(rv) generates a random algebraic variable. I am writing an algebra tutorial in CL and this code is from my DSL for the bit where I randomly generate algebra problems. (rv 2) would return a list of two variables one would reasonably find in a typical text. ie, x and y or m and n, but not x and a.
(dsb (a b c) (shuffle (cons 1
(random-primes 2 2 10)))
dsb is destructuring-bind. I did not use random-primes very oftwn so no abbrev. yet. :)
(dsb (x y z) (rpu 3 (r+ 5))
(rp n form) expands into a loop expression that repeats that many times collecting the result of the form shown. rpu is the version that ensures no duplicates (u for unique). (r+ n) generates a random number from 1 to n inclusive.
(m+- (m+- (ms* a (ms^ v x))
(m+- x y) generates either a mathematical expression tree my software will use for tutoring, randomly x+y or x-y
ms* generates a product as does m, but is smart about it and tosses a factor of 1. likewise ms^ returns a power but not if the exponent is 1, then just the variable. mss^ is supersmart and converts x^0 to 1.
(ms* b (ms^ (xqv v) y)))
xqv is short for mx-equiv, which copies a mathematical expression to get an equivalent expression. (mx-copy creates a Lisp copy that is "EQ" the original at the application's level of abstraction.
(ms* c (ms^ (xqv v) z))))))
Hmmm. This is a problem in factoring out the gcf of three terms ax^i + bx^j +cx^k.
Note that the above is as much about DSLs as it is about abbreviation, and I think if I wanted to delay shipping even further <g> I would break down and do a full parser of something like "ax^i + bx^j +cx^k,(abc)=[1 5],....".
