A Dynamic Computer Algebra System is the idea to use identities as rules for manipulation of algebra. Robert Fenichel's developed a system called FAMOUS in the 1970s using LISP which could.
A modern system DCAS has been implemented by Martin Johansen called DCAS Ether. The system works by selcting a class of identities based on the form of the input expression.
Here are two examples of identity collections, one for basic algebra, the other for boolean algebra.
/* Distributivity */
x*(a + b) = a*x + b*x;
/* Powers */
(a*b)^c = a^c*b^c;
(a^b)^c = a^(b*c);
/* add, sub */
solveequ(x, (gfvi(f(x)) + gfve(a(x)) = gfve(b(x)))) = solveequ(x, f = b - a);
solveequ(x, (gfvi(f(x)) + gfve(a(x)) + c = gfve(b(x)))) = solveequ(x, f + c = b - a);
/* mul, div */
solveequ(x, (gfvi(f(x))*gfve(a(x))*c = gfve(b(x)))) = solveequ(x, f*c = b/a);
solveequ(x, gfvi(f(x))*gfve(a(x)) = gfve(b(x))) = solveequ(x, f = b/a);
External links
Webpages of computer algebra systems