Dynamic Computer Algebra System

From Wikipedia, the free encyclopedia

Dcas is a dynamic computer algebra system featuring the idea of using identities as rules for manipulation of algebra. Robert Fenichel developed a system called FAMOUS in the 1970s using the LISP programming language pursuing the same aim.

A modern system DCAS has been implemented by Martin Johansen called DCAS Ether. The system works by selecting 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);