So what should i mod 0 really be equal to?

solve used to be one of Maple's strongest commands -- it even subsumed simplify in power.  But, over the years, dsolve slowly took over as the most powerful comand.  At the same time, people started realizing that within the framework of differential equations, the toolbox was actually larger than the one for algebraic equations (and most algebraic tools are still available).  So many tasks that one thinks of doing purely algebraically can also be done using differential equations, with perhaps the most surprising one is to factor multivariate polynomials via partial differential equations.

We are going to show a roundabout but rather effective method of solving some rather complicated (definite) integrals in closed-form via a rather unusual method: a special factorization of linear ODEs.  The example we will use is a 2 week old question that has yet to get an answer.

First, the problem: compute the integral

The following is extracted from Jakob Nielsen's weekly newsletter on usability.

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While in London for last week's conference, I stopped by the British Museum. Among other exhibits, I saw King George III's collection of antique coins. Because this was part of an exhibition about the growth of knowledge during the Enlightenment period, the collection was shown in the way the King had organized it.

His Roman coins were sorted chronologically, which is the same system the Museum uses to this day. But the Greek coins were sorted alphabetically according to the name of the ruler depicted on the coin. This meant that coins issued at the same time would be in widely varying parts of the collection. It also meant that coins minted in the same city state would be dispersed across the collection. Not surprisingly, the British Museum no longer uses George III's system for its collection (except for this special exhibit).

Information architecture lessons:

1. Alphabetical order is usually a bad way to structure items.
2. For a better structure, you need to understand the underlying dimensions of interest (the King didn't know enough about ancient Greece to correctly place the coins in time and space).
3. New info may cause you to restructure things for better access.
4. Two or more structuring principles may be better than a single one.

In a previous comment, J. Tarr asks "what is Maple primarily intended to do?", and suggests that I might have something to say on the topic.