their debut. We've also made many other quality-of-life enhancements.

Drop-down list boxes make your worksheets more tactile and interactive. The menu items can be defined in a matrix or vector, or in a table. You can return the index of the selected item, or return an entire row or column of a matrix.

An important use case is populating the contents of a drop-down menu with data from an external file. In movie below, we

  • import a database of steel shapes and their associated properties
  • populate the drop-down menu with the steel shapes in the first column of the imported data
  • based upon the selected shape, use ArrayTools:-Lookup to return a property
  • and finally perform a design analysis.

If you look carefully, you'll see that you can hide commands on a per-container basis to make your worksheets cleaner.

We have a large number of power system engineers who want to model electrical systems in phasor notation.

Entering a phasor is easy - just enter the magnitude, the angle character and then the angle. Phasors evaluate to rectangular complex numbers but can be recast to phasor format with the Context Panel.

You can also associate a unit with the magnitude and angle. On output, you can change units inline or via the Context Panel.

You can also prevent floating point approximation of phasors using the symbolic toggle on each container.

We've also made a raft of other improvements. Extracting slices of matrices is faster, and you can now enter units in 2d notation in the Context Panel (particularly useful when you want to change the units of everything inside a matrix).

As ever, the new features are driven by you. The only way you can point us the right direction is by telling us what you want. Don't be shy!

Featured Post

A checkerboard... that moves?



This recreation of an optical illusion was made using Maple Learn. For an interactive version where you can zoom into the plot and change the colors, check it out here: Optical Illusion: Moving Image. The buttons in the document were made possible by deploying the canvas from Maple using this Maple script.

Changing the colors creates cool visuals - and the motion of the image is apparent using some color schemes more than others.

   

   

 

How Does It Work?

If you zoom really far into the image, you can see that it is made up of a checkerboard in the background, with crosses (plus signs) covering each of the corners:

The checkerboard is made up of unit squares, and to create a cross with hieght=6d, centered at (x,y), polygons were used:

Polygon(
  [x+d,y+3d], [x+d,y+d], [x+3d,y+d],
  [x+3d,y-d], [x+d,y-d], [x+d,y-3d],
  [x-d,y-3d], [x-d,y-d], [x-3d,y-d],
  [x-3d,y+d], [x-d,y+d], [x-d,y+3d]
)

The key to the motion of the image lies in the alternating 1-1-2-1-1-2 pattern of the light/dark crosses along the diagonals.

Featured Post

I was working in my living room.  My computer was upstairs, but I had my phone and tablet.  I'm working on The Book ("Perturbation methods using backward error", with Nic Fillion, which will be published by SIAM next year some time).

I've discovered something quite cool, historically, about the WKB method and George Green's original invention of the idea (that bears other people's names, or, well, initials, anyway).  (As usual.)  Green had written down a PDE modelling waves in a long narrow canal of slowly varying breadth 2*beta(x) and slowly varying depth 2*gamma(x).  Turns out his "approximate" solution is actually an exact solution to an equation of a very similar kind, with an extra term E(x)*phi(x,t).  The extra term depends in a funny way on beta(x) and gamma(x), and only on those.  So a natural kind of question is, "is there a canal shape for which Green's solution is the exact solution with E(x)==0?"  Can we find beta(x) and gamma(x) for which this works?

Yes.  Lots of cases.  In particular, if the breadth beta(x) is constant, you can write down a differential equation for gamma(x).  I wrote it in my notebook using y and not gamma.  I wrote it pretty neatly.  Then I fired up the Maple Calculator on my little tablet, opened the camera, and pow!  Solved.

I wrote the solution down underneath the equation.  It checks out, too.  See the attached image.

Now, after the fact, I figured out how to solve it myself (using Ricatti's trick: put y' = v, then y'' = v*dv/dy, and the resulting first order equation is separable).  But that whole "take a picture of the equation and write down the solution" thing is pretty impressive.

 

So: kudos to the designers and implementers of the Maple Calculator.  Three cheers!

 



Am I using maple correctly?

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