A few days ago, I discovered the .get() method of the dictionary data type. It allows you to request the value corresponding to a key which a dictionary may not have, in which case you can specify what should be returned instead of rasing a KeyError. In PyDy, I had numerous cases where I was using if/else statements to check if a dictionary had a certain value, but by using the .get() method, I was able to eliminate about 50 or 60 lines of code and make the code a lot more readable and easier to maintain.
The progress on the trigonometric functions has been slow. Ondrej and I worked on some code together that handles most of the cases in the table by Fu et al., but not all. One of the things that has been a little challenging is to identify pi shifts in the argument to the trig functions and map the shift into the first quadrant (0, pi/2) and return the appropriate result, e.g.: sin(x+17*pi/18) –> sin(x + pi/18), etc. The approach has been to match x and r in the following generic argument:
As I see it, there are three cases to consider: 1) x==0, r!=0, 2) r==0, x!=0, and 3) x!=0, and r!=0. I am splitting the logic up in this fashion and am trying to deal with each case in the appropriate manner. In most cases, r will be of the Rational class, and therefore the modulo operator is needed to bring it to the interval (0, 2*pi), so I implemented the necessary code and sent a patch to the Sympy mailing.
Although the trig functions aren’t quite as they need to be yet, I was still able to manually get the simplifications that are presented by Fu et al. to work using the builtin Sympy commands, which hopefully will mean that simplifying the implementing the algorithm will be feasible with the existing Sympy tools and not too many extra functions will need to be created.