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The "." notation for the dot product of Vectors is very convenient and intuitive.  For example:

> <1,2,3> . <1,1,1>;

6

One sometimes annoying feature of it, however, is that by default Maple is using a dot product (suitable for Vectors with complex scalars) that is conjugate-linear in the first argument.  But let's say you will only be working with real scalars.  There's no problem if your Vectors have numeric entries, but...

Each of my two previous two blog posts (Maple Gems, More Maple Gems) contained five "gems" from my Little Red Book of Maple Magic, a red ring-binder in which I record...

In a recent blog post, I discussed five "gems" in my Little Red Book of Maple Magic, a notebook I use to keep track of the Maple wisdom I glean from interactions with the Maple programmers in the building. Here are five more such "gems" that appeared in a Tips & Techniques column in a recent issue of the ...

A tool tip came up which says I can see the operations performed step-by-step. Can someone tell me where that feature is (what it's called)?

I have:

>solve(x+y+sqrt(x^2+y^2)

(24*(x-12))/(x-24)

I want to see step-by-step how Maple got to that answer. Thanks.

Since coming to Maplesoft in 2003, I've kept a notebook of "gems" I've gleaned from consulting with the programmers in the building. I call it my "Little Red Book of Maple Magic." It really is red. The first spiral-bound notebook was little, and it was red. When it overflowed, I moved the notes to a red ring-binder. But it's not so little any more.

There are a few ways to view the source of a Maple procedure, such as by using the commands  showstat and print. And these work as usual for the exports of a module. But for procedures which are declared as local to a module these methods do not work right away since by default modules' contents are opaque.

One way around this is to change a setting, by issuing kernelopts(opaquemodules=false) prior to attempting...

If you want better performance then don't use 2D Math mode to enter procedures which call  `.` (dot).

The following timings are not the result of the order in which the cases are performed. The timings stay roughly the same if the blocks delimited by restarts are executed out of order.

The program mint, bundled with Maple, is a very useful syntax checker and program analyzer.

As provided, `mint` works best with Maple program source when contained in plaintext files. Inside Maple itself there is a command maplemint which does some of the same tasks as the stand-alone program `mint`. Unfortunately `maplemint` is quite a bit weaker than `mint` is, for quite a selection of procedures. Also, `maplemint` doesn't have the sort of flexible control that `mint` provides through its optional calling parameters.

I had previously posted a Maple language procedure for the purpose of calling out to `mint` while inside Maple (Standard GUI, or other). Here it is below, cleaned up a little. Hopefully it now works better across multiple operating systems, and also provides its optional parameters better.

Very few people would ever need this, I think, even while programming. But sometimes the details of the call stack are just what one wants.

So, for example,...

> h:=proc(x)
>   debugopts('callstack');
> end proc:

> m:=module() export f; local g;
>   f:=proc(x)
>     g(x^2);
>   end proc:
>   g:=proc(x)
>     global h;
>     h(x^3);
>   end proc:
> end module:

> m:-f(a);
[DEBUGSTACK, h, `debugopts('callstack')`, [a^6...

On some Linux distributions, the default font (Lucida Bright at size 12) for text mode in Maple's Standard GUI doesn't look as good as it might at the default magnification.

Here's a screenshot of Maple 12 and some text in a worksheet (on my very old Fedora Core 2).

Here's a first working shot at an external, programmatic mechanism for opening .mw worksheets/Documents as new tabs in an already running Maple Standard GUI session.

This involves a `sh` shell script, runnable in Unix/Linux/OSX/cygwin. Maybe someone could post a MS-Windows .bat batch file equivalent.

The basic idea is this: you have a GUI session open. But you want to be able to open other .mw files in that session without having to go through the GUI's File->Open menu every time ...

"I've seen this element before..." Often we are faced with the problem of building up sets incrementally, by removing pieces one at a time from a larger whole. The bottlenecks in this case are usually: 1) adding a small set X to a large set S (copies S and X, making this ~O(|S|+|X|)) 2) removing elements of the large set S from the small set X (binary search: |X|*log(|S|)) A classic example of this is a breadth-first-search. We start at one vertex of a graph and in each iteration we add the set of new neighbors X to the set of vertices S that have already been found. We can make this more useful by making the program return the sets of new neighbors found in each iteration, that is, the sets of vertices that are distance 1, 2, 3, etc. from the initial vertex.

This tip comes care of Dr. Michael Monagan at Simon Fraser University. Represent your sparse matrix as a list of rows, and represent each row as a linear equation in an indexed name. For example:

A := [[1,0,3],[2,0,0],[0,4,5]];

S := [ 1*x[1] + 3*x[3], 2*x[1], 4*x[2]+5*x[3] ];

To compute the product of the matrix A with a Vector X, assign x[i] := V[i] and evaluate. This can be done inside of a procedure because x is a table.

V := [7,8,9]: for i to 3 do x[i...